The Atom of the Universe: The Life and Work of Georges Lemaitre 9788378860501, 9788378860716

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translated by

LUC AMPLEMAN edited by

KARL VAN BIBBER

© Copyright by D. Lambert & Copernicus Center Press, 2015 © 2011 Éditions Lessius; 24, boulevard Saint-Michel, 1040 Brussels www.editionslessius.be Original title: Un atome d’univers. La vie et l’œuvre de Georges Lemaître Editing: Aeddan Shaw Cover design: Mariusz Banachowicz Layout: Mirosław Krzyszkowski Typesetting: MELES-DESIGN ISBN 978-83-7886-071-6 (cloth) ISBN 978-83-7886-050-1 (PDF) Kraków 2015

Publisher: Copernicus Center Press Sp. z o.o. pl. Szczepański 8, 31-011 Kraków tel./fax (+48) 12 430 63 00 e-mail: [email protected] www.en.ccpress.pl

Contents

Preface  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   9 Acknowledgments .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   15 Chapter I From Louvain to Namur  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   21 1 . The reed and the Universe  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   21 2 . Sources  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   23 3 . Guide to this work .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   31 Chapter II The early years: the Jesuits, mathematics and the mines (1894–1914)  .  .  .   33 1 . A Son from the Pays Noir  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   33 2 . At the Jesuit school  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   41 3 . The mines: a blind tunnel?  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   45 Chapter III The Great War: from student to artilleryman (1914–1919)  .  .  .  .  .  .  .  .  .   53 1 . The long walk to the Yser Front  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   53 2 . Back to the University: a new direction  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   60 Chapter IV The seminarian and relativity (1920–1923)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   67 1 . The Saint-Rombaut house  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   67 2 . Lemaître, theology and the Amis de Jesus  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   69 3 . Einstein’s physics viewed from Saint Rombaut  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   75 4 . Toward a new life  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   84 Chapter V The mathematician who became an astronomer  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   87 1 . A clergyman at Eddington’s house  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   87 2 . The time to sow: from Canada to MIT  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   93 3 . In the right place at the right time  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   114

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The Atom of the Universe

Chapter VI From the expanding universe to the primeval atom hypothesis (1927–1931).  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   121 1 . An expanding universe with no beginning or end  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   121 2 . From Einstein’s blame to Eddington’s mea culpa  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   132 3 . The hypothesis of the Primeval Atom  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   145 Chapter VII The Chinese connection (1927–1950...)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   165 1 . A disciple of Father Lebbe: from cosmology to the Chinese residence .  .  .   165 2 . Florescit et lucet  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   169 3 . “Servir”  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   173 4 . Lemaître’s Chinese Disciple: Tchang Yong-Li  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   174 Chapter VIII Arrival on the world scene? (1931–1939)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   179 1 . Travels and accolades  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   179 2 . Towards a theory of large-scale structures: the Lemaître-Tolman model  .  .  . 184 3 . A peek inside the black hole  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   192 4 . The defence of the “little lamb”  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   199 Chapter IX Science and faith: the theory of the two paths (1924–1936)  .  .  .  .  .  .  .  .  .   207 1. The origin of the “two paths”: a tripartite influence  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   207 2 . The Congress of Mechelen  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   215 3. The Pontifical Academy of Sciences .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   217 Chapter X An astronomer starstruck by algebra (1931–1957)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   221 1 . The Dirac equation redux (1931)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   221 2. The Projektive Relativitätstheorie (1933–1935) and Relativistic   Theory of Protons and Electrons (1937). .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   227 3 . The Fundamental Theory and the spinors of Cartan (1948)  .  .  .  .  .  .  .  .  .  .   234 4. The spinors: from the quantum field theory to history (1955–1957)  .  .  .   236

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Chapter XI From cosmology to calculation: the Størmer problem .  .  .  .  .  .  .  .  .  .  .  .  .  .   241 1 . The problem of the origin and nature of cosmic rays  .  .  .  .  .  .  .  .  .  .  .  .  .  .   241 2 . The determination of the orbits of cosmic rays: the Størmer problem  .  .   244 3. The first “Lemaître’s School”: 1933–1945  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   254 4 . The Størmer problem after 1945  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   259 Chapter XII A time of war (1940–1944)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   263 1 . Exodus  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   263 2 . A time for solidarity  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   266 3 . The time of isolation and reading  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   270 4 . A time of reprimand and trials  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   277 5 . Back to science  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   281 Chapter XIII Lemaître the master. A portrait of his pedagogy (1940–1944)  .  .  .  .  .  .  .   285 1 . Teaching and research, a seamless cloth  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   285 2 . Attending a class and passing exams with the Canon  .  .  .  .  .  .  .  .  .  .  .  .  .  .   292 Chapter XIV From mechanics to calculators and back again (1940–1944)  .  .  .  .  .  .  .  .   301 1 . Mechanics and cosmology: the nebulae and their clusters  .  .  .  .  .  .  .  .  .  .  .   301 2 . Numerical calculation  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   309 3 . Mesmerized by machines  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   315 4 . The apotheosis: the three-body problem  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   322 Chapter XV Faith and science: the Un’Ora problem (1951–1952)  .  .  .  .  .  .  .  .  .  .  .  .  .  .   331 1 . From Deus Absconditus to the natural beginning of the universe  .  .  .  .  .   331 2 . The Un’Ora discourse  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   337 3 . Lemaître’s reaction  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   340 4 . A small detour to Rome: the intervention of 1952  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   347

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The Atom of the Universe

Chapter XVI Monsignor Lemaître (1956–1964)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   353 1 . A little out of breath  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   353 2. The Presidency of the Pontifical Academy  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   355 3 . A mathematician in the spirit of Vatican II  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   362 Chapter XVII Mundus est fabula . The philosophy of a cosmologist  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   367 1 . Lemaître and the philosophers  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   367 2 . Lemaître: philosophy teacher  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   373 3 . An intelligible, non-deterministic and strange universe  .  .  .  .  .  .  .  .  .  .  .  .  .   375 4 . Teilhard listening to Lemaître  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   381 Chapter XVIII A “pair of Molière” and the “Nim-Pythagoras” fight  .  .  .  .  .  .  .  .  .  .  .  .  .  .   389 1 . A double star: Molière .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   389 2 . Let us calculate without fatigue!  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   393 Chapter XIX The last years (1962–1966)  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   405 1 . Last works  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   405 2 . To oppose “The sin against the Holy Spirit”: the ACAPSUL  .  .  .  .  .  .  .  .   411 3 . At the end of the “two paths”  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   414 Chapter XX Msgr. Georges Lemaître: a star that was without a double  (1962–1966).  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   419 1 . Unity of life  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   420 2 . Unity of work  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   422 Postscript ATV-5, the Georges Lemaître  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   429 Afterword When should one stop doing cosmology and turn to calculations?  .  .  .  .  .  .   431 Bibliography of Msgr. Georges Lemaître  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   437 Index of Persons  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   459 Photos  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   465

Phillip James Edwin Peebles Albert Einstein Professor of Science Emeritus Department of Physics, Princeton University Princeton, New Jersey, USA

Preface

T

he demonstration that our physical universe expanded from a very different state grew out of advances in the 1920s and 1930s that to a striking degree were the work of a single person, Georges Lemaître. Dominique Lambert’s biography, Un atome d’univers. La vie et l’oeuvre de Georges Lemaître, shows us how Lemaître’s remarkable work was informed by his life outside science, and the context within his other interests in natural science. This welcome English translation makes Lambert’s biography accessible to more people who take an interest in how we arrived at our present understanding of cosmic evolution from the dense early conditions Lemaître termed the “Primeval Atom” and Fred Hoyle renamed the “Big Bang.” Science builds on what came before. Critical for Lemaître was Einstein’s idea that a philosophically acceptable universe is the same everywhere, apart from small-scale irregularities such as our home on a planet near a star in a galaxy of stars. I see no indication Lemaître entertained doubts about Einstein’s idea; he seems to have been willing to work with it as a useful working hypothesis, as it has proved to be. Ideas can lead us to aspects of reality, on occasion. Einstein’s idea of large-scale uniformity was daring: there was no evidence, or motivation from a full theory. Surely it was more daring still to imagine that the very spacetime of our universe is evolving. My thinking on who put the idea together, which leads me to Lemaître, goes as follows. The Russian Alexander Alexandrovich Friedmann was the

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The Atom of the Universe

first to find the mathematical solution of Einstein’s general relativity theory for a homogeneous expanding universe of matter. It was a great accomplishment. The difficult conditions under which Friedmann worked, and his tragic early death, make it quite understandable that he did not recognize the astronomers’ observational evidence for his expanding solution. But science demands credible relations between theory and observation. The German mathematician Hermann Weyl did know about the evidence that starlight from distant galaxies of stars tends to be shifted to the red, as if the light were Doppler shifted by the motions of the galaxies away from us. Weyl showed that, in a special solution of Einstein’s theory that the Dutch astronomer Willem de Sitter had found, a homogeneous distribution of massless particles could move in the manner astronomers later observed: the rate of separation of any pair of galaxies would be on average proportional to their separation. But de Sitter’s solution contains no matter, quite contrary to all the stars we see around us, and in this solution spacetime is not evolving: massless particles move in a fixed spacetime geometry. Friedmann’s solution contains matter, and spacetime evolves, but evidently Weyl was not aware of Friedmann. Two years after Weyl, in 1925, the Belgian Georges Lemaître published his independent discovery of Weyl’s result, and in 1927 Lemaître presented his independent discovery of Friedmann’s solution for an expanding universe filled with matter. Lemaître showed that if this solution describes our universe then the rate of separation of the galaxies of stars is proportional to their separation, as Weyl had done for an empty universe. Two years later the American astronomer Edwin Hubble announced the first observational evidence of this relation between velocity and distance. Another year after that the community noticed Lemaître’s work, and he became famous. I see in this story several lessons on research in natural science. An idea may be discovered more than once, as in the independent recognition by Friedmann, Weyl and Lemaître of key elements of the idea of an expanding universe. A significant idea requires credible contact between theory and observation, as in the discovery that the-

Phillip James Edwin Peebles. Preface

11

ory and observation agree on the proportionality of recession velocity and separation. An idea becomes an advance when the community is ready to recognize this contact. The evidence that the galaxies are moving apart was known in the early 1920s, but by and large it was taken without consideration that our universe is unchanging. Lemaître had the good fortune to hit on the idea of expansion later in the 1920s, when the problem of understanding the astronomers’ redshifts had become pressing enough that people were willing to entertain Lemaître’s idea. And consider yet another lesson. Lemaître published his paper on a matter-filled expanding universe in Annales de la Société scientifique de Bruxelles. I am sure this is an excellent journal, but it was not read by leading astronomers and relativists, so it not surprising that the paper was overlooked until Lemaître wrote several letters pointing it out to Arthur Stanley Eddington, who had been Lemaître’s teacher during a visit to the University of Cambridge. A good idea should stand on its merits, but the community has to know about it. I draw a lesson on Lemaître’s character from the publication of an English translation of his paper in a widely-read journal, Monthly Notices of the Royal Astronomical Society, which Eddington generously arranged. The translation omits a footnote with comments on the relation between the recession velocity, v, of a galaxy and its distance, r, v = H r.    (1) In the missing footnote Lemaître points out that astronomers’ attempts to find a relation between v and r had indicated at best only a very weak correlation; the distance measurements were too uncertain. That is, he was not offering an explanation for a relation that was already known, he was offering a prediction. Despite the large uncertainties in galaxy distances Lemaître used them to find a value of the constant of proportionality, H, in equation (1) that is quite close to Hubble’s measurement of H two years later. That seems surprising,

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The Atom of the Universe

but the footnote explains. In a sample of galaxies for which Hubble had published estimates of distances, Lemaître divided the mean value of the velocities by the mean value of the distances. The mean helps average out the large uncertainty in each distance measurement. And under the assumption that distance and velocity are related by equation (1) Lemaître’s procedure yields an unbiased estimate of H. Why was this interesting footnote not published in the English translation? The admirable study by Mario Livio (in the journal Nature, 10 November 2011, p 171) makes it clear that this was Lemaître’s decision, not a plot to deny him credit. My guess is that Lemaître removed his comment on the lack of clear evidence of the relation in equation (1) because it had become out of date with Hubble’s claimed observation of this relation. That was after publication of Lemaître’s original paper but before publication of the English translation. And I can imagine that, since Hubble directly measured H from the slope of the relation between v and r, Lemaître decided the explanation of his indirect method was no longer needed. By eliminating the footnote he removed arguably out-of-date comments. He also obscured credit for his prediction of the relation in equation (1), but Lemaître showed no interest in self-promotion. Lemaître’s bold character is seen in this comment (in Nature, 9 May 1931, p. 706): Sir Arthur Eddington states that, philosophically, the notion of a beginning of the present order of Nature is repugnant to him. I would rather be inclined to think that the present state of quantum theory suggests a beginning of the world very different from the present order of Nature.

Eddington’s feelings seem natural; surely it was difficult to imagine our universe evolved from a very different state. But Lemaître welcomed the idea as an opportunity to expand the reach of natural science. He saw that one should look for fossil remnants of an old or-

Phillip James Edwin Peebles. Preface

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der; his candidates were cosmic rays and galaxies. The fossils prove to include a sea of thermal radiation left from the hot dense Big Bang, light elements formed by thermonuclear reactions in this hot state, and, as Lemaître argued, the galaxies, which are fossil remnants of the growth of slight departures from an exactly homogeneous early universe. Lemaître’s analytic solution for the growth of a mass concentration such as a galaxy, under the convenient approximations of spherical symmetry and negligible pressure, reveals the spacetime curvature fluctuations that are now a  carefully studied measure of the early universe. He conjectured that the early universe was cold; it proves to have been hot. But his interest in the role of quantum physics in the early universe is still very much on our minds. Einstein had adjusted his general relativity theory by adding a “cosmological constant,” Λ, that he expected would balance the attraction of gravity. When Einstein learned of the evidence that the universe is not unchanging he lost interest in Λ. Lemaître did not. His audacious idea was that Λ behaves as an energy density that surely has some physical significance. We know now that Λ is present and, in an appropriate though likely unintended tribute to Lemaître, it has been renamed “dark energy.” Its physical significance remains a puzzle. Times select leaders. In the 1920s and 1930s Edwin Hubble had the qualities needed to lead the great observational advances in what he termed the “Realm of the Nebulae,” or galaxies. Georges Lemaître had the qualities needed to lead the great theoretical advances in what he termed the “Primeval Atom,” or Big Bang. Research has moved in directions Lemaître could not have anticipated, but we are moving along paths he explored. Consider the modern flavor of this comment (in my translation from G. Lemaître, Revue des Questions Scientifiques, XX (4e série), 1931, p. 408): The evolution of the world can be compared to a display of fireworks that has just ended. Some red wisps, ashes and smoke. Standing on a well-chilled cinder, we see the slow fading of the suns and seek to reconstruct the vanished burst of formation of the worlds.

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The Atom of the Universe

I conclude by offering what I consider a profoundly valuable lesson found in G. Lemaître, “La culture catholique et les sciences positives” (Actes du VIe Congrès catholiques de Malines, Bruxelles, 1936, p. 70, in the translation from O. Godart and M. Heller, Cosmology of Lemaître, Tucson (Arizona), Pachart Publishing House, 1985, p. 173) on his life in the Roman Catholic Church and his work in natural science: In a sense, the researcher makes an abstraction of his faith in his researches. He does this not because his faith could involve him in difficulties, but because it has directly nothing in common with his scientific activity. After all, a Christian does not act differently from any non-believer as far as walking, or running, or swimming is concerned.

Acknowledgments

T

he work that will follow owes much to the competence and kindness of several people who did not hesitate to share their time, knowledge and memories. I will be forever grateful to them. This work would never have been possible without the initial suggestion of Professor Patricia Radelet and Dr. Jean-François Stoffel from the Centre Interfacultaire en Histoire des Sciences of the Université Catholique de Louvain (UCL) in fall 1994, the support and immense patience of Hedwige Rezsöhazy or the constant encouragement of Mr. Jean-Benoit Sepulchre of the “Association des amis de l’Université de Louvain” (AUL), Fr. Pierre Sauvage, N. Hausman and Dr. Jean Pierre Luminet from the Observatory of Meudon. I will remain eternally grateful to them. This book would have not been possible either without the continual stimulating advice, friendship and trust of Jacques Demaret from the Institut d’Astrophysique of the University of Liège to whom I am also greatly indebted. The development of this work was made possible thanks to the kind collaboration of André Berger and Mrs. Liliane Moens from the Georges Lemaître Institute of Astronomy and Geophysics, who opened the doors of the Archives Lemaître to me. Without their help and availability, this work would not have been possible. My thanks also go to Odon Godart and his wife, who dedicated long hours to me in recollections of the life and work of Msgr. Lemaître, with whom they were faithful friends. Obviously their personal testimonies strongly influenced this project. I would also like to extend my thanks to Dr. Lucien Bossy, whose information regarding cosmic rays was highly valuable.

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The Atom of the Universe

My gratitude goes as well to André Deprit from the National Institute of Standards and Technology in Gaithersburg, who wrote the first detailed historical notes on Msgr. Lemaître, and Mrs. Andrée Deprit-Bartholomé. Privileged collaborators of Msgr. Lemaître, they had the great kindness to put the results of their biographical and bibliographical research at my disposal. My thanks go also to Cécile Ducarme and the Ducarme-Deprit family for their cooperation. My study has also benefited from unique information communicated by other colleagues, collaborators and students of Msgr. Lemaître: Fr. Charles Courtoy, from the Department of Physics of the Université de Namur (FUNDP), René Dejaiffe from the Planetarium of Brussels, Jacques Masset, Jean Valembois, Roger Weverbergh and Fr. Julien Lizin; the professors Jean-Pierre Antoine and Jacques Weyers from the Department of Physics of UCL, Roger Broucke of the University of Texas, Roland Caudano of the Department of Physics of the FUNDP, Frans Cerulus of the Department of Physics of UCL and of KUL, Jacques Henrard of the Department of Mathematics of the FUNDP, Jean Ladrière from the Institut Supérieur de Philosophie, René Lipnik from the Department of Physics of UCL, Pierre Macq, honorary rector of UCL, Auguste Meesen of UCL, Paul Paquet, Director of the Royal Observatory of Belgium, Jacques Peters from the Faculty of Applied Sciences of the Katholieke Universiteit Leuven (KUL), P. Smeyers from the Instituut voor Sterrenkunde of the KUL, David Speiser from the Department of Physics of UCL, Georges Thill and Gérard Fourez from the department sciences-philosophie-sociétés of the FUNDP, and M. Delmer. All have my most sincere gratitude. May the family of Msgr. Lemaître also find here the expression of my deepest gratitude. With a boundless generosity, his family members have opened their doors and their archives to me, and they have answered my questions. I would like to especially thank Gilbert Lemaître, whose confidence and advice have been greatly appreciated, Mmes Christiane Houyet-Lemaître and Odette Dellenne-Lemaître, André Lemaître, Pierre Lemaître, Paul and Anne Houyet, Dr. Anne Maes-Lemaître and Dr. Vrins and his wife.

Acknowledgments

17

I would like to express my most cordial thanks to the following people: Guy Boodts, a genealogist who spared no effort in helping me to trace the origins of the Lemaître and Lannoy families; Claire Cabiaux and Dr. Chantal Tilmans-Cabiaux, whose information on the history of Courcelles was extremely valuable; Charles de Meurs, who enlightened me on the life of Lemaître during the First World War as well as Richard Mairesse and the adjutant Jos Bullens who provided me with information about the 3A (Third Artillery Regiment). Msgr. Edouard Massaux, honorary rector magnificus of UCL, Canon Roger Aubert from the Faculty of Theology of UCL, Fr. Louis Wuillaume and A. Jans, archivist of the archbishopric of Melechen-Brussels all enlightened me on the life and training for the priesthood of the cosmologist. Msgr. J. Billiauw, Msgr. G. Thils, Canons P. de Locht, J. Goeyvaerts, C. Vandewiel, F. Van Steenberghen and G. van Innis, the abbés Albert Caupain, Lenaerts and Van Steenberghen as well as Fr. Yves Nolet de Brauwere helped me to identify the role of Msgr. Lemaître within the ‘Amis de Jésus’. Stefano Bettini from the University of Florence, Marc Lachièze-Rey of the CEA of Saclay; Manuela Boodts-Nève, the Nève family of Mévergnies, Fr. Christian Papeians, archivist at the Saint-André abbey in Lophem and Professor Claude Soetens of the Faculty of Theology assisted me to accurately place the actions of Lemaître in regards to Chinese students and his relations with Dom Théodore Nève, Guy J. Baudoux of the “Institut des Hautes Etudes Chinoises” (IBHEC) who gave me also information concerning these Chinese students. I would also like to thank Sr. Madeleine Delmer, who provided me with one of the rare written documents concerning the ‘Un’Ora problem’; Marcel Nève de Mévergnies, Xavier de Maere d’Aertrycke, and Thomas Durt from the Department of Physics at VUB, Hubert Durt from the École Française d’Extrême-Orient and Sr. Émilie Fraipont who provided me with unique information on the life of Lemaître in Louvain after 1940. I am indebted to Br. Robert Graas who worked diligently to obtain information of great interest about the classes of Lemaître and de la Vallée Poussin; Jean Mawhin from the Department of Mathematics

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The Atom of the Universe

at UCL, who enlightened me on the latter and the thesis of Lemaître. Dr. Jean-Pierre Demoulin and the Fondation Teilhard de Chardin, Armand Panier from the Department of Chemistry of the FUNDP and Jean-Louis Maquet are all to be thanked for clarifying for me the insights of Lemaître on the works of Teilhard de Chardin. I also thank Charles-Bernard Demeure, Alfred van der Essen, Dr. D. Le Bon and Marthe Mahieux, who provided important indications on the ‘new numerals’ of Lemaître, and Dr. Lydie Koch-Miramond of the CEA in Saclay who revealed the influence of the works of Lemaître on the computerization of the CEAR. Rezsöhàzy and Pierre Arty explained the role of the Association du Corps Académique et du Personnel Scientifique de l’Université de Louvain (ACAPSUL). Luc Henriet, Yvon and Marie-Claire Lambert, Bernadette Naedts and Isabelle Piette of the team of Jean-Claude Polet helped familiarize me with the research of the cosmologist about Molière; and André Jaumotte of Université Libre de Bruxelles (ULB) provided me with his interesting notes on Jacques Cox. To complete this work, I had the chance to consult the archives of the Royal Palace of Brussels, thanks to the kindness of Gustave Janssens, archivist of the Palace, the advice of Colonel Thierry de Maere and the friendly mediation of Myriam and Michel Terlinden; I am profoundly grateful to them. I also had access to the archives of the UCL thanks to the help, devotion and competence of Françoise d’Arras, as well as to the archives of the International Academy of Philosophy of Sciences and those of F. Dockx, thanks to the Fr. Jean-Marie Van Cangh and to Mrs. Cambier. The documents related to the interactions of Msgr. Lemaître and the Institut Supérieur de Philosophie were provided by Jean-Pierre Deschepper of UCL, who I would also like to thank. Fr. Kail Ellis, Fr. Dennis Gallagher, and Franck P. Maloney of Villanova University have given to me some documents on the Lemaître stays in their University and on the Mendel Medal. Finally, I wish to thank Armand de Callataÿ, the Société Astronomique de Liège, André Lousberg and Arlette Noels of the Institut d’Astrophysique of the University of Liège, Pierre Marage of the

Acknowledgments

19

Department of Physics of ULB, Joseph Turek of the Catholic University of Lublin, André Ronveaux of FUNDP, Jan Govaerts and JeanMarc Gérard of UCL, Paul Bockstaele of KUL and Jacques Tits of the Collège de France for all their contributions. A biography always depends on the choices and the particular point of view adopted by its author. It should be made clear that the analyses herein are solely those of their author and not of the persons mentioned above. I want finally to express my deep gratitude to Bartosz Brozek who had the idea of this English translation and who supported its publication at Copernicus Center Press. Thank you very much also to my translator, Luc Ampleman who made his work with competence and enthusiasm. I also thank Karl van Bibber (Department of Nuclear Engineering, University of California, Berkeley) who encouraged this translation throughout and kindly agreed to read and edit the English manuscript. Last but not least, I want to express my deep gratitude to Phillip J.E. Peebles from the Department of Physics of Princeton University who wrote the preface and Michael Heller from the Pontifical Academy of Sciences, who strongly encouraged me from the beginning to the end of this work and who wrote the afterword.

Chapter I

From Louvain to Namur

1. The reed and the Universe

O

n Sunday 23 June 1963, a number of the members of the association of ‘Amis de l’Université de Louvain’, as well as journalists and people from various circles in Wallonia and Brussels, met at the Namur Bourse du Commerce in order to participate in an event called “Louvain at work: scientific research from recent years”. This event, organized by Philippe le Hodey, president of the ‘Amis de l’Université de Louvain’, aimed to illustrate the scientific vitality of their alma mater. Among the eight workshops conducted on that day, one was the responsibility of Msgr. Georges Lemaître.1 Without a doubt, Lemaître was the best ambassador to promote the vitality of research at the Faculty of Sciences at the University Louvain University (UCL). The audience attentively listened to the lecture delivered under the provocative title: “Univers et Atome” (The Universe and the Atom)2 in which Lemaître  Cf. the letters of Ph. le Hodey date from 5 and 30 April 1963, and the letter of A. Durant (secretary of the “Association des Amis de Louvain”) bears the date 7 May 1963, all three being addressed to Msgr. Lemaître to organize this conference. (Archives Lemaître, UCL, Louvain-la-Neuve). 2   The handwritten text, of which Msgr. Lemaître possessed only one copy, was given to the agronomist Professor Pierre-René Delvaux, on his request for a further publication. However, some judged that Lemaître’s handwriting was difficult to read (which is true) and that some parts of the text were at a high mathematical level (which is false). The publication project was abandoned and the manuscript remained forgotten for more than 30 years. Prof. Delvaux donated the manuscript to the Rare Archives of the Moretus-Plantin Library of Namur’s Facultés Universitaires Notre-Dame de la Paix (Université de Namur, or FUNDP) in 1996. The manuscript was edited, with an introduction by D. Lambert, in the book “L’itinéraire spirituel de Georges Lemaître” suivi de “Univers et atome” (inédit de G. Lemaître), Bruxelles, Lessius, 2007: 119-216. 1

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The Atom of the Universe

summarized and commented upon his famous hypothesis about the ‘primeval atom’ in relation to the purely natural beginning of the Universe. Members of the audience, perhaps somewhat overwhelmed by the technical details of Lemaître’s exposition, were unaware that they were witnessing the culmination of Lemaître’s defense of a hypothesis which was first formulated thirty years ago, an idea that constitutes today the standard cosmological model, or in other words, the theory of the Big Bang. The public was also unaware of how far the scientific contributions of the Louvain professor had gone beyond the field of relativistic cosmology, a field that he had partially forsaken after 1933, except in popular writing. Thus, what captured the attention of the people who had the chance to attend Msgr. Lemaître’s workshop was the audaciousness and optimism of his representation of the physical world as well as his trust in Reason. At the end of the academic year in 1963, he testified to his hope of obtaining the confirmation of a ‘primeval radiation’ that would be “analogous to fossils which testified to the primitive forms of life”. His allusion to a “fossil” radiation was prescient, as in 1965, merely two years later, Penzias and Wilson would discover precisely that, although in a somewhat different form than he envisioned. The discourse of Msgr. Lemaître therefore appeared not only as a model of scientific audacity, but also of a philosophical and religious one. Several members of the audience were even astonished by the departure made by the prelate, who was also the President of the Pontifical Academy of Sciences, from the theology of creation to his representation of the Universe’s origin, going as far as to see his hypothesis of the primeval atom as the antithesis of the world’s creation.3 This audacity is correlative of the confidence in the capacity of human intelligence. Far from being crushed by the immensity of the Universe evoked by Pascal in his Pensées, this intelligence can be found perfectly in the proportions of the physical dimensions of the cosmos. Man is indeed the Pascalian ‘thinking reed’, but – as asserted by George Lemaître at the end of his Namur’s confer3

  Original manuscript: 35. L’itinéraire spirituel de Georges Lemaître: 213.

23

I. From Louvain to Namur

ence – “the thinking reed (can) really dominate the Universe by recognizing it in its entirety”4. The questions that the ‘Amis de Louvain’ could have asked themselves at the conclusion of the Namur conference are still ours nowadays. Considering the priest-scientist that Msgr. Lemaître was, how can one explain the distance he preserved between his physical cosmology and the theology of creation? Was there in fact a fracture or at least a fissure between Msgr. Lemaître’s scientific ideals and his religious ones? From where did the ‘anti-Pascalian’ character of his implicit philosophy come from? Why did he never put into equations his hypothesis of the primeval atom? What was his preference in terms of mathematical research? Was cosmology the real focus of his theoretical concerns? In order to answer all of these questions, it is first and foremost necessary to understand the genesis and unity of the scientific thought of Lemaître, as well as fathoming its scope and magnitude. It is also necessary to understand the way in which faith and science coexisted at the heart of his public and private life. The present book aims to provide the reader with a few elements essential to answering the questions that one may ask about the life and work of Msgr. Lemaître. In doing so, we need to retrace the thread of George Lemaître’s physical-mathematical interests, to examine anew his sacerdotal life, and to map out the contours of Lemaître’s formulation of the science-theology landscape.

2. Sources Assimilating and synthesizing all the available sources dealing with Lemaître’s multidimensional life and work is a formidable task. The author was blessed with the proverbial embarrassment of riches given the sheer volume of chronicles and archives of this remarkable man. The present biography is a supplement to several other biographies,   Original manuscript: 37. L’itinéraire spirituel de Georges Lemaître: 214.

4

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The Atom of the Universe

and to which the present book owes a great debt. An exhaustive list of works prior to 1996, dedicated to the life and work of George Lemaître was compiled by Jean-François Stoffel.5 We highly recommend it to the serious Lemaître scholar. If one includes a few articles that were intended for popularization in newspapers, one may classify those works into three great periods that shows the progressive increase in interest for the man himself as well as for the works of the Louvain cosmologist during the thirty years between his demise and Stoffel’s compilation. The first period (1966-1972) that immediately followed the death of Lemaître is marked by eulogies and official ‘notices’ from academies.6 The second period (1972-1983) is characterized by the pioneering works of Odon Godart7 and Michael Heller8 who, starting from  “Mgr Georges Lemaître savant et croyant”. Proceedings of the colloquium held in Louvain-la-Neuve on 4 November 1994, followed by “La physique d’Einstein”, unpublished text of G. Lemaître, J.-F. Stoffel (ed.) Louvain-la-Neuve, Centre interfacultaire d’étude en histoire des sciences, 1996, Réminisciences 3: 168-175. 6  A. Bruylants, “Éloge funèbre de Msgr. Lemaître, Professeur émérite, pronouncé lors de ses funérailles à Louvain, le 24 juin 1966”, Louvaniensia, September 1966, no 3:17-21. “Monseigneur G. Lemaître”, Revue générale belge, Juillet 1966, no 7: 1-8; Ch. Manneback, “Hommage à la mémoire de Mgr Georges Lemaître” (speech given at the meeting of 2 July 1966), in Bulletin de la classe des sciences de l’Académie royale de Belgique, 5th Series, t. LII, 1966 : 1034-1039 (republication in Revue des Questions Scientifiques, t. CXXXVII (5th Series, t. XXVII), October 1966, no 4 : 453-461); J. Merleau-Ponty, “Cosmologie: mort d’un pionnier”, Atomes, October 1966, no 236: 560-561; G.C. McVittie, “Obituary notices: Georges Lemaître”, The quarterly Journal of the Royal Astronomical Society, t. VIII, September 1967, no 3: 294-297; P.A.M. Dirac, “The Scientific work of George Lemaître” (text presented on the 25 April 1968 during the plenary session of the Pontifical Academy of Sciences), Pontificiae Academiae Scientiarum. Commentarii, t. II, 1968, no 11: 1-18. Later, there would be the notice from C.V. Manneback, “Notice sur Monseigneur Georges Lemaître”, in Annuaire de l’Académie royale de Belgique, t. CXL, 1974: 87-115 (republication: “Monseigneur Georges Lemaître, membre de l’Académie” in Georges Lemaître et l’Académie royale de Belgique: oeuvres choisies et notice biographique (preface by Ph. Robert-Jones; editors J. Mawhin and A. Delmer), Bruxelles, Academie royale de Belgique, mémoire de la classe des science, 3e série, t. X, 1995 : 203-218). 7   Odon Godart (1913-1996) 8   Michael Heller, physicist and philosopher, priest and professor at the John Paul II University in Cracow and member of the Pontifical Academy of Sciences. He had the 5

I. From Louvain to Namur

25

the first-hand documents, attempted to delineate the specific contributions of Lemaître to cosmology and, at the same time, to clarify his approach regarding the relationship between the sciences and faith.9 This period began with the republication of the L’hypothèse de l’atome primitif (1946e)10 as well as of certain bibliographical notes from the Pontifical Academy of Sciences on the occasion of the fifth anniversary of Lemaître’s death.11 The impact of the works of Godart and Heller can be measured easily by consulting, for instance, the fundamental work of Helge Kragh, professor of the history of sciences at the University of Aarhus12: Cosmology and Controversy. The Historical Development of Two Theories of the Universe. One may assert that before 1983, more or less, the contribution of Lemaître was neglected in academic literature and in the general works of scientific popularization, especially in the Anglo-Saxon world. Obviously, there are some exceptions, for instance, the now-classic work of P.J.E. Peebles The Large-Scale Structure of the Universe.13 The third period (1983-1994) was initiated by the conference ‘The Big Bang and George Lemaître’ organized in 1983, in Louvainla-Neuve, by André Berger and l’Institut d’astronomie et de géophysique Georges Lemaître de l’UCL, on the occasion of the fiftieth anniversary of the publication of the seminal article of the Louvain opportunity to meet Odon Godart at a colloquium organized in Krakow in 1973 on the occasion of the 500th anniversary of the birth of Copernicus. This led to several long stays at UCL to study the personal archives of Lemaître. He was the laureate of the famous Templeton Prize and of the Lemaître Prize.   9   His work would lead O. Godart and M. Heller to write the first book exclusively dedicated to Msgr. Lemaître: Cosmology of Lemaître, Tucson, Pachart Publishing House, 1985, History of Astronomy Series 3. 10   From now, all references to the works and publications of Lemaître, are related to the bibliography that the reader may find at the end of this work with its alphanumerical classification. For instance, (1946e: 23) refer to the 5th publication of the year 1946 and to page 23. 11   “L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à l’occasion de sa mort (présentation of P. Salviucci)”, in Civitate Vaticana, Pontifica Academia Scientarum, 1972, Pontificiae academia scientiarum scripta varia 36. 12   Princeton University Press, 1996 (cf. page 58-59, 407) 13   Princeton University Press, 1980.

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The Atom of the Universe

cosmologist on the expansion of Universe.14 This conference would result in a major stimulus to the study of cosmology in Louvain. The conference would also lead, notably, to what could be considered the first critical biography of Lemaître by André Deprit15, Lemaître’s student and successor. The book is based on unpublished documents and testimonies gathered by André Deprit and his wife, Andrée Bartholomé, who was Lemaître’s assistant. These documents have been placed at my disposal.16 The hundredth anniversary of the birth of Msgr. Lemaître, 1994, was marked by two important conferences held in Louvain-la-Neuve. The first was organized by André Berger17 and the second by Patricia Radelet and Jean-François Stoffel from the Cen  “Discours prononcés lors de la cérémonie d’ouverture du symposium international organisé en l’honneur de Lemaître cinquante ans après l’initiation de sa cosmologie du big bang”; Louvain-la-Neuve, 10-13 October 1983, special issue of the Revue des Questions Scientifiques, t. CLV, 1984, no 2 : 139-224. also, “The Big Bang and Georges Lemaître: Proceedings of a symposium in honour of G. Lemaître fifty years after his initiation of Big Bang Cosmology”. Louvain-la-Neuve,10-13 October 1983 (A. Berger, ed.), Dordrecht, Boston, Lancaster, D. Reidel Publishing Co., 1984. 15   This biography in fact comprises four texts: (i) 20 extremely dense pages, added to the text of Odon Godart, “Monseigneur Lemaître, sa vie, son oeuvre” (in “Discours pronouncés…”, op. cit: 155-161); (ii) 31 pages annotated drawing from the favorite research themes of Lemaître as well as the most prominent characteristics of his personality and pedagogy (“Les amusoires de Monseigneur Lemaître’’ in “Discours pronouncés…” op. cit.: 193-224); (iii) a biographical text properly speaking of 29 pages (“Monsignor Georges Lemaître”, in The Big Bang and Georges Lemaître ..., op. cit.: 363-392) and finally (iv) a specialized study on his years of formation (“Georges Lemaître – les années d’apprentissage” in Quelques étapes de l’histoire de l’astronomie et de la géophysique en Belgique. Proceeding of Colloquium of 14 March 1986 (A. Berger and A. Allard, eds), Louvain-la-Neuve, UCL, 1987, works from the Faculty of Philosophy and Literature of Université Catholique de Louvain, XXXIV; Institut d’astronomie et de géophysique Georges Lemaître, Centre d’histoire des sciences et des techniques, III: 95-108. 16   With their originality and precision, the documents gathered by the couple DepritBartholomé have thrown new light on three important files: (i) to secondary school and university education. (ii) the military file, (iii) the journeys in several American research centers in. All these documents have been added to the AL. 17  Le centième anniversaire de naissance de Georges Lemaître, père du Big Bang: journée scientifique du 7 octobre 1994 à Louvain-la-Neuve, numéro spécial de la Revue des Questions Scientifiques, t. CLXV, 1994, no 3: 211-320. This hundredth anniversary also brought about a very interesting publication from several students and collaborators of Lemaître covering different aspects of his life and work: L’univers de Lemaître in Ciel et terre, t. CX, juillet-août 1994, no 4: 90-126. 14

I. From Louvain to Namur

27

tre interfacultaire d’étude en histoire des sciences de l’UCL18 These conferences not only highlighted but helped lead the rediscovery of the central and essential role Lemaître played in the development of contemporary cosmology by the general scientific community.19 Both conferences also attracted, beyond the scientific community, the interest of a large public for the life and the work of this famous professor of Louvain.20 More recently, a general biography of Lemaître was published by John Farrell, The Day Without Yesterday – Lemaître, Einstein, and the Birth of Modern Cosmology21 and a similarly important conference was organized by Rodney D. Holder and Simon Mitton, in Cambridge in 2011, Georges Lemaître: Life, Science and Legacy22. This conference underscored the fact that Lemaître was the first to compute in 1927 the value of what is called now the “Hubble constant” and to explain the law that would only be published by Hubble two years later in 1929. The current work, which was prompted by the aforementioned conferences, owes much regarding its scientific dimension to the largely unpublished records which are held in the ‘Archives of Lemaître’ (referred from now as ‘AL’) located inside the UCL at Louvain-laNeuve. The AL contains the scientific library, correspondence, manuscripts, notes and notebooks of Georges Lemaître23 as well as a part  Cf. Msgr. Georges Lemaître, savant et croyant..., op. cit.   In support of the role of these conferences in Lemaître’s scientific rehabilitation, witness the publication by Jean-Pierre Luminet (also a speaker at the first colloquium) of important texts of A. Friedmann and G. Lemaître [Essais de cosmologie précédés de L’invention du Big Bang by Jean-Pierre Luminet (texts chosen, introduced, translated from Russian and English and annotated by J.-P. Luminet and A. Grib), Paris, Seuil, 1997, Sources du savoir. Another witness that will be discussed later on is the magnificent technical work of Andrzej Krasinki, Inhomogeneous Cosmological Models (Cambridge University Press, 1997) that restored Lemaître’s place in the discovery of a particular model of inhomogeneous, symmetric and spherical universe. 20   Witness of this interest, the book of V. De Rath, Georges Lemaître, le Père du Big Bang (with the collaboration of J.L. Léonard and R. Mayence), Éditions Labor, 1994. 21   New York, Thunder’s Mouth Press, 2005. 22   Berlin, Springer, 2011, Astrophysics and Space Science Library 395. 23   The AL also contains the scientific documentation of two close collaborators of Msgr. Lemaître: Odon Godart himself, and Lucien Bossy. 18 19

28

The Atom of the Universe

of the furniture of his office and calculating machines, which he used (including the first computer the Burrough E101, from the Laboratory of Numerical Research of UCL). How has the AL been constituted? In October 1966, the landlord, wishing to rent the apartment of Msgr. Lemaître24 asked the family to take back what had belonged to Lemaître. Due to the loyalty of Odon Godart, and perhaps also a consequence of Lemaître’s will25, the Lemaître family entrusted him with the scientific documents.26 Godart transferred them first to his office at the “Institut de Physique” at Héverlé (Heverlee), where a first curation was done with the help of René Dejaiffe (1966-1967). When the Francophones left the Institute of Physics of Heverlee, in order to establish one at Louvain-la-Neuve, Odon Godart moved the archives to his own home at Bousval, near Louvain-la-Neuve where they were once more investigated and classified thanks to the contribution of Michael Heller. The documents later were returned to the Institute of Astronomy and Geophysics of UCL where the work of classification continued under the direction of André Berger, thanks to the unreserved devotion and skill of Liliane Moens, as well as the collaboration of Gilbert Lemaître27, physicist and computer scientist as well as nephew and godson of Msgr. Lemaître.   During this period the apartment was at “5 avenue du roi Albert” (now Dirk Boutslaan) in Louvain, a few steps from the “Collégiale Saint-Pierre”. 25   This is surmise, not established fact. According to O. Godart, Msgr. Lemaître wanted to leave him all his documents, rather than leave them to the UCL Faculty of Sciences, because of his being marginalized, in the early 1960s, from a project of a calculation center (oral communication, 19-03-95). Because of the lack of written documents or authentication of other witnesses, one is reduced to conjecture. 26   It is relevant to notice that the AL does not comprise any religious book (Bible, breviaries, missals, …) nor books of general literature (Ruysbroeck, Molière,…) for which one can establish with certitude the presence in the Lemaître’s bookshelf. What it does comprise, i.e. a  substantially complete collection of his scientific correspondence and manuscripts provide a comprehensive picture of the intellectual life of Lemaître. In the author’s opinion it is unlikely that the AL suffered any significant losses during its relocation in 1966. If any documents were eliminated or relocated during this period, it would probably only be from his strictly personal correspondence or works of religious and nonscientific nature (in fact it is known that Lemaître discarded much of his correspondence). 27  Gilbert Lemaître and the entire Lemaître family deserve much of the credit for collecting documents from their relatives and making them available to the AL. 24

I. From Louvain to Namur

29

The study of the sacerdotal life of Msgr. Lemaître was largely based on the analyses of the archives of the “Fraternité sacerdotale des Amis de Jésus” (these archives of the “Sacerdotal Fraternity of the Friends of Jesus”, will be referred hereafter as AFSAJ), to which Lemaître remained faithful all his life, following the suggestion of Abbé Maurits Lenaerts. These archives were held in the retreat house of Regina Pacis in Schilde, close to Antwerpen, from 193428 to September 1996, after which the house was sold and partially demolished.29 The history of the Fraternity was documented by Abbé Willocx, a collaborator of its Founder, Cardinal Mercier. These documents were given to the “Fond Mercier” of the UCL Archives by Professor Jean Ladrière who obtained them from F. Willocx before his death. For an analysis of the religious life of Lemaître, I have consulted some of the files which belonged to Canon Fernand Van Steenberghen30, famous professor at the Higher Institute of Philosophy (Institut supérieur de philosophie) of UCL and who for many years was also a member of the same Fraternity. Finally, I also had access to the documents that belonged to Msgr. Cammaert31, who was in charge of the Fraternity beginning in 1954. I also investigated the archives of the Saint-André Abbey near Bruges for information concerning the apostolate of Lemaître within the Chinese student community;32 these documents are complemented by   This house situated in the place called ‘Puttenhof’, was so to speak the motherhouse of the “Amis de Jésus”. Between 1934 and 1996, the different rectors of the house in Schilde were the abbés vaes, Boon, De Winter, De Vries, Goeyvaerts and Leenaerts (cf. V. De Winter, Geschiedenis van Puttenhof, handout, Schilde, 1973) 29   After the scission of the Diocese of Mechelen, and the creation of the new Diocese of Antwerpen, the “Fraternité sacerdotale des Amis de Jésus” of the Diocese of Mechelen-Brussels, was under the responsibility of Msgr. Cammaert who left the archives in Schilde. In 1995, I had the opportunity to inform his successor Canon Gonzague van Innis, about the location of the Archives, of which he admittedly had lost track. These Archives are now in Mechelen, in the Archives of the Diocese of Mechelen-Brussels. 30   I owe this opportunity to Abbé J. van Steenberghen’s generosity. 31   I had access to documents related to the Amis de Jésus thanks to the kind help of Canon G. van Innis. 32   I owe access to the archives of the Saint-André Abbey to the help of Father Christian Papeians, O.S.B., and to the invaluable assistance of Guy and Manuela Boodts as well as the Nève de Mévergnies familly. 28

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the archives of Fr. Lebbe, held in Louvain-la-Neuve. Professor Claude Soetens, from the UCL Faculty of Theology who studied these archives in depth provided the first detailed account of Lemaître’s dedication to the Chinese students of Louvain.33 These two parallel sources provide the specific theme of this biography, namely his twofold unity of thought and life. On the one hand, his unity of scientific thought insofar as the documents from the AL identify the thread that structures an important part of Lemaître’s scholarly work and extricating it from the limits of the cosmology itself. On the other hand, a unity of life, as illuminated by the AFSAJ, by which Lemaître achieved a synthesis harmonizing a deep interior life with an absolute commitment to the very forefront of scientific inquiry. The conclusions of this work will thus be found in distinct contrast to traditional analyses of Lemaître which portray, superficially in the author’s opinion, a sort of duality in his approach to natural and human realities, i.e. a man who followed two paths only intersecting at infinity. The studies of these two sources together allowed some previous gaps in the author’s previous research to be filled in. For example, there had been insufficient attention to situating Lemaître’s cosmological research34 within the historical development of the expanding universe. Similarly, the studies dedicated to the science-faith rela-

  The file “Chinese Connection” [connexion chinoise] (AL). The archives of the SaintAndré Abbey and those of Fr. Lebbe, completed by a few letters coming from the AFSAJ, constitute the main source of information regarding the activity of Lemaître in the Chinese community. It is not impossible that some documents still lie within the files of the “Société des Auxiliaires des Missions” (SAM). 34   There are some partial studies on non-cosmological research. One may mentioned the work of R. Dejaiffe, “Les contributions de Lemaître au problème general des trois corps’’, Hervelé, Centre de physique nucléaire, 1967, Institut d’astronomie et de géophysique Georges Lemaître, II ; of P. Lipnik, “Architecture de Mgr. Lemaître en arythmétique”, Revue des questions scientifiques, t. 168, 1997, no 2: 161-178. One may add the short studies that it is possible to find in the special issue of Ciel et terre (op. cit.). Nevertheless, there is no in-depth study about his works related to spinors (even if A. Deprit took up this topic in his paper: “A.S. Eddington’s E-numbers”, in Annales de la Société scientifique de Bruxelles, serie I, t. 69, December 1955, no 2: 50-78. 33

I. From Louvain to Namur

31

tionship in Lemaître’s works35 did not properly take into account two important and linked components of his sacerdotal life, namely his membership in the Amis de Jesus and his engagement with the Chinese student community as underscored by Fr. Lebbe. Thus, the full dimension of Lemaître’s interior life could have appeared to certain authors as marginal36 when compared to his scientific life, which was obviously not the case.

3. Guide to this work Readers who do not possess any scientific background or those who want to discover the aspects of the life of Msgr. Lemaître that are not related to mathematics or physics may read first chapters 1, 2, 3, 4 (except section 4), 7, 9, 12 (except section 3), 13, 15, 16, 17, 18 (except section 2), 19 and 20. Readers with a minimal scientific background may read without difficulty chapters 4 (section 4), 5, 6, 8, 11 and 18 (section 2). Only chapter 10 requires the reader to be conversant in algebra, along with a keen interest in this topic.

  O. Godart, M. Heller, “Les relation entre la science et la foi chez Georges Lemaître”, Pontificia Academia Scientiarum commentarii, Vol. III, no 21: 1-12; J. Turek, “George Lemaître and the Pontifical Academy of Sciences”, Vatican Observatory Publications, Vol. 2, 1989, no 13: 167-175; E. Boné, “Georges Lemaître, prêtre”, Louvain, Novembre 1992, no 33: 26-28; J.-Fr. Robredo, “Les idées cosmologiques de Lemaître entre science et religion”, Observatoire de Meudon, 1993, GDR Cosmologie et grandes structures. Histoire de la cosmologie; J.Fr. Robredo, “Entre fiat lux et Big Bang” in L’histoire cahée de l’astronomie, hors-série no 6, Ciel et espace, 1993: 38-43. 36   Witness of this opinion, the sentence of Isabelle Bris: “Il faut dire que depuis toujours, Lemaître, bien que peu actif en tant que prêtre, est plutôt bien vu au Vatican…” (one must say that since always, Lemaître, despite being scarcely active as a priest, is quite well viewed in the Vatican.”) (“L’abbé Lemaître: le père du Big Bang”, Ciel et Espace, April 1993, no 279: 58-63. The quote can be found on page 62). 35

Chapter II

The early years: the Jesuits, mathematics and the mines (1894–1914)

1. A Son from the Pays Noir

T

he life of Georges Henri-Joseph Édouard Lemaître began on 17 July 1894, at 10 Rue du Pont-Neuf in Charleroi, half-way between the bridge that gives its name to the street and the Rue de Montignies. The son of Joseph Lemaître1 and Marguerite Lannoy2, the young Lemaître came from a family with roots most likely in Courcelles in the northwest of Charleroi, dating from the 18th century. In fact, the ancestors of Georges had been present in Courcelles well before the foundation of the city of Charleroi.3 From 1718 until the 1760s, one could regularly find several ‘Lemaîtres’ in the administration of city affairs.4 The direct ancestors of Msgr. Lemaître, Pierre-Joseph (who died in Courcelles in 1774), Jean-Joseph (1720 Joseph-Achille Lemaître was born at Charleroi 10-03-1867 and died in Brussels 7-11-1942. 2   Marguerite Lannoy was born 9-04-1869 and died in Brussels 25-3-1956. She was the daughter of a brewer in Charleroi. 3   Letter of Alphonse Lemaître to “Monsieur le Flâneur’’ from the newspaper La libre Belgique dated 25 January 1960 (Copy sent to G. Lemaître by Abbé Oscar Leclerc, parish priest [curé] of Courcelles with a letter dating from the 17-02-1960, AL). My text owes much to the details provided by Alphonse Lemaître; at the time of this letter, the latter, architect and expert property surveyor, was communal councilor of Courcelles. Alphonse Lemaître is a descendant of Pierre, Hubert, Joseph and Pierre-Joseph Lemaître, the father of Clement. 4   Élie Lemal, Courcelles. Son histoire, 1930. I am grateful to Cl. Cabiaux and Ch. Tilmans for bringing my attention to this work. Between 1718 and 1728, one may find a man by the name of André Lemaître serving as alderman in Courcelles. 1

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The Atom of the Universe

1786)5, Pierre-Joseph (1759-1830)6 and Clément Lemaître all came from the area and were weavers by trade, a business passed down from father to son.7 It was as a weaver that Clément registered for an Infantry Regiment of Napoleon (“II 2ème de Ligne”) together with some other soldiers from the “Old Guard” from Courcelles. Twice wounded in action, he was demobilized after the Battle of Waterloo. Awarded the Médaille de Sainte-Hélène, Clément retained a respect for the deposed Emperor bordering on veneration. Alphonse Lemaître relates that Clément even carried the respect due to his emperor to the point that he stood to attention when someone said Napoleon’s name.8 Nevertheless, Clément’s military career did not end with the imperial downfall. This man with an impressive stature became, on 29 May 1831, a lieutenant of the Belgian Civil Guard, from which he commanded the 5th company, comprised of 110 men from Courcelles. He would end his life as a merchant, his body later being buried at Courcelles’ cemetery before the Calvary scene, in a grave surmounted by a sarcophagus made of stone. Édouard-Sévère-Joseph Lemaître (1824-1894)9 was the third child of Clément and Rosalie Desomme.10 Édouard-Sévère was only four years old when his mother died and his father Clément then wed Victoire Desomme11, the sister of Rosalie. Unfortunately, Rosalie in   He married Anne-Marie Mascaux 30-07-1741.   Born and died in Courcelles. Coalman (1820) and weaver (1824, 1830), he lived in the hamlet of Sartis in Courcelles. He married Marie-Catherine Mascau(x) 6-01-1781.   7   This was confirmed by in-depth research from the jurist and genealogist Guy Boodts. Genealogical research on the Lemaître side was first carried out by doctor Édouard Lemaître (godfather of Msgr. Lemaître) assisted by Mrs. E. Samain-Lemaître, from Courcelles (daughter of Julie Lemaître). More recently, this work has been carried on by Robert Possoz, and the entire Lemaître family tree has been digitally preserved thanks to M. Armand Watteyne.   8   A. Lemaître, Letter, op. cit.   9   The only official document concerning the birth of Edouard-Sévère is his baptismal certificate. This certificate would be recognized by the tribunal of Charleroi 01-041854, five months before his wedding. 10   Born in Courcelles 02-11-1799, married 19-07-1820, died in Courcelles 26-04-1828. 11   Born in Courcelles 15-04-1794, married 25-02-1829, died in Courcelles 12-12-1835.   5

  6

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turn died when Édouard-Sévère reached eleventh grade. His father subsequently married for the third time with Marie-Philippe.12 At the time of his wedding on 6 September 1854 to Alexise-Catherine-Joséphine Allard (1831-1898), Édouard-Sévère no longer lived in Courcelles, but in Montigny-sur-Sambre. He became the general manager of the Société des Charbonnages de Bonne-Espérance before adopting a career as merchant dealing in timber for mines. To date, there is no documentation that can help to clarify the precise history of Édouard-Sévère between 1829 and 1854. According to stories passed down through the Lemaître family, it seems that his departure from Courcelles occurred when he was relatively young and in difficult circumstances.13 However, what is more certain is Édouard-Sévère’s own personal interest and expertise in coal mining; indeed, since the 18th century, the Lemaître family has been occupied both with weaving and the coal trade. On 26 October 1774, the Marquis de Chasteler and Courcelles, Seigneur de Rianwelz, granted a claim to the Lemaître family which was situated in the place called Trieu des Agneaux. This concession, intended for the mining of the bituminous coal found there, was a part of Courcelles which fell under the Marquis’ jurisdiction, more precisely in the south of this area where the bridge on the brook called Claires-Fontaines serves as a natural boundary. The grandfather of Édouard-Sévère, Pierre-Joseph (+1830) the second child of his family, obtained on 27 February 1817 the renewal of the license for the mining the anthracite at Trieu des Agneaux  because he had supplied to the châtelain, according to family history, a particularly beautiful woven piece of cloth.14 However, individuals like the Lemaître family   Born in Gosselies 11-06-1801, died in Courcelles 18-04-1883.   Msgr. Lemaître’s nephew, André Lemaître, while acknowledging that the account was possibly apocryphal, stated: “…this history shows a young boy of 14 years old escaping his stepmother…And this is the arrival in Marcinelle, the work of a lamplighter in the mines […]; twenty years later Édouard-Sévère was director of the colliery of his childhood. (“L’oncle Georges”, testimony on the occasion of a tribute to Msgr. Lemaître, Collège du Sacré-Coeur, Charleroi, 26-10-1991.) 14   Continuing the testimony of Alphonse Lemaître. 12 13

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who exploited the bituminous coal deposits of Courcelles, sooner or later competed with, and came into conflict with more powerful operat­ing companies. The latter eventually won and Pierre-Joseph Lemaître lost the right to anthracite exploitation in the Trieu des Agneaux on 12 May 1821. The family was to regain this right thanks to a royal decree on 31 March 1845, and on 20 August 1849, the Societé du Trieu des Agneaux expanded its operations into the neighbouring district of Roux. In 1853, the Société Anonyme des Charbonnages du Nord de Charleroi, whose financial capital is predominantly French and whose headquarters is at Sart-lez-Moulins, acquired the lease of approximately 34 hectares of Trieu des Agneaux.15 It was in the following year that traces of the runaway Édouard-Sévère are to be found in Montigny-sur-Sambre, where he later became a director in the coal industry. Like his father, Édouard-Sévère was possessed of a strong personality. Freedom-loving and enterprising, both were leaders of men endowed with courage, great intellectual faculties and an undeniable originality. Edward Sévère was to have six children: two daughters, Maria and Laura, and four boys, Achille, Édouard-Justin16, Jules and Joseph who were to become scholars. The younger brother, Joseph, was the father of Msgr. Lemaître and studied law at the Université Catholique de Louvain before becoming director both of a marble quarry in Villers-le-Gambon17, and a glass factory on the outskirts of Chaleroi. Joseph was a generous and kindhearted man and his deep   For this information, I follow here E. Lemal, op. cit: 13-27. For a general history of the collieries in the region of Charleroi, I refer to a study of J.L. Dalaet, “Les charbonnages of Charleroi aux XIXe et XXe siècles” in Huit siècles de charbonnage. Colloque Meuse-Moselle II. Namur, 9-11 September 1999 (P. Wynants et H.-H. Herrman, eds), Namur, CERUNA, 2002. 16  Edouard-Justin would become a doctor and be chosen as godfather to Georges Lemaître. The godmother of the latter was Olympe Sablon, the mother of Marguerite Lannoy. 17  There exists a photograph published in the Belgian journal: Le Patriote illustré (26 juillet 1925, 48e année n° 30) showing Lemaître near Msgr. Heylen (bishop of Namur) and Mr. Broussier (Mine engineer, president of the Society of marble quarries during the celebration of the 25th birthday of the Society). 15

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faith and fidelity to the Church that was directed towards the essential without, however being overzealous.18 Consistent with this line of the family, Joseph was undoubtedly endowed with great intellectual originality. On August 30, 1893, Joseph married Marguerite Lannoy. Strength of personality also seems to have come to Msgr. Lemaître through the maternal line as well; she is famously quoted once as saying19: “If I were a man, I would have been at the top of the Himalayas.” Joyful by nature, she was also courageous, with a demanding attitude towards homework and an insistence on punctuality at mealtimes.20 She avowed unbounded affection for her son Georges, her “hero”21 but, nevertheless, her affection was sometimes very selective in relation to some of her grandchildren and her temperament revealed a certain rigidity from time to time. An intellectual woman, she also appears to have been a woman of deep faith,22 an attribute which was certainly passed down to her son. Joseph and Marguerite would have four sons: Georges, Jacques, Maurice and André23. A close-knit family, they lived for a while within the Charleroi community, in the ease provided by the income from   He humorously commented that “The shorter Masses are the best ones, because none can pray more than an hour without looking at the women’s dresses. (oral communication of Ch. Houyet-Lemaître, 03-08-95). 19   Oral communication of Gilbert Lemaître (24-03-95). 20   As reported by André Lemaître: “For her, duty, discipline, exactitude were not vain words. As much beloved as he was, her Georges was obliged to respect the hours of meals. I would not be surprised that she was the only person to whom he recognized fully her authority, though his sense of humor allowed him some escapes. Thus, this quip said with a deep voice, one day as he was entering the dining room, …at dessert time: “I don’t excuse myself, because I am inexcusable’ ” (“L’oncle Georges”, op. cit.). 21   She compiled several albums depicting Georges Lemaître’s career with the utmost care. These albums contain photographs and newspaper clippings that have helped us to establish the chronology of Msgr. Lemaître’s life with greater precision. 22   One significant example: when she learned about the fatal heart attack that had struck down her husband in a tram, while at “Rue de la Loi” in Brussels, on 12 November 1942, she went to her cousin saying at every step “Thy will be done” (oral communication of Ch. Houyet-Lemaître, 03-08-95) who accompanied her on that day. 23   Jacques (born 10-03-1896), Maurice (born 06-07-1898), André (born and died in 1901). 18

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their father’s glassware business. The inventiveness and originality of Joseph Lemaître led him to experiment with a new glass drawing process. This method also prefigured the technique that would make the reputation of the famous Glaverbel glass manufacturer. Unfortunately, a fire ravaged the company of Joseph Lemaître who, poorly insured, was left destitute. Despites this terrible ordeal, Joseph showed remarkable generosity, borrowing money from his cousins to pay his debts and especially to make sure that all of his employees were paid. His deep honesty and sense of social justice did not go unnoticed in the business community and undoubtedly helped him to find a new professional situation well-matched to his talents fairly quickly. He became, to all intents and purposes, a trustworthy man of the Société Générale in Brussels24, where he acted as a legal advisor to whom the bank entrusted large sums of money. Together with his family, he left Charleroi to settle in the capital in October 1910, more precisely at number 9, Rue Henri de Braeckeleer, a small quiet street not far from the Cinquantenaire and Saint-Henri’s Church. If the façade of the residence was pretty, the interior was comfortless, lacking even electricity. Madame Lemaître was to reign over the house until her death in 1956. Georges Lemaître enjoyed a deep attachment to his family throughout his life. He loved and respected his parents deeply, having frank and deep discussions with his father, often during the walks, especially when Joseph had to say something important to his children.25 The boundless admiration and affection Marguerite held for her son Georges was also in fact entirely reciprocal. Although George   He would specialize in questions related to the Belgian Congo. After his retirement, he rendered service at the Société Générale. It was while returning from one of his overtime days that he died. (Oral communication of Ch. Houyet-Lemaître (03-07-95) and G. Lemaître (21-5-99)). 25   On those occasions, he would thus say: “We are going to make a tour of the garden”. This is perhaps, as suggested by Gilbert Lemaître (oral communication 21-05-99), the origin of the well-known tradition of the walk that Georges Lemaître took after his lunch time at the restaurant Majestic in Louvain along with one or many collaborators (often Odon Godart before 1939 and after 1959) and during which the cosmologist was given to sharing his scientific or other concerns, 13-6-95; Cf. Godart, “C’était l’un des nôtres: Georges Lemaître (1894-1966)”, Louvain, Juillet 1983, no 2: 7-19. 24

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did not often send news26 to his mother during his stays in the United States before the Second World War, he never failed to show his affection when he returned to live with her between 1944 and 1956. In the late 1940s and early 1950s, George often accompanied his mother on vacation during the month of August in Switzerland, in Montreux or in Brunnen. His albums of photographs contain a remarkable number of photos of his mother.27 When she was sick, he lavished her with gifts and celebrated Mass in her room every day. The first act that Canon Lemaître performed a few minutes after his mother had taken her last breath was to celebrate Mass in rememberance of her soul. Georges Lemaître enjoyed great family holidays, birthdays, weddings28 and even small intimate meetings such as the New Year’s Day gathering with his brother Jacques, Christiane Houyet-Lemaître and her husband Michel, at the Hôtel de Postes in Dinant, south of Namur. George Lemaître was also interested in the life of his nephews   This was not surprising since Georges Lemaître never held any systematic correspondence with his collaborators or with his family. One journalist (J.K.) had published, in La libre Belgique (23 January 1960: 1), an article entitled “Portrait. Le chanoine Lemaître. Du Cosmos aux précieuses ridicules”. In this article, he told about Lemaître’s reaction when the latter saw him for the first time at the “Collège des Prémontrés” (ancient College of the Premonstratensians (Norbertines) built in 1571 and rebuilt in 1755, where was located the Institute of Physics in Louvain until some time in the 1960s): “This is you? So much the better, I won’t have to answer your letter!’’ I laughed. I did not tell him that one of my good colleagues just told me: “He would not answer you, he never answers. One needs to get him out of his lair [In French: Le débusquer de son gite; Translator’s Note]. In a letter dating from around 1960 (AL), Odette Lemaître wrote to his uncle: “I know that you hate to write but however, I would like so much to get informed […]”. O. Godart had told that he obtained almost no news from Lemaître regarding his work, who had departed for the United States, during his first years as a Ph.D. candidate, 1933-1934 (oral communication, 16-03-95). Mrs. Lemaître, not having news either, put O. Godard in charge of transmitting an urgent message to her son requesting an answer. After the transmission of a telegram, a laconic answer came back: “I am fine. Signed Georges”. After his return from the US, upon Godart’s questioning him: “Why you did not answer me?”, he received the lame answer “I could see that everything was fine!”. 27   I owe the opportunity to consult those albums to the generosity of Christiane Houyet-Lemaître and the friendly collaboration of Paul and Anne Houyet. 28   Georges Lemaître loved celebrating the weddings of his own family. (Cf. homily preached at the wedding of Christiane and Michel Houyet 03-07-1947, preserved, notably, at the AL). 26

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and nieces, whom he visited quite often and he concerned himself with their musical education.29 30 Msgr. Lemaître was keen on maintaining family traditions such as the “ladies toast”, which came from his father.31 During family meetings, as the meal had just started, he would rise and toast32: “I would think that I had missed my most sacred of my duties if I did not raise this glass to the health of the hostess of the house and the ladies who were willing to honour this family celebration with their presence”. Georges Lemaître would remain attached to his Charleroi roots. It was with great pleasure that he participated in the friendly regional celebration “à la Carolo”,33 gathering students from Charleroi in Louvain on the very same evening he was rewarded the Francqui Prize on March 17, 1934. It is not surprising, therefore, that the most faithful collaborator and friend of Lemaître was Odon Godart, a son of Charleroi and who came from the same College. The newly promoted President of the Pontifical Academy of Sciences accepted the invitation of Abbé Oscar Leclerc, priest of the parish Saint Lambert of Courcelles, to attend an academic session and to celebrate a Mass for the millennium of the parish, organized by his distant relative Alphonse Lemaître.34   Odette Lemaître, Jacques’ daughter, for example was invited at the age of eight by Georges Lemaître to attend a violin concert broadcast by the Belgian radio, then to a concert of Arthur Schnabel at the “Palais des Beaux-Arts” in Brussels (oral communication, Odette Delenne-Lemaître, 28-11-97). 30   Christianne Houyet-Lemaître recalled the frequent visits of her uncle in her house. 15 Rue du Jardin at Onhaye near Dinant. Her brother Pierre Lemaître holds pleasant memories of the visits of Georges Lemaître to his house in Winterslag in the Limbourg region and the long walks that he took with him. (Oral communication, 08-12-97). 31  The father of Msgr. Lemaître had a keen interest in classical literature, but also Walloon poetry in which he like to recite from time to time. (Oral communication, G. Lemaître, 21-05-99). 32   Oral communication of Ch. Houyet-Lemaître (03-07-95) confirming what was told by Gilbert Lemaître to V. De Rath (Georges Lemaître, le père du Big Bang [with the collaboration of J.-L. Léonard and R. Mayence]. Éditions Labor, 1994: 68). 33   Cf. O. Godart, “C’était l’un des nôtre…”,  op. cit. 34   Beside the two documents mentioned above, the files of AL covering the millennium event of Courcelles (Manifestations du Millénaire) comprise two letters (dated 31 March and 8 September 1960) addressed by Alphonse Lemaître to Msgr. Lemaître. 29

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2. At the Jesuit school Lemaître entered the Jesuit College of Sacré-Cœur in Charleroi in September 1904, to begin Greco-Latin humanities. The honours and certificates of merit35 he obtained during these six years of studies clearly illustrate his capacity to distinguish himself in mathematics as early as the second year. During the last two years, he added physics and chemistry to his list of achievements, but interestingly he never received any academic award for religion and it was not until he studied poetry and rhetoric that he obtained a certificate of merit in this branch. For poetry, he had Fr. Franz Charlier (1880-1963)36 who had just finished his classical philology studies at the Catholic University of Leuven and who would undertake, from 1933 to 1958, a career as professor of Greek at the Facultés Universitaires of Notre Dame de la Paix à Namur (Université de Namur), while for rhetoric he was taught by Fr. Goosens (1872-1943). Unlike his colleague Charlier, Goosens had made little progress in his secular studies. However, he was a forceful personality and a leader among the Caroloregian rhetoricians from 1909 until 1921, during the period when he was appointed as rector of the College of Mons. In 1914, he took charge of the field ambulance unit that had been established at the College. In the last two years of his studies in the humanities, Lemaître encountered a lively and creative professor of science, Fr. Ernest Verreux (1878-1938). It was Fr. Verreux, who during his stay in the Jesuit College of Verviers, in 1915, conceived and managed to set up the first Catholic radio station in the country. Verreux was the model of the scholar-priest who did not hesitate during science classes to undertake apologetic reflections with a mix of irony and eloquence which undoubtedly left an indelible impression on the young Lemaître.37   Archives of the “Collège du Sacré-Coeur” at Charleroi.   “Notice biographiques. Le P. Franz Charlier”, Échos, Février, 1964: 23-26 and “In memoriam. La mort du R.P. Charlier, S.J.”, Contacts, June 1963, no 25. 37   Father Verreux was extremely competent in mathematics and the natural sciences; nevertheless, his classes, while often original, were reputed to be unclear. 35 36

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Through contact with this kind of priest young Georges discovered that one could live a true life of faith along with an active openness towards science. In 1933, in an interview given to the journalist Duncan Aikman from the New York Times, Lemaître mentions an anecdote that shows that the Jesuits likely played a significant role in the development of his thought, regarding the relationship between science and faith, an issue that will be discussed later.38 Lemaître tells of a classroom scene in which he participated, an old father was expounding at the desk. Before him sat the lad who was to discover the expanding universe and who, even then, was full of science, in his eagerness the lad read into a passage of Genesis an anticipation of modern science. “I pointed it out” said Lemaître, but the old father was skeptical. “If there is, then it is a coincidence“, he decided, “it is of no importance. Also if you should prove to me that it exists I would consider it unfortunate. I would merely encourage more thoughtless people to imagine that the Bible teaches infallible science, whereas the most we can say is that occasionally one of the prophets made a correct scientific guess”.

At the Collège du Sacré-Cœur, Lemaître would do all of his humanities studies alongside Fernand Renoirte.39 The latter would become a professor of science and philosophical cosmology at the Louvain Institut Supérieur de Philosophie (Higher Institute of Philosophy), after moving one year ahead of his fellow Lemaître in the civil engineering applications. Their interest in science, and later their priestly vocation, would make them friends. As young priests, they

 “Lemaître follows two paths to truth. The famous physicist, who is also a priest, tells why he finds no conflict between science and religions’’, The New York Times Magazine, February 19, 1933: 3. 39   J. Ladrière, “M. Le Chanoine Fernand Renoirte, professeur à la Faculté des sciences et à l’Institut Supérieur de Philosophie. 1894-1958. Éloge académique prononcé aux halles universitaires le 16 mars 1959”, Annuaire de l’université catholique de Louvain, t. III, 1957-59:97-119. 38

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were often to be seen side by side in photos.40 Strangely, however, the two men who had everything to agree41 upon would keep their distance, with Renoître increasingly committed to philosophical research for which Lemaître had only slight interest.42 The departure of the Lemaître family for Brussels coincided with the matriculation of Georges at the advanced science class of the Nouveau Collège Saint-Michel in Etterbeek,43 not far from de Braeckeler Street. The young Lemaître, in the tradition of children of the Pays Noir had chosen, for the academic year 1910-1911, to prepare himself for the entrance exams of mining engineering studies. Within the advanced science class, mathematics was taught by Fr. Henri Bosmans, a good teacher44 and specialist of the history

  For instance: the picture of the 04-10-1926 showing the Abbés Lemaître, Renoirte, Théodore Genin and Léon Devisé (private collection of Mrs. de Biourge-Renoirte, sister of F. Renoirte). This picture can also be found in one of the albums of the Lemaître family (private collection of Mrs. Ch. Houyet-Lemaître). 41   It is worth mentioning here that as early as the 1920s, Renoirte would write two papers about special relativity: “La théorie physique. Introduction à l’étude d’Einstein”, Revue néo-scolastique de philosophie, November 1923 and “La critique einsteinienne des mesures d’espace et temps”, Revue néo-scolastique de philosophie, August 1924. To the best of anyone’s knowledge however, Renoirte never incorporated the general relativity and the relativistic cosmology in his philosophy of sciences. 42  According to the testimony of Etienne de Biourge, Renoirte’s nephew, Lemaître would have not appreciated the characteristic Neo-Thomism of his college fellow’s thought (oral communication, 04-05-99). The implicit philosophy of Lemaître that put the emphasis on this testimony will be analyzed further at a leater point. Curiously, the notorious course of Renoirte: Éléments de critique des Sciences et de Cosmologie (Louvain, Éditions de l’Institut supérieur de philosophie, 1945), does not make any mention of the writings of Lemaître, while Einstein, Eddington, Urey (Nobel Prize of Chemistry, 1934) as well as the mathematician Painlevé are mentioned. 43   The college was established in Etterbeek in 1905 after having moved from the “Rue des Ursulines”. For the history about the Higher Scientific Course [“Cours scientifique supérieur”], I refer to the paper of Fr. Jean Nachtergaele, “Une pépinière d’Officiers, d’ingénieurs et de pilotes. Le cours scientifique supérieur” in Les Jésuites belges. 15421992. 450 ans de Compagnie de Jésus dans les provinces belgiques, Brussels, AESM Éditions: 203-205. 44  At the archives of the French speaking province of the Belgian Jesuits, one may consult some manuals written by P. Bosmans. His “Notes d’algèbres, autographes” (Louvain, Editions Ackermans, 1902) contain some chapters which are most interesting, for instance the one on continued fractions (pages 41-76). 40

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of mathematics.45 Bosmans had a  distinct influence on Lemaître’s thought and, later in the methodology of mathematics class and courses of mechanics, he was to discover his strong interest in the history of mathematics. He preferred to read and comment upon original texts: Euclid in Greek; Euler, Gauss and Jacobi in Latin, etc. which enabled him to discover gems inaccessible to those who proceeded from secondary source materials. Furthermore, Canon Rome, a professor at the Université Catholique de Louvain, would request Lemaître’s assistance in establishing an analytical index of the historical works of Bosmans.46 In turn Lemaître, who would follow the historical works of Rome,47 would suggest in the late 1950s and early 1960s, that he should make his students work on texts of Greek astronomy in order to date some important discoveries with precision.48 It is plausibly during the years spent at the Jesuits that the appeal of the priesthood for Georges Lemaître began, an interest already detected at the age of nine, during the same month that he decided to become a scientist.49   H. Bosman (1852-1928) never undertook studies at the university in mathematics. Nevertheless, he would become one of the most important specialists of the history of mathematics in the Netherlands in the 16th and 17th century. He also had a thorough knowledge of Greek mathematics having studied them in the original (cf. P. Peeters, “Le R.P. Henri Bosmans, S.J.”, Revue des Questions Scientifiques, Vol.13, 1928: 201214; H. Bernard-Maître, “Un historien des mathématiques en Europe et en Chine: le P. Henri Bosmans, S.J. (1852-1928)”, Archives internationals d’histoire des sciences, Vol. 3, 1950: 619-656. 46  A. Rome, “Le R.P.H. Bosmans, S.J. (1852-1928) Notice biographique and index analytique de ces travaux historiques”, Revue des Questions Scientifiques, Série A, t.49, 1929, no 1: 112. 47   There is for instance at the AL, a paper from Canon Rome on the publications in history of mathematics (“Revue des recueils périodiques: -I. Histoire des mathématiques”, Revue des Questions Scientifiques, 4th series, t. XXII, September 1932, no 2: 261-288), with annotations from G. Lemaître. 48   According to René Dejaiffe, who worked with G. Lemaître and O. Godart between 1963 and 1965, some dissertations written by Canon Rome were supervised by both Lemaître and Godart (oral communication, 30-10-97). 49   “The Abbé proceedes to illustrate by his own life how it is possible for a priest to be a scientist […] He takes you back to a time when he was 9 years old, because it was then when most boys are interest only in games, that he decided to become a scientist […]. ‘What is most significant’ he continues ‘is that exactly at the same time, actually in the same month as I remember it, I made up my mind to become a priest.’”(D. Aikman, “Lemaître follows two paths to truth”, op. cit: 18.) 45

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He even briefly thought to enter the Society of Jesus.50 Before the Great War, he had already confided to his parents his desire to become a priest. His father, while admitting his pride in seeing his son pursue this path, however, asked him to continue his studies, as he thought Georges still too young.51 As shall be seen, this request of Joseph Lemaître proved wise.

3. The mines: a blind tunnel? After having passed the entrance exam to the Engineering School (Écoles Spéciales des Mines, des Constructions Civiles, des Arts et Manufactures, d’Architecture et d’Électricité) in Louvain, on 11 July 1911, Lemaître undertook his university career by registering in the first year of engineering studies, as well as in a bachelor’s degree in Thomistic philosophy, a complementary diploma of the Institut Supérieur de Philosophie, which allowed students of all disciplines to acquire some basics in neo-scholastic philosophy.52 At the time he started his bachelor’s degree, Msgr. Deploige was the president of the institute that had been founded in 1894 by the future Cardinal Mercier in order to foster a revival in Thomistic   “I did not know if I would become Jesuit or Benedictine or secular” (J.K. “Portrait. Le Chanoine Lemaître. Du cosmos aux précieuses ridicules”, op. cit.) Lemaître kept close contact with the Society of Jesus. This was confirmed by Fr. Charles Courtoy (oral communication, 17-10-95), physicist, who remembered the visit made by G. Lemaître to the young Jesuits of Louvain, who had invited him during the Second World War. The cosmologist insisted on the central role played by the Society to ensure that the Church would not “switch off from the scientific world”. 51   “I had the vocation: before the war, my father found me too young to decide by myself’’ (J.K. “Portrait. Le Chanoine Lemaître. Du cosmos aux précieuses ridicules”, op. cit.). It is not clear if “before the war” means before his engineering studies (1911) or during these studies (1911-1914). Nevertheless, the fact that he started the bachelors degree in Thomistic philosophy as early as the new term 1911, may lead one to believe that he had already informed his parents about his final choice to become a priest during his Cours scientifique supérieur. 52   Information concerning the philosophy class attended by Lemaître can be accessed by consulting the program of courses (1911-12 to 1919, Archives of UCL, Louvain-laNeuve). 50

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studies.53 George was probably introduced to philosophy by L. Christmas, whose thinking attempted to combine Thomism and Cartesian philosophy. He attended the class of philosophy of M. De Wulf as well as the courses in the metaphysics of theology of N. Balthasar. The scientists who enrolled in the bachelors studies were required to take a number of additional courses. In this context, he would also attend the courses of A. Thiery and A. Michotte in physiology, natural law and in social philosophy of Deploige. Thanks to the class of D. Nys, Lemaître would discover philosophical cosmology. Among the details which are perhaps not without importance for the future life of Lemaître, as we shall see, was the invitation to Vincent Lebbe to attend a series of conference entitled: “Impressions on Chinese Philosophy”.54 Georges Lemaître began his preparatory classes for the degree of mining engineer with Charles Manneback,55 who he would later meet as a colleague in the Faculty of Sciences of UCL. A deep friendship would bind these two scientists throughout their lifetimes. During the first two preparatory classes leading to the engineering degree, Lemaître attended the lectures of analysis of Charles de la   Cf. De Raeymaker, Le Cardinal Mercier et l’Institut Supérieur de Philosophie, Louvain, 1952. 54   According to the booklet containing the UCL academic calendar, those conferences took place during the academic year 1913-14, Wednesdays at 3:00 p.m. 55   Charles Manneback (09-03-1894 – 15-12-1975) was one of the closest friends of Georges Lemaître. He completed his study of engineering in 1920 before obtaining, three years prior to Lemaître, the title of Doctor of Sciences at MIT. After beginning his career as a telecommunications engineer, he was appointed lecturer [chargé de cours] of the Faculty of Sciences of UCL in 1922. Understanding quantum mechanics and knowing how to apply it, he naturally excelled in molecular physics. He worked with some of the most eminent scientists such as Debeje (1925-1927), Heisenberg (1928-29), Bohr (1931-32) and finally Fermi (1935-36). I refer the reader to the beautiful synthesis of Patricia Radelet, “Charles Manneback. 9 March 1894-15 December 1975. Les débuts de la mécanique ondulatoire”, Revue des Questions Scientifiques, t. 161, 1990: 289-308. This physicist of great distinction, a single man entirely devoted to science, had an influence on several of the research works of Lemaître. He was a valuable source of scientific information for Lemaître, who did not read specialized literature about physics during the second part of his life, (oral communication of O. Godart, 14-06-95). 53

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Vallée Poussin (1866-1962) ,56 the famous mathematician, a student of Jordan, Poincaré, Schwarz and Frobenius, whose works would influence the history of his discipline, in particular those relating to the famous demonstration of Gauss’ conjecture on the asymptotic distribution of prime numbers. Becoming president of the Pontifical Academy of Sciences, Msgr. Lemaître, would give, on 4 October 1962, a tribute to Charles de la Vallée Poussin, who had been a member of this Academy since its creation. The speech shows the influence left by the latter on his pupil (1962, p. 3): Eleven years ago, at the age of 85, he still held the Forum of the Scientific Society of Brussels, for which he had always been the Secretary. I retain an unforgettable memory of the enthusiasm, of the nearly childlike joyfulness with which he grabbed the chalk to draw figures and formulas on the blackboard with, it seems to me, the same greenness to the time where, as a student, I had my first introduction to mathematics.

Georges Lemaître encountered analytical mechanics in his studies, which would play such a significant role in his work, thanks to the lessons of Ernest Pasquier (1849-1926). This scientist, who had studied at the University of Ghent, was the student of Paul Mansion (18441920) who promoted the study of the geometry of elliptic space that one finds at the heart of the cosmological model of Lemaître.57 This   To place the professors of Lemaître in the context of the history of mathematics at UCL, I refer to the following studies: (1) A. Deprit, “Georges Lemaître – Les années d’apprentissage” in Quelques étapes de l’histoire de l’astronomie et de la géophysique en Belgique. Actes du colloque du 14 mars 1986 (A. Berger and A Allard, ed.). Louvain-la-Neuve, 1987, travaux de la Faculté de philosophie et lettres de l’UCL, XXXIV; Institut d’astronomie et de géophysique Georges Lemaître; Centre d’histoire des sciences et des techniques, Sources et travaux, III: 95-108. This study focuses on the formation of Lemaître (1910-1914); (2) J. Mawhin, “Une brève histoire des mathématiques à l’université catholiques de Louvain”, Revue des Questions Scientifiques, t. 163, 4e trimestre 1992, no 4: 369-386. 57  “Allocution de M. le Professeur Ch. Manneback”. (“Séance académique tenue à Louvain le 19 avril 1934 en l’honneur du professeur G. Lemaître, lauréat du prix Francqui en 1934”), Périodique de l’Union des ingénieurs de Louvain, numéro spécial, 1934: 32-33. 56

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class presented a recognizably modern treatment of analytical mechanics. As early as 1901, Pasquier placed mechanics in the context of all the new theories of vectors and built it up by means of a thorough discussion of the principles of this discipline. He was somewhat ahead of his time, and his critique of partisans of the existence of the absolute movement perhaps awakened the critical spirit in the young Lemaître, which would remain for him in its approach towards relativity. In his speech delivered at the funeral of Pasquier, Charles De la Vallée Poussin observed that58: Pasquier became acquainted with the relativistic theories only late in life, however, those theories could not surprise him and I would think rather that they pleased him. It is enough to recall the polemics with which he egged on the relativity movement and the clarity with which he exposed the weight of the metaphysical conceptions on which the support of the reality of an absolute movement was based. Moreover, the philosophical capacities of Pasquier naturally led him to be interested in this kind of question. Did he not bring his erudite collaboration to the Higher Institute established by Cardinal Mercier? He notably provided very beautiful lessons on the cosmogonic hypotheses that were published in the Revue Néo-Scholastique.

Pasquier was indeed in charge of the class on analytical mechanics that was proposed as an optional course for the students of the third year of the Higher Institute of Philosophy. It was in the second halfyear of 1896-97 that Pasquier gave a series of conferences on the diverse cosmogonic hypotheses. As was astutely noted by André Deprit,59 the published version of these conferences60 could not have escaped   “M. Ernest Pasquier, professeur émérite de la Faculté des science. Discours prononcé aux funérailles par M. le professeur Charles de la Vallée Poussin, le 10 avril 1926”, Annuaire de l’université catholique de Louvain, 1927-29: LIII-LVI. The quote can be found at the page LV. 59   “Georges Lemaître – Les années d’apprentissage”, op. cit.: 104-105. 60   E. Pasquier, “Sur les hypothèses cosmogoniques”, Revue néo-scolastique de philosophie, 1897: 282-297 and 347-366. 58

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the attention of Lemaître. Actually, one of the major references among Pasquier`s conferences61 can be found explicitly in one conference having practically the same title as the one Lemaître would give on 10 January 1945 for the Société Royale Belge des Ingénieurs et des Industriels (1945a) which constitutes one of the most famous chapters of his famous book “L’hypothèse de l’atome primitif: essai de cosmogonie” (1946b). The conferences of Pasquier would only confirm the modernity of its scientific thought. Pasquier provided, for instance, a summary of the astronomical knowledge of his time, which included some deliberations on variable stars, an analysis of the spectra of stars as well as on the dimensions of the universe. With extreme caution, and without neglecting any known objections, he shows a preference for the “nebular hypothesis” of Herschel, in which “nebulae”62 appears as “worlds in formation,” and in which “the stars are only the nebular material that would gradually be condensed.” The text ends by evoking the works about the stability of planetary orbits of Gylden and Poincaré which were the most modern of his time. Algebra and geometry were taught in the preparatory class of engineering by Gustave Verriest (1880-1990), the successor of Joseph Antoine Carnoy (1841-1906) whose books on algebra and analytical geometry had influenced several generations of engineers between 1892 and 1905. Verriest, who had prepared his thesis with de la Vallée Poussin, brought some methods of modern algebra from Göttingen (where he had been in contact with Hilbert) that inspired the members of the Bourbaki group considerably. Deeply attached to Flanders, Verriest was a supporter of a bilingual university of Louvain, but without the territorial separation of these two linguistics communities. Later, while leading battle against this separation, Lemaître would   Cf. the work of C. Wolf, Les hypothèses cosmogoniques, Paris, Gauthier-Villars, 1885. The reading of Lemaître’s paper (1945g) showed that the latter explicitly used this work. 62   With the state of the art of astronomy at that time, nebulae appeared as spots of weak and diffuse light of various forms, and which some already consider as distant “worlds”. 61

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often say63: “Alas, the University of Verriest no longer exists!” Lemaître did not seem to have been influenced by the teachings of Verriest.64 We do not find, therefore, the proper style of la Modern Algebra65 elsewhere in his writings or in his own classes. The second year of university for Georges Lemaître marked his first contact with the mathematical physics taught by the Canon René de Munynck. Instructed in research by the German universities, de Munynck had created a small library in the laboratory of Physics of the UCL that would prove of great benefit to the young Lemaître. De Munynck was a figure who easily accepted new scientific ideas and it is largely through him that Georges Lemaître became interested in relativity. He paid noteworthy tribute to De Munynck in the speech he would deliver on 19 June 1918, at his funeral (1948g, p. 270): His everlasting young spirit, showing an enthusiasm that was sometimes a bit naive, was open to all progress and ardently welcomed the novelties of the science at that time: the relativity, the atom of Bohr, and later the quanta [the quantum theory], the new particles, … His lessons of mathematical physics were remarkable and he brought a classic solid educational guidance to our generation, an indispensable basis for a healthy understanding of this kind of revolution of the physics that we have had to live through and which is without doubt not yet finished. Personally, I could never be sufficiently grateful to him for having suggested to me to participate in the competition for travel grants and to have encouraged my still-burgeoning interest in relativity. By redrawing, at this very moment, the stages of his life, I realize that he was only committing me to the way he had followed and had given direction to his career. The initiation into the personal search, to the journey abroad, can make all the difference between a simple teacher and a true master.   Oral communication of A. Meesen (August-September 1998).   A confidence from Verriest to R. Graas (oral communication, 18-10-95) subtly but clearly revealed the distance between the algebraist and the cosmologist. 65   There is one exception (Cf. chap 10). 63 64

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It was also during his second university year that George attended the lessons of Pierre-Jean-Edouard Goedseels (1857-1928).66 This Professor taught astronomy and geodesy, probability calculus and the theory of observational errors. Goedseels was a professor at the Royal Military Academy. He was then deputy inspector at the Observatory of Brussels as well as professor at UCL, where, to some extent, he succeeded Pasquier in astronomy, and Carnoy for courses of probability theory. He had a special interest in measuring instruments and the theory of errors. It is in this context that Goedseels developed some mathematical methods which caught the interest of Maurice Alliaume, who we will soon turn to, and to whom Lemaître would refer by correctly criticizing him in his own class on probability theory given during the war years (1940-1945).67 Goedseels had a passion for teaching calculation to small children, which is not without parallel, as we shall see later, what his student Georges Lemaître would attempt to undertake at the end of his life. Widowed, Goedseels entered the seminary of late vocations at the Archdiocese of Malines in 1923 at 66 years old, at the maison Saint-Rombaut, where he met Georges Lemaître. Contrary to what one might otherwise think, Georges had a great esteem for his master, which was reciprocal.68 Goedseels would indeed be, together with Alliaume, one of two “godfathers” who proposed the candidacy   “M.P-J. Goedseels, professeur honoraire à la Faculté des sciences”, Annuaire de l’Université Catholique de Louvain 1827-29: CVII-CXVII. 67   G. Lemaître, notes taken in the course of probabilities and the theories of errors by Brother Maxime-Léon (R. Graas) during the year 1941-42 (archives Dockx, FUNDP). 68   One could see it in his answer (1934b: 39): “[...] Abbé Edouard Goedseels, who followed me at the seminar and for whom the conversion marked by an inflexible good sense was not one of the least charms of the Saint-Rombaut house”. [translated from the original]. I do not agree here with A. Deprit (“Georges Lemaître – Les années d’apprentissages”, op. cit.: 107) when he asserts: “It is with great delight that two decades later, Lemaître would teach himself this course [concerning probabilities as presented by Goedseels] as if he wanted to take a form of malicious revenge, but on a more serious note since he was a priest, of pseudo-lessons on the least squares that a surveyor dressed up in cassock had inflicted upon him.” [translated from the original] In fact Goedseels wore the soutan only after 1923, i.e. three years after Lemaître had completed his scientific studies! 66

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of Lemaître as a member of the Société Scientifique de Bruxelles, in 1922.69 Being too old and failing to assimilate the Latin language that he had never learnt at school, Goedseels could not enter the priesthood to which he aspired. However, he received minor orders and wore the habit to the end of his days, which he spent in a home for elderly priests in La Hulpe (near Brussels). According to the results of exams, one could guess that Georges Lemaître was not especially motivated by the studies in mining engineering.70 One should imagine that Lemaître rather consented to the traditional path of the brighter children of the Pays Noir or to a paternal suggestion, rather than to follow his own innate interests. Put more positively, it could be said that his mining years led him to discover the kind of scientific subject which would suite him. In any case, Lemaître’s intellectual trajectory after the Great War clearly confirms that his future was destined not for the subterranean, but the cosmic.

  In the archives of this society, I have found the following text: “26 October 1922, on the presentation by circular of the general secretary (dated 14 October 1922), Charles de la Vallée Poussin, Georges Lemaître (doctor in physical sciences and mathematics), 84 rue de Mérode in Melechen, is admitted as a member of the Société Scientifique de Bruxelles (his godfathers are Goedseels and Alliaume) in the first section” (Archives du Secrétariat General de la Société Scientifique de Bruxelles, Namur, FUNDP) [translated from the original] 70   First year Bachelor. “Première candidature” (1911-12): great distinction; second year Bachelor, “Deuxième candidature”) (1912-13): distinction; first year for the degree of engineer of mines (1913-13): distinction. His results from the Ph.D. in mathematical and physical sciences would show, by contrast, that engineering studies were not the place where Lemaître could best apply himself. If one takes into account the interests of Lemaître in retrospect and if one observes in the same time the titles of courses offered in the first year for the degree of engineer of mines, it is possible to understand his lack of enthusiasm. Indeed, that year of course did not constitute mathematical courses properly speaking, but specifically courses of applied mechanics, physics and industrial architecture, topography, etc. (cf. Annuaire de l’Université Catholique de Louvain. 1911: 97-98). 69

Chapter III

The Great War: from student to artilleryman (1914–1919)

1. The long walk to the Yser Front

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he summer holidays of 1914 began as a happy event for the two brothers, Jacques and Georges, 18 and 20 years old respectively. They had planned a bicycle trip in the Tyrol with their friend Carlo Gérard, who later became a Jesuit. The invasion of Belgium in August 1914 transformed their trip to the Tyrol into a long walk to the Yser Front1. One may imagine the disillusionment felt by the lads whose dreams of freedom and happiness were shattered in a single instant. On the other hand, one can also appreciate their courage and self-sacrifice, offering up their health and youth in the defense of their country. Coming from a family of patriots who were deeply attached to Belgium and its King, they decided, without hesitation, to enlist, on 9 August 1914, in the “5e corps des volontaires”. 350 of these young volunteers, including Georges and Jacques, who had only received rudimentary military training, were sent beginning on 13 October to help   Information concerning Lemaître’s war years was obtained with the help of A. Deprit, Colonel Pierre Triest, of the Air Force (letters and documents, 26-3-84 and 12-1184, AL) and with the help of that great historian of the Belgian Royal Military School, Henri Bernard. The research of Colonel Triest was partially conducted with the aid of the basic sources of the Archives of the Brussels Military Museum. The main historical source providing information about the military itinerary of Jacques (regimental number 22311) and Georges Lemaître (regimental number 4260) are, of course, their military records themselves. 1

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one of the six divisions of the Armée de Campagne, the Third Army Division (3D.A.), without provisions or firepower, armed only with the older “Gras” rifles as the first units already engaged had been issued all the much superior “Mauser”. The 3D.A., under the command of General Léman, had already secured the positions between the forts of Liege, had subsequently fallen back under the orders of General Bertrand, to Waremme and Louvain, and the fortified position of Anvers. The volunteers of the 5th Corps, having deepened the trenches between the forts of Anvers, were transferred to different regiments of the 3D.A., which organised the positions east of the Yser that were determined by the line of Sint-Pieters-Kapelle-Leke-Keiem.2 Thus, Georges Lemaître was sent on 10 October to the “9èmede Ligne” (9th Infantry regiment). Lemaître didn’t have much time to rest with his division, which had been in reserve since the 15 October south of Furnes. The 18 of October saw the start of the infamous Battle of Yser, also known as the “Battle of Flanders”. The 9èmede Ligne was engaged with brigades belonging to the reserves of the 3D.A., which have been put at the disposal of the 2D.A., on 21 October. Certain elements of Lemaître’s regiment were caught during a rotation of the troops of this division during the daytime on the right bank of the Yser, and paid heavily in terms of casualties. The 9èmede Ligne was subsequently involved in a particularly heavy period of fighting together with the 3D.A. During the attack, this Iron Division was deployed to the coastal region and would lead to the reoccupation of Lombardsijde. Unfortunately, on 23 October, this area again fell into German hands. Lemaître, with his regiment put at the disposal of the French general Grossetti on 24 October, would take part in repulsing the German troops who had crossed the Yser on a makeshift bridge near Tervate. It was clear that the German breach on the Yser would not last long. After having reached the embankment of the railway of Nieuport in Dixmude and taken Ramskappelle on the 30 Octo  I suggest the book of H. Bernard: Guerre totale et guerre revolutionnaire, BruxellesParis, Brepols, 1966 (cf. T. I, Atlas, croquis 67) 2

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ber, the invaders were forced to retreat to the north shore of the Yser, because the field was flooded owing to the ingenuity of a group of civilians and soldiers who were familiar with the hydrographical possibilities of the region. Over four long years, the Belgian army would resist the invasion, staying along the famous railway. Georges Lemaître therefore took part, often on the front line, in the toughest moments of the Battle of the Yser.3 One may suspect that the engineer-student Lemaître might not have felt that his place was as an infantryman. He was probably satisfied, after nine months of infantry service, to be transferred on 3 July 1915 to the 39th Battery, which constituted, together with the 37th and 38th, the 2nd group of the third regiment of artillery (3A) of the 3D.A.4 His brother Jacques also followed him into the artillery. On 12 September 1916, he was transferred to the General Camp of the Artillery (Dépôt général de l’Artillerie), and on 27 December of the same year he joined the 38th battery of 3A. As could be predicted considering his academic orientation, he was sent to the CISLAA, the centre of instruction for auxilliary artillery officers, on 20 March 1917. He attended courses before joining his battery on 27 September 1917. After his transfer to the first battery of the second group of the 15th regiment of artillery on 5 February 1918, he joined, probably for a training period, the 38th battery via the CISLAA5 on 12 October 1918. His brother Jacques was appointed   The distinctions he received bear witness to this frontline action. Mentioned in dispatches (29-11-18): awarded for exemplary behaviour in a high act of war; “Croix de guerre avec palmes” (Royal Decree of 28-2-21); and the “Médaille de l’Yser”, received from the commander of the 3D.A. on the 15-11-22 (Royal Decree 16469 on the 4-1023), awarded to the 70,000 Belgians who participated in the “Battle of Flanders’’ [la Mêlée des Flandres]. Lemaître had ‘7 chevrons de front’ which indicates that he spent four years at the front (the first chevron being awarded after one year and the others after each six months of presence at the front). 4   Information concerning the 3A was provided by G. Nemery, specialist of the history of this regiment, to A. Deprit (letter, 14-4-86). I have benefited, moreover, from information from the Adjudant Jos Bullens, thanks to the assistance of R. Mairesse. 5   Georges Lemaître’s military records have a curious omission. One sees that he returned to the 38th Battery on 12 October 1918 from the CISLAA, however his transfer, after 5 February 1918, is nowhere mentioned. Did he return to the 38th because he had been dismissed from the course for auxiliary officers? 3

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adjutant on 11 November 1917, and then commissioned as an auxiliary “sous-lieutenant” of the artillery on 22 September 1918 and would finish the war as an officer. This was not the case with George Lemaître. Why? The latter would venture an explanation at the end of his life during an interview with a journalist from the Catholic newspaper La Libre Belgique6: 1914. I was committed. The Yser. The war was for everybody…I finished it as an adjutant. Why not an officer? Maybe because I had a bad character. Unless it was my Commanding Officer. Or maybe both. (Laughter)

From the oral tradition of the Lemaître family we learn that he dared to point out, during a ballistics class, the one remaining mistake in the military manual. A sanction would follow.7 After the armistice, Georges Lemaître was assigned to the temporary group of the military students of Louvain, on 20 January 1919, to which he would belong until his demobilisation on 19 August 1919. We have two testimonies that show that the young Lemaître had preserved and even enriched his knowledge and his scientific curiosity during all these years of turmoil. Charles Manneback8 states that “during the war, he found the possibility to familiarise himself with the ‘Optics and Electricity’ of Poincaré”. M. Goetals9, an engineer, who had fought with the 3A and Lemaître, said that he was touched by Lemaître’s capacity for detachment toward the terrible events around him. He maintained a great serenity during these years of combat and   J.K., “Portrait. Le chanoine Lemaître. Du cosmos aux précieuses ridicules”, La Libre Belgique, 23 January 1960: 1.   7   A. Lemaître, “L’oncle Georges, discours”, op. cit. 8   “Hommage à la mémoire de Mgr Georges Lemaître” (allocution pronounced at the séance of 2 July 1966), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. LII, 1966: 1034. 9   M. Goetals recounted the memories below to M. De Meurs, who had hired him in his firm. The latter told his son Charles, who in turn transmitted them to the author (oral communication, 17-08-97). 6

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often, during the watches, he liked to enlighten his comrades with scientific topics. After the war, Lemaître would remain attached to the 3A. During the 1950s, he undertook initiatives to join the Fraternity of the Regiment10 and, in the early 1960s, he vigorously insisted that his student, René Dejaiffe11, do its military service with the artillery and, if possible, with the 3A.12 The Yser was the crucible that forged some of the deepest and most long-lasting friendships for Lemaître. His insightful relationship with his brother Jacques was also sealed for life in the trenches. It was also in the trenches that friendships surpassing all social barriers were wrought. Lemaître often remembered his friend, a piano mover, who accompanied him when he was going on the front.13 Much of what was learned concerning Lemaître’s First World War period came from his correspondence with one Flemish soldier, Joris Van Severen. This correspondence, discovered and published by the Belgian historian Daniel Vanacker, is now preserved in the Archives of the Catholic University of Leuven (KU Leuven). Vanacker published also the war notebook of Van Severen disclosing the contents of his conversations with Lemaître14. The two soldiers remain friends untill the end of the war. But, afterwards, their friendship was broken as Van Severen evolved towards some radical political positions that were completely antithetical to Lemaître’s own15. The letters show that Lemaître, was already interested in cosmological questions, but also disclose his deep spiritual quest. He was considered at this time already as a very good mathematician but also as an ascetic.   Letter of the secretary of the “Fraternelle du 15A” (13-4-34, AL.) and the “Fédération nationale des volontaires de guerre” (18-5-34, AL). 11   Oral communication of R. Dejaiffe (30-10-97). 12   The motto of this regiment, now dissolved, was “Dans la lice” [which could be translated as ‘Into the Struggle’; Note of the translator] and could have been easily applied to the ‘marathon scientifique’ in which Lemaître took part in the 1920s. 13   Ch. Houyet-Lemaître (Oral communication, 3-7-95). 14   J. Van Severen, Die Vervloekte oorlog. Dagboek 1914-1918 (ed., introd. D.Vanacker), Kapellen-Ypres, Pelckmans-Studiecentrum Joris Van Severen, 2005. 15   All informations concerning this correspondence can be found in the author’s book : L’itinéraire spirituel de Georges Lemaître, Bruxelles, Lessius, 2007. 10

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The letters to Van Severen tell us what Lemaître read in between two battles: the books of Henri Poincaré, and the Bible (especially the Psalms and Genesis) but the letters also reveal a fascination with the books of Léon Bloy, a French Catholic writer and polemicist who made a symbolic hermeneutics of contemporary history. Bloy is perhaps best well-known as the godfather of the famous French Thomist, Jacques Maritain. During their leaves, many Belgian soldiers fighting on the Yser front went to Paris. Lemaître was so fascinated by this writer that he asked to meet him, during one of his leaves. He met Bloy, just before his death, in Bourg-la-Reine, near Paris, in the house which belonged to one of Bloy’s friends, Charles Peguy. Lemaître spoke to him about an essay entitled “Les trois premières paroles de Dieu” (The Three First Words of God16), he wrote in the trenches. It happens to be “an essay of scientific interpretation of the first verses of the Hexameron”. But Bloy did not appreciate the latter and advised Lemaître to deepen his knowledge in theology before writing on such a subject again. It is possible Lemaître completed writing this essay at the beginning of his theological training in Mechelen17, but shortly after, completely abandoned this approach to understanding the relationshiop between science and faith. (It was thought for a long time that this essay was written inside the Maison Saint-Rombaut, but in fact it predates the war.) This was either a work whose origins were found in the class on Holy Scriptures, or perhaps more likely a personal synthesis. Indeed, it is difficult to figure out how an intellect as preeminent as Lemaître’s and who was so personally engaged with both biblical revelations and the advancement of science, hadn’t tried to more accurately establish the limits of exegesis in the Book of Genesis for himself. According to its plan, style and

  His manuscript of six pages, which was never published by Lemaître, is preserved at the AL. It was edited in 1996. For the numbering of pages, I use this edition: cf. the bibliography of Lemaître: (1921a). 17   He put the date, 29 June 1921, on the final version of his essay (this left for some time the impression that the essay was written during his stay in Mechelen). 16

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object, this text reminds one indeed of the commentary of H. Faye18 on the first verses of Genesis: “Sur l’origine du monde, théories cosmogoniques des anciens et des modernes”. This book probably came to the attention of Lemaître through the previously mentioned articles of philosophical cosmology of Pasquier. Indeed, Faye, who was a member of the Institut de France and Professor at the École Polytechnique, tried to find interpretations of the biblical verses in term of rudimentary science, a discipline known by the Hebrews. Lemaître, meanwhile, followed the same approach, but interpreted the text in the light of the science of the early 20th century. Lemaître’s exegesis is in line with the encyclical Providentissimus Deus of Pope Leo XIII. Genesis is not a book of natural science; rather, its teaching concerns, first and foremost, the salvation of Man. Nevertheless, Lemaître pointed out that nothing prevents this biblical book from comprising some element of truth on the cosmos, since it had been inspired by the One Who Knows Everything: “the Holy Spirit hadn’t taught the science that he nevertheless knows perfectly, but he had perhaps adorned some pages as an ornament without importance beside the truths and the laws he proposed to our obedience and our faith” (1921a: 109). One cannot suppose that “science has any interest in seeing within the sacred text hypotheses to put to the test, since the main lines of the synthesis are already drawn”. The seminarian mathematician would thus show that there was effectively a certain concordance between the first biblical verses and the data of the physical sciences. A form of concordism indeed,19 but in a weak sense, as Lemaître does not directly establish a concordance between physics and the Bible taken literally, but rather a concordance between the former, and a particular biblical interpretation in a way where the concrete terms of the sacred Writer might been

  Paris, Gautier-Villars, 1907 (4e edition). Cf. the Chapter 1, “Moïse et la Genèse”, pp. 8-24. 19   On the meaning of this word, cf. D. Lambert, Science et théologie. Les figures d’un dialogue. Brussels/Namur, P.U.N, 1999. 18

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understood in a general abstract sense.20 Lemaître thus interpreted the expression “the earth was without form, and void’’21 as being an image of nothingness: […] There was not even any light. It is impossible that anybody could subsist without radiating light, indeed everybody at a certain temperature emits radiation of all wavelengths (according to the theory of Blackbody Radiation). Physically, absolute obscurity is the nothingness. One cannot see how it would be possible to understand this tenebrae otherwise than in this absolute sense preceding the Fiat lux; there was absolutely no light, there was thus, absolutely nothing. There was only the Spirit of God that prepared to create in the empty immensity: Spiritus Dei ferebatur super aquas.

This self-assured concordism of the youthful Lemaître would in fact crack under the objections of Eddington and Einstein, when another conception, ultimately more complex, would come to light at the end of the 1930s.

2. Back to the University: a new direction Still dressed in his uniform, George Lemaître returned to the University in Louvain for the academic year starting 21 January 1919 and would come to an end on 14 August 1919. He definitively abandoned his engineering studies for a Master’s degree in physics and mathematics. In order to be accepted in this second-cycle program, Lemaître had to pass a complementary exam22 to obtain a degree of the first cy  For instance, water should be interpreted as a “fluid without limit, without distinct contour. This term can therefore be use to describe the ‘mass of lights’ that fill the universe continuously to the Fiat lux. 21   The Vulgate says “Terra autem erat inanis et vacua”. 22   To help young people who had been held up by the war to acquire their diploma quickly, the Belgian government allowed universities to organize appropriate exams and supplementary exam sessions (Law of 14-2-1919; cf. Annuaire de l’université catholique de Louvain, 1919-20: 515). 20

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cle in physics and mathematics. He succeeded, achieving a Satisfactory grade, in July 1919.23 Two students passed this exam with a satisfactory grade during this year: Lemaître and Louis Reyntens.24 The latter, who was one year younger than Lemaître, was one of his dearest friends. He followed Lemaître in his studies of mathematics and physics before joining him in the seminary in 1923. From 1924 to 1939, he would teach science and supervise the special scientific class at the Institut SainteGertrude de Nivelles. A significant number of the students of this enthusiastic teacher, who knew how to generate interest in science25, would discover through him the personality and the first works of Lemaître.26 Reyntens thus hosted a circle of teachers of the Institut Sainte-Gertrude, which met over a cup of tea every Tuesday to discuss the most recent scientific topics. After having won fame in the Resistance as commander of the ‘Refuge Otarie’ network, which covered the region of Huy-Waremme, and after having been appointed director of the professional school Auguste Lannoy de Wavre, he died on 21 July 1947 in a motorcycle accident. During this heavily loaded second semester of the year 19181919, Lemaître completed, together with his friend Renoirte, courses that qualified him for the Bachelors degree in Thomistic philosophy. The latter would succeed with the highest distinction, while Lemaître would have to be content with a ‘simple’ distinction. To him, academic   Annuaire de l’université catholique de Louvain, 1920-26: 87.   H. Heyters, Louis Reyntens, Brussels, 1948. It is interesting to observe that this little brochure, published at the author’s own expense, was written by a very close friend of Lemaître. We will see, indeed that the Abbé Herman Heyters was a kind of spiritual father for Lemaître in the 1950s. Heyters, Reyntens and Lemaître all belonged to the sacerdotal fraternity called the ‘Amis de Jésus’ (cf. next chapter). 25   Louis Reyntens taught the Louvain philosopher, Jean Ladrière and transmitted to him his own deep interest in the sciences (oral communication from J. Ladrièere, 2610-94). 26   This was the case with Albert Caupain, who Louis Reyntens made read some of Lemaître’s publications. Albert Caupain, priest and ‘Ami de Jésus’, would attend Lemaître’s classes during his BA in mathematics that he would finish in 1946 (oral communication of A. Caupain, 23-03-95). 23 24

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degrees were not a reflection of one’s competence, but rather of one’s preferences (which the future would certainly confirm in his case). We shall later analyse precisely what, of the philosophy implicit in Lemaître, belongs to this Neo-Scholastic formation that he had received at the “Institut Supérieur de Philosophie”. It was also during this semester, in a city that still bore the traces of the war, that Lemaître began his first classes of his Masters in physics and mathematics. These classes were delivered in the beautiful building of the Collège des Prémontrés, 47 rue de Namur (Naamsestraat), where Lemaître would himself teach afterwards. This is a place full of Norbertine history, and where the adjutant artilleryman had the opportunity to frequent the “Cabinet de Physique”27 of De Muynck and the interesting library that was previously mentioned. Lemaître acquired, at the end of the academic year 1919-1920, the degree of Master in Physics and Mathematics with the highest distinction.28 The results spoke for themself: Lemaître had finally found studies that suited him. During these years 1919 and 1919-1920, he attended the courses of Professor Maurice Alliaume (1882-1931),29 who profoundly influenced Lemaître. He had succeeded Goedseels in 1919, notably, in classes of astronomy, geodesy and the theory of probability. In this latter discipline, he followed the footsteps of his predecessor by refining methods that allowed one to avoid the problems associated with the method of least squares. In the same year, he also became the substitute of Pasquier for the course on celestial mechanics. Alliaume was a good mathematician, mining civil engineer and doctor in physical sciences and   Cf. L’ Annuaire de l’université catholique de Louvain, 1919-1920: 47. The ‘cabinet’ was one of the two units that formed the laboratory of physics at that time. 28   Annuaire de l’université catholique de Louvain, 1920-26: 146. 29   “M. Maurice Alliaume, professeur de la Faculté des sciences. Discours pronouncé aux funérailles célébrées à Louvain le 29 octobre 1931, par S. Exc. Mgr. Ladeuze, recteur magnifique de l’université catholique” et “Éloge académique de M. Maurice Alliaume, professeur de la Faculté des sciences, pronounce à la salle des promotions le 22 décembre 1931, par M. Le professeur A. Van Hecke”, Annuaire de l’université catholique de Louvain, 1930-1933: CXXI-CXXIV and CXXV-CXLVIII. 27

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mathematics at the UCL. He deepened in his study of hydrodynamics that he had touched upon in his “Memoire” concerning the study of “Hydrodynamical Waves in Elastic Pipes”, during a two-year stay in Paris under the direction of Boussinesq. Prior to becoming professor at the university, he occupied the position of professor of mathematics, chemistry and drawing on the training ship Comte de Smet de Nayer. It is interesting to observe that several of Alliaume’s focal points of interest were shared, as we shall see, by his student Lemaître. The first was his affinity for celestial mechanics and related numerical calculations. Alliaume dreamt about the establishment of an office for astronomical and numerical calculations.30 Alliaume was also interested in the tools that facilitated mechanically performed numerical calculations, and especially nomographs.31 Second, there was his interest in relativity. Alliaume was one of the first, together with De Donder in ULB, who introduced the subject of relativity theory in Belgium,32 giving a Ph.D.-level course on this topic in 1921. Finally, Alliaume had a special predilection for the geometrical interpretation of mathematical results and the elliptic functions.33 Aside from his works on the history of science, which were praised by P. Bosmans in 1925, Alliaume wrote some magnificent syntheses of publications in astronomy and astrophysics between 1920 and 1930 for the Revue des Questions Scientifiques, which would amount to a volume of 460 pages. A year before his death, he expressed a desire to report   Lemaître realized his own such dream in the early 1950s when he founded his ‘laboratoire de recherches numériques’ [laboratory of numerical research]. Alliaume spent a great deal of time making tables, providing a concise way of representing the factorial values of the numbers from 1 to 1200 (the decimal system representation leading, of course, to kilometric expression). 31   It is significant that Alliaume wrote the very positive review of Maurice d’Ocagne’s book, “Vue d’ensemble sur les machines à calculer”, Paris, Gauthier-Villars, 1922, which described all that was known at that time on the mechanization of arithmetic, algebraic and integral calculation (Revue des Questions Scientifiques, 4e série, t. II, juillet 1922: 243-244). 32   Cf. For instance, “L’astronomie et la relativité” in “Revue des recueils périodiques. Astronomie 1922”, Revue des questions scientifiques, 4e série, t. 4, July 1923: 224-230. 33   He obtained, furthermore, a geometrical interpretation of a result of H. Leauté on the parameterization of certain curves by the Jacobi elliptic functions. 30

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the ideas of Lemaître concerning the expanding Universe; a wish however, that would go unfulfilled.34 His reviews of astronomy likely provided Lemaître with valuable information that would be crucial to his preparation after 1924 in England and the U.S., and also during the elaboration of his work on the expanding Universe in 1927. It seems that in the person of Alliaume, Lemaître could find somebody that would reveal to him the great themes that would constitute a meaningful framework for his scientific endeavours. These themes were classical mechanics, relativity and numerical calculations. If Lemaître steeped himself in the science of Alliaume, it seemed he might never keep his teaching methods extremely thorough and tidy, being reluctant to propose an exercise to students if he hadn’t himself prepared perfectly one day in advance. On this point, Lemaître would be closer to Goedseels, whose class35: […] was not an exposé of theories tidily prepared in advance, but an improvised development of one or other question, and it wasn’t rare that the lesson finished before one was able to get out of these difficulties. Deliberately, the professor had multiplied them in order to give the opportunity to make an in-depth analysis. In the following lesson, the problem wasn’t resumed, the students having conceivably found the solution by themselves. Another solution was addressed, which faced the same fate.

As with Goedseels, Alliaume greatly appreciated his student. Both men, as mentioned, were his godfathers at the Société Scientifique de Bruxelles. Lemaître chose Charles de la Vallée Poussin as the director of his Master’s thesis.36 Not having a preconceived notion about the topic   Cf. (1934b: 39).   “Éloge académique de M. Maurice Alliaume...”, op. cit.: CXXXVII. 36   In fact, as recalled by Manneback, it would consist of a direction rather than a nomination because Lemaître’s spirit of independence and the character of de la Vallée Poussin would have the consequence of making the student work independently from the master (Ch. Manneback, “Hommage à la mémoire de Mgr. Georges Lemaître”, op. cit. : 1034). 34 35

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he wanted to work on, what de la Vallée Poussin suggested to him was nothing less than a proof of the Riemann conjecture about the zeros of the famous Zeta Function, an issue that remains undemonstrated to this day. After a while, Lemaître came back to his professor admitting that he had no results to show, to which the latter told Lemaître: “So then, focus on triangular geometry37”. Lemaître was not discouraged and ask for another topic for his thesis. De la Vallée proposed a problem which was indeed closer to his research interests. In 1919, this famous international mathematician concluded a series of works on the question of the approximation of functions of one real variable.38 His interest in these questions already dated back to a work carried out in 190839 where he demonstrated, extending a method of proof used by Weierstrass in 1885, that one can, under certain conditions, find good approximations of functions of one real variable using algebraic and trigonometric polynomials defined by singular integrals.40 This result was found, independently, by Landau. The thesis of Lemaître consisted of having to “extend, to the functions with several variables, the theorems established for the representation of functions of a single real variable, by polynomials or trigonometric expressions”. The method and the results of this work, rather rote-like, were described by its author in the following way:41   This ‘incident’ was recounted by Lemaître himself to one of his students, R. Lavendhomme, who would become professor of mathematics at the UCL (oral communication, July 1994). 38   Leçons sur l’approximation des fonctions d’une variable réelle, Paris, gauther-Villars, 1919. Cf. J.C. Burkill, “Charles de la Vallée Poussin”, Journal of the London Mathematical Society, t.39, 1964: 165-175. 39   “Sur l’approximation des fonctions d’une variable réelle”, Bulletin de la classe des sciences de l’Académie royale de Belgique, 1908: 193-254. 40   In order to construct polynomials that converge uniformly toward a arbitrary continuous function f(x), Weierstrass integrated the product of f(x) with a function K(x,u) which has a step increase toward its maximum x=u. Charles de la Vallée Poussin used to generate his algebraic and trigonometric polynomials the kernel K(x,u) of the form: (1-(u-x)2)n and (cos(1/2(u-x)))2n. 41   G. Lemaître, Approximation des functions de plusieurs réelles, Manuscript, 1919, AL. This is in fact a draft of the thesis, preserved by Lemaître himself (translation from the original in French). 37

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I have followed the sequence adopted by M. de la Vallée Poussin in his lesson on the approximation of functions of a real variable. The methods that I have used are usually only straightforward generalizations of those developed in the first chapters of this work.

By perusing his thesis, one realizes that Lemaître was deeply engaged in the famous course of analysis of his professor42 as well in his work on the Lebesgue integral43 and, of course, especially, the work on the approximation of functions of real variables. However, in hindsight this constituted yet another, if minor, deflection of Lemaître’s real intellectual talent. The full force and originality of Lemaître’s mathematical ability was not put into play through this work, being as it was, largely a matter of “straightforward generalizations”. This comment likely more reflects his disillusionment than modesty. It is true that he did not have much time to complete his thesis because of his unsuccessful attempt at Riemann’s conjuncture. Thus the real measure of his talents which would ultimately reveal themselves were not those of de la Vallée Poussin, but rather of Alliaume: classical and relativistic mechanics, and numerical calculation. It is noteworthy that in 1962, in his tribute to the Belgian “prince of analysis”, Msgr. Lemaître would be pleased to remind his audience that “the interest currently addressed to the methods of numerical calculations has highlighted once again the fundamental contributions [that Ch. De la Vallée Poussin] brought in 1919 to the ‘approximation of functions of a real variable’”(1962b: 2).

  Ch. De la Vallée Poussin, Cours d’analyse infinitésimale, Louvain/Paris, UystpruystDieudonné/Gauthier-Villars (several editions from 1903 to 1938). 43   Ch. De la Vallée Poussin, Intégrales de Lebesgue, fonctions d’Ensemble, classes de Baire, Paris, Gauthier-Villars, 1916. 42

Chapter IV

The seminarian and relativity (1920–1923)

1. The Saint-Rombaut house

I

n October 1920, Georges Lemaître entered the Saint-Rombaut House.1 It was an annex of the great seminary of the Archdiocese of Mechelen opened on 8 December 1915 at No. 16 Marché-aux-Laines (Wollemarkt) in Mechelen in order to accommodate older seminarians. Only the preparatory courses in theology in this house were provided while the proper courses in theology were held in the main seminary itself. In October 1920, the Saint-Rombaut House was transferred to No. 84 Rue de Mérode (Merodestraat). By founding this annex of his seminary, Cardinal Mercier wanted to allow men whose vocational itinerary had been prevented by the war to advance towards priestly ordination. Throughout its existence, the house was supervised by Canon Jules Allaer, right-hand man of Cardinal Mercier. Around 1920, Abbé François van Beylen joined the director of the House in his capacity as bursar and professor of philosophy.2 Saint-Rombaut House was not a seminary like others; discipline was somewhat more lax than in the main seminary, which was located not far from there. For instance, seminarians could use their spare time in their own way while their fellows in the main seminary had to follow certain compulsory   Cf. Le Clercq, “La maison Saint-Rombaut”, Collectanea Mechliniensia, t. 5, 1930, 562-563. 2   Letter of Canon Constant Vandewiel (1-11-95). 1

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activities such as the regular walk to the country house, which was situated just outside the city of Mechelen, and which was more familiarly referred to as the Papenhof.3 The Saint-Rombaut House provided welcome to 104 students and the mixture of seriousness and liberty that characterized the house would be much to Lemaître’s liking, who would benefit from this formational experience both in terms of his life as a priest and as a scientist. At the Saint-Rombaut House, Lemaître met a young Chinese seminarian, Edouard Tchang-Hwai, who arrived in Belgium following the initiative of Fr. Lebbe.4 Lemaître was in charge of providing him with French lessons and catechism class. In return, Lemaître had Chinese lessons from his student. In the Archives of Louvain-la-Neuve (AL) one may still access a small notebook that served Lemaître in his study of Chinese language, most likely after his seminary.5 Apart from the study of Chinese pictograms and their pronunciations, Lemaître also studied one Chinese phonetic script that is not used nowadays in China. This form of writing perhaps played a role in Lemaître’s reflection that led him to propose a new representation of numbers after the Second World War. Edouard Tchang-Hwai would later renounce the priesthood, but Lemaître would not lose sight of him. He would find his student later, who had become a student in Pedagogy at the Université Catholique de Louvain. This encounter would be of primary importance in the life of Lemaître. As we shall see later, this is the encounter that would prepare Lemaître to his apos­ tolic activity amongst Chinese students at UCL. Upon meeting Cardinal Mercier before his entrance to the Seminary, Lemaître immediately found a person who could understand his spiritual and intellectual aspirations. At the spiritual level, Lemaître was   Oral communication with Canon J. Goeyvaerts (2-10-95).   Information transmitted by Claude Soetens (letter 13-11-96). 5   The sentences of the notebook seem to relate to a glossary of someone in charge of a residence for students, which Lemaître would be at the end of the 1920s in the context of the home chinois de Louvain. The translation of the notebook was conducted, on the 31-10-83, by Jia Xu, Ph.D., then a Bachelor’s student in Computer Science, at J. Steyart’s request. 3 4

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captivated by the ideas of Mercier regarding the priesthood that focused on the demanding imitation of Christ under the evangelical counsels and an internal life fed by prayer. As underlined by Msgr. Billiauw6: “the spiritual itinerary of Msgr. Lemaître was personally influenced by Cardinal Mercier as well as by the Cardinal’s books: À mes séminaristes (1907), Retraite pastorale (1908), and La vie intérieure (1918)”. At the intellectual level, the Cardinal and Canon Allaer allowed him to “study theology in parallel to the Theory of Relativity’’.7

2. Lemaître, theology and the Amis de Jésus The formal theological formation of Lemaître would last three years.8 If one compares his results to those of his fellow seminarians, it might appear that Lemaître was not particularly brilliant.9 The proper mode of reflection in theology, and perhaps more specifically in Neo-Scholastic theology as it was taught during this period, would seemingly be difficult or even foreign to Lemaître’s way of thinking.10 If theology as an intellectual discipline did not seem to inspire   Letter of the 5-11-95. Msgr. Billiauw, who was ordained in 1937, met with Lemaître in 1934 during the inauguration of the house Regina Pacis of Schilde while he was aspirant of the Fraternité des Amis de Jesus. He saw him each year in Schilde until 1960, approximately. This was confirmed by Msgr. Thils (oral communication, 28-1094) who spoke of the “admiration of Lemaître for Cardinal Mercier’’.   7   Letter of G. Lemaître to Ferdinand Gonseth dated from 21 January (very likely 1945).   8   According to the official directory of the archdiocese (25th year, 1922, p. 13 transmitted by A. Jans) the professors of the great seminary were: A. Croegaert (liturgy, pedagogy, oratory), C. Cruysberghs (theology, fundamental moral philosophy), J. De Jonge (spiritual director), A Gaugnard (moral theology), H. Naualerts (dogmatic theology), C. Ryckmans (Bible and Hebrew), V. Sempels (canon law and history of the church), P. Willems (plainsong).   9   The archives of the archdiocese of Mecheln-Brussels still preserve, in the registry of exam results (1914-1941) two series of grades concerning G. Lemaître for the period 1920-1924. However we do not know the scores of the other students, and thus his grades lack context (Communication of A. Jans, archivist). 10   The sentence, written during a retreat by Fathers Salsmans and Rutien in the Great Seminary of Mechelen in September 1924, may be significant in this regard: “it was requested of me to deal a bit every day with theology” (notebook of retreat, AL, translated   6

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him, it would be wrong to conclude that Lemaître was not seriously pursuing his own religious path, which he was charting for himself. It was clear that he was placing more emphasis on his spiritual preparation than his intellectual. From this standpoint, Lemaître had arrived at a fortuitous moment in the history of the episcopate of Cardinal Mercier. It was in 1920 that Canon Allaer, director of the Saint-Rombaut House, mentioned to the Cardinal the forming of some five groups of seminarians who desired to live the ideal of the priestly life, according to what is described in Cardinal Mercier’s retreat sermon to his priests in 1918 later published under the title of: “La vie intérieure. Appel aux âmes sacerdotales”.11 These groups were called the “phalanx” and later, the “phalanx of the pure”, because of the insistence they put on the consecration of their celibacy. They would be succeeded by another group that also met at the Saint-Rombaut House. The latter, called “Les Fils de Marie”, was abandoned shortly after Cardinal Mercier imposed upon them a program of life centered on prayer and poverty. During the 1920s, Canon Allaer wrote the provisional statutes of the “phalanx” that took, on 24 August 1921, the name of “Fraternité Sacerdotale des Amis de Jesus” following the inspiration of the Primate of Belgium himself.12 The seminarians could enter like aspirants in the fraternity, but their official itinerary would begin only after ordination. The aim of the fraternity was the sanctification of the clergy. After a certain probationary period, the priest pronounced, at the hands of the Bishop or his delegate, vows of poverty13, chastity from the original in French). Nevertheless all known documents (AL or AFSAJ) do not bear the trace of a reflection in theology properly speaking. 11   Translator note: the title can also be translated as ‘The interior life. Call to priestly souls’’. 12  For supplementary information, the reader may read the author’s paper: “Mgr Georges Lemaître et les ‘Amis de Jésus’’’, Revue théologique de Louvain, t. 27, 1996: 309-343. 13   This vow required the “Amis” to get rid of any surplus funds. They had to be accountable to the canonical head, and in the 1950s, to an “assistant” who verified, on the basis of a report, their fidelity to the vow of poverty. The spare money was put in a special fund for the “Amis” in times of need.

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and obedience, and a short time afterwards, the so-called votum immolationis, a vow of complete submission to the person of Christ.14 The priest “Ami de Jésus” undertook to make one hour of prayer after daily Mass and to participate, once a year, in a 10-day silent retreat. On his deathbed, 22 January 1926, Cardinal Mercier learned, from the mouth of the apostolic nuncio, Msgr. Micara, that the status of the “Fraternité Sacerdotale des amis de Jésus’’ was finally recognized by the Congregation of the Council.15 One day before, the Primate of Belgium had called in his Vicar General, Msgr. van Roey, to promise that if the latter became his successor, he would do everything to establish the “Fraternité” canonically. The latter gave his word, but without great conviction, because some, including Abbé Suenens16 who would later become Archbishop of Mechelen himself, were already worried that this “Fraternity” had become a kind of “state within a state”, a sort of elite privileged by authority. In conformity with its promise, Msgr. Van Roey, who became archbishop of Mechelen, established the “Fraternité” on the 27 December 1926.17 Nevertheless, he recommended absolute discretion to all his members   This curious provision, requiring a secular priest to pronounce religious vows, is linked to a somewhat deformed conception of the priesthood of the diocesan priest at that time. An idea largely shared in the Church then was that the ideal model of the sacerdotal life is one where the priest would belong to a religious order. But some bishops were opposed to this conception and thus would refuse the introduction of the sacerdotal fraternity of the “Amis de Jésus” in their dioceses. One example was André-Marie Charue, bishop of Namur (cf. A.-M. Charue, Le clergé diocésain tel qu’un évêque le voit et le souhaite, Tournai, Desclée, 1960: 52). After the Council of Vatican II the Church sided more with the view of this bishop. 15   At that time, this was the name of what we now know as the Roman Congregation in charge of the diocesan clergy. Its name comes from the fact that its mandate was to implement the decrees of the Council of Trente. 16   He made it known to the general secretary of the ‘Amis’ through a undated letter sent from Rome. There are two copies of this letter, one in the AFSAJ (dossier of positive and negatives reactions toward the Fraternity) and the other, in the Fonds Mercier in Louvain-la-Neuve (documents supplied by Abbé F. Willocx). 17   Long after, while attending the ceremony where the “Amis” were pronouncing their vows in Schilde, Cardinal Van Roey mentioned that if he had not felt obligated by his giving Cardinal Mercier his word, he would have never established the “Fraternité sacerdotale” canonically (oral communication of Canon Goeyvaert who had attended this ceremony, 2-10-95). 14

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and he had to reduce the influence of Canon Allaer who had been appointed head of the “Fraternité”. From 1926 to 1934 (the date on which the Cardinal Van Roey came to inaugurate the Regina Pacis and the Fraternity’s mother-house in Schilde, in the close suburb of Antwerpen), the “Amis de Jésus” were constrained to a quasi-clandestine existence. Organized in small local groups related to colleges, cities and the University of Louvain, the members would have little contact between themselves, except beginning in 1934 when many of them would meet during the silent ten-day retreat in Schilde. Significantly, the papers written by the members in their newsletter, Apostolus, were only signed by their initials. The death of Canon Allaer, on 3 October 1954, would weaken the Fraternity considerably, not to mention the questioning of the theological and canonical status of vows pronounced by secular priests, in the turbulence leading up to and following the Second Vatican Council. Georges Lemaître was not among the first group of the Amis de Jésus who pronounced their vows on the 28 April 1922 in the SaintRombaut House in the presence of Cardinal Mercier.18 However, Lemaître certainly kept them company and finally joined them as he participated in the general meeting of the Amis de Jésus organized with Cardinal Mercier 16-17 August 1923, in the Redemptorist convent in Essen.19 The first official list of the members of the Amis de Jésus preserved at the general secretariat of the Fraternity20 shows that on 31 December 1924, Georges Lemaître was effectively part of the Amis de Jésus linked to the local group of the Saint-Rombaut House. Lemaître would be faithful to his essential commitments within the Amis de Jésus for all of his life. However, as observed by Msgr. Thils,   Cf. A photograph taken in the garden of the Saint-Rombaut House on this day (AFSAJ and Fonds Mercier, Louvain-la-Neuve, documents transmitted by F. Willocx.) One may recognize Abbés Willocx, Hanon, Goeffoel, Allaer, Verbist, Moulart and Vermeylen, but not G. Lemaître. 19   Cf. Photography and documents, AFSAJ related to his general annual meeting (dossier III) 20   AFSAJ, correspondence, of the general secretary F. Willoxc with members, letters received by F. Willocx, 1924-1928, dossier I. 18

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eminent theologian at the UCL and a close friend of the Amis de Jésus, Lemaître was part of the “Fraternité” in his own way, with the freedom of spirit that always characterized him and not without a certain casualness in relation to institutional details of the “Fraternité”. A letter from Fernand van Steenberghen, the well known NeoThomist philosopher and active member of the Amis to Canon Allaer (dated 28 May 1932) is emblematic of the relationship that Lemaître had with the other members of the “local group from University of Louvain”, of which he became the head: My very dear Director, Your recent letter embarrasses me slightly: we have not had our group and section leader for the meetings since Easter; I met him one day and asked him for some news from the general council: he fell from clouds and didn’t remember a convocation; “there might be something behind that” he told me; I told him about our meetings and he told me that they were held on Wednesday at 2:30 but he could easily change the schedule. Since then, nothing! M. Lemaître is a very busy and very distracted man […] We could set up a group Lemaître-Torhout with an exemption from meeting in order to regularize the situation….

Nevertheless, the casualness should never be interpreted in Lemaître as a hint of superficiality or resignation towards the essentials of his vocation. He pronounced the four vows21 mentioned earlier which would not be without consequences for the remainder of his life.22 Several witnesses reported that he always undertook a long   The registry of vows of the AFSAJ reveals that Lemaître has pronounced his first temporary vows of one year on 12-8-1927 in Essen (Convent of the Redemptorists), his last temporary vows of one year on 9-8-1928 at the Saint-André Abbey of Bruges, his third temporary vows of one year on 1-8-1929 in Essen, his temporary vows of three years on 30 July 1930 in Essen, his three perpetual vows on 11-8-1933 in Zandhoven (study house of the Sacred Heart Fathers), the votum immolationis, on 12-8-1942 in Schilde (Regina pacis). 22   There are two letters of Jacques Lemaître to his brother Georges (22-10-1934 and 24-10-1934) in AL that demonstrate that the latter had helped the Amis financially with the construction of the Regina Pacis house in Schilde. The financial arrangement 21

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meditation after the daily Mass at the Collégiale Saint-Pierre of Louvain, at the church Saint-Henri23, when he left his parent’s house at 9 Rue de Braeckeleer, or even in their house when his mother was sick24. Every year, despite the several trips that he would make, generally to the U.S., he would never miss his long silent retreat, held in Schilde from 1934 until 1960. As mentioned by Msgr. Billiauw25: Since [1934] the Fraternity regularly organised a retreat of 10 days for members (at the house Regina Pacis at Schilde), particularly for those who during that year had pronounced their vows, but all the Amis are invited. Msgr. Lemaître was one of the rare members to attend all of them – 10 days of complete silence – very regularly until 1960, when the retreat was discontinued.

These retreats are unique and fascinating interludes for of the serious student of Lemaître’s thought. During the long period of silence, Georges Lemaître ran through things about his spiritual life, but also concerning his teaching work and the progress of his research. In several notebooks, he noted his spiritual resolutions, some notes of the preacher, but also, and above all, his program of research and ideas for calculation. If these fragments offer us a sort of distillation of his thinking, we are correct to believe that along with the silent meditation of Lemaître in the beautiful park of Puttenhoft in Schilde, there was also a continual torrent of formulae and calculations. Lemaître never commented on his belonging to the Amis de Jésus. Thirty years after his death, his family and close scientific colconceived by Jacques and Canon Allaer was carried out as told by Jacques to his brother Georges, “Without saying a word to mother”. The letters also implied that the money from the Francqui Prize to Georges Lemaître (17-3-1934), that he could not keep owing to his vow of poverty, likewise supported this project (this was confirmed by the penultimate rector of the Regina Pacis house, Canon Goeyvaerts, oral communication on 2-10-1995). 23   Testimony of Fr. Y. Nolet de Brauwere, O.P. (oral communication, September 1994). 24   Gilbert Lemaître (oral communication, 21-05-99). 25   Letter of 5-11-95 (translation from the original in French).

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laborators, those before and after the Second World War such as Odon Godart, Lucien Bossy or André Deprit and Andrée Deprit Bartholomé, did not know about his membership in the Amis and neither did Msgr. Massaux, his table companion at their daily meal at the restaurant Majestic in Louvain. However, the registry of vows26 and the report of meetings of the general council of the “Fraternité” to which Lemaître belonged during the 1950s27, as well as the testimony of the Amis 28 clearly reveals that one cannot minimize the importance of this aspect of his life.

3. Einstein’s physics viewed from Saint Rombaut   We have seen that at the seminary, Lemaître received permission to study the theory of relativity. Furthermore, the residence at the SaintRombaut House did not isolate him from the scientific milieu of Louvain. We have mentioned that his former professor, Goedseels, joined him in the Saint-Rombaut House in 1923. Nevertheless, Lemaître might have also kept contact with Alliaume29 since, as mentioned previously, Alliaume and Goedseels appointed Lemaître on 26 October 1922 as a member of the Société Scientifique de Bruxelles. As such, he regularly received the Revue des Questions Scientifiques and the

 AFSAJ   AFSAJ, secretariat de la Fraternité: dossier III cahier V: “P.V. des conseils généraux” (10-10-1954; 26-08-1958). 28   Between 1994 and 1998, I gathered the memories of several people who had known Msgr. Lemaître in the context of the Amis: J. Goeyvaerts, G. van Innis, P. de Locht, Msgr. Thils (who was not completely engaged in the Fraternité), A. Caupain, A. Vander Perre. I also have the opportunity to consult a letter sent by Canon F. Van Steenbergen to Msgr. Cammaert (personal archives of the Canon, folder FSAJ) in which he wrote about meetings of the local group of Louvain with Lemaître until 1966. 29   Alliaume was in possession, by 1921, of most of fundamental works about Relativity. Cf. his “Revue des recueils périodiques” (review of reviews) in astronomy (Revue des Questions Scientifiques, 4e série, t. II, juillet 1922: 172-199 and especially: “L’astronomie et la relativité: 183-199) in which he quoted (page 198) the work of Th. De Donder, La gravifique einsteinienne, Paris, Gauthier-Villars, 1921. 26 27

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Annales of this Society, which allowed him to keep abreast of the literature30 and in which he would publish all his life. The Société Scientifique de Bruxelles was founded 17 June 1875 and arose from the confluence of three earlier initiatives.31 The first was the “Cauchy groups”32, discussion circles founded by the engineering students of the University of Ghent by the Chevalier Lagasse de Locht and spread in Belgium by Doctor Struelens, Paul Mansion, Theodore Belpaire and the Jesuit, Father Carbonnelle. The second was a discussion group of Catholic intellectuals without any particular university ties, and third was a group of professors from the University of Louvain comprised of the physicist Gilbert, the inventor of the baro-gyroscope, the chemist Louis Henry, the doctor Lefebvre and François Walque. The main idea behind the Society, which was inspired by the first Vatican Council, was to bring Catholic scientists together and to show, according to a formula of Vatican I which became the motto of the Scientific Society of Brussels, that “nulla unquam inter fidem et rationem vera dissensio esse potest”.33 The first secretaries of the Scientific Society of Brussels were Fr. Carbonnelle, Paul Mansion and Charles de la vallée Poussin. The two publications mentioned above, the Revue and the Annales were in wide circulation until the end of the 1950s in Francophone   In the delivery of 20 July 1921 of the Revue des Questions Scientifiques (3ème série, t. XXX, juillet 1921), one can find a review of Eddington’s work “Espace, temps, gravitation”, translated to French by J. Rosignol (Paris, Hermann, 1921) of Philbert du Plessis (pages 513-524) as well as another of Fr. Dopp (529-531) in the 4th edition of Weyl’s book “Raum, Zeit, Materie: Vorlesungen über allgemeine Relativitätstheorie” (Berlin, Springer, 1921), 4th édition. 31   Cf. Annales de la Société Scientifique de Bruxelles (volume jubilaire. 1875-1926 cinquantième année), t. XLVI, Mai 1926: 22 – t. XXIV and B. Coveliers, B. Van Tiggelen, “La Société Scientifique de Bruxelles. La foi avec la science”, X. Dusausoit, “Ignace Carbonnelle, fondateur de la Revue des Questions Scientifiques”, in Les Jésuites belges. 1542-1992. 450 ans de Compagnie de Jésus dans les Provinces belgiques, Bruxelles, AESM éditions, 1992: 157-158 and 159. 32   First called “Leibniz groups” [in French: “groupes Leibniz”] and renamed “Cauchy” by Mansion. Cf. Chevalier Lagasse de Locht, “Paul Mansion”, Revue des Questions Scientifiques, 3ème série, t. XXVII, janvier 1920: 15-16. 33   Constitution Dei Filius, Chap. IV. (De fide et ratione), §3. 30

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countries34 and among various circles, schools and Catholic universities. Nevertheless, these publications were read and referenced classified  in non-Catholic research centres, especially in the Belgian, French, Canadian and even German astronomical observatories. In this light, if one considers that some mathematicians as prestigious as Boussinesq, Caratheodory, Puiseux and de la Vallée Poussin were members of the Society, one may understand why Lemaître cared about disseminating his own ideas through this channel. Only those unfamiliar with the French scientific milieu of the interwar period led some to be surprised that Lemaître had published in some “obscure” publications of the Scientific Society of Brussels. In the seminary, Lemaître also had contact with Canon De Muynck. The latter would suggest to him to apply for a travel grant.35 This competition was run every year by the Minister of Science and Arts (Article 55 of the Law of 10 April 1890) for students who had obtained their Masters within the previous two years. The selection trial consisted of two parts. First of all, the student candidate had to propose a main dissertation in a discipline of his choice as well as three complementary theses  (also original) in the same discipline, but not overlapping with the main dissertation. If the dissertation were to be accepted by the jury, composed of three people, it had to be defended orally in public. Any candidate who won the competition was given a grant; in 1920-1921 for example, the grant was for a trip abroad, equivalent to 8000 Belgian francs, distributed over two years. After the trip, the recipient had to provide an activity report. For this competition, Lemaître seems to have begun writing his dissertation as early as 1921-1922, and which appears as a personal synthesis on the special and general theories of relativity: “La physique   Between the two Wars, in France, la Revue des Questions Scientifiques was widely distributed by the Société de diffusion du livre (whose main office was at 8 Rue SaintSimon in Paris) founded by Pierre Goursat (Cf. B. Peyrous, H.-M. Catta, Le feu et l’espérance. Pierre Goursat fondateur de la communauté de l’Emmanuel, Paris, Édition de l’Émmanuel, 1994: 25-29.) 35   Every year, the course program of de UCL comprised information related to this competition (cf. academic year 1920-21: VI-X) 34

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d’Einstein” (“The Physics of Einstein”).36 This was the perfect moment, as the beginning of the 1920s was the period where the number of publications about the works of Einstein literally exploded in the French and English worlds.37 As it would would happen many times in his life, Lemaître arrived on the scene just at the right moment to aggregate all the relevant and useful information for his work. We have seen how Lemaître could keep up to date with the scientific literature on the Relativity principle. A note of Lemaître (1922b) in response to a request of the jury of the competition transmitted to him via Maurice Alliaume38, in order to demonstrate the originality of the dissertation, shows the range of references he was familiar with: Einstein39 of course, but also Théophile De Donder40 (and thus very likely his colleagues, H. Vanderlinden41, for in  This manuscript of 131 pages, finished on 31 May 1922, was never published by Lemaître. Preserved at the AL, it was edited in 1996 (Cf. bibliographie of Lemaître, (1922a); this book uses the page numbering of this edition). 37   Cf. the Bibliography in J. Becquerel, Exposé élémentaire de la théorie d’Einstein, Paris, Payot, 1922 and in A. Metz, La relativité. Exposé élémentaire des théories d’Einstein et réfutations des erreurs contenues dans les ouvrages les plus notoires, Paris, Chiron, 1923. 38   The note was written following a letter sent by Alliaume to Lemaître and dated 13 March 1923 (AL). The grade given to Lemaître (76%) for admissibility to the oral defence is similar to that of another candidate (72%). The jury wished to obtain more independent information regarding the originality of the work of Lemaître. One can understand the jury’s concerns, as the dissertation did not include any references, except an allusion to the seminal article of Einstein “Zur Elektrodynamik bewegter Körper”, Annalen der Physik, t. 17, 1905. 39   H.A. Lorenz, A. Einstein, H. Minkowski, Das Relativitätsprinzip, eine sammlung von Abhanlungen, Leipzig, Teubner, 1920. 40   Th. De Donder, La gravifique einsteinienne, op. cit. (this work was also published in the Annales de l’Observatoire royal de Belgique, 3e série, t. I, 1921); Théorie du champ électromagnétique de Maxwell-Lorentz et du champ gravifique d’Einstein, Paris, Gauthier-Villars, 1920. 41   Lemaître did not quote Vanderlinden, but the following references were unlikely to be unknown to Lemaître: H. Vanderlinden, “Les équations du champ de gravitation d’Einstein”, Bulletin de la classe des sciences de l’Académie royale de Belgique, séance du 7 février 1920: 43-52; “Les trajectoires d’un rayons lumineux dans le champ de gravitation d’Einstein-Schwarzschild”, Bulletin de la classe des sciences de l’Académie royale de Belgique, séance du 6 mars 1920: 90-97; Th. De Donder, H. Vanderlinden, “Théorie nouvelle de la gravifique”, Bulletin de la classe des sciences de l’Académie royale de Belgique, séance du 4 mai 1920: 232-245. 36

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stance), Langevin42, Pauli43 and Schwarzschild44. Even if he does not mention it, it is most likely probable that he read Eddington’s book Space, Time and Gravitation (1921) and his mathematical supplement, whose French translation had just been published.45 He could not avoid noting the book of Weyl, Raum, Zeit, Materie: Vorlesungen über allgemeine Relativitätstheorie (1918).46 “La physique d’Einstein”47 begins with an explanation of philosophical presuppositions in the style inescapably reminiscent of Eddington. The general plan of the dissertation accordingly sounds like an original reinterpretation of the mathematical supplement of Space, Time and Gravitation.48 For Lemaître, the very existence of an experimental science is related to a series of conditions. It is necessary for the material world to be intelligible. In this respect, it is necessary to have “an intelligent grip on the universe’’ which is “so marvellously adapted to all the forms of our activities” (1922a, p.226). The conditions of the intelligibility are, on the one hand, the regularity and the repeatability of phenomena and, on the other hand, the relative simplicity of the principles that describe them. But simplicity by itself   P. P. Langevin, “Sur la théorie de la realtivité et l’expérience de M. Sagnac”, Comptes rendus de l’Académie des sciences de Paris, 7 novembre 1921: 831-834. 43   W. Pauli, “Relativitättheorie” in Encyklopädie der mathematischen Wissenschaften, Band 5: Physik, teil 2, Leibzig, Teubner, 1922: 599-775. 44   K Schwarzschild, “Über das Gravitationfeld eines Massenpunktes nach der Einsteinschen Theorie”, Königlischen Preussischen Akademie der Wissenschaften, t. V, 1916: 189-196. 45   A.S Eddington, Exposé théorique de la relativité généralisée. Complément mathématique inédit de l’édition française d’‘Espace, temps et gravitation’ (traduction par J. Rosignol) Paris, Hermann, 1921. 46   The name of Weyl is in fact mentioned (1922a: 231). 47   One owes to Lucien Bossy, collaborator of Lemaître, the first detailed analysis of La physique d’Einstein (“La physique d’Einstein de Georges Lemaître” in Mgr Georges Lemaître savant et croyant. Actes du Colloque tenu à Louvain-la-Neuve le 4 novembre 1994 suivi de La physique d’Einstein, unpublished text of G. Lemaître, Louvain-laNeuve, Centre interfacultaire d’étude en histoire des sciences, 1996, Réminiscience 3: 9-19. 48   I say reinterpretation since Lemaître i) found the way to avoid the long development of tensorial calculations given by Eddington; ii) developed the cosmological part and iii) even ended, like the English astronomer’s work did, with a section about electricity, but without the extensions of Weyl-Eddington on general relativity. 42

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would be quickly overturned by the progressive accumulation of results having no connection with one another. Simplicity could only be maintained under the condition of the intelligence discovering unifying principles. For Lemaître, the history of physics was a succession of unifying theories: the geometry that unified the astronomical observations of the Greeks, Newton’s mechanics which explained astronomical phenomena in terms of the law of gravitation and finally relativity, which unified geometry, gravitation and electricity. However, the simplicity shown in these descriptions could be attributed, not to nature itself, but to the cognitive capacity of the subject. It would be appropriate then, to propose a condition of objectivity of the theoretical descriptions. For Lemaître, this condition is nothing else than this relativity principle or what one would call nowadays a principle of covariance: “the equations that express a physical law must keep their algebraic forms, when one makes an arbitrary change of coordinates”. (1922a: 229) And it is precisely this principle of general relativity that serves as a keystone for the reconstitution of the results of the special and general relativity by successively integrating geometry, gravitation and electricity. This way of proceeding was quite distinct from that of Einstein, who reformulated relativity by progressively extending classical mechanics, or that of De Donder, who undertook this formulation from a variational principle.49 From a formal point of view, one clearly perceives the influence of the “La gravifique einsteinienne” of Théophile De Donder.50 It is also interesting to witness his penetrating intuition at work that allowed him to adopt some changes of variables and some “good coordinates”51 enabling significant simplication of his calculations (1922b: 21-22).   According to this point of view, the relativistic equations are deduced from the stationary conditions (maximality or minimality) of a functional invariant under coordinate changes. 50   One sees evidence of this in the fact that Lemaître, like De Donder, does not use the “Einstein summation convention”, unlike the majority of authors. It is no coincidence that De Donder is mentioned twice in 1922b. Cf. Pages 20 and 21. 51   In order to demonstrate the tensorial character of mathematical objects introduced to describe physical phenomena, one must undertake long algebraic manipulations. Le49

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From an empirical perspective, reminiscent of the young Einstein, Lemaître analyzed the notions of measurement and the definitions of concepts of space, time and simultaneity. Considering the results of Einstein’s mechanics, contraction of length, time dilation, and the relativity of simultaneity, as “systematic errors” (1922b: 20), and effects of perspective related to some indirect measurement made by an observer external to the system analyzed, Lemaître managed to thwart some difficulties of interpretation related to the theory. The most interesting part of his thesis, in the author’s opinion, is the astronomical section. Here, Lemaître studied the motion of celestial bodies in a field of forces produced by masses that are immobile or endowed with a motion of rotation. In the case of the force field produced by immobile masses, he obtained the identical famous result as Schwarzschild dating from 1916 describing the gravitational field outside of a sphere of homogenous density. He then showed that the Schwarzschild field produced by an infinitely distant mass is formally analogous to the inertial force field produced by a body endowed with a uniformly accelerated rectilinear movement. The cosmological part of the dissertation was not really original. Indeed, Lemaître merely obtained the same solution that Einstein had found to his gravitation equations in 1917, and which corresponds to a universe formed with cosmic dust52 homogenously distributed within a static sphere of three dimensions53. In order to obtain this maître simplifies his task by showing that for every point of the space-time, there are particular coordinates, the “proper coordiantes” (geodesic) in which these manipulations become extremely easy since locally the universe becomes flat. (cf. W. Rindler, Essential Relativity. Special, General and Cosmological, Berlin, Springer, 1977: 131). 52   One can talk about dust when the pressure that is exerted between the particules is negligible. In his dissertation, never is any kind of pressure term involved in the energy-momentum tensor, which describes the source of the gravitational field. Cf. next chapter. 53   In contrast, the de Sitter solution, will be discussed later, was missing (in A. Eddington, Espace, temps et gravitation – the translation of Space, Time and Gravitation: an outline of the general theory of relativity, Cambridge University Press, 1920 – as well as in his Complement to the French translation); this solution is barely invoked and the cosmological part is more or less non-existent; this reinforces the opinion regarding a possible influence of these texts on Lemaître.

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solution, Einstein had to introduce a supplementary constant into his equations, the famous cosmological constant, without which one could not find a static universe, unless a negative pressure was introduced, something which was rejected by Einstein. Lemaître, who had shown in his dissertation that this constant appeared naturally in the most general form of Einstein’s equations, defended his introduction of it by showing that this constant helped to resolve some difficulties that appeared in the Newtonian gravitation theory when one presumed that the universe was filled with a constant density of stars and extending itself indefinitely54. This justification is worth noting since, eventually as we shall see, Lemaître would defend the necessity of maintaining a non-zero cosmological constant in the equations describing the expanding universes in accordance with Eddington and contrary to Einstein. Moreover, his insistence on three-dimensional spherical spacetime, the “elliptic space”, would always be related to an important philosophical assumption of Lemaître, which is manifest from the outset of the La physique d’Einstein: the universe must remain accessible to human knowledge and proportionate to it, which an infinite universe cannot be. Lemaître, as well as Eddington, would always reject actual infinity in physics, because it would be properly speaking inconceivable by human intelligence. The jury who evaluated the work of Lemaître was comprised of Maurice Alliaume, Théophile De Donder from the Université Libre de Bruxelles and H. Janne from the Université de Liège. Lemaître, being just ahead of another candidate who had written a dissertation on the theory of probability, won the competition after an oral defence during which he might have been accountable for work that should have been done since the submission of the dissertation and the reading of two references that he did not have in his possession in 1921:   Newton’s law cannot apply according to Lemaître since it would lead to the existence of an infinite global gravitational force. The cosmological constant allows one to obtain, in a first approximation, a modification of the classical equation of Poisson considering the density of constant matter on the whole universe. Moreover, it allows one to obtain a universe of finite size and ultimately a finite number of stars. 54

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a study of Fokker55 and the Mathematical Theory of Relativity of Eddington, which would play a key role in the next step of his work. The influence of the works of De Donder, which has already been highlighted in “La physique d’Einstein”, was confirmed again in the first scientific paper published by Lemaître (1923a)56. This was a paper in which he rederived, with the calculus of variations, identities57 which were previously obtained by De Donder in a series of notes completing his book, La gravifique einsteinienne. This technical paper, presented before the Belgian academicians on 7 July 1923 and submitted for publication by De Donder on 4 August 1923 during a meeting of the “Classe des sciences” (section of sciences) at the Royal Belgian Academy, would leave some trace in the work of the great physicist. Indeed, he quoted once more his Théorie invariante du calcul des variations58 in 1935. The first of Lemaître’s papers is interesting because it de facto confirms that in August 1923, Lemaître had already entirely read and understood the fundamental work of Eddington, The Mathematical Theory of Relativity, which was only finished 10 August 192259. In addition to all the seminary courses, Lemaître had deeply assimilated all of the most consequential works relativity, and in a mere three years. Moreover, he was now finally prepared for his meeting with one of the only people who, if one believes Einstein, had succeeded in presenting relativity in a rigorous and synthetic way: Eddington.

  A.D. Fokker, “De geodetische precessie: een uitvloeisel van Einstein’s gravitatietheorie”, Verslagen der Afdeeling Natururkunde, DI.XXIX, 1920-1921: 611-621. 56   In this paper, Lemaître deliberately made clear that he then adopted the Einstein summation convention of the tensor calculus. This shows perhaps that it was indeed De Donder who was his main reference toward La physique d’Einstein and that the influence of other sources (Einstein, Weyl…) was more significant by 1923. 57   The calculus of variations consists of identities concerning variational derivatives used to express that the integral of a multiplier is an extremum (maximum or minimum). A multiplier in the vocabulary of De Donder, is a scalar function which in a coordinate transformation, is multiplied by the Jacobian of the transformation. 58   Paris, Gauthier-Villar, 1935: 193. 59   Cambridge University Press, 1923 (the preface is dated 10 August 1922). 55

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4. Toward a new life Lemaître had submitted an application for a fellowship to the Commission for the Relief in Belgium (C.R.B.), under the auspices of the American Educational Foundation, the purpose of the Commission being to assist with the reparation of the war damage in Belgium. He obtained this fellowship in 1923. It was not surprising that Lemaître, who had just been ordained, would have received approval to submit such a request to study abroad. In fact, Cardinal Mercier was not only mindful to form a Christian intellectual elite to teach at UCL, but he was also sensitive to the international dimension of this formation. He was very familiar with the Commission for the Relief in Belgium and the university systems of the Anglo-Saxon world. Just one year before Lemaître came to meet him regarding his own admission to the seminary, Mercier had made a trip in September and October 1919, to the United States and Canada60. The goal of this journey was to thank the Americans who had contributed to the enterprise of Herbert Hoover dedicated to assisting the Belgian population affected by the German occupation, and from which a delegation came to greet the Cardinal during the war. Charlotte Kellogg, the spouse of one of the leaders of the Commission for the Relief in Belgium, had given several conferences to support the initiative of relief supplies to the Belgian population during the war, was also counting on this visit to stimulate the ideals of young Americans. In the course of this trip, during which he received a triumphant welcome, Mercier was invited to many universities including Harvard, Yale, Princeton and Columbia, among others, from which he obtained several honorific distinctions. Lemaître would obtain the fellowship of the Commission that would allow him, with the help of his travel grants, to be admitted as a research student at the University of Cambridge in England.   Cf. for instance, Le cardinal Mercier. 1851-1926 (F. Desmet, ed. avec la collaboration de E. Sterckx), Bruxelles, Louis Desmet-Vereneuil, 1927: 201-204 and CLXVCLXXXIV. 60

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At the end of his theological studies at the seminary, Lemaître received ordination at the Cathedral of Saint-Rombaut in Mechelen by Cardinal Mercier, on 22 September 1923. The day after, in the parish of Saint-Henri of Brussels, he celebrated his first Mass. On 25 September, in the parish of Saint-Christophe de Charleroi, he celebrated his second Mass before participating in a celebration organized by the family of his mother, the Lannoy family. Early in October 1923, Lemaître left Belgium. An extraordinary scientific adventure had begun.

Chapter V

The mathematician who became an astronomer

1. A clergyman at Eddington’s house

T

he young priest Lemaître discovered the Anglo-Saxon university world in Cambridge in the beginning of the academic year 19231924. He attended the courses of the renowned astronomer Eddington (1882-1944)1 as well as those of the physicist Ernest Rutherford (1871-1937), the father of nuclear physics. He completed his training in mathematics by attending the classes of G.W. Hobson on the calculus of variations at Cambridge University.2 Eddington, who came from a Quaker Family, had studied in Cambridge before coming back later as the director of the observatory and holder of the Plumian Chair of Astronomy. After having completed a series of works on the movement of stars and the determination of their mass using methods from classical mechanics, he became interested in the formidable problem of the internal constitution of stars at a time when no one had any idea about the mechanism by which stars were powered. Georges Lemaître met with Eddington at a moment when the latter was working on the computations that would lead him to the publication of the still current book, “The Internal Constitution   W.H.H. McCrea, “Recollection of Sir Arthur Eddington O.M., F.R.S., 28 December 1882 – 22 November 1944”, Contemporary physics, Vol. 23, 1982, n° 6 : 531-540; A.V. Douglas, Arthur Stanley Eddington, London, Nelson, 1956; D. Lambert, “Eddington. Entre astronomie et philosophie”, Ciel et Espace, avril 1999, n° 349: 64-67. 2   AL (Dossier Eddington). 1

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of the Stars”3 as well as the law relating the mass to the luminosity of a star. But Lemaître also knew of the Cambridge astronomer’s other line of work. It is certain from the recommendation of the jury of the travel grant competition, that Lemaître had read his “The Mathematical Theory of Relativity”.4 Eddington had become acquainted with Einstein’s works during the war thanks to his correspondence with de Sitter who had been able to continue his work in some peace owing to the neutrality of the Netherlands. He quickly synthesized relativity theory in a technical publication for the Physical Society5 and published a book which enjoyed considerable popularity, “Space, Time and Gravitation”6, also read by the mathematician-seminarians of the Saint-Rombaut house. Eddington may be best known for his famous astronomical expedition, together with the royal astronomer Dyson, in the aftermath of First World War. During the total solar eclipse of 29 May 1919, Eddington and associates, at two observational sites, one in Brazil and the other on the island of Principe in the Atlantic, confirmed one of the most cherished predictions of Einstein’s general relativity: the bending of the light rays of a star by the gravitational field of the Sun. Besides the heroic effort associated with this expedition, one should also appreciate the irony of a campaign designed to provide work for the British under the direction of a convinced pacifist7, in order to confirm the idea of a German! During his stay in Cambridge, Lemaître, who took up residence in a house for Catholic priests, St. Edmund’s house, carried out a research work drawing on Einstein’s physics. This work would be published at the end of his stay in Cambridge (1924a) and would profit from a presentation of Eddington himself, which clearly showed that   Cambridge University Press, 1923; this book was written between 1924 and November 1925. 4  Cambridge University Press, 1923. This book represented Eddington’s course in Cambridge on the general relativity. 5   “Report on the Relativity theory of gravitation”, London, Physical Society, 1918. 6   Cambridge University Press, 1920. 7   Eddington was a member of the Quakers, who were well known for their pacifism. Cf. E. Dommen, Les quakers, Cerf, 1990. 3

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the English astronomer acknowledged the significance of “La physique d’Einstein’’.8 In this work, Lemaître gave his own synthesis of relativity, starting with an analysis of the fundamental concepts, especially that of simultaneity. In his research at Cambridge, Lemaître would try to understand how the concept of simultaneity must be modified when one passes from special to general relativity9. In special relativity, simultaneous events are defined in a relative manner, with respect to systems of coordinate axes in uniform rectilinear motion (a so-called Galilean, or inertial reference frame). These moving systems of axes can be conceptualized by a rigid solid10, whose sides are determined by the axes. To generalize the notion of simultaneity, one may try to define the simultaneity of events with respect to a solid body not in uniform rectilinear motion. In spacetime, two events infinitely close together are simultaneous if the segment joining them is orthogonal to their geodesics.11 By integration, one may find a curve where all points are simultaneous with the first two. This line is called the “line of simultaneity”. If one can characterize all the points of this line by one sole coordinate, one can say that a “time of simultaneity” has been found. Lemaître followed Herglotz12 in distinguishing two kinds of movement of a solid body. In movements we term type A, the world   “Since the previous work on M. Lemaître’s problem – the intermediary between the special and general theories of relativity – is probably not very familiar to the English reader, a brief introduction may be desirable” (1924a: 164). This previous work can only be: La physique d’Einstein.   9   Cf. M. Jammer, Concepts of Simultaneity. From Antiquity to Einstein and Beyond, The Johns Hopkins University Press, Baltimore, 2006: 271-289. 10   A solid is rigid if the spatial measurements carried out on the lines of simultaneity stay constant during the movement. The rigidity only depends on the notion of lines of simultaneity and not on the existence of a time of simultaneity. 11   The “world line” is a curve that describes, in the space-time, the evolution of an event, i.e. its trajectory in position and time. If one takes a classical space-time diagram, the set of events simultaneous to a given event is a horizontal line orthogonal to the temporal axis, which is the world line of a point at rest at the origin of the system of axes. In relativity, one generalizes this notion by using a concept of orthogonality adapted to non-Euclidian spaces. 12   G. Herglotz, Annalen der Physik, t. XXX, 1909, p. 1 (1924a: 164). Cf. G. Nordström, “Einstein’s theory of Gravitation and Herglotz’s Mechanic of Continua’”, Koninklijke   8

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lines from the points of the solids are such that one cannot define lines and a time of simultaneity. These movements are entirely defined by those of an arbitrary point of a solid. The geometry of the space-time associated with this kind of movement, is in fact Euclidean. To illustrate type A, Lemaître considered rectilinear movement at variable speed, and the movement described by uniform acceleration. In the latter case, he obtained one of the results he described in his dissertation, concerning the analogy that exists in general relativity between the description of uniformly accelerating rectilinear movement and the gravitational field created by an infinite mass at infinitely distance.13 Movements of type B are those for which a time of simultaneity does not exist, even if there is always a way to build lines of simultaneity. However, in this case, the notion of simultaneity has lost its character of uniqueness in regard to a solid, because any event can be made simultaneous to any other by building an appropriate line of simultaneity. One example of type B movement is that of a uniformly rotating solid. Two simultaneous events with respect to a solid in a rectilinear uniform movement are not necessarily simultaneous with respect to a uniformly rotating solid, for example the Earth. This is well confirmed in experiments where one looks at the interference between light rays moving on a disc in uniform circular motion. This was experimentally verified by Sagnac14, for one, already mentioned in La physique d’Einstein. (1922a: 295). Type B motions correspond to the evolution in certain space-times where the geometry is non-Euclidean.15 One can appreciate that the research done by Lemaître with Eddington did not yet constitute actual cosmology. It was more of a refining and deepening of his understanding of formal Akademie van Wetenschappen te Amsterdam, Proceeding of the Section of Sciences, Vol. 19, 1916-1917: 884-891. 13   Described by the external solution of Schwarzschild. Compare (1922a: 292 and 345) with (1924a: 169). 14   G. Sagnac, “L’éther lumineux démontré par l’effet du vent d’éther dans un interféromètre en rotation uniforme”, Comptes rendus, 157 (1913): 708-710; E.-J. Post, “Sagnac Effect”, Review of Modern Physics, 39 (1967): 475-493. 15  In fact, in group theory these motions are characterized by four one-parameter groups acting on space-time.

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relativity, hearkening back to his previous year’s work. This in-depth study likely endowed Lemaître with the greater familiarity he would need for the interpretation of actual physical consequences of general relativity. It is interesting to note that Eddington himself would benefit from the presentation of the work of his student in order to illustrate what would become one of the most important themes of his philosophy of physics: the existence of “conceptual cycles”. Indeed, the English astronomer would show in his lectures at the University of Edinburgh from January to March 1927, that physical notions involve one another by forming a “cycle”, in such a way that none of these notions can be considered more fundamental than the others.16 Eddington’s presentation of Lemaître’s work demonstrates that this philosophical notion was already present as early as 1924 and the example of the conceptual cycles chosen by Eddington rely appropriately on the close connection that exists between simultaneity and that of the rigid body (1924a: 164): The definition of a rigid body appeals to space-measures: but simultaneity is involved in the separation of space-measures from time-measures; and simultaneity in its turn is relative to the rigid body. It is of interest to note how this logical tangle is approached.

Georges Lemaître was probably not enthusiastic about Eddington’s lectures. According to McCrea17, Eddington’s courses, in contrast to his popular conferences, were boring. On the other hand, Lemaître would be deeply influenced by the style and approach of Eddington’s scientific thought. The confluence of Eddington’s interest both in general relativity and the problem of astronomy and astrophysics would encourage Lemaître himself to focus on their   Cf. A.S. Eddington, The Nature of Physical Laws, Cambridge University Press, 1928: 260-268. 17  “Recollections…”, op. cit.: 536. 16

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intersection. It was precisely this fertile interplay that would lead to his seminal 1927 work on the expanding universe. It was also thanks to Eddington that Lemaître improved his knowledge of numerical methods for the solution of differential equations18. This would remain one of his favourite subjects for the rest of his days. Yet, the most consequential influence of the Cambridge astronomer on the young priest-scientist would be a suggestion for the topic of his Ph.D. thesis. This is one of the essential keys for understanding the coherence of Lemaître’s cosmological work. Unfortunately, there is little in the way of recorded detail of the life of the young Abbé Lemaître in England. From his correspondence we only learned that he befriended a Japanese astronomer named Yusuke Hagihara (1897-1979) who had studied at the University of Tokyo and had been sent to Eddington with a grant from his government. Years after, he would earn distinction by contributing important works on the stability of orbits in celestial mechanics, and later writing a monumental treatise on the subject.19 Both friends would meet for the last time in Berkeley at the beginning of the sixties. Neither do we know a great deal about the personal interaction, and perhaps friendship, between Lemaître and Eddington during his stay in Cambridge. Even if, as observed by André Deprit20, the pacifist Eddington might have had a different perspective than the artilleryman Lemaître on the recent world war, it is natural to imagine a closeness between them, both being single men deeply engaged in religious choices and scientific research. We shall see that Lemaître would develop a personal synthesis of science and faith quite similar to that of the Cambridge astronomer. If one takes into account Lemaître’s implicit philosophical standpoint21 it is easy to imagine   He accordingly thanked Eddington for this in his Ph.D. thesis at MIT (The gravitational Field in a Fluid Sphere of Uniform Invariant Density, According to the Theory of Relativity, Unpublished manuscript, AL: 27). 19   P. Herget, “Yusuke Hagiara”, Physics Today, June 1979: 71. 20   Oral communication, 10-11-95. 21   This aspect will be discussed in the next chapter. 18

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the powerful influence Eddington might have had on him. In particular, his operationalism, which supposes that physics never achieves reality itself, but only a set of measures resulting from the operations that we carry out on it, but also his idealism that made him say that he never did believe an experimental fact if it was not confirmed by … a theory! Lemaître would always retain a great admiration for his professor, and shortly after his death, he would write a note dedicated to him: “These few lines will only give, perhaps, a very incomplete idea of the work of the great English astronomer. They would not mention, above all, the influence of the professor in guiding and inspiring the untold number of beginners’ essays; neither will they tell of the regrets of all of those who would approach him and benefit from his lessons and advice” (1945d: 115; translated from the original in French). The admiration was surely mutual, as the English astronomer wrote to Théophile De Donder22 during Christmas 1924: I found M. Lemaître a very brilliant student, wonderfully quick and clear-sighted, and of great mathematical ability. He did some excellent work while here, which I hope he will publish soon. I hope he will do well with Shapley at Harvard. In case his name is considered for any post in Belgium I would be able to give him my strongest re­ commendation.

2. The time to sow: from Canada to MIT After a short stay in Belgium in June 1924, the young priest embarked for Canada in order to attend a series of scientific meetings. He was welcomed for a short stay at La Pointe, the magnificent summer residence   Quoted from J. Bosquet, “Théophile De Donder et la gravifique einsteinienne”, Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. LXXIII, 1987, n° 5: 209-253; The quote is found on p. 250. 22

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of Senator Alfred Thibaudeau and his spouse Emma (née Rodier), located at Beauharnois in southwest Montreal, along the St. Lawrence River23. How did Lemaître become acquainted with the Thibaudeau? The story goes back to the First World War. His friend Charles Manneback had a comrade-in-arms, Pierre Lamal, who came later to work as an engineer in Brussels. The latter had a cousin, the Belgium Consul to Montreal, a certain M. Mathys, who was a friend of the Thibau­ deau. The Senator and Mrs. Thibaudeau, as well as their daughter Madeleine24 befriended the young priest who would come back several times at La Pointe until the 1960s. With a tinge of nostalgia, two months before his death, Lemaître reminisced on the impression from his arrival in this country which was so dear to him25: [...] I retain such good memories of my several stays in your beautiful country as early as that distant time, when in 1924 the passenger ship which brought me from Belgium slowly ascended the St. Lawrence River from Quebec to Montreal, in the unforgettable sunset on the great river and its islands.

From 6 to 13 August, Lemaître accompany Eddington to attend a meeting of the British Association for Advancement of Science.26 The latter would make a lecture for the general public on relativity  Detailed information concerning the relationship between the Thibaudeau and Lemaître was provided by D. Bellemare, the grandnephew of Madeleine Thibaudeau, to A. Deprit (letter of 27-09-87). 24   According to the information provided by D. Bellemare, Madeleine Thibaudeau enjoyed an important position in the social life of Montreal and in Canada. The list of people in her network was impressive: Louis Blériot and Saint-Exupéry, Paul Claudel, Vladimir d’Omerson, Niels Bohr and Einstein, the thomistic philosopher Étienne Gilson and Jacques Maritain. To this list one must add, of course, the group of Belgian physicists Charles Manneback, Marc Hemptinne as well as the promotor of Lemaître’s thesis at the MIT, Paul Heymans and his friend Manuel S. Vallarta, as well as the professor of Sacred Scripture in Mechelen, Gonague Ryckmans. 25   (1967b: 153) translated from the original in French. 26   Cf. “The Toronto “Meeting of the British Association”, Nature, Vol. 114, July 1924, no 2856: 130-131; “Meeting of the British association at Toronto, 1924, August 6-13”, The Observatory, Vol. XLVII, November 1924, no 606: 325-328. 23

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and the other, a more technical talk on the radiation emitted by a star. One lecture in particular seized the attention of Lemaître, that of Ludwick Silberstein, a physcist of Polish origin but working in England. The presentation concerned the determination of the radius of curvature of space-time. Silberstein adopted the model of the universe described by de Sitter in 1917, a universe empty of matter, but which can be interpreted as expanding.27 Silberstein showed then that if one introduces an observer and stars in the form of “free particles” in purely inertial radial movement, the light observed from a body undergoes a shift in the wavelength towards the red or toward the blue proportional to its distance and inversely proportional to the radius of universe. From distance measurements performed on eight globular clusters28 in the Large and Small Magellanic Clouds29, he deduced a radius of the universe of 6.7 x 1012 astronomical units30. This relation established by Silberstein between general relativity and the observational data intrigued Lemaître, but astronomers would quickly point out that Silberstein had deliberately excluded data that did not agree with his law of spectral shifts. As underlined by Helge Kragh,31 this event was likely the source of mistrust in the astronomical community, which ultimately delayed the acceptance of Hubble’s law, when finally confronted with the relevant systematic data. Lemaître took inspiration from the talk and discussions with Silberstein to undertake his own study of the universe of de Sitter and to pursue the question   This will be the subject of a more detailed discussion in a later chapter.   The Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) are in fact mini-galaxies orbiting our Milky Way Galaxy, at a distance of about 170,000 lightyears. 29   The determination of distances and speeds performed on these objects does not allow one to obtain a linear law of proportionality between the distance and the spectral shift, specifically because they are gravitationally bound to our galaxy, and as such could not reflect the large-scale expansion of the universe. Hubble’s law, to be discussed later, established a linear relation between the distance of remote galaxies and the red shift of their spectra. 30   An astronomical unit corresponds to the average distance between the Earth and the Sun, or 149.6 million kilometres. 31   H. Kragh, Cosmology and Controversy, The Historical Development of Two Theories of the Universe, Princeton University press, 1996: 15. 27 28

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of spectral shift. In 1963, while paying tribute to his colleague Ho­ ward Percy Robertson (1903-1961), who was unsparing in his critique of Silberstein, commented:32 In fact, the errors of Silberstein have been very stimulating. I had myself long discussions with him in 1924 at the British Association Conference in Toronto and my work, as possibly later on the work of Robertson, results for a large part as a reaction against some unsound aspects of Silberstein’s theories.

Another important scientific meeting was held in Toronto virtually at the same time (11 to 16 August): the International Congress of Mathematics.33 Lemaître met Charles de la Vallée Poussin once again and most likely listened to the communication of Élie Cartan on the stability of homogeneous ellipsoids of fluid34 which involved calculational methods for which the Louvain priest would show a real predilection. Nevertheless, this congress did not seem to have played much of a role in the evolution of his thought. Owing to his contact with Eddington, his tastes were beginning to run more along astronomical lines, and his currents interest lay with Cepheid Variables.35 These variable stars are noteworthy, because their intrinsic luminosity, i.e. their absolute magnitude, is related to the period of their os  I refer here to the draft of (1963a) preserved at the AL: cf. page 6.   Proceedings of the International Mathematical Congress held In Toronto, August 1116, 1924 (J.C. Fields, ed.), University of Toronto Press, 1928. 34   Cf. E. Cartan, Notice sur les travaux scientifiques, Paris, Gautier-Villars, 1974: 106107. 35   For an history of observational astronomy related or not with cosmology, I refer to the three following contributions: M.S. Longhair, “Astrophysics and Cosmology’’ in Twentieth Century Physics, Volume III (Laurie M. Brown, Abraham Pais, Sir Brian Pippard, eds.), Bristol, Philadelphia, New York, Institute of Physics Publishing – American Institute of Physics Press, 1995: 1691-1821; D.E. Osterbrock, “The Observational Approach to Cosmology: U.S. Observatories Pre-World War II” in Modern Cosmology in Retrospect (B. Bertotti, R. Balbinot, S. Bergia, A Messina, Eds), Cambridge University Press, 1990: 247-289; The General History of Astronomy. Volume 4. Astrophysics and twentieth-century Astronomy to 1950 part A (O. Gingerich, Ed), Cambridge University Press, 1984. 32 33

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cillations in luminosity according to a universal law for Cepheids. This was discovered in 1912 by Miss Henrietta Swan Leavitt, who at the request of her patron Pickering, had inventoried more than one thousand Cepheids in the Magellanic Clouds. She classified the Cepheids graphically, plotting their absolute magnitude against their pulsation period, the resulting scatter-plot exhibiting the aforementioned law. Subsequently, Hertzsprung and Shapley recognized that Leavitt’s law was a characteristic property of all Cepheids, and the latter conceived that one could use Cepheid Variables as a ‘ruler’ or ‘standard candle’ to measure distances in the cosmos. Simply put, the ratio of a Cepheid’s intrinsic luminosity and apparent luminosity (that which is measured at the Earth) is proportional to the square of the distance to the celestial body. If one can find a manner in which to calculate the absolute brightness of a celestial body, it is therefore possible to find the distance. But this was precisely the case for the Cepheids since one could observe the pulsation period and the latter is related to absolute brightness by Leavitt’s law. Distances to remote galaxies could thus be measured out to even very great distances, so long as one could identify a Cepheid within it. From 1916 to 1918, Shapley would use Leavitt’s law to determine the distances of about one hundred globular clusters. Thanks to his work at the Mount Wilson Observatory, near Los Angeles in California, he succeeded in using around 1300 Cepheids in 62 globular clusters. Lemaître’s interest in the Cepheids, and consequently for the measurements of cosmological distances, would lead him to Ottawa and the Dominion Observatory, where he was welcomed by the director R.M. Steward together with François Henroteau (1889-1951)36, a former astronomer at the Royal Observatory of Belgium, who likewise was interested specifically in the Cepheids. In September, Lemaître went to the United States to start the academic year 1924-1925 once again in Cambridge but this time at the Harvard College Observatory that had been   Cf. “Necrology”, Journal of the Optical Society of America, Vol. 42, 1952, no 1-12: 589. This former ULB “docteur ès sciences” would distinguish himself by inventing a method to build very thin television screens. 36

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directed by Shapley (1885-1972)37 since his departure from the Mount Wilson Observatory in 1921. Lemaître was once again the beneficiary of a C.R.B. Graduate Fellowship grant38. Since he wanted to obtain a Ph.D. but the Harvard Observatory did not grant them, Lemaître registered as a student at the Massachusetts Institute of Technology (MIT) also located in Cambridge. To obtain an equivalency diploma, he was required to attend a series of supplementary courses in mathematics and physics that he had already attended in Louvain – MIT did not recognize his Masters degree, a fact that he did not omit mentioning in his report to the C.R.B.39 Lemaître also had the chance to attend experimental spectroscopy courses at Harvard. Additionally, he attended a class on the role of interference in spectroscopy provided by one of the great French specialists in optics, Fabry, who had come to the US as a guest professor.40 He also attended the classes of other guest professors: Olden­berg from Göttingen, Debye from Zurich and finally those of his former master, de la Vallée Poussin, who came to talk about functional analysis and integration theory.41 During his stay at Harvard, the young priest lived at 1 Cleveland Street in a house inhabited by the clergy serving the St. Paul Church.42 He took part in the daily life of the priests and their cele  B.J. Bok, “Harlow Shapley. November 2, 1885 – October 20, 1972”, Bibliographical Memoirs. Volume XLIX, Washington, National Academy of Sciences, 1978: 241-259. 38   This was a Ph.D. grant from the Committee for Relief in Belgium previously mentioned. The information about this period can be found in two reports written by Lemaître: “Rev. Georges Lemaître. Belgian fellow 1924-1925. D.Sc. Louvain, July 1920. Harvard Observatory and Massachusetts Institute of Technology. Astronomy” (January, 1925), “Physics and Astronomy’’ (Pasadena CA June 18, 1925), AL. 39   “Rev. Georges Lemaître…” (January 1925), op. cit. 40   The AL (“Dossier Eddington”) preserved Lemaître’s notes of this course, most likely from October 1924. 41   The AL (“Dossier Eddington”) also preserves some fragments of notes most probably related to courses on wave mechanics (Debye) and functional analysis, linear functionals, Stieltjes integrals, and the integral equation of Volterra (de la Vallée). 42   These details can be found in a letter sent by Lemaître to Canon Allaer, on 13-111924 (archives of the Archdiocese of Mechelen-Brussels, “Fonds Mercier”, XXV, 168; as related by A. Jans). 37

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brations. It was during this time, during the occasion of a dedication of a church, that he had the opportunity to be introduced to Cardinal O’Connell who had met Cardinal Mercier and the director of the Saint Rombaut House, Canon Allaer, during his 1919 trip43. Lemaître seemed to be entirely at home in the North American church. He was even invited to spend two weeks during the holidays at the personal residence of a bishop, who had an epistolary relation with Canon Allaer. His integration within the scientific community of Cambridge was also a success if one believes the list of circles he frequented: The Harvard Mathematical Club, The Association of Variable Star Observers44, and the seminar that gathered together Harvard and MIT scientists. Lemaître chose Paul Heymans (1895-1960)45 for his thesis supervisor, an eminent academic who would be a junior lecturer at MIT before becoming professor at the University of Ghent, and Minister of Economic Affairs, the Middle Class and Agriculture [Ministre des Affaires Économiques, des Classes moyennes et de l’Agriculture] during the year 1938-1939. Heymans’ supervision was perfunctory at best, as his interests did not correspond with those of the young priest. Indeed, he was a specialist of applied questions like photoelasticity and the measurement of small time intervals, for instance. However, the relationship between the two were excellent and Heymans had great confidence in Lemaître, as shown by the confidential information he gave him concerning a minor incident provoked by de la Vallée Poussin on 10 or   The 5 October 1919, the two cardinals attended a Mass celebrated at the Cathedral of the Archdiocese of Boston together in the presence of King Albert and Queen Elizabeth of Belgium. It was during this stay in Boston that King Albert was made Doctor Honoris Causa at Harvard University. P. Goemaere “A travers l’Amérique avec le roi des Belges”, Bruxelles, J. Goemaere, 1920: 47-52. 44   11 October 1924, no sooner was he in Cambridge than he attended the meeting of this association, which was held at the Harvard College Observatory. 45   Cf. Th Luykx, ‘’Paul Heymans’’ in Rijksuniversiteit te Gent. 1913-1960. Deel IV. Faculteit der Wetenschappen. Faculteit der Toegepaste Wetenschappen, Gent Uitgave van het rectoraat, 1960: 407-409. Some information was related by G. Fourez, P. Heymans’ nephew. 43

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11 November 1924, while he was introduced by Heymans precisely, at Cardinal O’Connell’s residence46. The scientific work carried out by Georges Lemaître during the year 1924-1925 was remarkably rich and concerned three different topics: astronomy properly speaking and specifically the study of variable stars, general relativity; and Eddington’s theory which was a unified theory of electromagnetism and gravity based on an extension of Einstein’s ideas. In the context of the Harvard College Observatory and under the supervision of Shapley, he developed a method that enabled the calculation of the period of pulsating variable stars47 of a given magnitude and spectral type. This method used the theory that Eddington applied to the Cepheids in order to verify the validity of the relation that was established between the mass and the luminosity of a star. Lemaître found a way to simplify the computations of the period, by using an appropriate diagram that enabled a rapid reading of the result. He exhibited a set of indices that suggested that the theory of stellar pulsation could be applied to stars other than the Cepheids and more specifically, to the variable stars with a short fluctuation period, or to the spectral type O and M stars.48 This research work would lead to an official publication at the Harvard observatory (1925d).49 Lemaître   De la Vallée Poussin complained about the slowdown in the construction work at the Louvain library that was being financed by the US. He attributed the cause of this slowdown to Butler, a philosopher and supporter of cosmopolitism and who would become the Dean of Columbia University and winner of the Nobel Peace Prize in 1931. Yet N.M. Butler was a friend of Cardinal O’Connell. The latter found it unseemly to put the responsibility of the situation unfairly on his friend as the slowing down of help to Belgium was, according to him, related to the participation of that country in the occupation of the Ruhr. He became angry and undoubtedly exceeding his intentions, he promised to talk about the incident with Cardinal Mercier and the Minister of Foreign Affairs in the US (Letter of Georges Lemaître to Canon Allaer, op. cit.). 47   Pulsating variable stars are stars whose periodic fluctuation of luminosity is related to pulsations in the upper layers of the atmosphere. 48   The letter M and O correspond to particular classifications of the spectra of stars. It was at Harvard that spectral classification was first employed to characterize stars. 49  Lemaître’s research works are quoted by Shapley in: “Reports of Observatories 1924-1925. Harvard College Observatory”, Popular Astronomy, Vol. 34, 1926: 24-29 (Cf. p. 28). 46

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had thoroughly studied the literature regarding variable stars such as eclipsing binary stars (e.g. β-Lyrae) whose luminosity fluctuations are related to the periodic passage of a companion.50 In his reading notes about the calculation of periodic orbits of such systems, one can already see his penchant for numerical analysis methods.51 The work of the young priest on general relativity started with a study of the de Sitter universe. Here it was not Eddington that had suggested this line of inquiry, but the provocative lecture of Silberstein at the Toronto congress.52 What is the de Sitter universe? It represents one of the three classes of solutions to Einstein’s equations of gravity53 describing a universe that is static (does not change over time: there is neither expansion nor contraction), homogeneous (the properties of space are the same independent of the position of the observer) and isotropic (at each point, there is no preferred axis, i.e. the properties of space are the same independent of the direction of observation54). Within this class, the first solution that corresponds to an empty universe of matter and without curvature is the Minkowski space-time, the universe   The AL preserves notes of lectures of Lemaître regarding the works of Shapley on β Lyrae and on the computations of eclipsing binary orbits. 51  All these calculations are related to the works of Darwin, “Periodic Orbits”, Acta mathematica, t. XXI, 1897: 99-242. 52   AL has preserved detailed lecture notes from a paper of Silbertsein that was published in May 1924 (“Determination of the Curvature Invariant of Space-Time”, Philosophical Magazine, Vol. 47, May 1924: 907). 53   These equations are denoted by Rmn - ½Rgmn = - kTmn - λgmn where k= 8pG/c4 (G the gravitational constant, c the speed of light in vacuum), λ is the cosmological constant, Tmn is the energy-momentum tensor which characterizes the source of the graviational field, and gmn is the metric tensor that enables us to compute distances in the space-time. Rmn and its trace R characterize the curvature of this spatio-temporal geometry. The metric tensor gmn is the unknown to be determined in the Einstein’s equations that express roughly that “the curvature of the space-time” is influenced by the energy-matter and by a cosmological term. In the case of a perfect fluid, we have Tmn = (rc2+p) umun – pgmn where (um represents the speed of the fluid, r its density and p its pressure. (cf. J.V. Narlikar, Introduction to Cosmology, Cambridge University Press, 2002 [1983]). 54   A homogeneous but not isotropic universe, would be one where for example, galaxies would be approaching the observer along one spatial direction, but receding from the observer along another direction. At each point, the space of this universe would appear either prolate (cigar shaped) or oblate (pancake shaped). 50

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of special relativity. The second is the universe of Einstein, which is a space-time for which the spatial part is a static sphere with three dimensions55 filled with a perfect fluid of uniform density and zero pressure. The third solution is that of de Sitter, which is a space empty of matter, but that possesses some very particular properties that distinguish it from the flat space of Minkowski. Specifically, if one introduces some small bodies of negligible mass into de Sitter’s space, with zero initial velocity, they will not stay at rest, but will tend to move towards or away from one another,56 in contrast to Minkowski space where the bodies would stay at a relative rest. Hence, from one point of view, one might say that de Sitter universe “gives the impression to be expanding”! If we consider, following Weyl57 and Eddington, a localized source of monochromatic light in a de Sitter space,58 a rather non-intuitive behavior arises, namely the wavelength of the light is progressively red-shifted as the source is removed to further distances. This begs two questions, first how can one understand this, and second, are there any observables that can be associated with this phenomenon. The spectrum of a source moving away from the observer will be shifted towards the red depending on the speed of recession, completely analogous to the familiar acoustical Doppler effect. One can thus interpret the spectral shift of the de Sitter’s space as a clue to the motion of luminous sources; this would soon be known as the ‘de Sitter effect’. Eddington, distinguishing the tendency of points to move away from one another, and the velocity red shift of sources59 to be   Such a space is finite without a boundary (an example being the surface of an ordinary sphere, which has a  finite surface area, but no boundaries). The analogue of a straight line in such a space is the ‘great circle’, i.e. a circle whose origin is the centre of the sphere. If we send a ray of light ahead of us in a three-dimensional sphere and waited long enough, the ray would ultimately return to us from behind. 56   This depends on the sign of the cosmological constant. If λ is positive, there is a tendency to move away. 57   H. Welt, “Zur Allgemeinen Relativitätstheorie”, Physikalische Zeitschrift, t. 24, 1923: 230-232. 58   With a positive cosmological constant, which was the case considered by Eddington. 59   This showed that Eddington always thought of redshift as a phenomenon related to 55

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distinct physical phenomena, focused on the latter to compare with spectra that Vesto M. Slipher60 had prepared for him at the Lowell Observatory. These observations showed indeed that almost all nebulae61, which had not yet been interpreted as galaxies similar to ours owing to erroneous distance estimations, manifested spectra shifted toward the red, interpreted as recession. The de Sitter universe thus could be credited in some measure for orienting the astronomical community towards red-shift measurements. An approximate calculation valid for short distances showed that the relative increase of the wavelength of light is proportional to the square of the distance.62 Some astronomers, Carl Wilhelm Wirtz in particular63, sought to verify if the observations corroborated this quadratic dependence. Silberstein, meanwhile, calculating another way, concluded that the relative shift of the wavelength would be linearly proportional to the distance of the source, and inversely proportional to the curvature radius of the universe. The relative shift also depended however on a sign ambiguity (plus or minus) which arose in the calculation64; The plus sign describing the case where the sources are receding from us (redshift), and the minus sign the case where these sources are approaching us (blueshift). The reliability of the observational data at that time however, was completely insufficient to distinguish the various calculational approaches.

a motion of light sources in the universe and not to an expansion of the universe itself bringing the sources with it. 60   A.S. Eddington, The Mathematical Theory of Relativity, Cambridge University Press, 1923: 162. The results provided by Slipher to Eddington only concern the speed of nebulae and not their distance. 61   The nebulae were first thought to be diffuse clouds, but later considered to be groups of stars close to us. Finally it was recognized that they were galaxies similar to our own Milky Way galaxy. 62   Cf. A. Sandage, “Practical Cosmology: Inventing the past” in The deep Universe (A.R. Sandage, R.G. Kron, M.S. Longair, eds.), Berlin, Springer, 1995: 97-99. 63   W.C. Seitter, H. W. Duerbeck, “Carl Wilhelm Wirtz. A Pioneer of the Observational Cosmology” in Modern Cosmology in Retrospect, op. cit.: 365-399. 64   The sign arises from the extraction of the square root of the element of spatial length.

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In certain mathematical representations of de Sitter space 65, that is, for some particular choices of coordinates, there is even a finite distance, the ‘horizon’, for which the spectral shift becomes infinite; and thus from which we cannot receive light. For Eddington the horizon could be an indication of a periphery of de Sitter space, a sort of massive ring used to sustain this space that is itself empty. Yet, he abandoned this hypothesis quickly by affirming that this massive horizon was only an illusion that is linked to a choice of coordinates representing a fictive singularity. This consideration of the mass horizon is not uninteresting as it shows that de Sitter space is in fact a space that simulates being massive, and thus drops a broad hint that the good way to link it to Einstein’s universe is to make a detour through the non-static universes, precisely as Lemaître would do a few years later. Just as the Earth can be described by different choices of geographical coordinates, so one may give different mathematical representations of de Sitter’s universe. Each of these representations is characterized mathematically by a metric, i.e. by an expression that allows the calculation, in its coordinates, of the element of the length of a curve drawn in this universe,66 the first of which was given by de Sitter himself in his 1917 paper,67 and used by Eddington under a different form.68 In his coordinates, the de Sitter universe is a static space-time where space is spherical. If one concludes as did Lemaître (1927c: 50-51), that this space-time is an ordinary sphere, the spatial   For example, the one chosen by Eddington in his book: The Mathematical Theory of Relativity, op. cit.: 161. 66   We have seen that the metric gmn is the unknown of Einstein’s equation. It allows calculating the distances in space-time from an infinitesimal version of the Pythagoras’s theorem: ds2 = gmn dxm dxn where a sum is performed when the indices are repeated up and down (Einstein’s convention). 67   W. de Sitter, “On Einstein’s theory of gravitation and its astronomical Consequences’’, Monthly Notices of the Royal Astronomical Society, Vol. 78, 1917: 3-28: ds2 = R2(-dc2 - sin2c(dq2 + sin2qdf2) + cos2cdt2) with R2 = 3/l; with the convention that c = 1. 68   Eddington rewrote the metric in such a way that one could compare it quite naturally with that of the problem of Schwarzschild interior. (Cf. below): The Mathematical Theory of Relativity, op. cit.: 161-169: ds2 = -g-1 dr2 - r2 (dq2 + sin2q df2) + gdt2 where g = (1-r2/R2), with the same convention as before. This is obtained from the one of de Sitter metrics by setting: r = Rsinc and t = Rt. 65

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sections are equivalent to the great circles crossing each other on the same diameter and the associated temporal lines are parallels of latitude orthogonal to these great circles 69. Lemaître would study this metric while showing that it does not fit the description of the de Sitter universe: note that the coordinates possess a center while the universe is homogeneous and isotropic, i.e. that all points are equivalent. To visualize this, let us take Lemaître’s spherical image and consider a great circle representing a spatial section. There is a special temporal line: the one represented by the only great circle that is orthogonal to this spatial section. The other temporal lines are smaller circles whose diameters decrease down to the pole, which represents the aforementioned horizon.70 Lemaître then adopted a metric already described by Lanczos in 192271 and that one may visualize as follows. All the temporal lines are meridians that cross one another at the same diameter and the spatial sections are the lines of latitude. One may see that as time passes, or in other words, when one progresses along one temporal line, space itself is modified as the radius of corresponding latitudes is not constant on the sphere. This change of coordinates provides the de Sitter universe, an image of a non-static world whose spatial distances are varied. For Lemaître, as for Eddington whom he referenced, the non-static character of the de Sitter space-time is not a problem as the astronomical observations seemed to indicate a phenomenon of recession of the nebula (1925c: 41).   To obtain the real geometry, one must add two supplementary dimensions to the space and pass from a real time coordinate to a pure imaginary time coordinate (Cf. N.D. Birrell, P. C. W. Davies, Quantum Fields in Curved Space, Cambridge University press, 1982: 129-138, where representations are given from the coordinates on a hyperboloid of one sheet. 70   In technical terms, one may say that the temporal lines are not geodesics, i.e. they do not describe lines of free particles. Only the central temporal line is a geodesic. If one releases a particle at rest in a frame placed at the centre, it remains there. In all other cases, the particles cannot stay at rest. 71   C.Lanczos, “Bemerkung zur de Sitterschen Welt”, Physikalische Zeitschrift, t. 23: 539-543. Lemaître wrote: ds2 =R2 (-cosh2t'(dc'2 - sin2c'(dq'2 + sin2q' df'2))+ dt'2). 69

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Eddington commented on this subject: “It is sometimes urged against de Sitter’s world that it becomes non-static as soon as any matter is inserted in it. But this property is perhaps rather in favor of de Sitter’s theory than against it.”72 Our treatment underscores this non-static character of de Sitter’s world that yields a possible physical interpretation of the mean recessional motion of spiral nebulae. Lemaître brings to bear his essential talents as a mathematician, which consists in quickly and intuitively seeing a transformation of coordinates, which reduces a complicated and not very symmetrical description to one which is much simpler because it is more symmetrical.73 By changing variables (1925c: 38), he shows that the de Sitter universe can be described as a Euclidean space, thus without curvature and without a preferred centre which expands exponentially over time. In this map, there is no trace of the horizon. It was thus a fictitious singularity. Lemaître’s purely mathematical elimination of singularities would play an essential role in his future works on relativity and in classical mechanics. Ironically, this metric of Lemaître which is, up to a factor of spatial dilation, equivalent to a Minkowski space, would be the foundation of the theory of the continuous creation of matter of Bondi, Hoyle and Gold,74 the great opponents of the theory of the primeval atom of Lemaître. The fact that the de Sitter universe can be interpreted as a Euclidean space was for the young astronomer a major obstacle since: We are led back to the Euclidean space and to the impossibility of filling up an infinite space with matter that cannot but be finite. de Sitter’s solution has been abandoned, not because it is non-static, but be  The Mathematical Theory of Relativity, op. cit.: 161.   A first change of coordinates: c = arcsin r/ t and t = ½ ln(t2 - r2) leads to a metric ds2 = R2/t2(dt2 - dx2 - dy2 - dz2). By posing dT = e dt/ t one is led to ds2 = R2(dT2 exp(2eT) (dx2 + dy2 + dz2)) where e = +1/-1. This solution would be rediscovered by Robertson in 1928 (cf. R.C. Tolman, Relativity, Thermodynamics and Cosmology, Oxford, Clarendon, 1934: 347). 74   Cf. N.D. Birrell, P.C.W. Davies, op. cit.: 130.

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cause it does not give a finite space without introducing an impossible boundary. (1925c: 41)

The argument of the finitude of the world that already appeared in the manuscript, “La physique d’Einstein”, constitutes here the fatal blow against the de Sitter universe. Throughout his life, Lemaître would never abandon this argument and he would always adopt the model of a finite universe. One may also observe that Lemaître was inclined to favour an interpretation of the recession of nebulae in terms of an expanding universe. Most of the ingredients were in place to enable his foundational work to germinate. Most, but not all. However, one of the missing links of his future work happened to be hidden in his own Ph.D. thesis we want to look at now. This thesis,75 which until then had not been widely read or assimilated76, was motivated by a problem that had been suggested by Eddington, probably when Lemaître was in England77, and which is more fully explicated in his Mathematical Theory of Relativity78 under the title of the ‘problem of the homogeneous sphere’. Eddington went in search of the gravitational field, described by the equations of Einstein, existing inside a sphere of perfect fluid of homogeneous density.79 This problem had been solved by the German astronomer Karl Schwarzschild in 191680 one year before Einstein found the solution  The title of this thesis preserved at the MIT library and at the AL is entitled: “The Gravitational Field in a Fluid Sphere of Uniform Invariant Density according to the Theory of Relativity” (50 pages). This Ph.D. thesis was nearly never studied and quoted. The first important work about the latter is that of Ian Steer, “Lemaître’s Limit”, Journal of the Royal Astronomical Society of Canada, April 2013 (arXiv: 1212.6566v1). 76   A part of the thesis appears in a rewritten form in the paper (1933e). 77  Indeed, during the congress of Toronto, Lemaître seemed to have one of his central results of his thesis as he wrote to Eddington on the 29 November 1925: “I would be very glad to know […] what your opinion might be on the physical significance of the maximum sphere with finite central pressure. I remember you were puzzled with this result when I told you in Toronto” (AL). 78   Op. cit.: 168-170. 79  The metric can be written in this case ds2 = -exp(A(r,t)) dr2 – r2 (dq2 + sin2qdf2) + exp(B(r,t)) dt2 representing the models of universes with spherical symmetry. 80   K. Schwarzschild, “Über das Gravitationsfeld einer Kugel aus incompressibler Flüssiggkeit”, Berlin. Sitzungsberichte, 1916: 424. 75

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corresponding to his static universe. The problem was then considered by Gunnar Nordström81 in Leiden and by Théophile De Donder.82 The solution of Schwarzschild contained a particularly noteworthy and consequential feature. The pressure in the centre of the sphere increases in function of its radius and become infinite for a finite value of radius.83 Thus physically, there cannot thus be a star for example, which would have a radius greater than this limiting radius. If the sphere contained water, the maximal radius would then be 370 million kilometres, which is twice the radius of Betelgeuse, this red giant whose diameter is estimated as more than 700 times that of the Sun. Eddington noticed that the problem of Schwarzschild was perhaps not fully rigorous relativistically. Indeed, density itself is not a relativistic invariant.84 When one make a change of reference frame the density does not stay invariant, which indicates that it is not a physically well-defined relativistic notion. Nevertheless, one may readily construct a relativistic invariant with the density (r) and the pressure (p) of the fluid,85 which is T = r-3p.86 At low pressures, this invariant should not much differ from the density and the solution of Schwarzschild constitutes a good approximation. But, at high pressure, in the vicinity of the limiting radius for instance, the solution of the German astronomer becomes inaccurate. Eddington suggested to Lemaître to explicitly solve the problem of the determination of the gravitational field inside a fluid sphere of constant invariant density T.

  G. Nordstrom, “Calculation of Some Special Cases in Einstein’s Theory of Gravitation”, Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings of the Section of Sciences, t. 21, 1918-1919: 68-79. 82  In La gravifique einsteinienne, Paris, Gauthier-Villars, 1921. 83   It is not possible to add matter to the sphere. (Cf. Th. De Donder, “Catastrophe dans le champ de Schwarzschild”: premiers compléments de La gravifique einsteinienne. Complément 3”. Paris, Gauthier-Villars, 1922). 84   It suffices to think of the fact that in special relativity, the mass is not an invariant since it can be transformed into energy by: E = mc2. 85   It consists technically in the trace of the energy-momentum tensor defined above: T = Tmm (with Einstein’s convention). 86   With the convention again being that the speed of light is unity. 81

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Lemaître started by first correcting his professor as the latter proposed that one must also modify, in the Schwarzschild approach, the condition expressing the fact that the fluid is perfect. Lemaître showed that this condition can be preserved as is. Then, he examined how Einstein’s equations are written for a spherically symmetric field of an inhomogeneous perfect fluid, but of constant invariant density T. He then obtained equations that were also found by Marcel Brillouin, but by another method.87 Brillouin’s method concatenated the Schwarzschild solutions of all the infinitely thin spherical shells constituting the whole sphere, and for which the density varies in a continuous manner from one layer to another. Taking the limit to infinity, he obtained the same equations as those of Lemaître. These equations are in fact those that characterized a model of universe that would be named after the 1930s, unfairly it must be said, the “Tolman model”. He tried to integrate these equations after having regularized the system of differential equations through some judicious changes of variables. He found the equations readily integrable for two specific cases, with remarkable solutions: the universe of Einstein and that of de Sitter. His equations defined a general framework that allowed imagining an interpolation between these two paradigmatic solutions of general relativity. He reinforced, in doing so, the affirmation of Eddington88: It seems natural to regard de Sitter’s and Einstein’s forms as two limiting cases, the situation of the actual world being intermediate between them. De Sitter’s empty world is obviously intended only as a limiting case; the presence of stars and nebulae must modify it, if only slightly, in the direction of Einstein’s solution. Einstein’s world containing masses far exceeding anything imaged by a astronomer, might be regarded as the other extreme – a world containing as much matter as it can hold. 87 88

  Proceedings of the Academy of Sciences of Paris, t. 174, 1922: 1585.   The Mathematical Theory of Relativity, op. cit.: 160.

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Nevertheless, this interpolation was still envisioned in the context of a model that did not vary in time. Not finding other exact solutions, Lemaître embarked on numerical integration, and his calculations, handwritten, are not simple. The upshot of all these lengthy calculations is that there is still, as with the case studied by Schwarz­s­­­child, a limiting radius beyond which a sphere of constant invariant density does not exist. Interestingly however, in this case, the pressure at the centre remained finite. As a function of pressure, the radius increases until reaching a maximum; thereafter it decreases, oscillating toward a finite limit as the pressure tends toward infinity. This result was even more paradoxical than the existence of Schwarzschild’s limit­ing radius, because89: Infinite pressure suggests that the equations cease to keep their physical meaning and, as it has been said, some kind of ‘catastrophe’ would occur. This way of eluding the difficulty is excluded in the case of a uniform invariant density.

This is precisely why Lemaître would later conclude that assuming a constant density, as does Schwarzschild, is a more reasonable option to address the problem of the homogeneous sphere.90 The student Lemaître thus showed that the suggestion of his professor at Cambridge was not as fruitful as it first appeared. As evidenced by a marginal note in a small notebook dated 1 September 1925, Lemaître had laboured long and hard to get to this point: “The numerical integration method caused me a lot of setbacks”.91 In the first version of his thesis, Lemaître had employed techniques for numerical integration without unduly worrying about the justification of the existence and the uniqueness of solutions in the neighbourhood   G. Lemaître, “The gravitational field…”, op. cit. (summary appended to Ph.D. dissertation: 6). 90   Cf. The report “Rev. Georges Lemaître…Physics and Astronomy” of 18 June 1925, op. cit. 91  AL. 89

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of the singularity that appeared, as is often the case, at the centre of the sphere. He applied a calculational method he discovered in Eddington’s theory of pulsating stars. However, his distinguished thesis committee (Norbert Wiener, H.B. Philips, Ph. Franklin and M.S. Vallarta) did not accept the first version he submitted 11 December 1925. The jury observed that his results “are left hanging in the air”92 relying as they did on the Picard method of resolution of differential equations, valid only outside a neighbourhood of a singularity. Yet, Lemaître used this method precisely within the neighbourhood of a singularity. The rejoinder of Lemaître is characteristic of his pragmatic mathematical philosophy favoring intuition and numerical experience over rigour:93 “I neglected to give a formal proof for this mathematical difficulty, as from the physical point of view, it seems clear that a solution must be determined by the value of the pressure at the centre of the sphere”. As an astute student of De la Vallée Poussin and desirous of his Ph.D., he wrote a five page addendum giving a rigorous justification of his calculations, convincing to the Committee who accepted his thesis on 15 December 1926.94 On 6 July 1927, Georges Lemaître was granted his Ph.D. in physics. Eddington’s suggestion had led to a negative result, but some equations emerged that that would allow some models of inhomogeneous universes with spherical symmetry to be constructed. On the other hand, another of Eddington’s proposals would lead Lemaître down the path to a total conundrum. At MIT, Lemaître deepened in his understanding95 of the unified theory of the gravitational and electromagnetic field that Eddington   “Report on the Doctoral Dissertation of G.H.J.E. Lemaître” joined to the letter of H.M. Goodwin, Dean of Graduate Students addressed to Lemaître and dated 31-121925 (AL)”, (AL). 93   Letter addressed to H.M. Goodwin, on 31-08-1926 (AL). 94   On the basis of the work done at MIT, the Committee would judge that it was not necessary that Lemaître be present for a formal oral defence of his thesis. (Letter of H.M. Goodwin to Lemaître, 15-12-1926, AL) 95   He already was familiar with this theory as he had read the Mathematical Theory of Relativity (last chapter) and the Exposé théorique de la relativité généralisée. Compléments mathématique inédit de l’Édition française d’“espace, temps et gravitation” (translation by J. Rossignol), Paris, Hermann, 1921: 116-149. 92

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had developed by generalizing Weyl’s theory.96 This theory, which is an early precursor of our contemporary gauge theories that have unified three of four of the fundamental interactions, is also an extension of Einstein’s general relativity. In general relativity, if one performs parallel transport97 of a vector along a closed curve in space-time, its direction will in general be changed upon returning to the starting point. Moreover the angle offset will depend on the specific path chosen, indicating the presence of the curvature of space-time, i.e. gravi­ tational forces. However in this theory, the length of the vector remains invariant. In Weyl’s theory, parallel transport on a closed path can change not only the direction of a vector that indicates the existence of gravitation as in relativity, but also its length. There is no standard length which is absolutely invariant at each point. Weyl has demonstrated that this last possibility corresponded in fact to the existence of the electromagnetic interaction. Eddington’s theory, meanwhile, went a bit farther by admitting that the variation of a vector during its parallel transport does not only depend on the path followed, but also on the orientation that it takes along this way. In the context of Eddington’s theory, Lemaître obtained equations describing the electromagnetic field that differed from the usual equations of Maxwell when the magnetic field was very intense98. In fact, Lemaître tried to develop the problem that would preoccupy Einstein during the

  Cf. M.-A. Tonnelat, Les theories unitaires de l’electromagnétisme et la gravitation, Paris, Gauthier-Villars, 1965: 225-266 (for Weyl) and 266-273 (for Eddington). A succinct presentation can be found in J. Becquerel, Exposé élémentaire de la theories d’Einstein, Paris, Payot, 1922: 190-195 (For Weyl) and 195-204 (for Eddington). 97   To form an idea about the parallel transport of a vector, the reader may wish to make a pen travel along a triangle drawn on the surface of a sphere in such a manner that the pen always makes a constant angle with the tangent to the sides of this triangle. The reader will see that upon returning back to the starting point, the pen has turned a certain angle. On a plane, this type of motion is nothing more than the ordinary parallelism and the vector does not undergo any rotation on a closed contour. 98   This is close to what Eddington is doing in the Exposé théorique de la relativité généralisée, op. cit.: 140-149. This “Exposé” is a mathematical supplement written by Eddington for the French edition of Space, Time and Gravitation (1921). This supplement be augmented and ultimately lead to his book: Space, Time and Gravitation (1923). 96

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second part of his career, posed by the problem of the electron99 or by the existence of elementary particles in the context of geometrical theories where everything might be deduced from a continuum. The young priest promptly abandoned this topic however, as the study of the simplest case showed incompatibilities with the empirical data.100 He would only regain some interest in this kind of unified problem six years later, once more under the inspiration of Eddington’s book, Relativity Theory of Protons and Electrons. Lemaître’s interest in this kind of problem is not surprising, as it was exactly in 1925 that Einstein was working on Eddington’s theory101 and as he himself contributed an appendix to the German translation of The Mathematical Theory of Relativity, related to the description of this theory by a variational principle102. But there is more. At MIT, where Lemaître was preparing his Ph.D., Norbert Wiener had a strong interest in the problems of the unification of gravitation and electricity. The father of cybernetics would later write a series of papers in collaboration with the Dutch geometer Dirk Jan Struik103 and with Vallarta about attempts of unified theories.104   Lemaître was likely familiar with this problem due to the Exposé théorique de la relativité théorique généralisée. Complément mathématique inédit de l’Édition française d’ “Espace, temps et gravitation” (translation by J. Rossignol), which has been mentioned (Cf. pages 116-149). 100   In a letter addressed to Eddington on 29 November 1925, Lemaître (who was back in Louvain) wrote: “I left aside the work I had begun on the in-tensor as I cannot find any answer you had made against it (it was a sign of the Poynting Vector)”. The “intensors” are tensors, which are invariant under a change of length scale. 101   Cf. V.P. Vizgin, Unified Field Theories in the first third of the 20th century, Basel, Birkhäuser, 1994: 204-218. A notebook preserved at AL makes clear that Lemaître had followed at least one of the works of Einstein regarding his approach of a unified theory of gravitation and electricity. 102   A. Einstein, “Eddingtons Theorie und Hamiltonsches Prinzip” in A.S. Eddington, Relativitätstheorie in mathematischer Behandlung (translated by A. Ostrowski and H. Schmidt), Berlin, Springer, 1925: 367-371. 103   Dirk Jan Struik was a student of Jan A. Schooten (cf. A.J. Kox, General Relativity in the Netherlands in Studies in the History of General Relativity (J. Eisenstaedt, A.J. Kox eds.), Basel Birkhäuser, 1992: 39-56). 104   Cf. P.R. Masani, Norbert Wiener 1894-1964, Basel, Birkhäuser, 1990 and more particularly the section “The work with Struik and Vallarta on the unified theory”: 120; V.P. Vizgin, op. cit.: 246.   99

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One may state that practically all the works of the young Lemaître are related to Eddington’s impulse. From variable stars to the gravitational field under spherical symmetry or even regarding the attempts of unified theories, the influence of the English astronomer is everywhere, although at each moment, and this was the special genius of the young priest, Lemaître knew how to correct or go beyond him to produce new ideas. Lemaître proves himself less a speculative intelligence who invented original and abstract lines of thinking than a penetrating and analytic intelligence, who needed the thoughts of someone else to deconstruct and recompose, or to prompt his own original contributions.

3. In the right place at the right time The timing of Lemaître’s trip to the US was impeccable. It was precisely during the years 1924-1925 that the observational data challenging the old thinking about the dimensions of the universe were publicized. The data specifically required a good working understanding of the theory of Cepheids, of which Lemaître became a specialist. From 30 December 1924 to 2 January 1925, Lemaître attended the 33rd meeting of the American Astronomical Society in Washington. The main event was the presentation given by Henri Norris Russell (1877-1939) entitled “Cepheids in Spiral Nebulae”, about the works of Edwin Powell Hubble (1889-1953)105 who could not be present at the conference. These measurements were performed with the 100-inch reflector of the Mount Wilson Observatory in California where Hubble had succeeded in identifying a number of variable stars on plates of two spiral nebulae, including the Andromeda Nebula. Hubble, who had pursued his scientific studies at Chicago and Law at Oxford and was also a talented boxer, was an expert in this   Cf. A. Sandage, “Edwin Hubble 1889-1953”, The Journal of the Royal Astronomical Society of Canada, 83, no 6, December 1989. 105

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field as he had done his thesis in 1917 on the study of nebulae which were barely visible by photographic methods. Hubble had definitively identified 12 Cepheids in the Andromeda nebula, that showed exactly the same period-luminosity relationship as discovered by Henrietta Leavitt at Harvard in 1912, in Cepheids of the Large and Small Magellanic Clouds. By using the Cepheids to measure the distance of the nebulae following the method that we have mentioned above, he concluded that these two nebulae lay at a distance of 285,000 parsecs, or 929,000 light-years. This vastly exceeded Shapley’s estimation of the size of our galaxy, and incontrovertibly demonstrated that there were several other galaxies like ours in the universe, of which the Andromeda was only one nearby example. A giant step in the understanding of our universe had just been taken. This communication of Russell put an end to the historical ‘Great Debate’ taken up between Herber D. Curtis of the Lick Observatory and Harlow Shapley in front of the National Academy of Sciences in Washington on the 20 April 1920. The former, using the Crossley reflector, defended the idea of the astronomer J.C. Kapteyn (1851-1922) of Groningen, one of the pioneers in the methods of counting the stars inside a nebula. According to this idea, the nebulae are in fact ‘island-universes’ comprised of millions of stars. The second rejected the idea of ‘island-universes’ situated outside our galaxy, owing perhaps to overconfidence in the measurements made by one of his friends, the astronomer Adriaan van Maanen106 working at Mount Wilson and who was finding smaller values for nebulae distances than Hubble, whose own numbers supported Curtis.107   In fact, the Swedish astronomer Knut Lundmark, combining the result of measures done in Uppsala and at the Lick Observatory, was led to believe that nebula M33 (one of the two studied by Hubble) might be further afield. He consequently criticized the results of van Maanen. 107   Paradoxically, Curtis held a grossly erroneous idea about our own galaxy, as his measured values of its size were 100 times smaller than suggested by Shapley, and further he placed the Sun close to its centre. Shapley, on his part, envisioned the universe as limited to our galaxy, but with the Sun at its periphery. Cf. D. Alloin, Les galaxies, Paris, Flammarion, 1998 and P.W. Hodge, The Physics and Astronomy of Galaxies and Cosmology, New York, McGraw-Hill, 1966. 106

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Lemaître was undoubtedly profoundly impressed by this communication and decided to improve his familiarity with astronomical techniques and data by visiting a series of American universities and observatories. Having benefited from a special grant provided, yet once more, by the Committee for the Relief in Belgium of the American Educational Foundation, Lemaître traveled to the Van Vleck Observatory of Wesleyan University in Middletown, Connecticut. He had been invited by Frederick Slocum (1873-1944) to attend the total solar eclipse of 24 January 1925108. Between his journeys, Lemaître continued notably to work on the text of his Ph.D. thesis and his other research. After short Easter holiday spent in the Canadian Rockies, he had the chance to attend the 133rd conference of the American Physical Society held in Washington, D.C. at the Bureau of Standards under the presidency of D.C. Miller and K.T. Compton, 23–24 April. There, Lemaître presented his work on de Sitter’s universe. His report basically covered his results described above, however, with an addendum pointing out that Silberstein’s Law was correct in absolute value, but not regarding the signs of speeds of recession.109 Silberstein had derived a linear relation between the spectral shift and the distance of the luminous objects in de Sitter’s universe, but admitted both red and blue shifts. Lemaître showed that it is not possible to maintain both signs of relative motion without violating the fundamental homogeneity of space-time. Thus Lemaître’s contribution specifically consisted in demonstrating that the inhomogeneity of the de Sitter universe is simply unnecessary. This is noteworthy as it was one of the elements that led him little by little toward his own enunciation of Hubble’s Law before its time.

  Cf. E.A. Fath, “The Eclipse of January 24, 1925”, Popular Astronomy, Vol. XXXII, 1924: 298-302. 109   “Proceedings of the American Physics Society”, Physical Review, Vol. 25, JanuaryJune 1925: 880-903. 108

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During the spring of 1925, he had the opportunity to hear Hubble expound his theories concerning the Cepheids in Washington, during a meeting at the National Academy of Sciences. Thus, in 1945, he would recall in a conversation with Gonseth110: In the spring of 1925, sometime before my return (to Belgium), I had the chance to attend a meeting at the Academy in Washington and hear Hubble presenting the discovery of Cepheids in the Andromeda nebula, which definitively established its distance and, therefore, the gener­al structure of the universe.

At the end of the academic year, Lemaître traveled to the Yerkes Observatory following an informal chance meeting of the astronomers in the Chicago area. He was invited by H. Vanderlinden, one of the collaborators of De Donder111 and member of the Royal Observatory of Belgium, and who was at that time a grantee of the American Educational Foundation at the University of Chicago. The discussions did not cover exactly his field of interest, as they largely dealt with questions about the asteroids and comets, but the meeting was an opportunity to meet with Leslie John Comrie (1893-1950).112 As observed by André Deprit, this was perhaps the decisive encounter which aroused Lemaître’s interest in mechanical computation. Indeed, Comrie would become a specialist in the mechanization of calculations, more specifically for the constitution of tables of mathematical and astronomical data. According to Deprit113, in the 1950’s, Lemaître liked to recommend to his students “the Table in 64 pages that Comrie was producing   Letter of 21 January 1945 (AL). He made an allusion to this talk in a review about the book of Paul Couderc, L’expansion de l’univers (1950b). 111   This showed once again that Lemaître could not have been ignorant of what was happening in the “Brussels School”. 112   Cf. “Obituaries. Dr. L.J. Comrie”, Nature, Vol. 167, January 6, 1951: 14-15. 113   “Les amusoires de Mgr Lemaître” in “Discours pronounces lors de la cérémonie d’ouverture du symposium international organize en l’honneur de Lemaître cinquante ans après l’initiation de sa cosmologie du Big-Bang; Louvain-la-Neuve, 10-13 October 1983”, Revue des Questions Scientifiques, t. 155, 1984, no 2: 216. 110

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in his computation facility, Scientific Computing Service Limited”. Lemaître did not have close contact with Comrie during his life, but it is possible that he remembered the man and his work while he was developing numerical calculation on machines himself, before and after the Second World War. A sentence in the obituary of Comrie could also be used to describe the capacities that would progressively develop in Lemaître:114 He was opposed to the building of special calculating machines but advocated always an examination of existing machines, available in considerable numbers, to see which was best adapted to the problem in hand. He was adept at devising special methods by which such machines could best be used, and in modifying the computational formulae to fit the machines.

The months of May and June 1925 would be particularly busy for the young priest. His goal was to pay a visit to Hubble at Mount Wilson, but beforehand, he would visit the Dominion Observatory of Victoria and the Lick Observatory where from the beginning of the century, astronomers such as Edward Fath had shown by spectral analysis that the nebulae were constituted of stars and where Herbert Curtis had strengthened the thesis of the ‘island universes’. Lemaître indeed met Hubble and took advantage of his stay in California to stop in Pasadena on 18 June, not far from Mount Wilson, at the famous California Institute of Technology, where he would later meet Einstein. At Caltech, he had a conversation with Robert A. Millikan, Chair of the Caltech’s Executive Council, and already a Nobel laureate in physics (1868-1953). It was the latter who, during a meeting of the National Academy of Sciences on 9 November 1925, coined the term ‘cosmic ray’ to designate the very high energy particles of extra-terrestrial origin impinging on our atmosphere. The meeting with Millikan would prove pivotal, raising a number of topics which would loom large   “obituaries…”, op. cit.: 15.

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in Lemaître’s conception of cosmology throughout his career. Time and again, the young priest exhibited an uncanny knack for being at the right place at the right time. Coming back from the West Coast, Lemaître discovered the Grand Canyon and the Lowell Observatory in Flagstaff, Arizona, where Vesto M. Slipher (1875-1969) had observed the high radial speeds from spiral nebulae spectrographically and most especially the velocity of the Andromeda nebula, which is approaching our Milky Way galaxy at a speed close to 300 km/s. Lemaître had no difficulty being introduced to Slipher as the latter enjoyed close relations with Eddington. On 8 July, Lemaître was back in Brussels. He had just managed to collect, in very short order and at a defining moment in the history of astronomy, essentially the complete toolkit that would help him to construct his own cosmology: the concept of an expanding universe (through the study of the de Sitter universe), the observational values of distances (through the study of the Cepheids and Hubble’s lecture) and the relative velocities of nebulae (owing to his interaction with Slipher). Along with all this was also the extragalactic nature of the nebulae, the equations of a non-homogeneous model with spherical symmetry (resulting from his Ph.D. thesis at MIT) and finally, the idea of the extraterrestrial origin of cosmic rays (due to his contact with Millikan). After his scientific barnstorming, the complete itinerary of which can now be retraced thanks to a number of post cards that Lemaître had sent to No. 9 rue Braeck­eleer, all the pieces of the puzzle were arrayed front of him. Nothing was missing.

Chapter VI

From the expanding universe to the primeval atom hypothesis (1927–1931)

1. An expanding universe with no beginning or end

L

emaître did not allow himself a long holiday in Belgium. From 14 to 22 July 1925, he went to Cambridge, England, to attend the second general assembly of the International Astronomical Union.1 There he encountered Henroteau, Vanderlinden and Jacques Cox (1898-1972)2, an astronomer who would become the rector of the Université Libre de Bruxelles from 1944 to 1947. The two became great friends. It was during this meeting that Lemaître heard Hubble describe his scheme for the classification of galaxies. In October 1925, Lemaître began his first year of teaching at the Université Catholique de Louvain, in the pleasant surroundings of the Collège des Prémontés, which housed the department of physics. As a lecturer, he replaced Simonart in delivering classes in analytical mechanics for mathematicians and physicists. For those under  Cf. E. W. Brown, “The International Astronomical Union at Cambridge”, Popular Astronomy, Vol. XXXIII, November 1925, no 1925: 569-574. 2  A.L. Jaumotte, “Notice sur Jacques Cox, membre de l’Académie”, Annuaire de l’Académie royale de Belgique, t. 151, 1985: 3-52. After the Second World War, Lemaître was invited by Cox to give a conference at the ULB. A group of fiercely anticlerical students wanted to prohibit Lemaître, as a priest, from entering the conference room. It was Jacques Cox who then intervened, declaring: “Sirs, it is possible not to like the (ecclesiastical) hat, but you should respect the spirit” and all returned to order (the anecdote was recounted by J. Cox himself to R. Desjaiffe; personal oral communication of the latter, 30-10-97). 1

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taking Doctoral studies (what is now the Masters degree), he succeeded de la Vallée Poussin in teaching the the history of science and the methodology of mathematics. Furthermore, a new course in the theory of relativity was added to the program especially for him. As part of his nomination for a faculty position at UCL, he was warmly re­commended to the rector, Msgr. Ladeuze, by Dr. Edouard Willems, secretary of the Fondation Universitaire. The latter had received a visit from Théophile de Donder himself in order to show him Eddington’s letter from Christmas 1924 mentioned in the previous chapter. Writing to Msgr. Ladeuze, Édouard Willems confided to him that3 “M. De Donder considers M. Lemaître as a ‘future genius of mathematics’ and was thus convinced to transmit the document to the Fondation universitaire.” Msgr. Ladeuze, an openminded man, recognized genius when he saw it and would grant him all of the permissions necessary for his research projects, even to the extent that at Lemaître’s request, he reduced his teaching load at the end of the 1920s and the beginning of the 1930s. Lemaître settled back in the city of Louvain where the signs of the Great War had started to fade little by little. He lived a few steps from the Collège des Prémontrés, and which would remain his residence for a long time: The Collège du Saint-Esprit, located at 40 rue de Namur (today Naamsestraat). No sooner was Lemaître back in Belgium, than he got in touch with the Amis de Jésus. After having consulted the person in charge of the Amis4, Lemaître was assigned to the local group called Louvain-Université together with Abbés Harmignies5 and Van Steenberghen, of the Institut Supérieur de Philosophie. The meetings of this group would last until 1966, adapting as much as possible to the travel schedule of the scientist-priest, his absent  Letter dated from 5 January 1925 (copy from AL).   Letter of the 7-11-1925, from Willocx, general secretary of the “Amis de Jésus”, to Lemaître (AFSAJ). 5   From a  letter of Harmignies to Willocx 8-2-1926 (AFSAJ), we know that Lemaître hurried to buy a Remington typewriter after his return from the US, the ‘latest model’ that might have captured the imagination of the ‘Amis’. 3 4

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mindedness and sometimes also to the lively character of the discussions that he provoked.6 During the years 1925-1926 and 1926-1927, Lemaître voraciously read everything he could about relativity and wave mecha­ nics.7 He gave a well-received talk on the empirical basis of the theory of relativity for the fiftieth meeting of the Société Scientifique de Bruxelles (1926a). The Belgian scientific community would also profit from his American experience. He gave a conference on the summary of his Ph.D. thesis at MIT to the Société Mathématique de Belgique8, and he published a French translation of his work on the movement of rigid solids in general relativity (1927h), a short and technically advanced version of his La Physique d’Einstein. Lemaître continued to reflect on the consequences of his work regarding de Sitter’s universe and on the observational data related to the motion of galaxies determined by their redshift, the scientific value of which was impressed on him during his visits to the Ameri­ can observatories. In addition, the discussions with Silberstein and follow-up work showed him that the de Sitter universe represented a mathematical framework within which one could readily support a law of redshifts. But the space-time of the Dutch astronomer was unsuitable both because it was devoid of matter and it relied on Euclidean geometry. Neither, however was the Einstein space-time workable, as while being filled with matter, it was unable to account for   There is a letter from Willocx to Lemaître dated from 22-02-1926 where the former thanked Lemaître for a text that summarized in a “clearer and more courteous manner” some remarks that he had previously formulated in a discussion. 7   His works reflect the deep familiarity gained by this program of study (1927b). The AL has preserved a notebook of readings where Lemaître summarizes a series of the ideas of Louis de Broglie, Léon Brillouin, Erwin Schrödinger and Bohr. This is one of the last times that Lemaître would write Schrödinger’s equation (cf. Chapter X). In his note, one may see as well that Lemaître had a profound knowledge of the book of E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, with an Introduction to the Problem of Three Bodies, Cambridge University Press, 1904 (cf. Chapter XIV). This book helped him to understand the role of the Hamilton-Jacobi equation in the constitution of the wave mechanics of de Broglie. 8   On 18 June 1927. The title of the communication was “L’univers fini et sans borne” [“The finite and boundless universe”] . 6

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global movement of galaxies. One needed to construct a universe achieving an interpolation between that of Einstein and de Sitter, retaining the desired features of both, that is one that would be both dynamic and massive. The idea was already suggested by Eddington in his book, The Mathematical Theory of Relativity9: “It seems natural to regard de Sitter’s and Einstein’s forms as two limiting cases, the circumstances of the actual world being intermediate between them’’. Lemaître’s Ph.D. thesis at MIT, the writing of which he completed upon his return to Louvain, and the supplements requested by the thesis committee strongly persuaded him that intermediate solutions between Einstein and de Sitter could indeed be built. Nevertheless, in his thesis, such solutions all corresponded to static universes (inhomogeneous with spherical symmetry) and drew on the idea of Schwarzschild, which did not bring anything new to the problem of the recession of galaxies. Lemaître’s stroke of genius was to surmount the inhibition that weighed on the entire astronomical community and that chained it to the idea of a static universe. This was only done with trepidation and called for a fair degree of courage, as the fame of Einstein held sway on the side of a static solution of the equations of general relativity. Lemaître admitted in 196310: [Robertson and I] had some hesitations about considering non-statical solutions or as Robertson called them “dynamical solutions” but I was better prepared to accept them, encouraged by the opinion of Eddington.

In his seminal paper of 1927 entitled “Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactiques” (1927c), he adopted the formal expression of the “spherical and static” Einstein’s solu  9 10

  Cambridge University Press, 1923: 160.   (1963a). I refer here to the draft of the article preserved at the AL.

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tion11 but additionally supposed that that the radius of the universe was variable over time12, as in his representation of the flat and exponentially expanding de Sitter universe. As he explained in his paper13: “In order to find a solution presenting simultaneously the advantages of those of Einstein and of de Sitter, we are therefore led to study a universe of Einstein where the radius of space (or universe) varies in some way.” Lemaître then wrote down the equations of Einstein’s gravitational field corresponding to a spherical universe of variable radius, filled with a perfect homogeneous fluid of constant mass. In Einstein’s equations, he maintained the famous cosmological constant; this constant was introduced by Einstein, then by de Sitter in order to obtain their solution and whose effects are only felt at long distance, which explains the use of the qualifier ‘cosmological’.14 The solutions of the equations obtained by Lemaître in fact described all possible homogeneous and isotropic universes, filled with a perfect fluid and with positive15 constant curvature. Unknown to him, Lemaître had also found a result that had already been discovered   The metric of this universe filled with a perfect fluid of density r and of zero pressure is written ds2 = c2dt2 - RE2ds2 where RE is a constant radius of this universe given by RE = 1/(lE)1/2 with a value of the cosmological constant lE = 4p Gr/c2 and ds is the length element of the three dimensional sphere of unit radius. 12   He starts with a metric of the type ds2 = c2dt2 – R2 (t) ds2 . 13   In the draft of the article of 1927, he indeed first wrote “a universe of constant mass and of variable radius…” but then had replaced the last qualifier by “increasing”. In a letter to Gonseth dated 21-01-1945, he told him: “in 1927, I published ‘a universe of constant mass and variable radius explaining the radial speed of the extragalactic nebulae’ presenting the space of variable radius as an intermediate between two solutions of Einstein and de Sitter, the latter solution being put under the form of Lanczos’” (AL; the author’s italics). 14   The cosmological constant has the dimension of the inverse of a square distance. The most general form of the equations of Einstein that satisfied a relativistic equation of energy-matter conservation might involve a term with this constant. 15   The sphere is a space of constant positive curvature. In such a space, the sum of the angles of a triangle is greater than two right angles. A hyperbolic space, i.e. a saddleshaped surface, has constant negative curvature. The sum of the angles of a triangle is less than two right angles. In a Euclidean space, which is a space with constant zero curvature, the sum of the angles of a triangle equals exactly two right angles. 11

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in the period 1922-1924 by the Russian Alexander Friedmann, who had solved the Einstein field equations corresponding to homogeneous and isotropic universes with positive16 and negative17 constant curvature. Nevertheless, in his work, which had no link with astronomical data, he had not considered the case where the pressure of the perfect fluid filling these universes was anything other than zero.18 Lemaître showed that a solution of these equations corresponds to a spherical space that expands exponentially with time (as with his Euclidean representation of de Sitter’s space) and was identical with Einstein’s universe infinitely far in the past. Lemaître’s universe thus was without any beginning. For an infinitely long duration, the universe of Lemaître would appear to be as static as Einstein’s unstable universe that hesitated in the face of expansion! Lemaître’s universe also did not have a temporal end. At an infinite time in the future, the Lemaître universe, which has an infinite volume and finite mass, would possess zero density, thus corresponding exactly to de Sitter’s universe. Lemaître had finally found a dynamic universe achieving the desired interpolation between Einstein and de Sitter. In Lemaître’s universe, light emitted from a remote source, such as a nebula, undergoes a red-shift related to the expansion of the universe.19 Lemaître derived a law linking the distance r of a source to its recessional  A. Friedmann, “Über die Krummung des Raumes”, Zeitschrift für Physik, t. 10, 1922: 377-386. Cf. A. Belenkiy, “‘The waters I am entering no one yet has crossed’: Alexander Friedmann and the origin of modern cosmology” in Origin of the expanding universe: 1912-1932, ASP Conference Series, Vol. 471 (J. Way, D. Hunter eds), Astronomical Society of the Pacific, 2013. 17  A. Friedmann, “Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes”, Zeitschrift für Physik, t. 21, 1924: 326-332. 18   The so-called Friedmann-Lemaître equations are written: 3(R’/R)2 + 3 kc2 / R2 = c2 (l + krc2) and (R’/R)2 + 2R’’ / R + kc2 /R2 = c2 (l - kr) where R’ and R’’ denote the firstand second derivative of R(t) with respect to t. These become the Einstein equations for the model of a homogeneous and isotropic universes whose metric is given by ds2 = c2dt2 – R2(t) ds2 and ds2 = dr2 / (1-kr2) + r2 (dq2sin2q df2) with k = + 1, 0, - 1 for the elliptical, Euclidean or hyperbolic spaces. Lemaître considered k = +1; Friedmann considered k = +1 and -1 but with p = 0. 19   More precisely, the nebulae do not change their positions in the universe, but rather the space itself expands, with the red shift reflecting this uniform stretching. 16

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speed: v=a·r where the coefficient a depends on the relative rate of change of the universe’s radius. This coefficient prefigured what, after 1929, would be known as the Hubble constant20. Aided by the measurement of the distances of galaxies published by Hubble in 192621 and by the average speeds of 43 extragalactic nebulae published by Gustaf Benjamin Strömberg (1882-1962)22 in 1925, Lemaître determined the actual value of the coefficient to be approximately 625 kilometres per second for the objects located at a distance of one megaparsec (625 km/sec/Mpc)23. This particular solution held a special place in the class of all possible solutions of his equations, constituting a boundary case between “bouncing universes” on one hand and “hesitating universes” on the other24. A bouncing universe is a spherical universe without temporal beginning or end. Its radius decreases with time, reaching a minimum, and then regains its monotonic growth. A hesitating universe begins its history with a radius of zero, then increases until the moment it reaches a certain value where it seems to dwell briefly, seemingly undecided between growth and decay. After that, it resumes accelerated growth25. Lemaître had calculated both types of solutions but   Mathematically, if one designates the radius of the space by R, the constant a of Hubble is given by R’ / R, this expression evidentally with the time. The law deduced by Lemaître is customarily writen R’ / R = v / cr (1927c: 55). 21   E.P. Hubble, “Extra-galactic nebulae”, Astronomical Journal, Vol. 64, 1926: 321-369. 22   G.B. Stromberg, “Analysis of Radial Velocities of Globular Clusters and Non-Galactic Nebulae”, Astrophysical Journal, Vol. 61, 1925: 353. This information hade been picked up by Lemaître during his passing through the Mount Wilson observatory in 1925. 23   One million parsecs is written as 1 Mpc, where 1 parsec (pc) = 3.26 light years. Thus the value of the Hubble constant is expressed in units of km/sec/Mpc. 24   We refer the non-specialist reader to H. Kragh, “ ‘The Wildest Speculation of All’: Lemaître and the Primeval-Atom Universe” in Georges Lemaître: Life, Science and Legacy (R.D. Holder, S. Mitton, eds.), Berlin, Springer, 2012: 35 (Fig. 2). By slightly perturbing the solution of Lemaître, one can obtain “bouncing” or “hesitating universes”. Cf. also J. Demaret, Univers, Les théories de la cosmologie contemporaine, Aixen-Provence, Le Mail, 1991 (figure 89) or J. Heidmann, Introduction à la cosmologie, Paris, P.U.F., 1973 (figure 178). 25   Lemaître would always consider the case l > lE and k = +1. For the cases k = 0 or -1, we can have behaviours of R(t) presenting an inflection point like in Lemaître’s 20

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rejected both for observational reasons: the beginning of the expansion of the universe would date back to only a billion years ago, which is too short in regards the scale of stellar evolution. Indeed, the inverse of the Hubble constant, i.e. the inverse of the parameter a mentioned above, has the dimensions of a time (1/a = r/v) and gives some estimation of the duration of the expansion phase of the universe which we are in. But, if we carry out the computation from his value of 625 km/sec/Mpc, we find an expansion of approximately 2 billion years, which is of the order of the age of the Earth computed from the residual radioactivity in rocks. Problematically the history of the universe flirts with becoming shorter than that of the Earth. This is the reason why Lemaître preferred to reject the beginning of the expansion of universe in the infinite past. It should be obvious that the idea of a universe with no beginning, or more precisely with a beginning in an infinitely remote past, is incompatible with Lemaître’s implicit philosophy as it appeared in his La Physique d’Einstein, which assumed that the intelligibility of the universe implied a finite space-time. This was only a superficial incompatibility however, as Lemaître, following a principle inherited from Eddington, had learned not to attach too much physical reality to the mathematical descriptions of instability phenomena involving temporal processes of infinite duration.26 For Lemaître, then, this universe with no beginning and no end is only an approximation; he even said it explicitly to Gonseth27: “The integrable solution is not presented as the exact solution, but as an approximation whose exact solution cannot differ so much, so one has at its disposal a duration longer than 2 × 109 years.” Later, he would show that his exponential growth solution is actually physically indefensible, as Einstein’s hesitating universe for positive values of l positive inferior to lE. This would be further discussed later on (Chapter 8). 26   “As Eddington observed on this topic, the logarithmic infinite that is introduced in problems of unstable equilibrium must be interpreted with caution. (1934g: 367). Cf. also (1958g: 33). 27   Letter to Gonseth of 21 January 1945 (AL).

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universe is in fact unstable. If one introduces small density fluctuations, its equilibrium is broken, and the universe begins to evolve rapidly in time. To push back the breaking of equilibrium infinitely far in the past, it would be necessary for the universe to be perfectly homogeneous everywhere in the Einstein universe (1934g: 367). Yet, Lemaître, who had attended classes at MIT on wave mechanics and who had a keen interest in the applications of the uncertainty principle of Heisenberg (1931a), well knew that quantum fluctuations of matter would guarantee immediately a spectrum of inhomogeneities in the early universe. To summarize his conclusions at this juncture: a bouncing universe would provide too short an expansion to be reconciled with our knowledge of the solar system and the stars, but neither is the exponential model physically defensible. Lemaître would be led to propose a third type of model to which he made a brief allusion in his 1927 paper – the “hesitating universe”. Lemaître’s equations allowed other kinds of solutions, for example a universe for which the radius increases from zero to a limiting value or decreases from this value to zero (later dubbed “Einstein-Eddington universes”) and “Phoenix universes”, to borrow the expression of Eddington28, i.e. universes, whose radius periodically oscillates between zero and a maximum value in the manner of a cycloid. That Lemaître computed and graphically depicted all these other solutions in detail cannot be established with any certainty. The archives (AL) contain a graphic showing evolutions of the “hesitating universe” type, but the figure is not dated.29 It is not impossible that it was drawn by Lemaître around 1927, even if the notations that are found with the graphic are not those from the article (1927c). Never­   Cf. A.S. Eddington, The Nature of the Physical World, Cambridge University Press, 1928: 85 (based on the course delivered by Eddington in January 1927 at the University of Edinburgh). 29  These graphics were reproduced by M. Heller in his paper: “Question to the Infallible Oracle” in Physics of the Expanding Universe, Berlin, Springer, 1979: 202. They are also reproduced in the beautiful album of M. Lachièze-Rey and J.-P. Luminet, Figures du ciel. De l’harmonie des spheres à la conquête saptiale, Paris, Seuil/Bibliothèque nationale, 1998: 155. 28

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theless, during this time, these solutions were not of primary interest to Lemaître, and the possibility cannot be excluded that they were considered only after the publication of one paper of de Sitter30 where the latter depicted on the same graphic the “Phoenix”, the “hesitating” and the “bouncing” universes. The originality of the work of Lemaître was neither purely mathematical, nor purely astronomical. It is at the same time both one and the other. At that time, it required real courage to propose an explanation of the galactic redshifts based on a new solution to the general relativistic equations along with a bold interpretation of observational data, of which he was still a neophyte. Many indeed attributed redshift to the motions of galaxies in the universe that does not evolve in time or, like Hubble, interpreted it only in the framework of de Sitter’s universe. Another novelty of his 1927 paper was to propose a thermodynamical interpretation of cosmic evolution under the conditions of adiabatic expansion, i.e. without heat exchange31. This link to thermodynamics would play a major role in his “primeval atom hypothesis” and would represent the headwaters of many seminal works on the relationship between general relativity and thermodynamics32, a burgeoning field of research today – thermodynamics of black holes, definition of the entropy of the universe, etc. At that time, Lemaître ascribed the expansion of the universe to radiation pressure (19227c: 59). It is interesting to observe that during approximately the same period and following a similar intellectual path, Howard Percy Robert  W. de Sitter, “On the Expanding Universe”, Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings, t. XXXV, 1935, no 5: 596-607. The figure could date from a previous paper of de Sitter: “The Expanding Universe. Discussion of Lemaître’s solution of the Equation of the inertial Field”, Bulletin of the Astronomical Institute of the Netherlands, t. 5, 1930, no 193: 211-218. 31   He was led to an equation formally equivalent to the one expressing the conservation of the energy in thermodynamics: dQ-pdV = dU with dQ = 0 (i.e. an adiabatic process) and U = rV. Here dQ is the heat absorbed or released, -pdV the work of mechanical pressure, p the pressure, dV the element of volume, and dU the element of internal energy of the system). 32   Cf. the work of the Caltech chemist and theorist of relativity Richard C. Tolman (see particularly his famous work Relativity, Thermodynamics and Cosmology, Oxford, Clarendon press, 1934) that was influenced by Lemaître. 30

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son was led to comparable results to those of Lemaître, without venturing however to propose a relationship between a spherical universe of a variable radius and redshift of nebulae. He had presented his thesis in Caltech in 1925 and the young Abbé Lemaître could possibly have met him when he traveled there on 18 June 1925. Nevertheless, it is unlikely for this encounter to have taken place, as a quote of Lemaître by Robertson only appeared in the 1930s, after his postdoctoral visit to Göttingen and furthermore, by the end of the 1920s, Lemaître had not yet mentioned the work of his American counterpart. As early as 1924-1925, Robertson, who had studied The Mathematical Theory of Relativity deeply, had the idea to look for mathematically solutions of Einstein’s equations corresponding to dynamical universes that evolve in function of time, and within which the space is “conformally Euclidean”, i.e. equivalent to a flat tridimensional space of the classical geometry, up to a scale factor.33 He discovered four families of solutions, notably one hyper-sphere of variable radius, a particular case of a solution found by Kasner and a dynamical version of Schwarzschild’s solution of the gravitational field at outside of a mass with spherical symmetry. In Göttingen, he criticized the works of Silberstein and was led to the same conclusion as Lemaître regarding the interpretation of the recession of nebulae in de Sitter space.34 According to Sandage35, Robertson would have mentioned his work on the relationship between redshifts and distances of nebulae to Hubble during the years 1927-1928. It is then also possible, but not certain,  H.P Robertson, “Dynamical Space-Time which contains a Conformal Euclidean 3-space”, Transactions of the American Mathematical Society, Vol. 29, July 1927, No. 3: 481-496. This paper was presented to the San Francisco section of American Mathematical Society on 19 June 1925 at the very moment when Lemaître was at Caltech. Thus it is unlikely for the two men to have met in Pasadena. Lemaître was during that time more concerned with astronomical questions than by general solutions of Einstein’s equations. Lemaître never studied the works of Kasner, for instance, who was well known in the early 1920s. 34   H.P. Robertson, “On the Relativistic Cosmology”, Philosophical Magazine, Vol. V. suppl. May 1928: 835-848. 35   A Sandage, “Practical cosmology: Inventing the Past” in A. R. Sandage, R. G. Kron, M.S. Longair, The Deep Universe. Saas-Fee Advanced course 23. Swiss Society for Astrophysics and Astronomy (B. Binggeli, R. Buser, eds), Berlin, Spinger, 1995: 96. 33

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according to Sandage, that this conversation could have had some influence on Hubble in 1929. Finally, his knowledge of universes conformally equivalent to Euclidean geometry led Robertson to consider, like the young priest, the space-time of de Sitter as an infinite Euclidean and expanding space. We can see that Robert­son was led close to the target reached by Lemaître. Nevertheless, he did not reach it, even if his mathematics was leading him down the path of a dynamic universe. Lacking full confidence in the observational data, or being too much under the influence of Weyl in Göttingen, Robertson could not escape from the shackles of the de Sitter universe. More mathematician than most astronomers and more astronomer than most mathematicians, as he would characterize himself, Lemaître had just laid the foundation stone of a new paradigm of relativistic cosmology. The freedom of thought which enabled this step would always remain the hallmark of his work.

2. From Einstein’s blame to Eddington’s mea culpa Lemaître’s 1927 paper did not immediately attain the fame it deserved. This was not a question of the journal that had accepted it, the Annales de la Société Scientifiques de Bruxelles nor to its circulation; Lemaître himself had insistently pointed out that during this time, the Annales was published by the famous French publishing house PUF (Presses Universitaires de France). In fact, immediately upon publication, the paper was listed in the Astronomisher Jahresberichte36 and in the Bulletin de l’observatoire de Lyon37, among others38. Simply put, if the article had not received the attention that it deserved at the time, but only   T. 29, 1927, ref, no 8830 (the paper is classified under the rubric ‘Nebel’ and not ‘relativitätstheorie’). 37   Bulletin of Lyon, 9, 170B. 38   The paper is also mentioned in Mathesis, a case book of mathematics for the use of special schools and teaching education, t. XLI, 1927, 488. In France, this journal was printed and published by Gauthier-Villars. 36

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much later, it was primarily because the scientific community was not ready to accept the idea of an expanding universe. Hubble would hold to the idea of a static universe for a long time or at least, of a de Sitter universe, which only mimicked a dynamic universe. Einstein, on his side, threw the whole weight of his reputation to limiting the consideration of theories consistent with an expanding universe. It is well known that he slowed down the publication of a paper by Friedmann, claiming an error of calculation, when in fact the mistake was his.39 Lemaître had the opportunity to meet Einstein at the 5th Solvay Congress held in Brussels between 24 and 29 October 1927.40 By this time, Einstein already knew of Lemaître’s paper “that a friend made him read” (1958d: 129). This friend was perhaps De Donder with whom he had had contact in 1926 in preparation for the Solvay conference. Einstein had been admitted on 2 April 1926, with the explicit approbation of King Albert, as a member of the scientific committee of the International Solvay Institute.41 While he was walking in the Allées of Brussels’ Leopold Park in the company of Auguste Picard, Einstein made some technical observations to Lemaître which were most likely favourable on the mathematical aspect of its paper, however “he concluded by saying that, from the physics perspective, this seemed to him absolutely abominable” (1958d: 129). Lemaître had probably some difficulty in defending the relevance of his own point of view since he told the following story (1958d: 159; translated from the original in French): As I was trying to pursue the conversation, Auguste Picard, who was accompanying us, invited me to get into a taxi with Einstein, who was to visit his laboratory in Brussels. In the taxi, I talked about the speed   Concerning the studies of the reaction of Einstein: A. Friedmann, G. Lemaître, Essa­ is de cosmologie, op. cit.: 43-48; A. Belenkiy, “ ‘The waters I am entering…’ ”, op. cit. 40   Les Conseils Solvay et le début de la physique moderne (P. Marage, G. Wallenborn, eds.) Brussels, ULB 1995: 161-193. 41   Cf. the book: Albert Einstein 1879-1955, Bruxelles, Académie Royale de Belgique, 1981: 24-28. 39

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of nebulae and I had the impression that Einstein was not aware of the current astronomical facts.

During his meeting with Einstein, Lemaître had been informed about the paper of Friedmann of 1922, of which he was not previously aware.42 This was probably related to the fact that Lemaître was more interested in the astronomical literature than to articles of physical theory, especially when those were written in German, a language that he had not mastered as well as English. In the future, referring in his publications to the equation describing the variation of the radius of a spherical, homogeneous and isotropic universe, mentioned in his famous 1927 paper, he would always call it the “Friedmann equation”43, without trying to emphasize his own contribution. One day, in front of an amphitheatre of Bachelors students, remembering that he had not acknowledged Friedmann’s works in 1927, said44: Anyway, it is simpler to solve a problem by yourself than to find the solution in the existing literature.

Einstein’s reaction did nothing to reassure Lemaître, but the latter was not the kind of man to be overawed. He continued to fully trust his idea of an expanding universe as evidenced by the paper given on 31 January 1929 in front of the Société Scientifique de Bruxelles (1929a). He was convinced that this concept provided a thoroughly satisfying explanation of the movement of galaxies. In this he was absolutely correct, because in 1929 Hubble would publish his famous   In (1929a: 216), Lemaître thanked Einstein for having pointed out the work of Friedmann. 43   It is the equation: (dR/dt)2 = -1+a/(3R)+lR2/3 (a is a constant and l is the cosmological constant), obtained by putting b = 0 in Equation 10 of (1927c: 53). Formally the equation is analogous to the one expressing the classical conservation of energy. The left hand part of the equation represents the kinetic energy. This equation often led Lemaître to interpret the expanding universe described by R(t) as a process achieved under the action of two opposing forces. One is a gravitational force with a 1/R potential, and the other is a repulsive one with a R2 potential. 44   Personnal communication of G. Fourez (17-06-1999). 42

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paper where he definitively confirmed the relationship between the recessional speed and the distance of 24 extragalactic nebulae45, although still associating the relationship to a “de Sitter effect”. Moreover, Lemaître would never seek out the support of anybody that could have defended his ideas, such as Eddington or de Sitter. It is significant in this regard, that he did not attempt during his participation in the meeting of the International Astronomical Union46 in Leiden between 5-13 July 1928, to plead his case to the two illustrious astronomers. There is no evidence to indicate that Lemaître had sent his article to Eddington in 1927. What is sure, however, is that the latter did not acknowledge the article prior to 1930. On 10 January of that year, during an informal meeting of the Royal Astronomical Society, de Sitter expressed some doubt regarding the relevance of the static universe of Einstein in describing the observational data. Eddington then suggested that one of his students, McVittie, find some dynamic models of universes giving at least, as particular cases, those of Einstein and of de Sitter. The school of Eddington was stimulated by the purely mathematical work of Robertson of 192947 in which he derived   E. Hubble, “A Relation Distance and Radial Velocity among Extra-Galactic Nebulae”, Proceedings of the National Academy of Sciences, Vol. 15, 1929: 168-173. Hubble had the benefit of the work of Slipher on the measurement of speed, and of Milton L. Humason, a specialist at Mount Wilson for the redshift observations. The latter had started his career by riding mules that transported the material for the construction of the Mount Wilson Observatory. The value of the so-called Hubble constant was estimated in 1929 to be between 465 and 513 km/s/Mpc, which implies an expansion lasting between 1.9 and 2.1 billion years. This constant might be more properly called the “Lemaître-Hubble constant”, as Lemaître was the first to propose the correct theoretical interpretation for it. 46   Cf. Transactions of the International Astronoical Union, Vol III. Third Assembly held at Leiden. 5-13 July 1928, Cambridge University press, 1929. Lemaître was member of the I.A.U. since 1925. 47  H.P. Robertson, “On the Foundation of Relativistic Cosmology”, Proceedings of the National Academy of Science, Vol. 15, 1929: 822-829. Cf. the observation of Eddington in the “Report of the Council to the Hundred and Eleventh Annual General Meeting”, “the Expansion of the Universe”, Monthly Notices of the Royal Astronomic­al Society, Vol. 91, 1931: 414 and L’univers en expansion (translation of J. Rossignol), Paris 1934: 60. 45

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a general metric for homogeneous and isotropic universes. This research project was published in the February issue of the Observatory Journal48, that Lemaître regularly read. When he took found this article, Lemaître was visibly surprised as he thought that Eddington had gotten wind of its publication. Without waiting more, the Louvain priest wrote to his former professor in Cambridge49: Dear Professor Eddington, I just read the February n° of the Observatory and your suggestion of investigating a nonstatistical intermediary solution between those of Einstein and de Sitter. I made these investigations two years ago. I consider a universe of curvature constant in space but increasing with time. And I emphasize the existence of a solution in which the motion of the nebulae is always a receding one, from time minus infinity to plus infinity.

After writing the letter and informing his professor that Einstein considered his physics conclusions to be “indeed abominable”, Lemaître attached several copies of his article to his letter and asked Eddington to send a copy to de Sitter. Eddington would do so immediately since he found in the work of his student what was missing in Robertson’s works – real contact of general relativity with wellestablished astronomical data. In a letter dated 19 March 193050, he informed de Sitter that his suggestion had been realized by Lemaître and that he had the intention of publishing Lemaître’s work in the Monthly Notices:51 “to call the attention of astronomers to his paper”. De Sitter realized immediately the importance of the work of Lemaître, because he had himself looked for, without success, an interme  Vol. 53, February 1930: 33-44.   Draft of the letter preserved at the AL. 50   I thank P.J.E. Peebles of Princeton University for having transmitted a copy of this letter (coming from the archives of de Sitter in Leiden). 51  An English translation of the paper of 1927 would be published in 1931 (1927d) where Lemaître would add references to the works of Friedmann and Tolman. 48 49

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diary solution between his own and that of Einstein. In turn, he wrote to him from Leiden on 25 March 193052, to tell him that he was going to take his work into account in his future publications. The Dutch astronomer would keep his word53, and his prestige, combined with the celebrity of Eddington, would contribute to propelling the young priest of Louvain to the pinnacle of scientific fame. The reputation of Lemaître in the eyes of the astronomer of Leiden would never fail, and more especially since the physicist-priest succeeded in demonstrating how to overcome a difficulty that de Sitter has raised54 concerning the two results (the average movement of the extragalactic nebulae in an expanding universe) that were at first glance incompatible (1930b). In 1931, thanks to the strong support of Eddington, an English translation of Lemaître’s paper (1927c) would be published (1927d). On 17 February 1931, on behalf of the Royal Astronomical Society, William Smart, the Editor of Monthly Notices of the Royal Astronomical Society sent a letter to Lemaître55 requesting him to submit an English translation of his 1927 paper and to propose to him to become a member of this Society. Smart gave his colleague the freedom to add or to correct something in his original paper. In March 1931, the translation was published (1931b). Surprisingly however, some  Letter preserved at the AL and published in A. Friedmann, G. Lemaître, Essais de cosmologie précédés de L’invention du Big Bang by Jean-Pierre Luminet (texts chosen, introduced, translated from Russian and English and annotated by J.-P. Luminet and A. Grib), Paris, Seuil, 1997, Sources du savoir: 303. The answer of Lemaître would come after 5 April 1930 (Ibid: 304-305). 53   Cf. W. de Sitter, “The Expanding Universe. Discussion of Lemaître’s Solutions of the Equations of the Inertial Field”, Bulletin of the Astronomical Institutes of the Netherlands, Vol. 5, 1930, no 193: 211-218; “On the Distance and the Radial velocities of Extra-galactic Nebulae, and the Explanation of the Latter by the Relativity theory of Inertia”, Proceedings of the National Academy of Sciences, Vol. 16, 1930, 474-488; “The Size of the Universe”, Publications of the Astronomical Society of the Pacific, Vol. XLIV, April 1932, no 258: 89-104. 54   W. de Sitter, “On the Motion and the Mutual Perturbation of Material Particles in an Expanding Universe”, Bulletin of the Astronomical Institutes of the Netherlands, Vol. VII, September 1933, no 249: 97-105. 55   This letter was discovered by Mrs. Liliane Moens in the AL. 52

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thing important disappeared from the English version. The paragraph where Lemaître computed the expansion rate from the astronomical data he had at his disposal (what is now known as the “Hubble constant”, H) is suppressed. Why? This paragraph is important because it is the first time, in a scientific paper, the Hubble constant is deduced from observations and explained from relativity. Some historians have suggested that this was due to the influence of Hubble who published “his” law in 1929 and could have been motivated to protect the priority of his own work56. But this is not in fact true as was conclusively shown by Mario Livio57. When Lemaître translated his own paper58 he “did not find advisable to reprint the provisional discussion of radial velocities (of the galaxies) which is clearly of no actual interest”59. In fact, in 1927, Lemaître had already plotted the velocities (v) of 43 galaxies measured by Vesto Slipher and published in 1925 by Gustav Strömberg of the Mount Wilson Observatory, against the distance measurements of the galaxies (d) performed by Hubble’s team in 1926. If one looks at the velocity-distance scatter-plot of all this data, it would be somewhat of a stretch to propose the linear law, v = H·d. Lemaître’s intuition was ultimately proven correct, but rigorously the data at his disposal in 1927 cannot be said to strongly support Hubble’s law. But by 1930 the situation had changed significantly. In 1929, Hubble had published his law on the basis of additional and more precise observations which rendered the “Strömberg list” obsolete. It is easy to see that Lemaître, as a rigorous astronomer, had decided to give up on his old data60.   Cf. D. Block, “Georges Lemaître and Stigler’s Law Eponymy” in Georges Lemaître: Life, Science and Legacy (R. Holder, S. Mitton eds), Berlin, Springer, 2012: 89-96; D. Block, K. Freeman, Shrouds of the Night. Masks of the Milky Way and Our Awesome New View of Galaxies, Berlin, Springer, 2008: chapter 7. 57   M. Livio, “Mystery of the Missing Text Solved”, Nature, 479 (2011): 171-173. 58   This is substantiated by a letter from Lemaître to Smart (9 March 1931), and discovered by Mario Livio with the help of Peter Hingley and Bob Carswell of the Royal Astronomical Society. 59   Letter from Lemaître to Smart, 9-03-1931, AL. 60   J.-P. Luminet, “Editorial note to A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae”, General Relativity And Gravitation, 45 (2013) 1619-1633. 56

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We have seen that the explanation of redshifts led Lemaître to posit what would in 1929 become “Hubble’s Law”. It would be more accurate to call it the “Hubble-Lemaître Law”. For years, the scientific contribution of Lemaître had been underestimated or even unknown. Today the situation is being remedied as can be seen for example by the fact that the European Space Agency decided to give the name “Georges Lemaître” to the 5th Automated Transfer Vehicle (ATV-5) of the International Space Station, which was launched on 29 July 2014 and successfully docked with the ISS on 12 August 2014. Nevertheless, Lemaître would never try to claim any kind of paternity for the discovery of this law. On the contrary, with exemplary scientific honesty and intellectual modesty, he insisted in his critique of the work of Paul Couderc, L’univers en expansion61, on the fact that62: Naturally, before the discovery of the clusters of nebulae, it was out of question to establish Hubble’s Law, it was only possible to calculate its coefficient…I am sorry to rectify these details that are a bit too personal, but this seems to me necessary as the legend, more beautiful than the reality, is presented by the author like an argument and a guarantee of a very firm truth.

It has to be noticed here that this modesty was a bit excessive and what Lemaître termed a “legend” caused a lot of distress to Couderc63, and was not so far from the truth. The reaction of Lemaître perhaps revealed more about one of his character traits. He could quickly lose his temper when he thought that someone did not respect his convictions, scientific projects, ecclesiastic dignity64 or   Paris, Presses Universitaires de France, 1950.   I refer here to the draft of the proceeding (1950b) preserved at the AL. 63   Letter dated 16-10-1950, from D. Barbier, Editor-in-Chief of the Annales d’astrophysique within which it is published (1950b), to Lemaître who speaks of the sentence tagging the text of de Couderc as “legend”: “[this sentence] had seriously upset Couderc, who almost saw in it, an attack on his honor. It is unnecessary to tell you that it should not be changed if it adequately expressed your thinking.” 64   To Fr. S. Dockx, O.P., founder of the International Academy for Philosophy of Scien­ 61 62

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the ideas of a unified Alma Mater located in Louvain. In the present case, Lemaître’s reaction could be interpreted in the following way. Couderc had certainly vexed Lemaître by not acknowledging his astronomical prowess and by minimizing the actual dissemination of his 1927 publication. Couderc said, indeed65: “Beside Eddington, the theoreticians quoted were not professional astronomers: their universe of variable radius were found and proposed before the empirical discovery of an expansion, or in complete ignorance of this discovery made by astronomers”, and “[the work of Lemaître was] published in a bulletin of Brussels which was scarcely accessible and remained without recognition until Eddington had drawn attention to him”. This elicited Lemaître’s rejoinder66: “[My bibliography was] perfectly upto-date about astronomy” and “[… ] our scarcely accessible Bulletin, the Annales de la Société Scientifique de Bruxelles were at that time published at the Presses Universitaires de France”, the publishing house that had just released the book of Paul Couderc! Lemaître knew how to tease an adversary delicately to put a situation aright, but without wounding. At the beginning of the thirties, Lemaître was interested in a subject that was highlighted at the end of his 1927 paper: the cause of the expansion of the universe. As for Eddington, McVittie, Sen or McCrea67, Lemaître was interested in the question of the instability of the static universe of Einstein. A perturbation with this unices, who called him “Monsieur L’abbé” Lemaître answered with a letter dated from the 28-10-1947 and written at Jupille: “Allow me to remind you that I was appointed a canon a long time ago” (Archives of this Academy, letter transmitted by Fr. J.-M. Van Cangh and Mrs. Cambier, secretary of P. Dockx). This was confirmed by the testimony of G. Thill, former student of Lemaître. “During the class of mathematical methodology (at the Master’s level) where he showed that a certain translation of Euclid in French was deficient, a student interrupted Lemaître to ask him a question calling him “Monsieur”. He was vexed and openly made the observation that he should be called “Monsieur le Professeur’’ [Mr. Professor] or “Monsieur le Chanoine” [Mr. Canon]. (Communication of 25-06-97). 65   Op. cit.: 160-161. 66   I refer here to the draft of the critique. 67   Cf. A. Eddington, The Expanding Universe, Cambridge University Press, 1933: 52.

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verse inevitab­ly leads it to evolve as a function of time. Nevertheless, while the others simply identified this perturbation to the formation of “condensation” of matter in the universe, i.e. to density fluctuations, Lemaître showed that one must in fact consider another more fundamental phenomenon: that of ‘stagnation’. In his work, Lemaître divided the Einsteinian universe into cells bounded by surfaces of separation. By studying the formation of condensation with spherical symmetry, toward the centre of each cell, with the mathematical techniques he had learned when writing his Ph.D. thesis at MIT68, Lemaître showed that the radius of the Einsteinian universe begins to change not in function of the degree of concentration of the matter induced by the condensation, but in function of the variation of pressure that was exerted on the boundary between the neighbouring regions (1931b)69, this pressure corresponding in fact to the average kinetic energy of particles exchanged between these regions. If the pressure at the boundary decreases, this means that the exchange of matter decreases, and that the kinetic energy “stagnates” close to the centres of condensation. What Lemaître terms “stagnation” which launched the expansion of universe, is found in his own words (1946e: 79): One observes that the equilibrium breaking depends on the value of the pressure on the boundary of the (space) cells, i.e. on what could be called the neutral zone between the condensations. If the pressure at the neutral zone were zero, the condensations would be without influence on the equilibrium of the universe. But, any growth in pressure produces a contraction while any decrease in pressure leads to an expansion of the universe.   It is worth reminding ourselves that this thesis was focused on the determination of the gravitational field produced by a sphere of inhomogeneous perfect fluid. Condensations in the universe can be modeled by such inhomogeneous spheres. 69   Eddington commented on the article (1931b), saying “I am inclined to think, however, that Lemaître’s treatment goes to the root of the matter” and he added in the footnotes: “Lemaître’s paper (…) seems to me very obscure, but I have had the advantage of verbal explanations from the author” (The Expanding Universe, Cambridge University Press, 1933: 52). 68

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As he declared in the conclusion of his 1927 paper, it was indeed pressure that played a central role as a cause of the expansion of the universe, but not in the way he had anticipated; it was a collateral effect of radiation pressure. This idea of ’stagnation’ that would provoke a controversy among McCrea, McVittie and Lemaître70 is intriguing as it occurred just at a transitional moment in Lemaître’s thinking. This idea led him to question the formation of large structures in the universe, such as galaxies. Calculations provided support for the notion that structure formation could not be unrelated to global cosmological evolution, as a local diminution of the pressure would in consequence also drive the expansion of the universe. The equilibrium breaking of Einstein’s static universe thus also provided a paradigm for galaxy formation. Moreover, Lemaître also found yet one more reason to reject the model of a universe with exponential growth. Let us start from a given non-zero pressure on the boundary of a condensation cell and let us introduce a pressure variation. The weaker the pressure variation would be, the sooner the equilibrium breaking and the beginning of the expansion would be reached. One might think then that the expansion could begin at a date as far back as one wants. Lemaître recognized that this could not be the case however, as the “influence of the diminution of pressure on the time at which expansion commenced is extremely slow. To push back the very beginning of the expansion approximately one billion years, one must reduce the drop in pressure by half. To reach ten, twenty, or thirty billion years ago, it is necessary to reduce the pressure drop to the thousandth, millionth, billionth, etc., and such a reduction would lead to nonsense in physics” (1931h: 402). Practically, what Lemaître would say is that that the beginning of the expansion could not have physically occurred more than 100 billion years ago, and consequently, that the model of a universe with exponential growth without a beginning   Lemaître spoke about the 'controversy' in his letter to Gonseth of 21-01-1945 (AL). In fact, McVittie and McCrea had first believed that condensation would lead to a contraction of the universe, but later McVittie sided with expansion as its consequence (cf. A. Eddington, “Reports of the Council…”, op. cit.: 415). 70

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and end that would correspond to an infinitesimal perturbation of the initial pressure would not make any real sense in physics. The choice of a hesitating universe then seems to be the most physically appealing. But, this hesitating universe represents a very peculiar initial state as its radius is reduced to zero. Could there be a sensible physical interpretation of such an initial state? Lemaître would provide his answer by developing the primeval atom hypothesis. The possibility of a missing or hidden link between the famous 1927 paper and the hypothesis of the primeval atom deserves some attention. As we have seen, in the English translation (1931b) of his 1927 paper, Lemaître dropped outdated astronomical data and the numerical derivation of Hubble constant thereby. But interestingly, he retained a paragraph at the end of his paper concerning what he proposed was the cause of the universe expansion: radiation pressure71. At the time of the translation of his paper, Lemaître was fascinated by a hypothesis of Robert A. Millikan and one of his students, G. Harvey Cameron on the origin of cosmic rays72. Millikan believed that cosmic rays were the electromagnetic radiation result from the mass defect associated with the fusion of particles randomly colliding in space73. This, Millikan maintained, erroneously as it would turn out, could restore some degree of physical order and thus enable a decrease in entropy. This hypothesis was motivated by an attempt to circumvent the second law of thermodynamics which he considered, for philosophical reasons,

  H. Kragh may be the only author to have emphasized the importance of that paragraph: “Lemaître argued that the expanding universe needed a cause for its increasing departure from the static Einstein world. At the time he could not say what this cause was, except that it might have been ‘set up’ by the radiation itself, as he somewhat cryptically expressed it. Yet the mere willingness to look for a cause for the expansion is remarkable, as it underlines the physical nature of his model.” (Matter and Spirit in the Universe. Scientific and Religious Preludes to Modern Cosmology, Imperial College Press, 2004: 130). 72   R.A. Millikan, G.H. Cameron, “The Origin of Cosmic Rays”, Physical Review 32 (1928): 533-557. 73   Cf. also R.A. Millikan, Electrons (+ and -), Protons, Photons, Mesotrons and Cosmic rays, The University of Chicago Press, 1947 (1935): 551-555. 71

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as unacceptable74. According to the Nobel laureate, radiation gives rise to particles, whose subsequent fusion produce nuclei, but accompanied by radiation whose energy corresponds to the mass defect of the fusion reaction, i.e. the difference between the initial and final masses. Lemaître gave some credence to the Millikan-Cameron hypothesis, but was unwilling to go so far as repudiate the second law of thermodynamics. What was most interesting to him was the prospect that one could ascribe the production of all matter in the universe beginning from radiation. Adapting this notion in the framework of his expanding universe he explains (1930a, p.182): “The possibility is now admissible that light was the primordial state of matter and that all matter condensed in stars was formed by the process proposed by Millikan”75. Here may be seen the continuity of Lemaître’s thought: the cause of the expansion could be radiation pressure and the origin of all matter could be primordial radiation. Thus one can say that, in 1930, Lemaître is already thinking about a kind of primeval state of the universe, and this state being primordial radiation. But Lemaître knew well the notions about quantum mechanics he learned at Cambridge and at MIT, and it is impossible to avoid making the connection between this “primitive radiation state” to what would become in 1931 the “primeval atom” considered as the initial unique quantum of the universe. Lemaître would never again refer to his 1930 paper and its connection to Millikan-Cameron ideas. Another factor would soon arise to catalyse the birth of his primeval atom.

  Cf. H. Kragh, Matter and Spirit in the Universe. Scientific and Religious Preludes to Modern Cosmology, Imperial College Press, 2004: 84-95. 75   Our translation. The paper was originally written in French, perhaps explaining why it is so rarely quoted. 74

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3. The hypothesis of the Primeval Atom The great ideas of Lemaître often originated in confrontation with the ideas of someone else. The hypothesis of the primeval atom is no exception, having taken for its inspiration his own reaction to a statement made by Eddington on 5 January 1931 at the British Mathematical Association in the form of a communication entitled significantly “The End of the World from the Standpoint of Mathematical Physics”.76 “Philosophically,” Eddington asserted77 “the notion of a beginning of the present order of nature is repugnant for me”, a position he continued to espounse during his conferences at the University of Edinburgh, from January to March 1927.78 According to thermodynamics, the entropy of the universe increases in a monotonic way. This entropy measures the degree of disorder, of disorganization of systems existing in the universe. Thus79: Travelling backwards into the past we find a world with more and more organization. If there is no barrier to stop us earlier we must reach a moment when the energy of the world was wholly organized with none of the random element in it.

For the English astronomer, this led to the idea of an initial organization of the world and and thus perhaps also of a “great organizer80”: This has long been used as an argument against a too aggressive materialism. It has been quoted as scientific proof of the intervention of the Creator at a time not infinitely remote from today. But I am not   Supplement to Nature, March, no 3203: 447-453. “The idea of the primeval atom came to me after reading a paper of Eddington ‘The End of the World…’ ” (Letter to Gonseth, 1 January 1945, AL). 77   Ibid.: 450. 78  A.S. Eddington, The Nature of the Physical World, Cambridge University Press, 1928. 79   Ibid.: 84 80   Ibid.: 84-85. 76

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advocating that we draw any hasty conclusions from it. Scientists and theologians alike must regard as somewhat crude the naïve theological doctrine which (suitably disguised) is at present to be found in every textbook of thermodynamics, namely that some billions of years ago God wound up the material universe and has left it to chance ever since. This should be regarded as the working hypothesis of thermodynamics rather than its declaration of faith. It is one of those conclusions from which we can see no logical escape – only it suffers from the drawback that it is incredible. As a scientist I simply do not believe that the present order of things started off with a bang; unscientifically I feel equally unwilling to accept the implied discontinuity in the divine nature. But I can make no suggestion to evade the deadlock.

It was Georges Lemaître who would make the suggestion which would allow them to evade the deadlock and that suggestion, published in Nature under the title “The Beginning of the World from the Point of View of Quantum Theory” (1931d), is nothing other than the primeval atom hypothesis. This hypothesis is opposed to that of Eddington on both the scientific and theological planes. Contrary to Eddington, Lemaître would demonstrate that physics could give meaning to an initial state of minimal entropy, that is to say, of maximal order and not in the infinitely remote past. Thus for him, the idea of a beginning of the universe was hardly “scientifically repugnant”. At the time when Lemaître wrote his note for Nature, he was also working on a paper regarding an application of the uncertainty relations of the quantum mechanics (1931a). His reflections led him to apply quantum uncertainty to the description of the universe. For Lemaître, the universe possesses a constant energy that is distributed among several quanta. Moreover, thermodynamic reasoning81 persuaded him that the number of quanta must always grow during spontaneous transformations and that, correspondingly, this growth of quanta number as well as their dispersion should be accompanied by 81

  Cf. (1931h: 404-405) and (1946e: 85-86).

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an increase in entropy. One may therefore conclude that, if one goes back in the past, the number of quanta would decrease, as well as the disorder due to their dispersion, until a physical state of minimal entropy corresponding to a single quantum emerged. At this level, the entire universe would be gathered into one unique ‘atom’ in the etymological sense of the term. The atomic weight of this atom would correspond in fact to the total mass of universe. By putting together thermodynamics and quantum mechanics, it is thus possible to give a sense to a natural beginning and, as expressed by Lemaître: “such a beginning of the world is far enough removed from the present order of nature to not be repugnant”. What it seems Eddington found “repugnant” were physical concepts stemming from our immediate experience applied to situations far away from our experience base. Until now, this presentation of the natural beginning of the universe did not involve general relativity and in particular the notion of space-time. Lemaître was conscious of the difficulty of unifying, in the same description, the continuous character of space-time, which can be represented as a four-dimensional surface, and the discrete nature of atoms. In order to resolve the conundrum, he went so far as to suggest that space and time would lose their sense at the atomic level. They would only acquire their sense at the statistical level, as an average is performed on a large ensemble of particles. In other words, it would not be possible to apply the geometrical framework of general relativity at the atomic scale, but rather the continuum of spacetime is only an approximation valid in the limit of a large number of particles but an inappropriate description at the microphysics scale. This line of thinking would prove prescient in the quantum theory of gravity. Indeed, when we go down to the scale of elementary particles, quantum fluctuations render the notions of surface and distance, and even perhaps of geometrical points, devoid of meaning, as for example when one tries to use the notions of classical geometry to describe fine-grained phenomena such as the foam originating from the crashing of seawater or the shape of clouds. Thus the beginning of space-time coincides, for Lemaître, with a certain numerical

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multiplicity and specifically the multiplicity engendered by the disintegration of this atom which gives rise to all cosmological matter. But this beginning should not be confused with the notion of beginning of the world itself, which refers to the beginning of the atomic universe itself. Lemaître formulated the distinction that “the beginning of the world stands just prior the beginning of space and time, which only acquired their meaning progressively as the particle multiplicity increased” (1958f: 6). This sentence is in itself ambiguous, begging the question of how can one speak of ‘before’ if there were no time. But Lemaître did not undertake to speak of a chronological priority devoid of meaning, but of the logical priority of the atom-universe on space-time, in the sense whereby the emergence of space-time could be inferred from the former. In 1948, Lemaître would synthesize his vision about the relationship between the atom-universe, space-time and the beginning of the natural world with an appealing ‘parable82 of the conic glass’83: This origin appears to us in space-time as a background that challenges our imagination and our common sense by presenting them with a barrier that cannot be crossed. The space-time may seem like a conical glass to us. We progress towards the future by following the generating lines of the cone to the exterior of the glass. We make the tour of the space by browsing in a circle normal [perpendicular] to the generating lines. We go through the course of time with the idea that   Part of Georges Lemaître’s style was to employ a little story, often amusing to express an idea (communication of Gilbert Lemaître, 21-05-99). 83   (1948a: 40; translated from the original in French) Two examples of his sophisticated sense of humor are in order. During the 1950s, Lemaître pretended that his physician, Dr. Cornélis, had prescribed him to drink champagne for a remedy. One day, when Lemaître was sick, his friend Charles Manneback came to visit him. Odon Godart introduced him in his apartment, and the bedridden canon added to the surprise by welcoming him with a thunderous “Bonjour Charles!”, with a glass of champagne in his hand (oral communication of O. Godart). A similar incident occurred in the early 1960s, when he was at the Louvain University hospital after his first cardiac incident. One of his physics students who visited, Roland Caudano, remembers with delight being offered champagne by the famous prelate (oral communication of Professor R. Caudano). 82

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when we then approach the bottom of the glass, this unique instant that did not have a “yesterday” because yesterday, there was no space. Thought cannot conceive of anything pre-existent prior to the natural beginning of the world, as it is space itself that begins and we cannot conceive anything without space. Time seems to be capable of being prolonged at will, both towards the past and the future. But space must have a start, and time cannot exist without space; thus one may claim that space strangles time and prevents it from propagating below the bottom of space-time. But this is an origin which is also the beginning of multiplicity. It is an instant where all matter is a lonely atom, an instant where the static notions that presume multiplicity are useless. One should ponder if under these conditions the notion of space in this limit does not become evanescent, and only progressively acquires sense with the fragmentation of the primordial atom, and the multiplication of beings.

Initially, it seems that Lemaître also intended to demonstrate that the idea of a beginning of the world was not “theologically repugnant” either. Eddington, for one, would not admit of any divine intervention or metaphysical discontinuity in the purely physical description of the universe. From his 1931 paper, it seems clear that one of Lemaître’s objectives was to show that one could easily think of a beginning of space-time in a purely physical way while preserving the relevance of a religious approach to the notion of origin or the creation of the world. Indeed, this manuscript contains the following concluding paragraph which was deleted by its author before its publication84: I think that one who believes in a supreme being supporting every being and every action, also believes that God is essentially hidden and may be glad to see how present physics provide a veil hiding the creation. 84

  Manuscript preserved at the AL.

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This passage is comprehensible in the context of his previous comments. Relativistic physics only starts with space-time, which itself can only be said to begin with a certain multiplicity of particles, which requires the disintegration of the atom-universe. Paradoxically, physics can only reach the natural beginning through the initiation of a process of disintegration. The problem of the existence of the atom itself, no longer called the primeval atom by Lemaître himself, exceeds science, but not necessarily philosophical and theological reflection. This atom, containing all the matter of the cosmos, could in reality have been propelled into existence by a creative Will.85 And this is indeed the way that Lemaître, as a Catholic priest, conceived of the situation and he was still reminding his friend Msgr. Massaux of it in the 1960s in Rome.86 The hypothesis of the existence of the initial quantum, as well as the suggestive image of its disintegration, allowed him to show that the problem of the existence of the world itself, of the being of the universe, is distinct from the problem of the beginning of the “space-time-matter”. In other words, Lemaître asserts that there is no physics without the presupposition of a reality which is “always already there”, symbolized by the atom-universe, and that its being as such is forever veiled to the eyes of a science that must not be confused with metaphysics. This was no more and no less than the measured reaction of a man formed at the Thomistic school of the Institut Supérieur de Philosophie of Cardinal Mercier where one respected the various approaches to reality, but without confusing them. Lemaître, however, deleted this passage, most likely to avoid it being wrongly interpreted as simple concordism. Wasn’t there in fact a real risk associated with the atom-universe of seeing ‘God’s hand’ triggering the disintegration process in too facile a way? This is precisely the con  It could have existed since the beginning of the eternity in a self-sufficient way, but this remains once again a metaphysical position that could not be resolved by science itself. 86   Lemaître told Msgr. Massaux at the beginning of the Council Vatican II, “Of course, the primeval atom is created by God” (oral communication of Msgr. Massaux). 85

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fusion of epistemological levels that Lemaître desperately wanted to avoid in his cosmological talks and papers. Prudently then, he withdrew this passage. The future would prove him right. An important element of the constitution of the hypothesis of the primeval atom is Lemaître’s participation in the colloquium held in London 21-29 September 1931 to celebrate the hundredth anniversary of the British Association for the Advancement of Science (BAAS).87 Lemaître was invited to take part in a discussion on the evolution of the universe88 with no less than J. Jeans, E.A. Milne, W. de Sitter, A.S. Eddington, R.A. Millikan, J.C. Smuts and O. Lodge. A discussion also joined by the Bishop of Birmingham, E.W. Barnes, who had trained as a mathematician in Cambridge. James H. Jeans (1877-1946) defended the idea that the cosmic rays detected in high altitude were caused by the annihilation of proton-electron pairs occurring in the spiral nebulae or by the spontaneous transformation of the matter of stars into radiation similar to radioactive disintegration. For him, stars might have contained transuranian elements that disappeared progressively by emitting highenergy radiation. This hypothesis was diametrically opposed to that of Millikan, who attributed the origin of cosmic rays to the energy release that is produced during the formation of helium from hydrogen.89 The proton of the hydrogen atom was produced, in other words, by the materialization of radiation streaming in the universe. Lemaître attended the debate between Jeans and Millikan that took place during this BAAS colloquium with an audience of more than two thousand people. The young priest had written an article a year before (1930a) in which he incorporated Millikan’s hypothesis into an expanding universe, where he computed the attenuation of radiation   Cf. “Centenary Meeting of the British Association”, Nature, Vol. 128, August 1931, no 3223: 230. 88   “The Evolution of the Universe”, Supplement to Nature, October 1931, no 3224: 699-722. 89   M. De Maria, A. Russo, “Cosmic and Cosmological Speculations in the 1920s: the Debate between Jeans and Millikan” in Modern Cosmology in Retrospect (B. Bertotti, R. Balbinot, S. Bergia, A. Messina, eds), Cambridge University Press, 1990: 401-409. 87

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due to the expansion of the universe (this prefigures the computations that will be done later to characterize the properties of the cosmological background radiation). Lemaître would not unilaterally support either Jeans’ or Millikan’s positions, but rather would selectively choose from each of them the elements necessary for his own hypothesis. Unfortunately, the choices made would prove physically incorrect, diminishing his relevance and currency later in his career, when nuclear physics emerged as a fundamental pillar of early universe cosmology. From Jeans, he retained the idea that there are in the universe atoms of very large atomic number, which decay to transuranics, uranium, and other elements which will emit further radiation due to their decay. Lemaître was mindful of one of the keen insights of the English astronomer: if one can still observe atoms today that have not yet decayed, it implies or at least strongly suggests that the universe is still relatively young, of an age not incommensurate with the decay lifetimes of these atoms. Further, it dovetailed well with Lemaître’s idea of the irreversible evolution of the universe intrinsic to his cosmology. By the same reasoning writ large, as we can see many galaxies in close proximity to our own, in an epoch where the universe is still in expansion, one would conclude that our Milky Way could not have formed too long ago either. We have seen above that Lemaître attributed the expansion of the universe to the phenomena of ‘stagnation’. This phenomenon allowed us to go back to the beginning of the expansion, but on condition of effecting some variations of pressure which are absolutely infinitesimal and devoid of physical sense. This condition established an upper limit to the age of the universe of a hundred billion years. Yet, according to the classical theory of Jeans, this time was definitely too short for the formation of the very dense cosmological structures that we observe today, i.e. galaxies. Thus what seemed to be called for was a cosmology that both yields a relatively recent initiation of expansion, but also a much more rapid structure formation, that produces galaxies and stars faster than the classical model of the Laplace

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nebula, based on a slow diffusion and aggregation of matter. Thus, Lemaître appealed that (1931e: 705): A complete revision of our cosmological hypothesis is necessary, the primary condition being the test of rapidity. We want a ‘fireworks’ theory of evolution. The last two thousand million years are but a slow evolution: they are the ashes and smoke of bright but very rapid fireworks …

Lemaître then adopted the idea that ‘cosmology is atomic physics on a large scale’ (1931e: 705) and that the history of the universe started with the disintegration of a primeval atom90. This atom broke up, giving rise to atoms of large atomic number; these representing the “original atoms” from which Lemaître imagined the formation of stars (1931e: 705): The birth of a star would be an atom of weight somewhat greater than the actual weight of the star, and the star would be formed by the super-radioactive disintegration of its original atom. It is conceivable that the greater part of the products of disintegration would be kept back together by the gravitational attraction of such a massive atom, although a considerable part, say one thousandth, should be able to escape into free space at the beginning of the evolution, before the products of disintegration are numerous enough to form an atmosphere.

This picture contains a correlative explanation for the origin of cosmic rays; they would be constituted of products from the disintegration that succeeded in escaping from the primitive atoms and from stars before the formation their atmospheres (1931e: 705):

  The term appeared in (1931e: 706): “At the origin, all mass of the universe would exist in the form of a single atom: the radius of the universe, although not strictly zero, being relatively small. The whole universe would be produced by the disintegration of this primeval atom.” 90

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Cosmic rays would be glimpses of the primeval fireworks of the formation of a star from an atom, coming to us after their long journey through free space …

Later, in 1945, when he would publish his famous work L’hypothèse de l’atome primitif, largely a collection of previously published popular articles, he would admit to Gonseth91 that the idea of an atom, which in disintegrating would however retain its decay products by gravitational attraction, was an “unfortunate” idea. He would thus abandon the notion of stars being immediately formed from the disintegration of the “original atoms”, but he would retain the more general idea that all existing matter in the physical universe ultimately comes from the disintegration of the primeval atom. Thus for Lemaître, cosmic rays not only represented the ‘smoking gun’ validating this picture, but would provide powerful clues towards a more detailed early universe cosmology and the evolution of structure. Cosmic rays, constituted of photons, alpha particles, electrons and other particles (1931g: 20), would be the ‘fossils’, or ‘hieroglyphs’ informing us of the beginning of cosmological history (1931h: 406): Our universe bears the traces of its youth by which we may hope to reconstitute its history. The documents in our possession are not hidden under the stacks of fired bricks of the Babylonians, nor does our library risk being destroyed by any fire; it is the vast empty space where luminous waves are better preserved than the wax of phonographs. […] One of the most curious hieroglyphs in our astronomical library is the ultimate penetrating radiation: cosmic rays. Can we date them? Can we read them?

For more than 20 years, Georges Lemaître would try to understand the trajectories of the cosmic rays which are detected on Earth. He was then to hypothesize the existence of a cosmic “fossil radia91

  Letter, 21 January 1945, Al.

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tion”, a relic testimony of the first instant of the universe. Indeed his intuition was to be borne out, but not exactly as he had envisioned. This “fossil radiation” was not made of energetic charged particles, but rather of a thermal distribution of photons with a temperature of 2.7 K, the Cosmic Microwave Background (CMB) discovered by Penzias and Wilson in 1964-65. Lemaître was mistaken on the detailed nature of cosmic rays, the understanding of which would require a development of the fields of nuclear and particle physics that did not exist at that time, and furthermore of which he had no competence or interest. (Lemaître disparaged elementary particle physics as ‘entomology’, classifying a vast set of particles without mastering their production mechanism. One gathers from his reading notes that Lemaître approached the study of the physics of elementary particles only after 1958, and then only superficially)92. In regard to Millikan, he rejected the idea that cosmic rays were related to the annihilation of electron-proton pairs, and here his intuition served him well. The American scientist had suggested that electromagnetic radiation could materialize into a proton, but conservation of both momentum and energy forbid such a process in free space. On the other hand, a high energy photon interacting with the electric field of an atomic nucleus could materialize into a massive particle-antiparticle pair, a result already well-known in the 1940s, the fact of which Lemaître either did not know or did not accord much importance. Thus, he blithely proposed a process for the materialization of photonic radiation to explain, in 1949, the production of protons in the universe, and consequently the large abundance of hydrogen in the cosmos (1949e). His argument, involving a deceptive analogy between the process based on massive particles and others   One finds allusions to a work of Collins (1958) and to an enumeration of the products of decay of certain particles (e.g. the S+) with a mention of isotopic spin and strangeness. These notes are likely from the conference “L’étrangeté de l’univers” (1960a: 4) [The Strangeness of the Universe]. This particle consisting of two “up” quarks, and one “strange” quark), has Strangeness quantum number = -1, and +1 electric charge. It has a mass of 1,189.37 MeV/c2, making it a little more than 25% heavier than a proton or neutron. 92

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of zero mass is the following (1949e: 1162-1163; translation from the original in French): Some examples of the materialization of energy are well known: photons of sufficient energy can in certain conditions materialize into electrons. The cosmic rays themselves produce in the atmosphere particles of mass intermediate between those of electrons and protons, the mesons. It is therefore natural to imagine that for energies a thousand times higher, a process of materialization can give birth to protons.

Charles Manneback, his friend and fellow physicist, expert in relativistic quantum mechanics, was not at all pleased with the publication of this idea.93 And after the death of Msgr. Lemaître, he declined, for this reason, a project to publish the complete works of Lemaître that he had initially planned.94 Talking about a publication of the cosmologist McCrea, Charles Manneback confided to Odon Godard95: McCrea does not mention the physical hypothesis of the primeval atom: The ‘Quantum Giant’ nor about cosmic rays. So much the better. Because I always disagreed with Lemaître on this topic.

Lemaître would partially amend his hypothesis of the materialization of the energy in 1958 by proposing that energy be converted into massive particles in gaseous clouds which often sup  I refer the reader to Ch. Manneback, “Rayons cosmiques et mesons” in “La physique aux États-Unis. 1939-1946”, Revue des Questions Scientifiques, 20 Octobre 1947: 570597 and “Progrès récents de la théorie quantique des champs et du meson”, Relationes de Auctis Scientiis Tempore Belli (Pontificia Academia Scientiarum), A. 1939-1945, no 17: 3-26. Likely, Lemaître did not want to take into consideration these contributions. 94   Communication of Ch. Manneback to O. Godart (oral communication of O. Godart, 16-03-95). Manneback only took part in the binding of publications of Lemaître for the archives of the Academie Royale de Belgique (cf. Letter of Manneback to Godart, 29-05-1970, AL). 95   Letter, 29-05-1970, AL. Translated from the original in French. 93

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port intense magnetic fields96 (1958a:479; 1958g:18). Nevertheless, no allusion to the relativistic conservation laws of energy and momentum is mentioned by Lemaître, and the argument remains at the purely qualitative level. The only way to save Lemaître’s hypothesis regarding the production of hydrogen from primeval radiation would be to presume that the physical laws at the beginning of the universe were not the same as they are today, and by implication neither were the conservation laws. Dirac was indulgent with the physicist-priest in this matter, supporting this somewhat charitable interpretation of his hypothesis97: Lemaître supposed that there might have been some process of materialization that turned the very large kinetic energy of the early cosmic rays into hydrogen, or possibly helium within gas clouds. Such a process of materialization is not known in present day physics, where we have the conservation of baryons, but I think it is worth considering, because there is no certainty that conditions have not changed greatly since those early days. With an evolutionary universe of the type proposed by Lemaître it is possible that the laws of nature are also evolving and are not as immutable as is usually supposed.

While the hypothesis of the primeval atom did not fit Lemaître’s model of a universe with neither beginning nor end, nevertheless, it was still compatible with the spherical model of a hesitating universe. He definitively opted for the latter in November 1931, and would remain committed to it for the rest of his life. In this model, the history of the universe pivots around critical moments.

  These fields will be the object of further comments in the section on the formation of galaxies and clusters. 97   P.A.M. Diac, “The Scientific Work of Georges Lemaître”, Pontificiae Academiae Scientiarum Commentarii, t. II, 1968, no 11: 16. Dirac himself had developed a cosmology where the fundamental constants of physics could vary over the course of time. 96

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1) First of all, the universe undergoes a period of fast expansion from a state where the radius of the universe was zero. This ‘initial singularity’ of general relativity, where spatio-temporal geometry emerges, corresponds to the disintegration of the primeval atom. The zero value of the radius is in fact only an idealization as, for Lemaître, the notion of space and time fades into irrelevancy at the moment where we approach the primeval atom (1958a: 477). The physical beginning which fits the solution of Friedmann’s equation starting from R = 0 is provided by the Primeval Atom Hypothesis. Here the word ‘Atom’ should be understood in the primitive Greek sense of the word. It is intended to mean absolute simplicity, excluding any multiplicity. The atom is so simple that nothing can be said about it and no question posed. It provides a beginning that is entirely inaccessible. It is only when it has split up into a large number of fragments by filling up a space of small, but not strictly zero radius, that physical notions begin to acquire some meaning.

During the first phase of expansion, space-time is created at the same time as the products of the disintegration of the primeval atom (cosmic rays, primitive atoms and stars) fill it. It should be noted that, for Lemaître, the whole of the history of the universe is not foreordained in the primeval atom. From a totally non-deterministic perspective, Lemaître envisioned that (1931d: 706): Our world is now understood to be a world where something really happens; the whole story of the world need not have been written down in the primordial quantum, like a song on a phonograph record. All the matter of the world had to be present at the beginning, but the story it has to tell needs to be written step by step.

He maintained this position until the end of his life and, two months before his death in an explicit opposition to the determin-

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ism of Laplace, he would assert (1967b): “one could turn the famous quote of Laplace on its head and say that whoever knew the primeval atom or the final stages of its division could not in any way deduce the particularities of the universe that began with it.” This first phase of expansion, which began with a theoretically infinite speed, decelerated until reaching a radius corresponding roughly to an Einsteinian universe of the same mass. 2) The universe then remained in a quasi-static state for a certain time98 during which it behaved like an Einsteinian universe. The universe was then filled with a ‘gas’ of stars and atomic dust, as well as cosmic rays. This gas would condense under the action of its gravitational self-attraction to generate the nebulae, and the phenomena of stagnation would then yield to the breaking of equilibrium of the quasi-Einsteinian universe. 3) This equilibrium being broken, the hesitating universe resumed its expansion, this time with an acceleration removing the nebulae further away from one another, as seen today via their redshifts. This model of the hesitating universe coupled with the hypothesis of the primeval atom, summarizes the whole of Lemaître’s cosmological work: the second and the third moment in the history of the universe correspond to an evolution similar to that of the “1927 universe” with no beginning and no end, and asymptotic to an Einsteinian universe in the past. In the same time, these two moments represent the break in equilibrium of the Einsteinian Universe studied by Lemaître by means of stagnation. Finally, the second moment corresponds to   The duration of this quasi-static phase, beginning when the radius approximates that of the corresponding Einsteinian universe, depends on the value of the cosmological constant. By varying the latter, one may shorten or lengthen the age of the universe. This was useful at the time of Lemaître’s work as the value of the Hubble constant only gave a duration for the expansion of the order of two billion years, which was of the order of the age of the Earth. To resolve this conundrum, it was natural to say that the inverse of the Hubble constant only measured the duration of the second phase of expansion, whereas the actual age of the universe could be made to be whatever one wanted, by an appropriate choice of the cosmological constant. Lemaître chose a positive value of the cosmological constant l which was a bit higher than the one that characterizes the static Einsteinian universe of the same mass: l > lEinstein = l/(REinstein)2. 98

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the formation of the condensation of matter with spherical symmetry, which can be simulated within an inhomogeneous spherically symmetric model that Lemaître had developed in his thesis at MIT. To obtain a hesitating universe, one must introduce a cosmological constant, as Einstein did in order to obtain a static universe. Nevertheless, Einstein was not satisfied and discovered in 1932, together with de Sitter99, that it was possible to obtain a geometrical model of an expanding universe that is Euclidean but with zero cosmological constant. The ‘hesitating’ models were at this time progressively abandoned because the observational data did not seem to show a phase of acceleration in the expansion, but also for other more theoretical reasons. The hesitating model of Lemaître would come back in vogue in 1967 when Shklovsky would demonstrate its utility to explain a particular value of the redshift of quasars100. But it was soon noted that the required value was not characteristic of all quasars. The model was abandoned once more. Nowadays, Lemaître’s ideas have come back in fashion as measurements made on the most remote supernovae indicate that the universe is currently in a phase where its expansion is indeed accelerating, and it seems possible to fit it with a hesitating model of positive cosmological constant. A reprise of this topic will be found further on.101 Although Lemaître never abandoned the model of the “hesitating universe” after 1931, one should not necessarily conclude that his con  A. Einstein, W. de Sitter, “On the Relation between the Expansion and the Mean Density of the Universe”, Proceedings of the National Academy of Sciences, Vol. 18, 1932: 213-214. This is a universe of dust (and thus of zero pressure) that marks the boundary between the “Phoenix universe” (with a constant positive curvature) and the universe with infinite growth (with a constant negative curvature). 100   Cf. W. Rindler, Essential Relativity: Special, General, and Cosmological, Berlin, Springer, 1977: 277. The redshift of quasars depends only on the ratio between the actual radius of the universe R0 and the radius of the universe R1 at the moment when a light ray was emitted from the quasar. In the hesitating universe of Lemaître, the radius of the universe can remain quasi-stationary for a long time. This means that during this period, two very distant quasars can have the same redshift as the shift only depends on the ratio of the radii. In 1967, we thought that all quasars were located at z = 2, with 1+z = R0 / R1, z being the ratio of the radiation's wavelength compared to that in a stationary, or laboratory, frame of reference. 101   Cf. Chapter VIII.   99

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cept of the “primeval atom” remained immutable thereafter either. In fact, his hypothesis was largely independent of the mathematical detail and underwent some evolution. Lemaître first abandoned the idea of the formation of stars from super-radioactive primitive atoms, in the 1932-1933 time frame. It was difficult to imagine an effective process in which gigantic atoms decayed while keeping their decay products handy to form the constitutive matter of the stars we observe today. It was also difficult to find an efficient energy loss mechanism that would be needed to rapidly dissipate the random motion of a vast multitude of pre-existing stars into a very dense “nebula”.102 But Lemaître himself cautioned that the “primeval atom” concept should not be taken literally and exactly as a physical model (1946e: 153): “…too much importance must not be attached to this description of the primeval atom, a description which may have to be modified, perhaps when our knowledge of atomic nuclei is more perfect”. While in 1931, it merely consisted of a sort of undifferentiated quantum or an atom of prodigious atomic weight, a sort of radioactive “super-transuranium”, it became in 1945 an “isotope of the neutron” (1945f; 1946d: 142). It consisted then of an enormous nucleus solely formed of neutrons and whose size was approximately an astronomical unit103: “The primeval atom must not be considered to be a transuranic. It could be an isotope of extremely large mass of the actual elements, and even more likely of the neutron” (1948b: 328; translated from the original in French). It is then clear that the initial singularity of radius zero would clearly be inconsistent with such a description. Again, one must remember that he does not attach absolute importance to his model, but regarded it only as an idealization that loses its precise interpretation going back closer to the beginning of the universe. The hypothesis of the primeval atom thus represents a stimulating image, a fertile intuition able to provide a kind of physical inter  Lemaître made a brief retrospective of his ideas on this purpose in the letter to Gonseth, 21 January 1945, AL. 103   The radius of the earth's orbit around the Sun, about 150 million kilometres. 102

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pretation of the model of the hesitating universe, but this hypothesis should not be confused with a rigorously defined theory. In fact, Lemaître never wrote down any equation nor made any calculation related to the description of the primeval atom as such. To do so, he would have had to use the notions of nuclear physics that were developed in the late 1930s and early 1940s, mostly in the United States. Lemaître however had not studied quantum mechanics after the end of the 1930s and even less the relativistic quantum mechanics whose spectacular applications would begin after the Second World War. Thus he could not translate his model of the primeval atom into mathematical language, which his relativistic cosmology suggested to him. Rather, it would be Maria Mayer and Edward Teller of the University of Chicago104 who would carry out calculations of nuclear matter germane to the problem of such a neutron star with a 15 km radius. Gamow105 had already taken up this problem in 1942, but in a slightly more grandiose context, a polyneutron comprising the entire mass of the universe. By examining the mechanical stability of neutron spheres, Mayer and Teller showed that the latter might quickly cover themselves with small balls of 10-12 centimetres that would then detach from the neutron star, undergo beta decay transforming some neutrons into protons and electrons), and ultimately reconstitute as atomic nuclei. Calculations proved that it was possible to account for the relative abundance of the heavy elements106, but not for light elements as hydrogen or helium, which constitute by far the largest proportions of the elements in the universe. Despite the suggestion of his collaborator Odon Godart107, Lemaître never wanted to meet Gamow108. Neither did he make any effort to meet with Teller   Cf. “Polyneutrons and improved calculation”, in H. Kragh, Cosmology and Controversy. The historical development of two Theories of the Universe, Princeton University press, 1996: 123-127. 105   Cf. G. Gamow, La création de l’Univers (trad. Guéron), Paris, Dunod, 1954: 56-59 106   More precisely the elements whose number of protons in the nucleus is higher to 34 (Bromine, Krypton, Rubidium…). 107   Oral communication, 16-03-95. 108   Gamow sent to Lemaître a preprint of his paper: “The Evolution of the Universe”, Nature, 162, 30 October 1948 and wrote on the cover some kind words. 104

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during the 8th Solvay Congress that was held in Brussels 27 September – 8 October 1948 when the latter came to present his results regarding the ‘polyneutron’. Was he disappointed to see his idea being taken in different directions or was it simply a lack of patience with the nascent field of elementary particle physics? It is impossible to divine at this late stage. Nevertheless, it is certainly not a coincidence that in year following the Solvay Congress, he attempted to solve one of the problems in the Teller-Mayer model by proposing the strange explanation “à la Millikan” of the abundance of the hydrogen mentioned previously. Ultimately what perdured from the original intuition of Lemaître is the necessity to find unification of quantum mechanics and general relativity in order to truly understand the early history of the universe. In the end, cosmology also justified Lemaître in regard to the existence of “fossil radiation”, even if its nature was hardly that imagined by Lemaître. It must be said bluntly that Lemaître’s scheme for the formation of elements proceeding by a hierarchical decay from a simple and homogeneous primordial atom to a large multiplicity proved completely invalid. The contemporary standard model of cosmology proceeds by just the opposite hierarchy: one begins with a soup of elementary particles (quarks, leptons etc.) to reach progressively more complex moieties, i.e. nuclei, atoms, and ultimately large-scale structure. Lemaître’s cosmology, distilled for the 11th Solvay Congress (1958f, g), underscores the real genius of Lemaître being his ability to play off confrontations of his thoughts with another’s to achieve a yet more original synthesis. Most notably and successfully was his interaction with Eddington, resulting in the Big Bang; also notably if less successfully with Millikan and Jeans regarding the specific mechanism for the formation of stars and structure.

Chapter VII

The Chinese connection (1927–1950…)

1. A disciple of Father Lebbe: from cosmology to the Chinese residence

G

oing through the personal files of Msgr. Lemaître, one discovers a series of documents gathered by Odon Godart under the title of the “Chinese Connection” that allows us to see the cosmologist of Louvain in a different light. While the young priest Lemaître was constructing the basis of his revolutionary cosmology in the secret recesses of his apartment in the College du Saint-Esprit or in his office of the Collège des Prémontés, and while one could readily imagine him completely absorbed by the equations of general relativity, he was also living perhaps the richest apostolic experience of his priestly life. It has already been mentioned that Lemaître had taken care of a Chinese seminarian during his stay at the Saint-Rombaut House. He had pursued his study of the Chinese language with some difficulty as the method was written in German.1 After his stay in the United States, Lemaître was particularly concerned with the problems of foreign students. In 1927, he confided in his retreat journal2:  Seidel, Chinesische Konversations-Grammatik, Heidelberg, Julius Groos, 1923, Lehr-bücher-Methode Gaspey-Otto Sauer. This book as well as a booklet preserved in Lemaître’s bookshelf of (AL) were heavily annotated by Lemaître. More particularly, Lemaître thereafter used the book's way of writing numbers. 2  It consists of a notebook with a black cover with the inscription on first page “Retraite au grand séminaire, 1927, prêchée par les Fr. Salsmans and Fr. Rutiens, s.j.’ [Trans: Retreat at the grand seminary, 1927, preached by the Fr. Salsmans and Fr. Rutiens, S.J.](AL). 1

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My responsibility within my state [as a priest] is more vast than I was aware. I could have the opportunity to take care of students. Should Picard3 be reminded of his resolution to entrust me with his international circle? If I don’t start anything of this kind, would I ever do any­thing?

The chance would be given to him but not to take charge of Msgr. Picard’s circle, the chaplain of Action Catholique de la Jeunesse Belge (ACJB)4 an organisation created after the First World War, but to work on behalf of the Chinese students in Belgium. This was established, for the first time, by Claude Soetens, professor of history at UCL. Several Chinese students who had worked in France during the First World War went to Belgium after 1918.5 We also know that at the end of the 1920s Pius XI consecrated the first six Chinese bishops in Rome. The Pope had taken this initiative partly at the behest of Fr. Vincent Lebbe (1877-1940) who had been a missionary in China since 1901. Fr. Lebbe succeeded in opening in Louvain, in October 1926, the “Home Chinoise” (Chinese residence). Located at 29 Place du Peuple (which later became Place Ladeuze and currently Ladeuzeplein) in the house of a chaplain of students, Abbé François6, the Home Chinois hosted an important group of Chinese students who were at UCL.7 As early as 1927, a priest of the diocese of Liège and   Msgr. Louis Picard was a leader of the “Action Catholique” (a movement of social Catholicism). 4   In 1924-1925, a branch of the ACJB for women was organized. For several decades, the latter was led by Miss Christine de Hemptinne, who was also a guest at La Pointe, the famous residence of the Thibaudeau family. 5   The Federation of Franco-Chinese Students, founded by the rector of the University of Peking, allowed certain Chinese to come and study in a French university under the condition that they also agreed to working part-time in factories whose staff had been depleted between 1916-1918 due to the war. After the cessation of hostilities, the Chinese students were fired to free up jobs for people coming back from the Front (cf. K. De Ridder, “Les premiers étudiants chinois in Belgium”, Courrier Verbiest (Fondation Verbiest-Institut Chine Europe), t. IX: 7-8). 6   The latter became later Fr. Augustin, most likely at the Benedictine Abbey of MontCésar in Louvain. There was some friction between François and Lemaître, because the former wanted to continue to live partially at the house that he was leasing. (Letter of Georges Lemaître to Dom Theodore Nève, 6-10-1929, AL.)   7   In Louvain, Fr. Lebbe benefited from the help of his sister and her husband, Professor 3

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who collaborated with Fr. Lebbe, Abbé Boland (1891-1955), became the chaplain of the Home after a priest-student, living at the Collège du Saint-Esprit, had assumed this task. Having to manage the Home and the spiritual activity of the Chinese students in Belgium and in France, Abbé Boland decided to pass on the responsibility. Naturally, he considered the Collège du Saint-Esprit and asked Lemaître to replace him as the chaplain of the Home Chinois. Lemaître, who had just met Edouard Tchang-Hwai once again (who had become a student in pedagogy after leaving the seminary8), accepted the proposal in 1927 or 1928. Lemaître was clearly well matched to this task and he took to his apostolate among the foreign students with conviction and alacrity. On Christmas Eve 1928, he baptized a Chinese student to whom he had taught catechism.9 At the end of the academic year 1927-28, he conceived of a strategy to bring around Abbé Boland to the Chinese bishops’ appeal to introduce the “sacerdotal fraternities of the Amis de Jésus” in China. To this end, he wrote to Abbé Fernand Willockx, general secretary of the Amis10: My dear Fernand, I am sending you the bulletins of the ACJS11 that on p.14 alludes to the “auxiliaries of the apostolate”, priests affiliated with the Amis de Jésus. Abbé Boland informed me that the Chinese bishops would like to establish the Amis de Jésus in their diocese and that the auxiliary priests would be most agreeable to be part of it, if the Fraternity were to be organized in the dioceses where they are assigned. This is the sense of Jacques Thoreau, who taught geology at UCL. The brother of the latter, Édouard, was a monk at the Saint-André Abbey (near Bruges), which had played an important role in the history of Chinese students in Belgium. Cf. V. Thoreau, Jacques Thoreau, Un homme de science, un homme de foi, Didier Hatier, 1991.   8   Lemaître would stay in contact with E. Tchang after his return in China until at least 1933 (his final letter dated 14-11-1933, AL).   9   Letter of Lemaître to the priest Gilson (probably living at the “Collège Préuniversitaire Chinois”), 20-12-1928 (AL). 10   AFSAJ. Translated from the original in French. 11  “Action Catholique des Jeunes Spécialisée”.

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the text as I read it, which was perhaps deliberately vague. It appears that in fact, they are prepared to carry out the establishment of the Fraternity there on their own. Don’t you think that it would be quite useful if Boland and maybe one of those young priests could attend the meeting at Lophem12? They would then be fully apprised of the organization that has been requested, and most of all of the spirit of the Fraternity; in fact I talked with him and he was very eager to take part in the meeting. I suspect that he is not enthusiastic about the project but perhaps this visit could bring him around. Would you talk about it to the director13 or would you prefer that I wrote to him directly?

On 28 June, Willockx would indeed write to Boland to invite him to Lophem, not telling him that the initiative came from Lemaître himself.14 In 1926, at the request of Fr. Lebbe and under the crook of Abbé Boland, a sacerdotal society dedicated to training secular priests was born. These priests were at the disposal of the Chinese Bishops and under their jurisdiction. This society took the name of the name of the “Société des Auxilaires des Missions” (SAM)15. Some “auxiliary” seminarians spent their philosophical year at the Leo XIII seminary (Séminaire Léon XIII) and Abbé Boland himself served as spiritual director for some of these seminarians. The young students of the Leo XIII Seminary were caught up in a wave of enthusiasm for service to the Chinese Church. One person distinctly unenthused with this project was the Seminary’s president, Abbé A. Brohée16, who feared too strong an influence of the SAM and of Abbé Boland on the Seminary,   This meeting was the general assembly of the Amis de Jésus that would take place on 9 August 1928 at the Saint-André Abbey near Bruges (Lophem). It was during this meeting that Lemaître would renew his three temporary vows of poverty, chastity and obedience. 13   i.e. Canon Allaer. 14   AFSAJ (Secretariat I. Letters sent by Willockx 1924-1954). 15   La Société des auxilaires des missions (préface de S. E. Mgr Kerkhof, évêque de Liège), Editions SAM, 1962. 16   Communication, Cl. Soetens (letter, 13-11-1996) 12

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which was after all, dedicated to the service of the Belgian dioceses. Brohée elevated the issue to Cardinal Van Roey, and Boland was removed from Leo XIII Seminary. According to Claude Soetens, this gambit was probably responsible for putting an end to the idea of an affiliation between the SAM and the Amis, which were under the canonical jurisdiction of Cardinal Van Roey. Nevertheless, the seeds already planted were fruitful regarding assistance to the Chinese. This explains why one of the Amis and close friend of Lemaître, Louis Reyntens, welcomed a contingent of Chinese students in his “special scientific class”17, at the Collège Sainte-Gertrude of Nivelles.

2. Florescit et lucet18 In Belgium, assistance for Chinese students was organized in Catholic circles by the Foyer Catholique Chinois (FCC), a not-for-profit association under the direction of Fr. Théodore Nève, the abbot of the Benedictine Saint André abbey (now Sint-Andries abdij van Zevenkerken), in Lophem (now Loppem) near Bruges (Brugge). This “Sino-Benedictine” connection was hardly coincidental. Dom Théodore had met Fr. Lebbe in Rome in 1900 and again in Belgium in 1913. The abbey had edited the Bulletin des Missions beginning in 1921, a journal to which Fr. Lebbe himself contributed starting in 1924.19 In June 1926, Abbé Boland and Fr. Lebbe came to Saint André abbey just when Fr. Theodore had been elected abbot. The latter agreed to help Fr. Lebbe   Oral communication, Albert Caupain (23-03-95). Cf. also H. Heyters, Louis Reyntens, Bruxelles, 1948: 3 (a copy of this book may be found in the library CDRR (Centre de documentation et de recherches religieuses), University of Namur. 18   Motto of the Nève family that also appears in the stained glass of the Saint André Abbey in Lophem, alluding to the rose and the star that decorate the family coat of arms. 19   Between 1924 and 1927, Fr. Lebbe would publish six articles in the Bulletin des Missions. Teilhard de Chardin’s analysis of the Bulletin is an interesting study (Lettres intimes de Teilhard de Chardin à Auguste, Bruno de Solages et Henri de Lubac (introduction and notes by H. Lubac), Paris, Aubier Montaigne, 1972: 188; letter of 2-4-1929 to Fr. Valensin). 17

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managing his charitable works, one of the resulting initiatives being the FCC. Established 28 January 1927,20 the FCC assumed responsibility for the operation of the Chinese home in Louvain as well as the Chinese pre-university college of Gemmenich21. Remarkably, numbered among the monks of Saint André was Fr. P.C. Lou Tseng Tsiang, none other than the former Prime Minister of the Chinese Republic, who would later become vice president of the FCC. Lemaître struck up a working relationship with Fr. Theodore Nève, likely going back to the general assembly of the Amis de Jésus held in Saint André in August 1928, the same year, the physicist-priest became a member of the FCC. Their correspondence testifies to the great esteem the two men held one another. This mutual admiration would provide solace and support to Lemaître when problems would arise later on between Boland and himself. On 11 October 1929, while living at the Collège du Saint Esprit, Lemaître took on the oversight of the Chinese home22. It was clear however, that the home was too confessionally identified for Chinese nonbelievers to feel comfortable meeting there. He thus suggested to Dom Théodore Nève that he would open the apartments of the Collège du Saint Esprit to all comers23: “I shall organize an initiative for the ‘pagans’ in the form of a ‘Suen Wen circle’ at my place. Several students, who would hardly come to the ACJS even for a meal24, would accept the invitation of a professor who will receive them at his own home!” During the time he frequented the home, Lemaître had met a number of important personalities, including Fr. Germain, rector of the Aurora   Date of the last visit of Fr. Lebbe to Saint André.   The reason for siting the pre-university college in Gemmenich (near the German border) was the fact that the subsidies supporting the Collège were mostly German. It only existed there for two years, after which it was transferred to Louvain, where it did not function as well. 22   Letter of Lemaître to Dom Boniface Janssens (AL). He took this task very seriously, monitoring the visits of Chinese students and supervising their academic development (Cf. letter to Abbé Gilson, 20-12-1928, AL). 23   Letter, 6-10-1929 (AL). 24   Meaning his own home, 29 Place du Peuple (Ladeuzeplein). 20 21

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University25 (Zhendan Daxue), a Catholic university with a good reputation for preparing Chinese students wishing to go to Europe. Lemaître did not restrict his interest to just the circle of students; he also tried to raise awareness of the difficulties met by the Chinese in Belgium more broadly, and therefore he would convince, for example Charles de la Vallée Poussin to help them out financially.26 Lemaître’s activities on behalf of the Chinese would go far beyond the limit of his Alma Mater. In July 1929, he was chosen by Msgr. Ladeuze as the UCL representative at the Comité Interuniversitaire Sino-Belge (CISB, the Sino-Belgian Interuniversity committee), which had been in charge of the distribution of study grants to Chinese students coming to Belgium since 1927. Lemaître would sometimes find himself caught in a bind between the University that was reluctant to finance certain projects of the Committee, and some members of the Committee who thought that his activities were too focused on apostolic aims27. At home, Lemaître had to share an office with Abbé Boland. But, the two men, both possessed of strong personalities, had their own opinions on the best manner by which to lead the mission among the Chinese students. As a result, Abbé Boland wanted to transfer the management of the home to the auxiliary priests which he was in charge of. Matters deteriorated when the relocation of the home was being considered. Lemaître had begun negotiations with a certain Abbé Jacobs for the purchase of a building, although the project was financially risky and the young professor finally decided to propose the less ambitious idea of renovating the residence at 29 Place du Peuple. Then a new opportunity arose for acquiring a suitable building at   Cf. the photograph (p.8) of the paper “Les premiers étudiants chinois en Belgique”, op. cit. (The author is grateful to Canon Wéry for drawing his attention to this document). 26   Letter of Lemaître to Théodore Nève dated 23-12-1929 (archives of the Saint André Abbey, henceforth referred to as the AASA). 27   Correspondence between Lemaître and Mr. van der Essen, secretary of UCL (letters, 6-08-1929 and 12-08-1929); letter of Lemaître to Mr. Pieters, General Secretary of the CISB (20-08-1929); letter of M. Pieters to Boland (15-09-1929), preserved at the AL. 25

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28 Rue des Joyeuses-entrées (Blijde Indomstraat). The deal was close to being finalized and Lemaître was already planning the erection of the new center. Abbé Boland, however had other plans to use this house for the head office of the SAM28. A growing mistrust had arisen between the two men, and the situation came to the ears of the president of the FCC. On 19 December 1929, Fr. Édouard Neut reported the problem to Dom Théodore with Neut proposing that he remove Boland.29 On 21 June 1930, Abbé Boland wrote a letter to Lemaître requesting him to cease and desist all involvement in the search for the Chinese house, since, he declared: “I do not see the possibility of two heads in the house” and moreover “we sometimes differ, ‘using charitable terms’, in terms of our opinions and methods”30. The cosmologist wrote to Dom Théodore that very evening to bring him up to date on the affair. Dom Théodore responded on 30 June, confirming Lemaître’s assignment of the residence at Rue des Joyeuses-Entrées and his position of Director31. Abbé Boland counterattacked by writing not only to Dom Théodore32 to complain about his decision, but likely also to Cardinal van Roey and certainly to Msgr. Luigi Drago, General Secretary of the Conseil Supérieur de la Congrégation de la Propagande (High Council for the Propagation of the Faith33). To the latter, he wrote that the Primate of Belgium did not deem appropriate that Georges Lemaître should remain as head of the Chinese home.34 The motivation of the Archbishop of Mechelen will never be known for sure but, it is obvious even prior to 1934 that he had reservations in regard to the Amis, and in any case, he was always careful not to give them any advantage. This was surely not helpful for Lemaître’s   This house would become effectively the house of studies of the SAM (La Société des Auxilaires…, op. cit.: 9). 29   Letter preserved at the AASA. Fr. Neut informed Dom Théodore that Lemaître was learning Chinese. 30  AASA. 31   Letter of 28 June 1930 (AASA). 32   Letter of 28 June 1930 (AASA). 33   Sacra Congregatio de Propaganda Fide (Congregation for the Propagation of the Faith) old name of the Congregation for the Evangelization of Peoples. 34   A duplicate of the letter to Msgr. Drago 7-09-1930 is preserved at the AASA. 28

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cause. There is a more prosaic interpretation as well: Abbé Lemaître’s wide reputation for inattention and disinterest in organizational detail, which the FCC itself ultimately admitted.35 Nobly, Lemaître accepted that he must cede his place to Abbé Boland36, not before personally directing the outfitting of the residence at Rue des Joyeuses-Entrées. In retrospect it was the prudent and correct decision as his scientific trips during the 1930s would not have allowed him to welcome Chinese students to Louvain appropriately, while the SAM was well prepared for this task.

3. “Servir” In spite of these events, Lemaître did not lose interest in the cause of Chinese students. At the beginning of the 1950s, he took care of the operation of the Academic Committee for the Chinese Students of Louvain of which he served as President37. This Committee had the goal, according to its statutes, of the “formation of a Catholic Chinese elite”, whose future was threatened by the political events of the moment. In order to carry out their mandate, the Committee welcomed Chinese priests and laymen in a residence entitled “Servir”.38 Aided by a priest of Scheut (a Belgian congregation of missionaries), Fr. Bongaerts, Lemaître would supervise this new apostolic project in conjunction with the other members of the Committee. Among them, there were Dom Théodore Nève, Professor Thoreau, Fr. Litchtenberger39, S.J., two representatives of the SAM, his Superior General,   In Saint-André, Dom Théodore Nève admitted to some of Lemaître’s management difficulties (6-09-1930, AASA). 36   Lemaître would not bear any grudge towards Boland, as reflected in the tone of the letter he wrote him 23 January 1931 (AL); the attitude of Boland toward the cosmologist was reciprocal in this regard. 37   The documents concerning this Committee are preserved at the AL. The head office of the Committee was at 21 rue des Bogards. 38   The residence “Servir” would welcome 10 Chinese priests in 1952 (report of the 2110-1952, AL) [Translator: ‘Servir’, literally in English ‘to serve’] 39   Litchtenberger would continue his correspondence with Lemaître when the latter 35

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the Abbé Gilson, Fr. Hanquet, and also Canon Jacques Leclerc, who during that time had started editing his famous book: “La Vie du P. Lebbe. Le tonnerre qui chante au loin”40. On this Committee, there was also one of Lemaître’s closest friends: Canon Jardin. Priest of the diocese of Namur, the latter had been the founder of the Cercle International des Étudiants Étrangers (CIEE) and of the first restaurant for foreign students situated at Place Hoover (now Ladeuze Plein) in the heart of Louvain. Before the Second World War, at the end of his ritual constitutional following lunch at the restaurant Majestic, he often visited Canon Jardin41. This connoisseur of pipe smoking, who shared Lemaître’s spirit of bonhomie, simplicity in human relations and a proclivity to thrive in a ‘happy mess’, accompanied him on his trips to Italy at the end of the 1930s, and again in the 1950s. Within the Academic Committee, Lemaître once more had to countenance a number of institutional problems. Typical of these was the matter that, having been attracted by the prestige of UCL, some Chinese priests joined the Alma Mater without the authorization of their bishops. Lemaître helped reassure the ecclesiastic authorities by getting the Congregation for the Propagation of the Faith to intervene at the appropriate moment.42

4. Lemaître’s Chinese Disciple: Tchang Yong-Li If Lemaître was moved by the plight of the Chinese in Belgium, conversely, many Chinese students were deeply influenced by him as well. Among them, the most well known is undoubtedly, Tchang Yong-Li (1913-1972).43 This student was born in Kweiyang (Kweiwas at the residence Saint-Ignace in Saigon (letter 29-08-1958). 40  This biography of Fr. Lebbe was ordered by the SAM (cf. P. Sauvage, Jacques Leclerc. 1891-1971. Un arbre en plein vent. [préface of L. Guissard], Paris / Louvainla-Neuve, Duculot, 1992). [Translator: the title of Leclerc’s biography in English is: ‘Life of Father Lebbe. Thunder that sings from afar’]. 41   Oral communication, Odon Godart (14-06-1995). 42   Letter 27-08-1952 from Lemaître to a Cardinal of this Congegation. (AL). 43   The information concerning Tchang Yong-Li was provided by his sons Haowen and

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chow). After obtaining his BA at the Aurora University in Shanghai in 1934 and having taught in a secondary school in Kweiyang, he came to Louvain, thanks to the Comite Interuniversitairs Sino-Belge. He obtained his doctorate in mathematical sciences in 1938, having defended his dissertation on the theoretical explanation of two particular effects characteristic of the trajectories of cosmic rays detected at the Earth’s surface.44 Lemaître, his collaborator Odon Godart, and Tchang Yong-Li became fast friends. Lemaître quickly sized up Tchang Yong-Li as mathematically quite capable, and in the year 1936-37 introduced him into a group of physicists and chemists in Louvain working on deuteroethylene, a molecule derived by substituting a deuterium atom45 for an atom of hydrogen in ordinary ethylene C2H4. At the Collège des Prémontés which housed the Institute of Physics, Marc de Hemptinne directed the overall deutero-ethylene research program. Deuterated compounds were prepared by the chemist Jungers, involving catalytic and photochemical techniques, and Raman spectroscopy46 of these new heavy ethylene molecules was performed by Delfosse. The Institute was particularly well positioned to carry out high quality measurements, as de Hemptinne had become interested in Raman spectroscopy during his time in Zurich where he had studied with Debye, and thus had set up on his own lab47 with advanced equipment Zhuwen Zhang (Tchang), his spouse and one of his students, Chen Zhongxuan, to André Deprit thanks to the mediation of a Chinese student at UCL, Xu Jia. This information, as well as the photographs, was transmitted by A. Deprit to the AL. 44   The thesis of Tchang Yong-Li corresponds to the two following publications: “VI. Cônes des rayons cosmiques infiniment voisins de l’équateur”; V. Trajectories voisines de l’équateur”, Annales de la Société Scientifique de Bruxelles, série I, t. LIX, 1939: 285-300; 301-345. 45   Deuterium is an isotope of hydrogen. Its nucleus contains one neutron and one proton. This element was discovered in December 1931 by Harold Clayton Urey of Columbia University. 46   C.V. Raman, Indian physicist; received the 1930 Nobel Prize for the elucidation of characteristic molecular rotational and vibrational spectra by inelastic scattering of light. 47   de Hemptinne’s generosity was worthy of note. In a period where the finances of UCL were extremely modest, he provided laboratory equipment out of his own resourc-

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in the basement of the Collège des Prémontés upon his return. Lastly theoretical work on the spectrum of vibrational modes of the molecule was carried out by Charles Manneback48 with occasional help from Lemaître. That year, the chemist Hugh S. Taylor49 of Princeton came to Louvain as holder of the Francqui Chair granted to him by the department of chemistry, and on 16 June 1937 Msgr. Ladeuze conferred on him the title of doctor honoris causa. Shortly after the discovery of deuterium, electrolytic techniques were developed to increase the concentration of this isotope. Taylor quickly realized the enormous scientific potential of ‘marking’ molecules by substitutional introduction of heavy hydrogen in order to study chemical reactions in detail, for example the mechanism of catalysis. Taylor and his group became specialists in the production of deuterated molecules and especially heavy water. The Princeton chemist, who had published several papers with Jungers beginning in 193350 and advised de Hemptinne on the equipping of his laboratory, became an active member of the deutero-ethylene team at the Collège des Prémontés, and lauded them for their spirit of collaboration:51 es, and was even known to supply textbooks for his courses at no cost to the students. 48   Manneback gave a lecture of the famous “Chaire Francqui” under the direction of P. Debye, on 5 December 1934, “Calcul et identification des vibrations des molécules” (published by Editions E.D.K., 132 rue Féronstrée, Liège). The lecture dealt with work done with his student M. van den Bossche who wrote his Ph.D. in Louvain in 1932. 49   C. Kemball, “Hugh Stott Taylor, 6 February 1890 – 17 April 1974” in Biographical Memoirs of Fellows of the Royal Society, Vol. 21, 1975: 517-547 (London, Royal Society). 50  H.S. Taylor, J.C. Jungers, “The Deuteroammonias”, J. Amer. Chem. Soc., Vol. 55, 1933: 5057; “The Mercury Photosensitized Decomposition of the Deuteroammonias”, J. Chem. Phys., Vol. 2, 1934: 373; “Deuterium as an Indicator of Mechanism in the Photodecomposition of Ammonia, ibid, Vol. 2, 1934: 452; “The Mercury Photosensitized Decomposition of the Deuteroammonias”, J. Chem. Phys., Vol. 2, 1934: 373; “Deuterium as an Indicator of Mechanism in the Photodecomposition of Ammonia”, ibid., Vol. 2, 1934: 452; “The Mercury Photosensitized Polymerisation of Acetylene and Acetylened2”, ibid., Vol. 3, 1935: 338; Exchange Between Ammonia and Deuterium on Cataytic Iron surface’, J. Amer. Chem. Soc., Vol. 57, 1935: 660; “The Decomposition of DeuteroAmmonia on Tungsten Filaments”, J. Amer. Chem. Soc., Vol. 57, 1935: 679. 51   “Report to the Francqui Foundation by Hugh S. Taylor, Titulaire de la chaire Franc-

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In the Institute de Physique, a body of interesting research on heavy isotopes and their compounds was carried out in which the writer was pleased to collaborate. An admirable example of cooperative research of the most fruitful type was the work on the synthesis, the Raman spectra and the theoretical physical analysis of the deutero-ethylenes, the heavy hydrogen derivatives of ethylene.

Taylor’s collaboration with the Louvain group would come to an end after his return to Princeton52. It is interesting to see how the structure of the College, with the physical proximity of the labs and the daily meeting of professors at tea-time, facilitated such an interdisciplinary program that the modern era prides itself on having invented. Lemaître was periodically sought out for advice or some physical insight towards the resolution of problems encountered by his team of friends and his colleague de Hemptinne. His contributions were appreciated, even if some feared his appearance near fragile experimental apparatus; nonchalantly leaning on a delicate diffraction setup one day earned him a reputation as a theorist to be kept far from the lab! (The equipment bearing the thumbprint of Canon Lemaître has been preserved for posterity in the very lab where this incident took place.53) For the study of monodeuteroethylene, C2H3D, Manneback needed Abbé Lemaître and Tchang Yong-Li working together on the calculation of the molecule’s vibrational modes. This is not an easy problem, as the substitution of a deuterium atom for ordinary hydrogen breaks the simple symmetry of ethylene, and required searching for the roots of a ninth-order equation. It so happened however that Lemaître and Tchang Yong-Li were familiar with this class of problem and possessed the numerical techniques to solve it. (It should be remembered that the young qui. Université de Louvain, 1937”, AL. 52   H.S. Taylor, P. Capron, J.M. Delfosse, M. de Hemptinne, “The Separation of the Carbon Isotopes by Diffusion”, J. Chem. Phys., Vol. 6, 1938, p. 656. 53   Oral communication of Fr. Ch., Courtoy, S.J., who had worked at the laboratory of de Hemptinne before and after the Second World War (17-10-95).

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priest had taken a course on spectroscopic techniques during his stay at MIT.) Very likely using the Mercedes mechanical computing machines possessed by Lemaître, to be discussed later, the three scientists succeeded in determining the eigenmodes and frequencies of the planar vibrations of the molecule. Thus they succeeded in predicting the intensity and the polarization of the lines of these infrared spectra54 and Raman spectra (1937a and b). Tchang Yong-Li would return to China with his spouse who had accompanied him in Louvain, and in 1940 he would be appointed professor at Aurora University. From 1941 to 1949, he would teach in three university institutions in Kweiyang, and became Head of the Department of Mathematics and Physics at the University of Kweichow. During this time he returned to the old problem he worked on with Lemaître concerning the detailed calculation of the trajectory of cosmic rays and comparison with their observation at the Earth’s surface55. From 1949 to 1972, he was professor at Yunnan University in K’un-ming and occupied several important positions in various Chinese societies of physics.56 He kept his interest in spectroscopy alive in K’un-ming, and many of his publications in Chinese concerned the Sagnac effect57 a relativistic effect observed with an optical interferometer. Evidently, the disciple had not lost anything that he had learned from his master58 in Louvain.

  An enduring core competency in infrared experimental spectroscopy would truly be developed at the Collège des Prémontrés only after the Second World War as a consequence of the thesis of Ch. Courtoy (oral communication 25-06-1999). 55   In an article written in French (“Cônes de rayons cosmiques entre les latitudes magnétiques 30ºN et 30ºS”, Séries mathématiques et physiques. University of Kwei-Chow, 1946, no 1: 1-41), Tchang Yong-Li applied, in Lemaître’s style, techniques of harmonic analysis in order to determine the flux of cosmic rays in a band of 60º latitude centered on the equator and for a fairly wide energy range. 56   He was member of the Commission for Theoretical Physics of the Chinese Society of Physics and vice-president of the Physics Society of the Province of Yunnan, a mountainous province bordered by Tibet, North Vietnam and Burma. 57   The Sagnac effect had been investigated by Lemaître himself in 1922a: 261-262 and 1924a: 173. 58   The French name, Lemaître is translated into English as the Master! 54

Chapter VIII

Arrival on the world scene? (1931–1939)

1. Travels and accolades

A

t the end of the academic year 1931-32, Lemaître left his residence at the Collège du Saint-Esprit and moved to an apartment on the second floor of a building, 7 Place Foch (Fochplein and, since 2011, De Somerplein) in Louvain1, above the De Belva bakery, bread and cake shop. Between 1932 and 1939, however, he would be absent from Louvain for a total of two years, corresponding to trips of more or less a semester each to the United States. As a faculty member, he was surely cognizant of the debt of gratitude he owed for the indulgence of his rector, Msgr. Ladeuze and his colleagues who covered his teaching assignments while he was gone. His first journey spanned from August 1932 to February 1933, the first two months of which were spent at the Harvard College Observatory to study the clusters of galaxies with Shapley2 and MIT to perform computations on cosmic rays. The last two months were spent at Caltech on cosmological models in the company of Richard Chace

  Letter to Jean (surname unspecified) and letter to Msgr. Ladeuze, dated 04-08-1932, AL 2   In a research project that accompanied his CRB Fellowship application before his departure to the United States in August 1932 (AL), he explicitly expressed his interest in working with Shapley. 1

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Tolman,3 professor of physical chemistry and mathematical physics. Tolman had already acquired a great reputation for his work at the interface of general relativity and thermodynamics.4 It was during this stay in Pasadena that Lemaître would have his first long and friendly discussions with Einstein, in contrast with the chilliness of their first encounter at the 1927 Solvay conference in Brussels. The two would meet yet again in May 1933. After a semester back in Louvain, he returned to the US from September 1933 to March 1934, where he was a guest professor in the department of physics of the Catholic University of America in Washington, D.C. He gave a course on the astronomical applications of relativity.5 He returned to Belgium on 15 February 1934 for two semesters during which his collaborator, Odon Godart, who had just started working under Lemaître the previous year, could at last benefit from his advisor. His opportunity was limited as Lemaître was already planning another trip. From September 1934 to June 1935, he was a guest at the prestigious School of Mathematics of the Institute of Advanced Studies of Princeton where Einstein had finally settled. He would interact extensively with Veblen about algebraic questions, and it was during this trip that the last of the ‘walking discussions’ of Lemaître with the father of the relativity took place. In 1935-1936 and 1936-1937, it was his American colleagues who reciprocated by visiting Lemaître on his home turf. He welcomed his friend Vallarta from MIT for a year6 as visiting professor under the auspices of an advanced fellowship from the American Educational

  In the research project for his CRB Fellowship (AL) Lemaître likewise expressed the desire to work with Tolman in Pasadena. 4   We refer the reader to R.C. Tolman, “On the Use of the Entropy Principle in General Relativity”, Physical Review, Vol. 35, 1930, no 7: 896-903, research performed within models of static universes with spherical symmetry (pages 901-903). 5   The Catholic University Bulletin, March 1934, p.7. 6   From September 1935 to July 1936. 3

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Foundation. It was also during this period that he also collaborated with Hugh Taylor from Princeton. These two years marked a short break before Lemaître was back on the road, this time as visiting professor in the department of mathematics of Notre Dame University in South Bend, Indiana, from February to August 1938.7 He participated in a symposium on algebra and logic alongside some of the most important names in modern algebra, such as Emil Artin, Adrian Albert, Oystein Ore, the father of the category theory Saunders Mac Lane, and finally no less than John von Neumann. On the first day of the symposium, the South Bend News-Times carried a front page photo8 of Lemaître and Professor Huntington, a logician from Harvard. During his stays in the United States, Lemaître was disconcerted to find himself the object of unexpected attention and popularity. During the fourth general assembly of the International Astronomical Union, Eddington directed the attention of journalists to Lemaître in attendance, quoting the works of the Belgian ecclesiastic9 in his 7 September 1932 lecture entitled “The Expanding Universe”. Such publicity from one of the most important astronomers of the time, propelled Lemaître into the limelight of a public attuned to the latest discoveries on the cosmos and related questions on the relationship of science and faith. From that moment on, the peregrinations of the physicist-priest would be followed closely and his views picked up by the most widely circulated newspapers in the US. Typical was the article printed by The Tower (7 December 1933) covering his stay at Catholic University: The noted Belgian priest-scientist who is a guest professor at the Catholic University for the winter semester has made a profound impression on the scientists in this country at his every appearance. Two   “Many new teachers join faculty”, Notre Dame Scholastic, 24 September 1937: 4.   Friday, 11 February 1938. Other visiting professors at Notre Dame of note from that period include Kurt Gödel and Eugene Guth from University of Vienna. 9   The Observatory, Vol. LV, November 1932, no 702: 301. 7 8

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weeks ago he spoke before the National Academy of Sciences meeting in Cambridge, Mass., and the story of his picturization of the universe was carried on front pages of the leading newspapers of the nation. It was described by one publication “as an overflowing bucket of soapsuds”, with the universe as the bucket and the individual bubbles constantly rising over the bucket as the vast collection of stars called nebulae.

Lemaître would even be consulted by President Roosevelt himself. In a letter addressed from the White House dated 24 September 1935, the President would ask him for his help in order to better understand the living conditions in the US, then in the throes of a deep economic depression.10 The second half of the 1930s brought him many formal accolades crowning a decade of work that changed the course of cosmology forever. The first major award he received was the Mendel Medal, conferred 15 January 1934,11 an award established in 1928 by the Order of the Eremite Fathers of St. Augustine, recognizing a Catholic scientist that had contributed significantly to the sciences.12 The award, which is still conferred to this day, was presented by Fr. Edward V. Stanford, President of Villanova College (now University) under the direction of the Eremite Fathers, during a gala dinner with one hundred guests. The dinner was graced with the special presence of Msgr. James H. Ryan, Rector of Catholic University. Lemaître was the first priest laureate of this medal bearing the name of the founder of genetics who was also a father of the Augustinian order. The previous year’s Mendel award   Roosevelt wrote to Lemaître: “I shall deem it a favor if you will write me about conditions in our community as you see them. Tell me where you feel our government can better serve our people.” (AL) 11   The author is grateful to Fr. Kail Ellis, O.S.A., Dean of the College of Liberal Arts and Sciences, Fr. D. Gallagher, archivist, and Dr. F.P. Maloney from Villanova University for their valuable information they have provided. 12   For the history of this prize, I refer to R.M. Churbuck, “The Drama Behind a Coin: The Mendel Medal”, The Tagastan (Publication of the Students of Augustinian College, Washington D.C.), Vol. 15, Winter 1951, no 1: 2-20. 10

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was the Princeton chemist and friend of Lemaître, Hugh Scott Taylor; Teilhard de Chardin would also be so recognized in 1937. On 17 March 1934, Lemaître received the Francqui Prize from the hands of King Leopold III of Belgium.13 A triumphal tribute was reserved for the priest during his return to Louvain; he even had to show himself at the window of his apartment in order to answer the acclamation of students from the street below. On 19 April, a solemn meeting was organized in honour of the laureate at the Salle des promotions of the Halles of Louvain.14 Lemaître, accompanied by his parents, listened to the acknowledgments and congratulations expressed by Msgr. Ladeuze who was present despite the formal warning of his doctors. Opened by the Dean of the Faculty of Science, the chemist P. Bruylants, this meeting would be remembered for its brightness and warmth, in contrast with relative indifference of some of the faculty on the occasion of his appointment as President of the Pontifical Academy of Sciences not many years later. Charles Manneback had the honor of summarizing his friend and colleague’s scientific work, after which Lemaître delivered his address beginning with a tribute to his mentors, Pasquier, Goedseels and especially Alliaume. His conclusion showed clearly that throughout the years of intense work, his faith had not been suffocated by the dramatic unfolding of scientific knowledge, nor had these developments been in vain in regard to returning glory to God (1934b: 43; translation from the original in French): I wish to take advantage of this occasion to reaffirm (to Msgr. Ladeuze) my resolution to continue with all my efforts, together with all of you, to serve science. Science is beautiful; it deserves to be loved for itself, as it is a reflection of God’s creative thought.  Cf. Foundation Francqui. VIIIe Rapport. 1er octobre 1977-30 septembre 1982 (50ème anniversaire), Bruxelles, 11 rue d’Egmont. 14   “Manifestation en l’honneur de M. le Professeur Georges Lemaître, lauréat du prix Francqui”, Annuaire de l’Université de Louvain, 1934-1936: 686-703. “Halles” is the name given, in Louvain, to the administration builiding, which previously had been a market. 13

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On 30 May, he received a Ph.D. honoris causa from McGill University as along with three other personalities, including Adélard Godbout, Minister of Agriculture of Québec. This University was one of the first institutions that he had visited during his stay on the American continent in 1924. On 10 June 1936 it was the turn of the Société Astronomique de France to recognize Lemaître with the Prix Jules Janssen, previously only awarded to Eddington (1928), Einstein (1931), Shapley (1933) and de Sitter (1934).15 Lemaître was not only honoured by his scientific colleagues. He would also be recognised by the Church that had made him “honorary canon” of the chapter of the Cathedral Saint-Rombaut in Melechen on 27 July 1935.16 He would also be honored by his native region. The ASBL (“Les Amis du Hainaut”) would award him on 4 October 1935, during their general assembly, their own prize, along with Bordet, Destrée and Rousseau, attesting that Lemaître had “truly contributed to the glory of Hainaut”17.

2. Towards a theory of large-scale structures: the Lemaître-Tolman model In his thesis at MIT, Lemaître had studied a model of the universe with spherical symmetry and whose density could vary not only in time, but also in space. This is the model that led him to conceive of an interpolation between the Einsteinian universe and that of de Sitter. His the  “Prix et médailles décernées par la société”, Bulletin de la Société Astronomique de France, 1936: 315. 16   This distinction is purely honorific, and was accorded systematically to professors of universities and of seminaries. This recognition, of which Lemaître was quite proud, allowed him to bear the title of canon and to be attired on certain solemn circumstances, choir vestments similar to that of titular canons, including the pectoral cross, and the mozetta over the rochet. A photograph preserved in the AL (published in this book) shows Canon Lemaître beside Cardinal Van Roey during one of his visit to Lemaître’s parish of Saint Henri in Brussels. 17   Letter dated 11 May 1935 addressed by the President and the Secretary of the ASBL “Les Amis du Hainaut” to the Rector of UCL (UCL Archives, copy at the AL). 15

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sis research also proved to be a kind of seed-crystal for deep intuitions concerning the formation of galaxies and their clusters. The development of a theory of structure would take form in two distinct stages. During the academic year 1931-32, Lemaître first realized that his inhomogeneous model with spherical symmetry could explain why the condensation of matter can occur in the universe. He proposed to his student, Joseph Wouters, that they would team up on this project. Curiously, this would be Lemaître’s only student who would work with him on general relativity over the entirety of his career. The conceptual outline beginning from Lemaître’s MIT thesis and his initial ideas on galaxies and structure is first found in a Communication of Wouters in the first (mathematical) section of the 28 January 1932 Société Scientifique de Bruxelles.18 Wouters’ thesis reveals that during that period, Lemaître held that the universe was already filled with a gas of stars, prior to the formation of galaxies,19 but Lemaître will show in 1934 that this hypothesis is not relevant. At this juncture, Lemaître did not appreciate that his model might provide an explanation of the existence of galactic clusters. It was his second voyage to the New World that would focus his attention on structure formation. During the second stay in the United States, Lemaître had the chance to participate in the fourth general assembly of the International Astronomical Union held at MIT, 2-9 September 1932. It so happened that a significant number of participants of the general assembly remained in Cambridge 9-10 September for a symposium related to extra-galactic objects; this sidebar meeting being comprised of three sessions. The first one was devoted to the structures of our Milky Way galaxy, the second to systems closest to ours, and the third about the “super systems” of galaxies, i.e. clusters.20   The title of the Communication was ‘Sur la formation des nébuleuses’ [Trans: ‘On the formation of nebulae’]. 19   In the abstract of Wouters’ thesis, one finds: “I will compare the universe filled with stars to a gas…” (Annuaire de l’Université de Louvain, 1931-1932: 504). 20  A.S.E., “The Fourth General Assembly of the International Astronomical Union”, The Observatory, Vol. LV, 1932, no 702: 301. 18

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The formal sessions were followed by more presentations and discussions. It was during this symposium that it dawned on Lemaître that the model developed in his thesis could provide an explanation for cluster formation. It was also very likely that Lemaître had the opportunity to work with Harlow Shapley, from the Harvard College Observatory (with whom he had interacted beginning in 1924), and to benefit from his most recent galaxy data in 1932. As Lemaître would explain to Ferdinand Gonseth in 194521: I returned to America for the meeting of the Astronomical International Union in the fall of 1932. It was at this moment that my thinking on the significance of nebulae clusters all came together.

The ideas of Lemaître on galaxies and clusters led, in 1933, to three provocative papers that can be considered the foundation of all his cosmological work.22 Indeed, these ideas would undergo no significant modification after the mid-1930’s.23 Lemaître had fixed on a certain representation of the evolution of the universe, which he would elaborate and exploit for the rest of his career,24 of which a brief synopsis follows. Lemaître derived a solution to Einstein’s equations with a cosmological constant, of an inhomogeneous universe with spherical symmetry. Generalizing what he had done in his thesis, he now presumed that the pressure of the matter that fills the universe was not necessarily isotropic.25 He then obtained what is called now a “Tolman   Letter, 21 January 1945, AL.   1933c and 1933d integrated the thesis work of Joseph Wouters while adding his ideas on clusters; 1933e represented a comprehensive synthesis of his thesis at MIT. 23   The reader may wish to compare 1933c (page 903) and 1958f (page 18). 24   Lemaître would produce a review of his ideas presented at the end of the 1930s in a manuscript which would remain unpublished for a long time (1985a), and another at the end of the 1940s (1949d). In these syntheses, the theoretical framework does not differ essentially from that of 1933e. 25   Technically, this means that he made the choice following components of the stress– energy tensor: T44=r, T11= -p, T22 = T33 = -t where the pressure p and the tension t have different values (here c =1). 21 22

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model”26 and which would be independently rediscovered several times after him.27 Tolman (1881-1948) and Lemaître discussed these issues extensively between late 1932 and January 1933 at Caltech, and Tolman subsequently had used the model of the Louvain cosmologist in order to study the effect of inhomogeneities in cosmological models, properly crediting him. Unfortunately, the Lemaître’s contributions would go long unrecognized while Tolman’s were ensconced in history.28 It was to the great merit of the Polish cosmologist Andrzej Krasinski to give the Belgian cosmologist his due, producing an English translation of the paper (1933e)29 in 1997, and proposing the model be renamed “Lemaître-Tolman”. After having obtained this very general solution30, Lemaître studied certain particular cases, the ‘quasi-static fields’31, as an example. The latter comprise the inner solution of Schwarzschild32 that he had provided in his thesis and which corresponds to the gravitational field that exists within a sphere of perfect fluid (thus, with isotropic pres  R.C. Tolman, “Effect of Inhomogeneity on Cosmological Models”, Proceeding of the National Academy of Sciences of the U.S.A., Vol. 20, 1934, pp. 169-176; published again by A. Krasinski in General Relativity and Gravitation, Vol. 29, 1997, no 7: 935943. We refer also to R.C. Tolman, Relativity, Thermodynamics and Cosmology, Oxford, Clarendon Press, 1934, pp. 250-252. Curiously Tolman did not refer to (1933c, d, e), but indeed (1931b). In his paper of 1934, he cited nevertheless (1933e). Considering the fame of Tolman’s book, this may explain one of the causes of Lemaître’s ‘oblivion’. 27   We refer the reader here to the excellent review of A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, 1997) that gives a complete panorama of these models and of the relations linking them together; also: J. Plebanski, A. Krasinski, An Introduction to General Relativity and Cosmology, Cambridge University Press, 2006: 294-366. 28   The model is sometimes called “Tolman-Bondi” in reference to the paper of H. Bondi, “Spherically Symmetrical Models in General Relativity”, Monthly Notices of the Royal Astronomical Society, Vol. 107, 1947: 410-425. 29  (1933g). 30   The metric of the Lemaître-Tolman model is: ds2 = -a2(c,t) dc2 – r2 (c,t) (dq2 + sin2q df2) + b2(c,t) dt2 such that: (c/b)2 rt2 = – c2 (1-(1/a2) rc2) + 2Gm/r + (lc2/3)r2. The subscripts of r refer to partial derivatives related to indexed variables; c and G are the speed of light and the gravitational constant; m corresponds to the mass in the sphère of radius c; l is the cosmological constant. 31   These correspond to rt = 0. 32   Whose metric is given by ds2 = -a2 (dc2 +sin2c (dq2 + sin2q df2)) +(f1-f2cosc)2 dt2 where f1 and f2 are constants. 26

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sure33) of constant density. Having found the universes of Einstein34 and de Sitter35, as specific cases of this internal solution, his interest was rekindled in the famous problem of the “Schwarzschild radius” limit, beyond which any sphere of a homogeneous fluid cannot exist, the pressure becoming infinite for this radius.36 Eddington had proposed solving this problem by using the relativistic invariant density instead of the energy density itself, but Lemaître’s MIT thesis had shown that this did not lead in a fruitful direction.37 In his 1933 work, Lemaître harkened back to an idea already in his thesis38: the apparently paradoxical character of a limiting radius supposing that the sphere was filled with a perfect fluid. It is paradoxical because if it was assumed that sphere was constituted of layers of matter which were supported by transverse stresses as it is the case for a vaulted ceiling, one may legitimately assume a constant pressure or even zero pressure everywhere in the sphere. In this case, no limiting radius exists, and spheres filled with matter, arbitrarily large, could exist in the universe. Lemaître also analyzed, in his work of 1932-1933, how the equilibrium breaking of quasi-static fields could be produced and, in particular, of the one corresponding to a static universe of Einstein. It should be noted, as pointed out by Krasinki39, that the Lemaître-Tolman model does not describe the entire class of the models   p = t.  f2 = 0 and k rc2 = 2l. Where k = 8pG/c4. We follow Lemaître, setting c =1. 35  f1 = 0 and r = 0. 36   Lemaître gave a  presentation at the “first section” of the “Societé Scientifique de Bruxelles”, 30-01-1930 entitled: “Sur le Paradoxe de Schwarzchild”. The pressure is given by p = r f2 cosc/(f1-f2cosc). c = 0 corresponds to the center and one can see that f1=f2 coincides with an infinite pressure in the center. 37   Lemaître provides numerical results to Eddington’s problem in this work and proposes an interpretation of it. The pressure at the centre of the fluid of constant invariant density remains finite at the limiting radius. This is so, because if one increases the central pressure, the radius of the sphere grows, which increases the energy of the matter compensating for the increase of the pressure, and thus preventing the latter from tending towards infinity. 38   Preserved at AL. 39   Krasinski, “Editor’s Note: The Expanding Universe by the Abbé Georges Lemaître”, General Relativity and Gravitation, Vol. 29, 1997, no 5: 637-640 and “Early Inhomogeneous Cosmological Models in Einstein’s Theory” in Modern Cosmology in Retrospect 33 34

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of inhomogeneous universes with spherical symmetry. For example, Datt40 has shown that a model exists of a spherically symmetric universe with zero cosmological constant and pressure, which can not be obtained from the Lemaître model. It also seems, according to Ellis, that in 1917, de Sitter had already written the equations of the Lemaître-Tolman model, but without solving them41. Lemaître’s style of working is also revealing. He pursued ideas that interested him without paying much attention to the existing literature or to other groups that might be working on the same topics. Consequently, he was oblivious to the work going on in the school of De Donder in Brussels, concerning the general relativistic description of an electron within a spherically symmetric field42. This work, along with that of Lemaître, had been the subject of a 1930 paper by de Donder himself, in a special volume published on the occasion of the Centennial of Belgium’s Independence43. The interest of the contributions (1933c, d, e) from the cosmological point of view was precisely that Lemaître was tackling the problem of condensations in an expanding universe. Such a condensation can be represented naturally as a particular solution of his spherical and inhomogeneous model when pressure and tension disappear44. (B. Bertotti, R. Balbinot, S. Bergia, A Messina, Eds.), Cambridge University Press, 1990: 115-127. 40   B. Datt, “Uber eine Klasse von Lösungen der Gravitationsgleichungen der Relativi­ tät”, Zeitschrift für Physik, 1938, t. 108: 314. The class of models studied by Datt can be generated by considering rc = 0. As noticed by Krasinski, if one assumes that, in the Lemaître-Tolman model, one gets a singular global metric. The Datt models cannot be obtained as a natural limit of the one of Lemaître-Tolman models. 41   Krasinski, “Early Inhomogeneous…” (Discussion), p. 127. 42   M. Nuyens, Études synthétiques des champs massiques à symétrie sphérique, Brussels, Castraigne, 1925. In this study, the author drew on a method developed in 1924 by Henri Janne from the University of Liège. The latter took part in the jury that evaluated ‘La Physique d’Einstein’ of Lemaître. Cf. also M. Nuyens, “L’électron à tension internes” dissertation presented 2-04-1927 at the class of sciences of the Académie Royale de Belgique, mémoire no 1366. 43   Th. De Donder, “La physique. B. Physique mathématique” in La Patrie Belge, Bruxelles, Les editions illustrées du “Soir”, 1930: 333-335. 44   p = t = 0. Then, the metric is written ds2 = – (rc)2 dc2/f(c)2 – r2 (dq2 + sin2q df2) + c2 dt2 such that (rt)2 = – c2 (l-f(c)2) + 2Gm/r + (lc2 /3) r2 and f (c) = (1/a) rc.

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Lemaître represented the condensations of dusts in the universe as concentric spherical layers of different density that do not interact with one another. As his model related to inhomogeneous fields with spherical symmetry, he observed that each material layer is described by an equation that looks formally like the Friedmann equation, called the Lemaître-Tolman equation45. The latter can be integrated with the Weierstrass’ elliptic functions.46 The Lemaître-Tolman equation reproduces, in a  specific case, the equation of Friedmann describing homogeneous and isotropic universes, mentioned previously47. The latter led Lemaître and his student Wouters to observe that the Lemaître-Tolman equation can describe situations where each spherical layer evolves independently, like different homogeneous and isotropic universes.48 In particular, the equation describes a situation where a spherical condensation is localized within a spherical homogeneous and isotropic universe, expanding without limit in time. This condensation, after expanding, then contracts increasing the local matter density. Between the contracting zone and the rest of the expanding universe, there is a limit that remains in equilibrium, as the case of Einstein’s static universe. Lemaître hypothesized that the zone of contraction corresponds to a galaxy in formation. After the Cambridge conference, Lemaître would identify the equilibrium zone as   Specifically the equation (rt)2 = -c2 sin2c + 2Gm/r + (lc2 /3) r2 obtained by putting f = cosc in the equation of the previous footnote. Lemaître termed this the “Friedmann equation” (equation 8.21 of (1933e), cf. pages 23 and 24-27), even though the equation is more general that those described in homogeneous and isotropic models. 46   The equation of his model equivalent to the one of Friedmann can be written: dp(u)/ du = -2 ((p(u) – e1)(p(u) – e2)(p(u) – e3))1/2 that defines the function p of Weierstrass. This function that allows the parameterization of elliptic curves, plays an important role in the context of the proof of the last Fermat-Wiles theorem. 47   One can find this equation by putting r = R sinc and m = M sin3c where M is a constant. By setting c = 0, one obtains the Euclidean universe, and for imaginary values of this variable, the hyperbolic universes. Lemaître however was interested only in spherical universes (c real). 48   If one take for instance r = R sin4c as in (1958f: 18), one sees that according to the values of the variable c that defines the concentric layers, these behave like Friedmann-Lemaître spaces but evolving differently. The Tolman-Lemaître model allows for a patchwork of homogeneous and isotropic universes with distinct temporal evolutions. 45

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the characteristic limit of a cluster of galaxies. During his stay in the United States, Lemaître would have the chance to meet Hubble and compare his theoretical predictions related to clusters with the observations that the latter had made with Humason, on eight clusters of galaxies and in particular on the Coma cluster. This comparison confirmed his intuition49: The first calculations of the theoretical mass of nebulae, in excellent harmony with the data of Hubble, were done in his office with his data for the Coma Cluster.

In 1934, a study of Shapley’s data50 conducted on 25 clusters provided yet further confirmation of his hypothesis (1934a). It was also during this year that he became aware that stars could not have formed before galaxies. Essentially, by comparing the gravitational energy of the distribution of matter in a galaxy to that of the sum of its stars, one concludes that the stars would lose a non-negligible percentage of their gravitational energy while entering the cluster; this would pose several difficulties. On the other hand, supposing the initial matter to be only dust, it is possible to explain how gravitational energy would be lost as the galaxy formed, by inelastic collisions transforming gravitational energy into heat, and progressively leading to the formation of stars. This description of the formation of galaxies and their clusters could be introduced in a consistent way in his “hesitating universe” model. The universe is a spherical space, therefore finite but without boundary. During its first expanding phase, it contains only dust. The stars, galaxies and clusters are formed by statistical fluctuations during the transition to the quasi-static phase where the universe resembles an Einsteinian universe. The clusters are in fact the “fossils” of   Letter to Gonseth, 21-01-1945 (translated from the original in French).   H. Shapley, “Luminosity Distribution and Average Density of Matter in Twenty-Five Groups of Galaxies”, Proceedings of the National Academy of Sciences, Vol. 19, 1933, no 6: 591-596. 49 50

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this quasi-static epoch in cosmological history. According to his previous ideas, one can establish a link between the restart of the expansion during a third characteristic moment of the hesitating universe, and the stagnation of matter associated with its condensation in an unstable universe similar to that of Einstein. One can thus easily fathom that the longer this quasi-stable phase lasts, the larger the number of clusters will be formed. But this is a number than could be estimated by observation, and which ultimately enabled Lemaître to estimate the duration of the expansion of the universe to be approximately 5.6 billion years. Lemaître would further develop his ideas of galaxies and clusters after the Second World War by incorporating the proper motion of galaxies in the cluster, which was not reckoned with here. However Lemaître’s work would not gain much traction, in part because most cosmologists at that time preferred to work on homogeneous spaces, and with Einstein, were rejecting models with non-zero cosmological constant.

3. A peek inside the black hole The homogeneous and isotropic universes of Friedmann-Lemaître involves models that are characterized by initial singularities: zero radius at zero time. But this appeared to be in contradiction with the existence of a minimal radius conceived by Schwarzschild’s exterior solution describing the static gravitational field with spherical symmetry which exists outside of a point mass m. One can readily show that at a radius r = 2Gm/c2 from the field source, the corresponding metric of this solution becomes singular. This crucial problem was in fact the object of vigorous discussion at the Collège de France in April 1922 on the occasion of Einstein’s visit.51   Cf. J. Eisenstaedt, “Histoire et singularité de la solution de Schwarzschild (19151923)”, Archive for History of Exact Sciences, Vol. 27, 1982: 157-198. 51

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Lemaître’s thesis at MIT had drawn attention to the problem of the limiting radius of Schwarzschild’s interior solution. On the other hand, his work on de Sitter space had demonstrated that some singularities that appear in the solutions of general relativity may simply be due to a particular choice of coordinates. He therefore undertook to demonstrate (in 1933e), that the above-mentioned limiting radius is in fact one such example of a fictious singularity. After having shown how the Schwarzschild external solution can be derived from his inhomogeneous model with spherical symmetry, he found a change of coordinates that made the singularity disappear.52 Put in other terms, there was physically no obstacle to approaching the source of the gravitational field even down to a distance smaller that the “Schwarzschild’s radius”, i.e. the radius corresponding to the singularity. Lemaître’s coordinates arose naturally from his derivation of the Schwarzschild metric from the Lemaître-Tolman model, which shows once again, the Tolman’s role in promoting awareness and appreciation of Lemaître’s contributions. Finally, it should be noted that the origin r = 0 represents a true singularity of the gravitational field that cannot be eliminated by a simple change of coordinates. This singularity belongs to the very structure of the space-time being considered.53 This was an extremely consequential result as it constituted one of the paths towards a theory of black holes, as such singularities are popularly termed. The singular Schwarzschild radius represents in fact a “horizon”. When a star of mass m collapses on itself after having burned all of its thermonuclear fuel, if its radius becomes less than its gravitational horizon, r = 2Gm/c2, no observer would ever be able to see it thereafter. No signal, no information at all, emitted from inside the horizon could be detected outside.   In Lemaître’s coordinates, the metric is written: ds2 = - 2m dc2/r - r2 (dq2 + sin2q df2) + dt2 (here c = G = 1). 53   On the problem of the singularities in cosmology, I refer to the beautiful book of John Earman, Bangs, Crunches, Whimpers, and Shrieks. Singularities and Acausalities in Relativistic Spacetimes, Oxford University Press, 1995.

52

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Prior to Lemaître, Eddington54 had already transformed the exterior metric of Schwarzschild into a non-singular metric, but had not realized its importance. His coordinate transformation would be rediscovered and generalized by Finkelstein in 1958.55 Nevertheless, as would be demonstrated by Synge in 1950, and independently yet again by Fronsdal in 1959, the system of coordinates used by Lemaître and Eddington represented a map that only covered half of the space-time of Schwarzschild’s56 metric. In 1960, Kruskal57 and Szekeres58 came up with a coordinate system allowing them to extend the domain of the Lemaître-Eddington-Finkelstein solution to the total geometrical space described by the Schwarzschild space-time. This would be the basis of a method of analytical continuation of spacetime domains developed by Walker and later by Penrose and Carter. A simple analogy is in order. To describe the terrestrial globe, one needs at least two geographical maps because its surface cannot be spread out on a plane without tearing it. Synge and Fronsdal would be like cartographers who showed that the map used to describe the ancient world had to be extended as the geographical reality it describes is larger than the one shown. Kruskal, Szekeres, Penrose, Carter and Walker then provided the actual way of constructing good coordinates and maps allowing the entire Earth to be covered.

 Eddington, “A Comparison of Whitehead’s and Einstein’s Formulae”, Nature, Vol. 113, 1924: 192. According to Eisenstaedt (op. cit.: 195), Paul Painlevé may have done work similar to Eddington’s, but would not have been aware of the interest in the regularized metric. 55   D. Finkelstein, The Physical Review, Vol. 110, 1958: 965. The metrics of Finkelstein are based on the coordinates that describe the geodesics of photons that move towards the centre or outside of the field source. The Eddington metrics only considered photons moving one way, i.e. those falling towards the field source. 56   I refer here to the class of Professor Jacques Demaret, Introduction à la géometrie riemannienne et à la théorie de la relativité générale, chap. 5, University of Liège, Unpublished; cf. also W. Rindler, Essential Relativity. Special, General and Cosmological, Berlin, Springer-Verlag, 1977 (1969): 150. Cf. also: R. Penrose, Cycle of Time. An Extraordinary New View of the Universe, London, The Bodley Head, 2010: 106-121. 57   M.D. Kruskal, The Physical Review, Vol. 119, 1960, p. 1743. 58   G. Szekeres, Publ. Math. Debrecen, Vol. 7, 1960: 285. 54

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The paper (1933e) also contained the answer to a problem Einstein posed to Lemaître. In January 1933, at the end of his second visit to the US, Lemaître was at Caltech when Einstein arrived after a long journey due to his exile from Germany. On 11 January, the father of relativity would attend the seminar on cosmic rays that Lemaître was giving at the Mount Wilson Observatory. Einstein should have given a seminar of theoretical physics held at Norman Bridge Laboratory the previous evening; nevertheless, he would not go and the seminar had to be called off. Why? In fact the answer was made public by the press who had been tracing every movement and even the slightest actions of Einstein59: Shortly before dinner tonight [Jan.10], Dr. Einstein and Father Georges Lemaître, the Belgian physicist, strolled about the Athenaeum60 grounds, the serious expressions on their faces indicating that they were debating the present state of cosmic affairs.

In fact, as Lemaître would himself reveal (1958d: 129-130; translation from the original in French): I met again with Einstein (…) in California, at the Athenaeum in Pasadena. Speaking of his doubts concerning the inevitability, under certain conditions of the singularity (the zero value of the spatial radius), Einstein proposed a very simplified model of the universe for which I had no difficulty in calculating the energy tensor. This episode revealed a lot to me about his way of thinking and dealing with uncertainties by deciding to follow specific well-chosen cases. He concluded that the loophole of which he had thought did not work out.

  “Einstein Relaxes for Day. Father of the Relativity Lolls in Sun at Caltech as Wife Goes Shopping for California Oranges”, L.A. Times, January 11, 1933 (by a Times staff correspondent). 60   The Athenaeum is the official guest house of the California Institute of Technology where Lemaître, Einstein and his spouse Elsa were staying. 59

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What was this loophole? Einstein had rederived a solution of his equations corresponding to a ‘Phoenix universe’ without a cosmological constant in 1931.61 This kind of universe expands and contracts periodically in a manner of a cycloid, each evolutionary period being bracketed by two singularities, where the radius of the universe goes to zero.62 Einstein was not happy about these kinds of singularities where the matter density becomes infinite and where the usual laws of physics lose all meaning. He was thus looking for situations described by his general theory that made it possible to avoid the radius of the universe going to zero. He thought that the singularities might come from the assumption of isotropy in the Friedmann-Lemaître models and suggested to the Abbé that the singularity might disappear in anisotropic models63. Lemaître then undertook to solve the Einstein equations in the context of a simple anisotropic and homogeneous model nowadays known as the Bianchi I64, to see if one could “blunt the tip of the cycloid” of Einstein’s model, by anisotropic effects. Alas, the attempt failed; anisotropic effects did not prevent the universe from passing through a state of zero volume. The “Phoenix” can rebound again and again without any problem. The importance of this result would only be appreciated later, when Hawking and Penrose would derive general theorems on the in-

 A. Einstein, “Zum Kosmologischen Problemem der Allgemeinen Relativitätstheorie”, Preussiche Akademie der Wissenschaften. Sitzungsberichte, 1931: 235-237. 62   These singularities would nowadays be termed as the “Big Bang” and “Big Crunch”. 63   An anisotropic solution of the Einstein equations had been studied at the beginning of 1920 by E. Kasner, “Geometrical Theorems on Einstein’s Cosmological Equation”, American Journal of Physics, Vol. 43, 1921: 217-221, but treated it as a purely mathematical solution without cosmological implications. 64   The metrics obtained by Lemaître are of the type: ds2 = - c2dt 2 + A(t)2dx2 + B(t)2dy2 + C(t)2dz2. To obtain the solution of Kasner, one must choose A(t) = t2p1, B(t) = t2p2, and C(t) = t2p3 where the sum of the pi’s and the sum of their squares equal to 1, one of the pi’s being negative. In anisotropic models, the universe can become singular either while contracting in one spatial direction and expanding in the other two (pancake singularity), or contracting in two spatial directions and expanding in the other (cigar singularity). At the end of the 1930’s, Lemaître was very familiar with this kind of behaviour (1985a: 27-30) through the works of Tolman. 61

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evitable existence of singularities in certain cosmological models65. Penrose also proposed a principle of “cosmic censorship” banning the presence of “naked singularities” in models of space-time, i.e. singularities not “hidden” by a horizon of the type that appears in the Schwarzschild field66. Thus Lemaître’s study concerning both the characterization of Schwarzschild’s horizon and the inevitability of the singularity in the Phoenix model can be considered as one of the pioneering works that paved the way for the subsequent fruitful explorations of Hawking and Penrose. It is clear that Lemaître was aware that situations where the radius of the universe goes to zero marked a limit to the applicability of general relativity. Effectively, according to Lemaître, the force between elementary particles, “ultimate” as he called them, might arrest the complete contraction of the universe. Using the value of the number of protons in the universe suggested by Eddington of 1078, and assuming that one particle could not approach another within a distance of 10-12 cm, he calculated that the universe could not go below a value of 10(78/3)-12 = 1014 cm, or equivalently ten times the radius of the earth’s orbit around the sun. He then concluded that (1933e: 37; translation from the original in French): […] only subatomic nuclear forces seem able to stop the contraction of the universe, when the radius of space is reduced to the dimensions of the solar system.

One can immediately see the conundrum this simple calculation posed for Lemaître. The presumed incompressibility of nuclear matter would result in the final state of the universe being a sphere of fi  S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge, University Press, 1973: 256-298; S. Hawking, R. Penrose, The Nature of Space and Time, Princeton University Press, 1996. 66   One meets such situations with the Kerr-Newman metrics that describe gravitational and electromagnetic fields of massive bodies that are electrically charged and rotating (cf. A. Krasinki, Inhomogeneous Cosmological Models, op. cit.: 197). 65

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nite radius, not unlike the ‘polyneutron’ of the Gamow school, except that it would be constituted of protons. This is in sharp contrast with his conception of the primeval atom which implied a true initial singularity of the universe, i.e. an initial state of radius zero. And this explains why the concept of the primeval atom remained somewhat fuzzy all throughout Lemaître’s life. Furthermore, Lemaître dismissed the Phoenix model according the following argument (1933e: 37; translated from the original in French): From a cosmological point of view, the zero of space must be treated like a beginning, in the sense that each previously existing astronomical structure would have been destroyed there. The time of this beginning, or if one wishes, of this re-beginning, must certainly date before the formation of the terrestrial crust and the organization of the solar system, i.e. a strict lower limit of 1.6 x 109 years from the present measured radioactivity of rocks.

But Einstein’s cycloidal model led to a lower limit of the duration of the expansion phase of the universe, to which Lemaître would conclude wistfully: From the aesthetic point of view, it [the failure of the cycloidal model] is unfortunate. Such a solution, where the universe repeatedly expands and contracts to an ‘atom’ the dimension of the solar system, had an irresistible poetic charm, reminiscent of the Phoenix of legend.

In the popular scientific literature, Lemaître’s contributions to cosmology are most often restricted to his first major paper (1927c). Hopefully the scientific community will come to recognize the fresh originality of his works in 1932-1933. Lemaître introduced the major concepts that are the very fabric of cosmology today: singularities (the Big Bang, Big Crunch), his theorem on the inevitability of singularities, the concept of an event horizon, inhomogeneous and anisotropic models.

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4. The defence of the “little lamb” One of the topics of discussion and a source of controversy between Einstein and Lemaître during his stay in Pasadena concerned the famous cosmological constant, previously mentioned. Years later, Lemaître would remember (1958d: 130; translated from the original in French): I had during this period several conversations with Einstein, generally while walking, and almost always, then as later, about the cosmological lambda that he had brilliantly introduced into his equation, but which he was never happy with and furthermore tried to remove. Some journalists overheard that we were talking about the little lambda, that they amusingly renamed the “little lamb”, which supposedly followed us on all our processions.

This controversy in fact would continue at Princeton in 1935, even to the late 1940’s, on the occasion of the preparation of a paper by Lemaître that he had prepared for a testimonial book in honor of the father of Relativity edited by Paul Arthur Schilpp (1949g). Einstein had introduced the cosmological constant into his equations to obtain his spherical static universe67. As soon as the idea of the universe’s expansion became widely accepted, however, he renounced the cosmological constant. As recounted by Abraham Pais, Einstein divulged his mind on the topic to Hermann Weyl in 1923 on a postcard, in which he wrote68: “If there is no quasi-static world, then away with the cosmological term.” With de Sitter, in 1932, Einstein would show that one can obtain a Euclidean universe of zero pressure and cosmological constant even with expansion, which would reinforce   If one abandons the cosmological constant in this case, one can only find a solution of the Friedmann-Lemaître equations by assuming negative pressure. 68  A. Pais, Subtle is the Lord…The Science and the Life of Albert Einstein, Oxford University Press, 1982, quoted by S. Weinberg, ‘The Cosmological Constant Problem’, Review of Modern Physics, Vol. 61, 1989, no 1: 2. 67

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Einstein’s intention to definitively jettison the cosmological constant. Einstein regarded the introduction of a term containing the cosmological constant in his gravitational equation was contrary to a ‘principle of logical simplicity’ of formalism of which he was convinced without being able to articulate why.69 For Lemaître, the notion of ‘simplicity’ is a relative question as one can easily suppose that the most general form of Einstein’s equations of gravitation, containing the cosmological constant, is of such evident simplicity since it could be deduced from some simple principles.70 Eddington insisted on preserving the constant because he saw in it a fundamental constant71 of physics bridging quantum mechanics and general relativity. On his part, Lemaître maintained three motives for adhering to the “little lamb”.72 First of all, the constant is required for the self-consistency of relativity. The identification of energy with mass is at the very heart of the theory. But energy is only defined up to an arbitrary constant, providing a merely conventional reference from which one measures, while mass cannot possess such a constant. It is thus necessary, for the formalism to be consistent, that there exists a way of compensating for the effect of an arbitrary choice of the energy constant, and this is the cosmological constant. Einstein’s rejoinder to Lemaître was that as energy is identified with inertial mass, there is no need for any such compensation73. In fact, in 1947 Lemaître would acknowledge74 that his argument was adequate only because he had assumed that matter or energy   Letter to Lemaître dated 26-09-1947 (AL): “ I found it very ugly indeed that the field law of gravitation should be composed of two logically independent terms which are connected by addition. About the justification of such feelings concerning logical simplicity, it is difficult to argue. I cannot help but feel it strongly and I am unable to believe that such an ugly thing should be realized [in nature].” 70   Observation in a letter to Einstein dated 3-10-1947 (AL). 71   In fact, Eddington insisted on keeping the value of the cosmological constant corresponding to Einstein’s static universe. 72   Elaborated in a letter to Einstein of 30-07-1947 (AL), and in (1949g). The first reason appeared in (1934a: 12). 73   Letter 26-09-1947, op. cit. 74   Letter 3-10-1947, op. cit. 69

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were conserved, which was not the case in general relativity. However in 194975, he would return to defending his line of reasoning. Furthermore, the constant allows one to arbitrarily lengthen the quasi-static phase of the oscillating universe, permitting the age of the universe to exceed the limits provided by the radioisotope dating of the oldest rocks on earth. Even in 1949, Lemaître’s estimate for the duration of the expansion of the universe, based on the measured Hubble constant of that time, was a mere 1.72 billion years, still too close to the age of the rocks (1949g: 446). The universe needed to be a little older, and the only way to do so, according to Lemaître, was to introduce a positive value for the cosmological constant. Lemaître interpreted the (positive) cosmological constant as a sort of repulsive force counterbalancing the gravitational force at large distance scales,76 with the Einsteinian static universe corresponding to the case of perfect equilibrium between them. Such an equilibrium however, is unstable but precisely such an instability would enable the condensations required for the formation of galaxies and clusters. Thus, for Lemaître the cosmological constant appeared deus ex machina to provide for the theory of structure! What should we think of all this nowadays? One knows that the value of the cosmological constant can only be positive77 and very small; otherwise its effects would have been readily observed centuries before, for example on the orbit of planets. For some while, it was thought that the cosmological constant should have been strictly zero. This could in fact be reconciled quite naturally with the predictions of the Theory of Inflation78 introduced to resolve a conundrum of the Big Bang theory: the “problem of the horizon”.   (1949g: 443-444).   From Friedmann’s equation we get: (dR/dt)2 = - h + 2Gm/R + (lc2/3)R2 where h is a constant. The term involving 1/R can be interpreted as a gravitational potential and the term containing R2 as the potential of a repulsive force. 77  If it were negative, it would contribute to the attractive effect of gravity and the universe would quickly collapse, which has not been observed. 78   P. Coles, F. Lucchin, Cosmology. The Origin and Evolution of Cosmic Structure, New York, Wiley, 1995: 118-156; I. Moss, Quantum Theory, Black Holes and Inflation, New York, Wiley, 1996: 99-112. 75 76

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As information cannot propagate faster than the speed of light, our knowledge of the universe is limited to what lies within a spherical frontier, the “horizon”, whose radius grows in time. One can show that, going back in time, the radius of the horizon decreases faster than that of the universe, and, thus at one point the radius of the universe exceeds the horizon. Early in its history therefore, there would be regions of the universe that could not yet have been in communication (i.e. were “causally disconnected”) and thus could not have exchanged energy or matter required to make the universe globally homogeneous. It was thus quite unexpected that the cosmic microwave background discovered in 1964 displayed such homogeneity and isotropy of the universe79. Our best solution to this puzzle posits that a small homogeneous patch of the universe for a very brief interval expanded in a superluminal way (“inflated”), the observable universe being just that patch. Just as with a sphere whose radius became extremely large, and for which any small neighborhood would look like a plane, our observable universe became almost exactly Euclidean. If the Theory of Inflation is correct, therefore, sophisticated measurements would show that its geometry is ‘flat’ – which exactly is what is observed. In Friedmann-Lemaître models, a Euclidian (‘flat’) universe is one whose total energy density (both the energy associated with matter and with space itself, the so-called ‘vacuum energy’) is equal to a certain critical density. If the density exceeds the critical density, the geometry of the universe is spherical, corresponding to a ‘closed’ universe; if the density is less than the critical density, the geometry is hyperbolic, and the universe is ‘open’.80 If the cosmological constant is   One could assume that this homogeneity had been absolutely perfect since the beginning, but astrophysicists do not like such hypotheses, as they require an initial condition which is “too” particular; what is called in the parlance “fine tuning”. 80   What is determined absolutely from the equations of the Friedmann-Lemaître Models are the parameters of total density: W0= WM+Wl = (r/rcr)0 such as WM = kc2(r0c2)/3H02 and Wl = lc2/3H02 and W0= 1+ (kc2/H02R02). The subscripts ‘0’ refer to present values. H = (dR/dt)/R is the Hubble constant, k = 8pG/c4, r the density, rcr = 3H2/8pG the critical density. For k = 1,0,-1 we have universes which are spherical, Euclidian and 79

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zero, matter energy determines the geometry, depending on whether it is above or below critical density, and by how much. To date, astronomers have been unable to find enough ordinary visible matter81 or dark matter82 to account for critical density and explain the observed flatness of the universe, nor have physicists succeeded in discovering more exotic (non-baryonic) dark matter;83 motivating a non-zero cosmological constant, or some other form of vacuum energy to make up the deficit.84 In 1967, Yakov Zeldovich demonstrated that the cosmological constant can be interpreted as a contribution to the energy of the quantum vacuum, a fundamental and irreducible positive energy density, due to the continual production and annihilation of virtual particles.85 As Nobel laureate Steven Weinberg86 observed, Zeldovich’s was led to consider the origin of the cosmological constant by pondering several attempts to explain why a significant number of quasars, first discovered in the 1960’s, all had the same redshift.87 As mentioned previously, such a phenomenon could be effected within Lemaître’s hesitating universe in conjunction with a positive cosmological conhyperbolic respectively. If k = 0, then W0=1 and r0 = (rcr)0. For H0 = 60 km/s/Mpc, one obtains (rcr)0 = 6 x 10-30 g/cm3 corresponding to a little more than 3 atoms of hydrogen in a volume of 1000 litres. 81   Specifically visible baryonic matter, i.e. anything formed of protons and neutrons that constitute the nuclei of ordinary matter. 82   Non-luminous baryonic matter, i.e. objects such as brown dwarfs, or cold gas clouds. 83   It seems well established now that there must be exotic dark matter whose density exceeds that of ordinary matter in the universe by a factor of 6 or 7. Some well-motivated particle candidates exist arising from theoretical extensions of the Standard Model of particle physics, the so-called WIMP and axion being among them. 84   This contribution is characterized by Wl. 85   Quantum theory predicts that particles are continually created and annihilated according to the Heisenberg uncertainty principle. A manifestation of such vacuum fluctuations is the Casimir effect. Quantum mechanically particles correspond to waves, each with its own wavelength. Between two metallic plates which are extremely close together, the spectrum of virtual particles with wavelengths greater than the separation is suppressed, whereas the spectrum outside the plates suffers no such suppression. This leads to a tiny but measurable imbalance of force of the plates, tending to push them together. 86   S. Weinberg, op. cit.: 3. 87   Cf. Chapter VI.

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stant. It was then natural that Zeldovich worked on a possible explanation of the non-zero value of the little lambda. Unfortunately, Zeldovich’s calculation would show that the total contribution of all virtual particles leads to an extremely large energy for the vacuum, astronomically higher than the upper limit allowed for the cosmological constant. A conventional field theoretical approach to l appeared stymied. The original ideas of Lemaître are today quite consonant with the situation in modern cosmology. In 1998-99 groups from Berkeley and Harvard published convincing evidence that the universe was not only expanding, but accelerating; both teams had employed Type-Ia supernovae to extend the Hubble plot more than half-way back to the Big Bang.88 These observations are consistent, and in fact require, a positive cosmological constant or more general vacuum energy.89 Moreover, these observations determine the total energy density of the universe to be close to the critical density; the matter and vacuum energy contributing respectively 30% and 70% (in rough numbers) to this total density. There are several theoretical frameworks that may explain why the value of the cosmological constant or vacuum energy, can be so small, but non-zero. Peebles, for example,90 predicts that the cosmological constant should diminish as the universe expands.91 More ambitious supernovae surveys will soon determine whether the cosmic acceleration is due to a simple cosmological constant, or a more   A supernova is a star whose life ends with a spectacular explosion: the energy released in this process is, in a few months, equivalent to that produced by the Sun during a hundred million years. 89   The reader is referred to the excellent synthesis of the theoretical and observational results made by Elisa Di Pietro from the Institute of Astrophysics of the University of Liège: ‘Les Supernovae au secours des cosmologistes’, Revue des Questions Scientifiques, t. 169, 1998, no 4: 367-402. 90   P.J.E. Peebles, Principles of Physical Cosmology, Princeton University Press, 1993; P.J.E. Peeble, D. Schramm, E. Turner, R. Kron, “L’évolution de l’univers”, Pour la scien­ce, Décembre 1994 and P.J.E. Peebles, “Evolution of the Cosmological Constant”, Nature, Vol. 398, 4 March 1999: 25-26. 91  For example C. Hogan, R. Kirshner, N. Suntzeff, “Des supernovae pour sonder l’espace-temps”, L. Krauss, “L’antigravité” in the issue: “La revolution cosmologique”, Pour la Science, mars 1999: 35-49. 88

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dynamical form of vacuum energy. Even if this new data shows that Lemaître was not wrong in defending the cosmological constant, it should be borne in mind that the universe as we know it today corresponds to a very high degree to a Euclidean geometry rather than the elliptical space with which he seemed infatuated.92 The progress of modern astrophysics and cosmology nothwithstanding, the most impressive lesson however, is how much these earliest notions from the 1930s retain such currency, and that the “little lamb” can still be seen accompanying astrophysicists on their promenades today!

  It should be noted that the equations of the Friedmann-Lemaître models admit as solutions Euclidean universes with a positive cosmological constant whose expansion follows a curve similar to that of the hesitating universe of Lemaître. 92

Chapter IX

Science and faith: the theory of the two paths (1924–1936)

1. The origin of the “two paths”: a tripartite influence

W

e have seen how strongly Lemaître’s scientific life was influenced by Eddington. His fundamental works in general relativity and cosmology were all more or less reactions to Eddington’s claims. Similarly Lemaître was in all likelihood deeply impressed by the way the Cambridge astronomer lived a profound synthesis between his deep faith and Quaker commitments, and his extraordi­narily productive scientific life. According to Eddington, through an analysis of the implicit presuppositions of a physicist’s work, one can get a sense not only of the mathematical world, but also of a spiritual world properly so called. This thought was rooted in the structuring of the discourse of physics in the conceptual cycles that have already been mentioned above1. When a physicist tries to define a notion, he needs to refer to concepts that already exist previously, thus all terms are defined by defining one another without being able to arrive at any ultimate foundation of knowledge. Thus, to define gravitational force in relativity, one refers to potentials that are themselves defined in relation to a metric that is used to calculate intervals between events. Yet, the latter can only be defined operationally with measuring sticks or clocks that are pieces   Cf. Ch. V. and A.S. Eddington, The Nature of the Physical World, Cambridge University Press, 1928: 260-265. 1

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of matter. But, what is matter? One can only define it in physics by referring to interactions and therefore, to notion of force. According to Eddington, to go beyond the conceptual cycles and find a firm foundation for a true knowledge of things, one is ultimately forced to acknowledge a knowing subject, to an intelligence. Therefore, the Cambridge astronomer demonstrates that the foundation of physics is not accessible to physics, which is held hostage to conceptual cycles, but only to a spiritual nature. Individual human minds are themselves but one element of a more general spiritual reality. Borrowing the thought and turn of phrase of the English mathematician William Kingdon Clifford (1845-1879),2 often quoted in his books3, Eddington posits the foundation of all reality and all universes to be “mind-stuff”, or “spiritual substance”: The mind-stuff is the aggregation of relations and relata that form the building material for the physical world. Our account of the building process shows, however, that much that is implied in the relations is dropped as unserviceable for the required building. Our view is practically that urged in 1875 by W. K. Clifford.

As pointed out by Luciano Boi, in a seminal work dedicated to the mathematical problem of space4, we are here in the presence of a sort of materialist monism where physical reality and its representation in our mind are merely two faces of the same fundamental spiritual reality. Eddington could not endorse Clifford’s materialism, but he retained the idea of the unity between spiritual and material dimen  Cf. E. Bréhier (1932) [1981] Histoire de la philosophie. III/XIX-XX siècle. Paris/ Quadrige/P.U.F: 808-810; W.K. Clifford, Mathematical Papers (R. Tucker, ed.), New York, Chelsea Publishing Company, 1968 (Reprint after the edition of 1882 with an introduction by H.J. Stephen Smith). 3   For instance, in Space, Time and Gravitation (Cambridge University Press, 1921: 77, 152, 192) or in The Philosophy of Physical Science (Cambridge University Press, 1939: 4). The quotation can be found in The Nature of Physical World, Cambridge University Press, 1928: 278. 4   L. Boi, Le problème mathématique de l’espace. Une quête de l’intelligible, Berlin, Springer, 1995: 423-431. 2

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sions that does not blur their distinction. Moreover, the highlight of this spiritual dimension in the basis of human experience constitutes the foundation of religious experience5: It is in this background that our own mental consciousness lies; and here, if anywhere, we may find a Power greater than, but akin to, consciousness.

Lemaître would inherit from Eddington the manner of scrupulously respecting the distinction between the order of the physical, natural, material reality and that of the spiritual reality, which is experienced in the depths of human consciousness. Yet, for Eddington, as Lemaître, this distinction could never correspond to a separation. There was a deep unity, but which could not be apprehended via the scientific perspective. Lemaître, like his Cambridge professor, considered that the scrupulous distinction between the material and spiritual dimensions helped protect the transcendence against a sort of reduction which is completely antithetical to religiousness. Lemaître used to quip6: “I have too much respect for God to make Him a scientific hypothesis”.7 One can find this respect in Eddington, who similarly did not fail to underline the danger of reducing theology to mathematics8: And yet if the scientist were to repent and admit that it was necessary to include among the agents controlling the stars and the electrons an omnipresent spirit to whom we trace the sacred things of consciousness, would there not be even graver apprehension? We should suspect an intention to reduce God to a system of differential equations,   The Nature of the Physical World, op. cit.: 282.   Communication with A. Caupain (22-03-1995). 7   During a conference on cosmology given by Lemaître in Louvain, a nun attempted a reconciliation between what Lemaître just said and a statement about God. Lemaître, visibly embarrassed, finally answered her: “Your God is certainly not my God!” (oral communication. M. Xavier de Maere, 12-07-1997). 8   The Nature of the Physical World, op. cit.: 281-282. 5 6

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like other agents which at various times have been introduced to restore order in the physical scheme. That fiasco at any rate is avoided. For the sphere of the differential equations of physics is the metrical cyclic scheme extracted from the broader reality. However much the ramifications of the cycles may be extended by further scientific discovery, they cannot from their very nature trench on the background in which they have their being – their actuality.

The bond that unites Eddington to Lemaître did not go unnoticed. It was explicitly highlighted in a number of publications and certain opponents of Lemaître’s ideas would predictably point out the relationship between the two.9 Three years before his death, Msgr. Lemaître harkened back to Eddington, underscoring his vision of the science-theology relation10: Perhaps he went farther than merely seeking to define the frontier between science and religion, but the quote I will read you clearly shows that he had not confused the two spheres. After having quoted (loosely) a sentence of Hermann Weyl, he commented on it as follows: “The physical science is led to recognize a domain beyond its frontier, but not to annex it”. He would no more scientifically entertain a supernatural creation of the word, than I myself would.

During his trips to the United States, in the 1930s, the American population discovered, not without a certain astonishment, that this high level scientist who freely discussed the deep matters of the uni  Cf. D. Aikman, “Lemaître follows two paths to truth, the famous physicist, who is also a priest, tells why he finds no conflict between Science and Religion”, New York Times Magazine, February 19, 1933: 3. While Aikman is rather sympathetic to the position of the two scientists, Paul Labérenne, in ‘L’astronomie et l’histoire de la pensée humaine’ (Encyclopédie de la Pléiade. Astronomie (sous la direction of E. Schatzman), Paris, 1962: Gallimard: 6-25) unfairly reproaches them for trying to justify the divine creation by physical cosmology (page 24). 10  “Univers et atome”, in D. Lambert, L’itinéraire spirituel de Georges Lemaître, Bruxelles, Lessius, 2007: 200 (original manuscript: 3). 9

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verse with Einstein, Millikan and Hubble, was also a priest.11 Yet, for many Catholics and Protestants of this time of a more fundamentalist bent, this was a stumbling block. How was it possible to reconcile a literal reading of the first texts of Genesis with a picture of an expanding universe, of no fixed coordinates. Lemaître was often forced to clarify his position in public debates or in interviews with the press, concerning the way he conceived the relationship between science and faith. After Eddington, this was a second external factor stimulating him to articulate his position on their relationship. The interview he granted to Duncan Aikman of the New York Times Magazine in 1933 is illustrative in this regard. Lemaître made clear he did not share the literal interpretation of the Bible, claiming that its aim was not to teach scientific truths, but the way of salvation. Mixing wit with wisdom, Lemaître compared those who attempted to find some scientific instruction in the Scriptures, with those who would try to extract theological content from the binomial theorem! For Lemaître, the conflict between science and the Bible vanishes if one adopts a more symbolic exegesis12: But the Bible says creation was accomplished in six days, you protest. “Isn’t that a direct, literal statement?” – “What of it” retorts the priest. “There is no reason to abandon the Bible because we now believe that it took perhaps ten thousand million years to create what we think is the universe. Genesis simply tries to teach us that one day in seven should be devoted to rest, worship and reverence – all which are necessary for salvation”.

An efficient solution against a fundamentalist reading of the Bible, the purely symbolic exegesis of Lemaître is the natural complement   From time to time, American or Canadian journalists made Lemaître into a Jesuit! Cf. New York Times, December 11, 1932. AL has preserved a large number of newspaper clippings which belonged to Lemaître documenting their astonishment of seeing a priest who also was a world class scientist. 12   D. Aikman, “Lemaître follows two paths…” op. cit.: 3. 11

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of the position that he seemed to have inherited from Eddington and which implied keeping some distance between science and theology. Lemaître would formulate this position using the image of “two paths toward the truth”. One of these paths is that of science and the other is revelation. The first one concerns the truths related to the physical universe and the second conveys truths conducive of man’s salvation. These two paths are respectful of one another, but do not intersect. The requirement of rest on the seventh day, for example, has nothing to do with the question of the origin of the universe! The unity of the two paths, of the two approaches, cannot be situated at the level of any rational principle. Rather the unity is found insofar as it is the same person that elects to follow them13: There were two ways of arriving at the truth. I decided to follow them both. Nothing in my working life, nothing I have ever learned in my studies of either science or religion has caused me to change that opinion. I have no conflict to reconcile. Science has not shaken my faith in religion and religion has never caused me to question the conclusions I reached by scientific methods.

How to explain then that there could be, at least historically, conflicts between science and theology such as the infamous ‘Galileo affair’ for instance. Lemaître answered strangely: Oh, Galileo was mildly disciplined for being an indiscreet reporter of a private conversation in the Pope’s household and for using some of his scientific findings to promote a veiled attack on the teachings of the Church. In a word, he was another scientist who did not understand the limitations of science or the purpose of the Bible.

One finds Lemaître here closer to the traditional position of that time in the Catholic world whose main proponent was the physicist13

  Ibid.: 18.

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chemist and historian Pierre Duhem. For the latter, physics has no ontological scope, it does not describe reality as such, but simply undertakes to “save the phenomena”, i.e. to find the most concise means of incorporating and reproducing the experimental results. In this view, Galileo erred in affirming that the Sun was really in the centre of the World. He should have said that his ideas were simply a way to “save” the astronomical observations. He was thus misled on the status of science; he erroneously gave it metaphysical stature, and thus his reprimand was to be expected. Not surprisingly Lemaître had been exposed to Duhem’s thinking earlier in his career. Essentially, both were outstanding scientists and men of deep faith, and were criticized for wanting to use science for the profit of Catholic theology. With supreme intellectual honesty, both men sought to clearly distinguish science and faith, and they did so by radically separating the two spheres, negating any appeal to metaphysics in physics. The intention was commendable, but was the method entirely valid? The somehow doubtful nature of their ‘solution’ to the ‘Galileo Affair’ shows its limitations14. In fact, one may legitimately wonder if by radically excising metaphysics or theology from natural enquiry, one is not de facto compromising an important part of its intellectual credibility. Besides the influence of Eddington and the encounters with American fundamentalism, there was a third element that would force Lemaître to hone his position regarding the relationship between his cosmological work and his faith. It was Einstein. Lemaître always maintained that his motivation for his model of the universe in 1927, and later the hypothesis of the primeval atom, were exclusively scientific in nature. Indeed, on the face of it the primeval atom was rooted solely in quantum mechanics, thermodynamics and general relativity, to the exclusion of all philosophical or religious ideas. However,   Invited by Paul Germain to give a conference at the Sorbonne, in the context of the Association of the French Catholic Scientists, Lemaître answered a question concerning what he thought about Galileo. He said: “Galileo was a good Christian who has a real and authentic right to remain Christian! Then you have to respect him” (oral communication, of Paul Germain, Rome 25-5-2000). 14

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Lemaître faced the misunderstanding of Einstein who saw within the hypothesis of the primeval atom a metaphysical and religious dimension that Lemaître endeavored to exclude. Lemaître recounted that during his stay in Pasadena in the early 1930s, each time he attempted to discuss the primeval atom with Einstein, the latter withstood him: “No, not this, this suggests too much creation” (1958d: 130). Ironically it was Lemaître, the Catholic priest, who defended a purely materialist stance on the beginning of the universe by refusing to invoke a theological concept, whereas Einstein in the name of a theological concept rejected a purely scientific model! Clearly the negative reaction of Einstein would contribute to reinforcing Lemaître’s resolve to distance cosmology from any philosophical or religious reflection. At the terminus he would make the radical affirmation15: “The hypothesis of the primeval atom is the antithesis of the supernatural creation of the world”. Similarly, when Paul Dirac told him that he thought that his cosmology was the branch of the science that was the closest to religion, Lemaître dissented, and ventured that it was rather psychology.16 The separation of the spiritual and material dimensions of reality that was entirely absent from Lemaître’s mind during the first World War, and his years at the Saint-Rombaut house, as it appeared in “Les trois premières paroles de Dieu” (1921a), seemed to emerge at the beginning of the 1930s. This principle of the “non-overlapping magistera” was likely radicalized following Einstein’s categorical rejection of the primeval atom hypothesis. Nevertheless, the separation of the “two paths” could not but provoke tension in Lemaître’s thought, and it is not surprising that he tried to solve it theoretically, precisely as he attempted to do at the 6th Catholic Congress at Mechelen.

 “Univers et Atome”, edited in D. Lambert, L’itinéraire spirituel de Georges Lemaître, Bruxelles, Lessius, 2007: 213 (original manuscript: 35). 16   P.A.M. Dirac. “The Scientific Work of George Lemaître”, Pontificia Academia Scien­tiarum. Commentarii, t. II, 1968: 14. 15

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2. The Congress of Mechelen In his conference paper “La culture catholique et les sciences positives (The catholic culture and the positive science)” (1936b), Lemaître proposed a working relationship between science and faith based on two methodological principles. First of all, a principle of reciprocal respect. One should neither minimize nor overvalue science with respect to other modes of human enquiry. Certainly science is one “of the higher human activities” (1936b: 65) concerning as it does research towards truth. It is not however essential for a human as the latter “is also a child of God, and the blooming in him or her of divine grace does not depend in an essential way on the blooming of his or her intelligence” (1936b: 65). Secondly, a principle of unity without confusion and separation. The scientist “must keep the same distance between two extreme attitudes. One would treat the two aspects of his life like two carefully isolated compartments where he would receive, depending on the circumstances, his science or his faith; the other that would mix and confuse lightly and indiscriminantly that what should remain distinct” (1936b: 69). The first principle can readily be accepted with its emphasis on the “two paths towards the truth”. It is simply a matter of not overvaluing one approach to the truth over another. The second principle is more challenging as the methodological distance between the two paths can create real tension within the mind. Lemaître resolved this problem in a similar way as he did in the aforementioned 1933 interview. A unity of approach between science and faith is possible, without confusion or separation, but not at the level of thought, building a sort of conceptual or theoretical ‘bridge’ between scientific knowledge and the content of the revelation. Rather, such unity is to be sought on the level of action. Thus the content of science – theories, observations, experimental data – possess no direct theological value in themselves: the researcher “can put his faith into brackets during his research” (1936b: 70). Nevertheless, scientific research is a human activity which the faith of the scientist cannot help but color. By endowing his own acts with

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divine meaning, by living this sense in his daily activities, is how the scientist-believer realizes this unity between science and faith. According to Lemaître, there is no difference between the scientific research of a believer and of a non-believer17. Futhermore, it is not by studying equations and examining photographic plates from a telescope that one would learn something about the content of revelation. The unity of science and faith is successful at the moment when the scientist, solving equations or observing photographs of galaxies, entrusts his work to God and places it in His hands (1936b: 70): […] his faith gives a supernatural dimension to his greatest as well as his smallest activities! He remains a child of God when he put his eye to the microscope, and as well, in his morning prayer, where the entirety of his activity is to place himself under the protection of his Father in Heaven. When he thinks of the truths of faith, he knows that his knowledge of microbes, atoms or suns will neither be a benefit, nor a hindrance to approach the inaccessible light, and, as for any man, he would need to try to have the heart of a little child to enter the kingdom of heaven. Thus, faith and reason, without undue mixture or imaginary conflict, are unified in the unity of human activity.

One can then understand that Lemaître never wanted to undertake any theological interpretation of the hypothesis of the primeval atom or of any such scientific result, short-circuiting the two paths towards truth. One also understands why Lemaître lived without any tension or intellectual schizophrenia regarding his sacerdotal status. As he reached the unity of the two approaches during his meditation following the Mass, whether at Saint Paul in Cambridge, Saint-Pierre in Louvain or Saint-Henri in Brussels, his daily scientific activities had nothing to do, at least directly, with theology.   Lemaître contended that the only advantage that the believer possessed over the non-believer is a sort of “sane optimism”, as the former knows that the enigma of the universe is a solution because it is the product of an intelligence (1936b: 70). 17

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3. The Pontifical Academy of Sciences Lemaître’s position regarding the relationship between science and faith very much found a home within the Pontifical Academy of Sciences. The Academy was founded in 1936 by Pope Pius XI to succeed the Accademia Pontificia dei Nuovi Lincei (Academy of the New Lynxes)18, which had by then fallen into disuse.19 Under the purview of the Roman Pontiff himself, distinguished scientists were welcomed without distinction as to their philosophical or religious views. Following the wishes of Pius XI and of its first president Edoardo Gemelli (1878-1959), it was thus a Pontifical academy and not an academy of the Catholic Church. The very premise of the Pontifical Academy is the harmonious coexistence of natural sciences with revelation of which the Magisterium is the guardian, and acknowledgement of their proper mutual spheres, as Gemelli himself personified. He was a converted Marxist who entered the Friars Minor in 1903, and trained in neurology. After extensive visits to laboratories abroad, Hans Driesch guided him towards experimental psychology, a discipline he ultimately taught at the Cattolica of Milan that he himself had set up in 1921. For the entirety of his life, he stayed faithful to both his Franciscan and scientific vocations, without any interference between them. The personality of Gemelli commanded respect among many close to Lemaître. As observed by Régis Ladous20: Like Gemelli, Lemaître was a priest. Like Gemelli, he taught in a Catholic university, that of Louvain. Like Gemelli, he was loved by   This academy was linked to the Accademia dei Lincei (Academy of the Lynxes) founded in 1603 and of which Galileo was an active member. The name of the Lynx was chosen in reference to the strong eyesight of this animal, symbolizing scientific perspicacity. The Accademia Pontificia dei nuovi Lincei was founded by Pius IX in 1847, as a revival of the old Accademia dei Lincei. 19   Regarding the history of the Pontifical Academy of Sciences, the reader is referred to an excellent book by Régis Ladous, Des Nobel au Vatican. La Fondation de l’Académie pontificale des Sciences, Paris, Cerf, 1994. 20   R. Ladous, Des Nobel au Vatican, op. cit.: 169 (our translation from the original in French). 18

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his students and did not qualm participating in their meetings “in the middle of tobacco smoke and beer steam that flowed abundantly”21.

The only difference between the two was their attitude towards political engagement. Gemelli was always a militant, while Lemaître, as reported by Ladous22: (…) was the opposite of a militant or a politician; he never engaged in Catholic Action nor any movement whose acknowledged goal was to restore the social royalty of Christ, or, using another formula of primitive Christianity, to seek a theocratic organization of society.

Not surprisingly when Mgsr. Lemaître would launch his campaign in favour of the unity of Louvain, he displayed a political naivety in sharp contrast with the political sophistication and skill of Gemelli. Gemelli had a friend in Louvain, the psychologist Albert Michotte. The latter certainly told him about Lemaître, who had attended some of his lectures at the Institut Supérieur de Philosophie. On the advice of the apostolic nuncio in Brussels, Msgr. Clemente Micara, Lemaître was proposed by Gemelli to be put on the list of the first members of the Pontifical Academy published on 28 October 1936, in the Acta Apostolicae Sedis. Lemaître found within the Academy a place to promote the thesis he had developed in the Congress of Mechelen. The Pontifical Academy allowed him not only to enrich his scientific connections, but also to further explore his approach to the dialogue between scien­ce and faith. From the very beginning of the Academy, Lemaître enjoyed an excellent reputation with the Vatican authorities, in particular the   O. Godart, “Monseigneur Lemaître et son OEuvre”, Pontificiae Academiae Scientiarum. Scripta ex Aedibus Academicis in Civitate Vaticana, 36: 27 (our translation from the original in French). 22   Ibid.: 169. 21

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State Secretary of Pius XI, Pacelli, who would later become Pius XII. Eugenio Pacelli was appointed by the Pope to organize, at the international level, consultations toward the drafting of the Academy’s constitution23; he thus had an intimate knowledge of the institution in which he participated as an “honorary academician”. When Pacelli became Pius XII, he asked Lemaître to pronounce a eulogy for the Father of nuclear physics and Nobelist, Lord Rutherford during the meeting that opened the fourth academic year of the Pontifical Academy, in the presence of the Pope, the diplomatic corps and the College of Cardinals on 3 December 193924. Lemaître who made the trip during those troubled times despite rumours of an imminent war, had an opportunity for a discussion with the recently elected Holy Father.25 This meeting left him with indelible memories he recounted during a conference, after the Second World War, in a Jesuit College26: It is difficult to adequately describe the magnificent setting within which these solemnities took place, at the seat of the headquarters of the Academy, the villa of Pius IV in the middle of the gardens of the Vatican City. The Holy Father was seated at a table in front of the assembly; in the foreground, the purple of the cardinals highlighted the apparel with which the diplomats were bedecked and the mantillas of some of the ladies, while on the benches on either side of the room,

  R. Ladous, op. cit.: 90-91.  “Discorso per la Sessione plenaria dell’Academia”, pronounced by Pius XII on this occasion can be found in: Discorsi dei Papi alla Pontificia Accademia delle Scienze (1936-1993), Città del vaticano, Pontificia Academia scientiarum, 1994: 31-41 (English translation in: Papal Addresses to the Pontifical Academy of Sciences 1917-2002 and to the Pontifical Academy of Social Sciences 1994-2002 (pref. Prof. N. Cabibbo; introduction by H.E. Msgr. M. Sanchez-Sorondo), Scripta Varia, 100, Pontifical Academy of Sciences, 2003: 80-90). 25  As a souvenir of this event, Lemaître would keep a large framed photograph of Pius XII surrounded by the cardinals, academicians and diplomats. His album also includes a photograph of a discussion between Pius XII and himself, in company of Gemelli. 26   Only a draft of this conference is preserved at the AL. There is nothing identifying the specific college in question. (Our translation from the original in French). 23 24

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the academics, adorned with golden necklaces were prepared to listen to the teachings of the Holy Father.

All of his life, he retained a great veneration for Pius XII, and gave no credence to the reproaches that some made of him27: The Holy Father addressed the academics, representing a delegation of scientists from around the world, of all religious and philosophical beliefs. The Holy Father, spoke in the name of the Church as its head and shared his thoughts with the scientific body gathered around him on how he conceived good relations between faith and science.

Lemaître’s attitude of extreme respect towards the Pope facilitated the mitigating of his position regarding the “Un’Ora problem”, discussed later.

  This was confirmed by the testimony of R. Dejaiffe (Oral communication, 3010-1997), by the manuscript “Univers et Atome” of his conference to the “Amis de l’Université de Louvain” (1963), and by a letter of Abbé Heyters to Sr. Madeleine Delmer, O.S.B., 24-12-1951. The two documents will be discussed later. 27

Chapter X

An astronomer starstruck by algebra (1931–1957)

1. The Dirac equation redux (1931)

I

n contrast to his colleague Gustave Verriest (1880-1951) who had frequented Göttingen, Lemaître was not an algebraist according to the standards of the “modern algebra” school of Artin or Noether. By nature, he was not inclined towards the kind of syntheses that unified mathematics by subsuming them under abstract concepts like the “structures” of the Bourbaki School1 or Lawere’s “categories”. What primarily interested Lemaître was the manipulation of formulas, numbers and geometrical figures, and this is where Lemaître’s mathematical genius shone forth. In lecture, he would start from a specific case where “something happens”. Without following a strictly rigorous method, and often by trial-and-error, Lemaître would conjure up a new interesting result. Never the one to systematize or generalize,   In the 1950s, Lemaître began to read a copy of “Les Eléments de Mathématique” of Bourbaki preserved today, and underlined in red or a blue pencil as was his habit. These readings however, had no influence on his work; at best one can find a passing allusion to modern synthesis in (1967d). Albert Caupain, who visited Lemaître in the early 1950s, found him studying set theory (oral communication, 23-03-1995). In January 1957, he began to study algebraic topology: homotopy, homology, de Rham cohomo­ logy, Hopf fibration, etc., also attending the lectures of Professor Hirsch of ULB (There is preserved a 55-page notebook of his dedicated to algebraic topology [AL]; interestingly of all Lemaître’s notebooks, it is this one which was most meticulous.) But none of this had any influence on Lemaître’s research. It was in Lemaître’s preparation for his class where he was able to discover the “Kustaanheimo-Stiefel transformation” by himself (cf. chapter XIV). 1

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Lemaître played on formulas as one might improvise at the piano, but without a thought to compose any kind of symphony. If Lemaître displayed any interest in algebra at the beginning of the 1930s, it was solely for the purposes of physics and more specifically to Dirac’s discovery in 1928 of the equation describing relativistic electrons. Lemaître had studied quantum mechanics at MIT, and at the end of January 1931 had written a brief report concerning Heisenberg’s uncertainty principle applied to Coulomb’s law (1931a). Never­theless, Lemaître never concerned himself with quantum mechanics, partly because of a lack of time, but also because he did not see how it could be unified with general relativity (which remains a problem to this day). But the Dirac equation renewed hope that the two disciplines could be unified. This intrigued Eddington, first because it appeared to lead to the unified theory2 he would pursue his whole life3, and also because the Dirac equation forced him to question some of his a priori assumptions regarding the necessary basic tools for the description of the physical world.4 Eddington thought that the whole of physics could be built from tensors, but the Dirac equation showed that this was not the case as the description of the relativistic electron required, not tensors, but what Paul Ehrenfest would later term spinors5.

  Eddington had produced a  unified theory of electromagnetism and gravitation that Lemaître had studied in 1925. He subsequently searched for a path by which to build a theory that would link quantum mechanics and general relativity, a problem unresolved to this day. 3   Cf. on this topic the excellent book of C.W. Kilmister, Eddington’s Search for a Fundamental Theory, Cambridge University Press, 1994. 4   Philosophically, Eddington thought that one could generate the whole formalism of physics from an a priori analysis of the necessary conditions of all representations of the emprirical world. For instance, to build a  world description, one needs first and foremost a concept of relation R, after which one might be able to compare relations R and R’. But this requires a priori a second theoretical tool B such that R’ = BR; this is exactly this kind of consideration that leads to the notion of a tensor (cf. A.S. Eddington, The Nature of the Physical World, Cambridge University Press, 1928: 230-239). 5  Cf. Budinich, A. Trautman, The Spinorial Chessboard, Berlin, Springer-Verlag, 1988: 4. 2

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Eddington had shown that one could deduce from the Dirac formula an expression that will be called here the “Eddington equation”6: (A1p1+A2p2+ A3p3 – imc B3) Ψ = 0 where m refer to the mass of the electron, c the speed of light, i2 = -1 and where the Ai and the Bj are 4x4 matrices. Eddington considered, in a general manner, 6 antisymmetric matrices Ai (i =1,2,3) and Bj (j=1,2,3) whose square is equal to the unit matrix. The matrices Ai commute with the matrices Bj but the Ai of different indices, as well as the Bj of different indices, anticommute7. If one considers all the sums of monomials formed by products of matrices Ai or Bj or of both Ai and Bj, one obtains an algebra of dimension 16 that Eddington christened the “algebra of Sedenions” or the “E-number algebra”, but which was already known in algebraic literature by the name of “quadriquaternions”.8 It represents a particular case of an algebraic construction that would prove important later in noncommutative geometry and in statistical mechanics to describe spin systems in a periodic lattice.9 In the early 1930s, some Belgian students of Théophile De Donder worked on a generalization of Dirac equation. Lemaître had read   It is unfortunately not possible to appreciate the contributions of Lemaître without a minimum of mathematical technicality. The reader unfamiliar with higher mathema­ tics may omit this chapter without serious detriment. 7   Working within the field of complex numbers, we can use the set of matrices Ai and Bj to generate algebras of quaternions. Within the field of real numbers, matrices Ai and Bj whose squares are unity generate the so-called “hyperbolic” or “Gödel quaternions”. 8   Cf. “Nombres complexes, (exposé d’après l’article allemand de E. Study)” in Encyclopédie des mathématiques pures et appliquées, I.5, Paris, Gauthier-Villars, 1904. The name “quadriquaternion” comes from the fact that one multiplies between them two algebras of complex quaternions (dimension 4). 9   Let us consider for each element x of a set of n points (e.g. a network), an algebra generated by two matrices A1(x) and A2(x) such that Ai(x)r = +1/-1, and A1(x)A2(x) = q A2(x) A1(x) where q = exp (2pi/r). Moreover Ai(x) Aj(y) = Aj (y) Ai(x) for all i and j, and x different from y. The sums of terms consisting of products of all such matrices define an algebra G2n (r) of dimension r2n (cf. P. Martin, Potts Models and Related Problems in Statistical Mechanics, World Scientific, 1991: 276). In the case considered by Eddington-Lemaître r = 2 (Ai(x)2 = +1, hyperbolic quaternions) n= 2. 6

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the paper of Jules Geheniau entitled “Sur l’équation de Dirac généralisée” (“On the generalised Dirac equation”)10. Lemaître, familiar with the works of Dirac, Eddington and Darwin, found a way to simplify a problem and make it more suitable for manipulation (1931c). He completed the equation in a way to make it more symmetrical, and obtained an equation generalizing that of Eddington: TΨ = (A1p1+A2p2+ A3p3 + B1q1+B2q2+ B3q3) Ψ = 0 In this form, the study of the covariance11 of the equation becomes particularly simple. This is plainly seen if Ψ is transformed into Ψ’ = KΨ, by means of a 4x4 matrix K with real elements, and if, at the same time, one assumes the following transformation law for T:12 T’ = (K’)Tr T (K’) where the superscript ‘Tr’ refer to the matrix transposition, and K’ to a 4x4 matrix. The form of the equation is preserved through the transformation T’Ψ’ = 0, if the condition K’ = K-1 holds. If one considers a matrix K of determinant unity, one may observe that the determinants of T and T’ are equal. Thus, one may readily calculate the square root of this determinant from the representation of the matrices Ai and Bj, the square root being: (det T)½ = p12+p22+p32 - q12-q22-q32 = (det T’)½ . This implies that K (and also -K) is a transformation that preserves a “(pseudo-) distance” in a space of six dimensions that generalizes the Minkowski space-time of special relativity. In such a space,   Bulletin de la Classe des Sciences de l’Académie Royale de Belgique, 3e série, t. XVI, no 12 (séance du 6-12-1930): 1442-1445 (paper presented by Th. De Donder). 11   The study of transformations that leave the form of the equation invariant. 12   Lemaître assumed that T transforms as a covariant tensor of the second order. 10

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the “distance” is given by an expression such as p12 - q12 - q22 - q32. By studying the matrices K, Lemaître observed that the transformations K form a group generated by 15 generators13, of which one subgroup corresponds to the Lorentz group of special relativity. Without knowing it, Lemaître was exploring what would later be called a “spin group”14. Lemaître had generalized the Eddington equation by additionally enforcing the requirement of symmetry. Should he have pushed this generalization further? In fact, the answer is no since dimension six is the maximal dimension for which these “spin groups” can be expressed simply in terms of classical groups15. Lemaître had just made an incursion into a fertile domain of contemporary mathematics and physics: the theory of spinors16. These spinors are the objects Ψ that transform themselves by means of the elements K of   The Lie algebra of the group is given by the six products AiAj, BiBj and the nine products AiBj. The six first matrices, of negative square generate ordinary rotations, and the remaining nine, of positive square, generate pseudo-orthogonal transformations (hyperbolic rotations). 14   This is the group Spin (3,3) whose element connected to the identity is isomorphic to SL(4,R), itself related to the group of the pseudo-orthogonal transformations SO (3,3). The latter possesses the subgroup SO(1,3) corresponding to the Lorentz group of special relativity. Cf. H.B. Lawson, M.-L. Michelson, Spin Geometry, Princeton University Press, 1989: 12-20; L. Dabrowski, Group Action on Spinors, Napoli, Bibliopolis, 1988: 21-26. 15   Lemaître could have pushed his study further and explored the complex version of the Spin group: Spin(6,C) isomorphic to SL(4,C), he would have at his disposal a frame that would have been sooner or later extremely fertile since that latter group involves as a subgroup SU(2,2) which is isomorphic to the component connected to the identity of the group Spin(4,2) which is itself related to the group of conformal transformations of the Minkowski space. Moreover, SU (2,2) is closely linked to the Penrose Twistor Theory (cf. I.T. Todorov, Conformal Description of Spinning Particles, Berlin, Springer-Verlag, 1986: 21-30; R. Penrose, “On the Origins of Twistor Theory”, in Gravitation and Geometry (W. Rindler, A. Trautman, eds.), Napoli, Bibliopolis, 1987: 341-361. 16   Let us remember that PSL(2,H): = SL(2,H)/Z2 is isomorphic to the component connected to the identity of SO(5,1), where H is the algebra of usual Hamilton quaternions (cf. J. C. Baez, The Octonions, Bulletin of the American Mathematical Society, 39 (2002): 145-205; http://math.ucr.edu/home/baez/octonions; J. C. Baez, J. Huerta, “The Strangest numbers in String Theory”, Scientific American, May 2011, Vol. 304, no 5: 44-49). If one uses the algebra of Gödel quaternions one is led (but you have to be careful because this situation is not completely analogous to the previous one!) to the component connected to identity of SO(3,3). This shows the link between Lemaître’s work and the Gödel quaternions. 13

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a spin group defined from a quadratic form (“norm”) characterizing the space under consideration. In 1933, Lemaître would encounter spinors again, but this time in connection with general relativity. It was this year that Einstein, returning from the United States decided not to go back to Germany due to Nazi threats. He stayed in Belgium four months, at De Haan (Le Coq-sur-Mer) in the Villa Savoyarde, which still exists today, under the protection of the Belgian Royal Family. He was invited to give a series of lectures on the Theory of Spinors at the Fondation Universitaire in Brussels. These lectures would be more properly described as informal discussions, and Lemaître was in charge of moderating the sessions on Saturday 17 May at 15:00. Einstein was left impressed by his interaction with Lemaître. Professor Max Gottschalk asked Einstein if all of the people in his audience understood him, to which Einstein answered: “Professor D. [probably De Donder] perhaps, Canon Lemaître surely, the others, I don’t think so.”17 The Einstein’s talks were likely devoted to the spinorial formulation of general relativity based on “tetrads” (Vierbein)18, which De Donder proposed translating as “quadruped” (“quadrupède” in French!), much to Einstein’s amusement19. But the Canon would never use the spinorial formalism of general relativity, but solely the Eddington form of the Dirac equation. Einstein left Belgium 9 September 1933 and went to England and from there to Princeton.

  Bulletin de la centrale d’oeuvres sociales juives, juin 1955, no 9: 4, quoted from Albert Einstein. 1879-1955, Bruxelles, Palais des Académies, MCMLXXX: 87-88 18   It is necessary to define spinors locally on the space tangent to a space-time manifold. One uses a local base, a ‘quadruped’, in which the metric is Minkowskian. One can then define locally some objects that are transforming under the spin group associated with Minkowski space-time, i.e. SL(2,C). These objects are the spinors. It is possible to rewrite tensors as the products of spinors. 19   Cf. (1958d: 130-131). 17

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2. The Projektive Relativitätstheorie (1933–1935) and Relativistic Theory of Protons and Electrons (1937) In 1935, Lemaître was invited by Veblen (1880-1960) to the School of Mathematics of the Institute of Advanced Studies at Princeton where Einstein, Alexander, von Neumann and Weyl had all located. Veblen was a specialist of differential geometry and had just finished an important book on one extension of general relativity, projective relativity.20 This theory aimed to give an interpretation that satisfied the Kaluza-Klein theory unifying gravitation and electromagnetism, by introducing an additional fifth dimension in the formalism of general relativity. As measurements in physics involve only four dimensions, it is required that the metric describing the space in five dimensions does not depend on this fifth variable, interpreted at that time as merely an ancillary concept. In order to give a satisfactory mathematical foundation to this so-called “cylindricity condition”, Veblen interpreted the transformations of the fifth coordinates as changes of proportionality factors of the homogeneous coordinates of a projective space. Kaluza-Klein theory thus became a theory of a projective space-time. Veblen discovered that the very spinors used by Eddington and Lemaître could be studied from a projective geometry that in a particular case, reduced to the projective theory of relativity. At the Institute, the Louvain cosmologist once again found himself at the right place at the right time. A brief excursion into the relationship between spinors and projective geometry is in order, along the lines traced by Gary Gibbons of Cambridge University two decades ago.21 If one considers the Majorana spinors, i.e. spinors with four real components, one can imagine their components as projective coordinates characterizing the point in   O. Veblen, Projektive Relativitätstheorie, Berlin, Springer, 1933.   G.W. Gibbons, “The Kummer Configuration and the geometry of Majorana Spinors” in Spinors, Twistors, Clifford Algebras and Quantum Deformations (Proceedings of the Second Max Born Symposium held in Wroclaw, Poland, September 1992), Dordrecht, Kluwer, 1993: 39-52. 20 21

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projective space with three dimensions on the field of real numbers. It is possible to build a group of transformations of this projective space onto itself, from linear transformations of the real space of four dimensions22. One can then show that this group is isomorphic to the spin group considered by Lemaître. Certain spinors thus have such a natural projective interpretation. This result was in fact the foundation of the seminal work of Plücker. The latter showed that one can associate to each line of an ordinary three-dimensional space23, a line of isotropic vectors belonging to the quadratic equation: x12+ x22+ x32y12- y22- y32 = 0. To draw out the internal coherence of Lemaître’s thought, (which he never took pains to explain himself) it is necessary to show that the projective space of three dimensions on the field of real numbers is nothing else topologically than the elliptic space he used in his cosmology24. While Lemaître never explicitly stated it, it seems that the covariance group that he exhibited for the Dirac equation revisited by Eddington and that he himself generalized, was a group intimately related to his favourite model of universe. At the end of the 1940s, after having systematized his ideas on the geometry of elliptic space25, partly after having read Clifford’s work26 and the book of Blaschke   If one considers matrix transformations of the determinant +1, this group is SL(4,R) which is isomorphic to the component connected to the identity of Spin(3,3). This component is also the double cover of the component connected to the identity of SO(3,3). 23   One must remember that one can always establish a correspondence between a projective space of a certain dimension and an affine space of the same dimension. 24   This geometry is that of the three dimensional sphere: S3 for which two diametrically opposed points have been identified. It consists in fact of S3/Z2 where Z2 is the finite group of order 2. Further, the projective space of dimension n on the field R of real numbers, Pn(R), is topologically equivalent to Sn/ Z2. 25   In the AL, it is possible to find a  notebook dedicated to elliptic geometry. In this text, one can also find a reference destined for the Encyclopédie catholique japonaise (1985a: 3-6), which leads us to believe that Lemaître immersed himself in the work of Clifford at the end of the 1930s. 26   Clifford was the first person who was interested in the notion of parallelism on the sphere of three dimensions. The sphere of three dimensions can be foliated by a family of tori and two circles, in the same way that the ordinary sphere can be foliated by a family of circles (the “parallels”) and two points (the “poles”). The analogues of the parallel lines in the elliptic geometry of the sphere in three dimensions are the 22

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published during the Second World War27, he would explain in a pedagogical paper the relationship between elliptic geometry and quaternions (1948d). However, the spinors were no longer present. The year following his return from Princeton, Lemaître received a letter from Eddington28 asking him to proofread his book Relativity Theory of Protons and Electrons29, in which he tried to establish the foundations for a unification between relativity and quantum physics, using an a priori deductive method based on properties of the algebra of quadriquaternions. This 336-page book was highly speculative and ignored the development of the theory of spinors that had taken place between 1931 and 1936 under the impetus of Cartan, Veblen, Schouten, and van der Waerden30. Not surprisingly, it was not well received by critics.31 Nevertheless, the book comprised a series of ideas that were stimulating for an understanding of the numerical values of fundamental constants. Lemaître was readily taken in by Eddington’s project of a purely algebraic explanation of the fundamental constants of physics, outlined in his book. The latter envisaged finding, for instance, a theoretical reason for the value of the “fine-structure constant”32 1 / 137.036..., that appears in the correction to the energy levels of hydrogenic atoms when one takes into account relativistic effects and the spin of the Villarceau circles. These circles, obtained by a section of the torus by a plane tangent to two circles of right section, were already known by the architects of the Renaissance. On a torus, there are two family of such circles and therefore two types of parallels. These circles representing the “parallels lines” of the elliptic geometry are also the fibers of the Hopf fibration discovered in 1931 and the kernels of the so-called Kustaanheimo-Stiefel transformation used in the problems of regularization (and which Lemaître could have had discovered; cf. chaper XIV. 4). 27   W. Blaschke, Nicht Euklidische Geometrie und Mechanik, Teubner, 1942. 28   Letter, 27-02-1936 (AL). 29   Cambridge University Press, 1936. 30  Eddington’s approach is rather based on his knowledge of the work of Clifford, quoted on p. 2. 31   I refer the reader to the excellent analysis of C.K. Kilmister, Eddington’s Search for a Fundamental Theory: A Key to the Universe, Cambridge University Press, 1994: 187-222. 32   This number is the approximate value of (1/4pe0)e2/ħc the charge of the electron, h Planck’s constant and e the dielectric constant of free space).

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electron. The reasoning goes as follows. If one describes two particles interacting electromagnetically, one should use two algebras of quadriquaternions (as the wave function describing each particle is described, according to Eddington, by a quadriquaternion). The product of these two algebras results in an algebra of dimension 16x16=256. Due to the impossibility of distinguishing identical particles in quantum mechanics, the mathematical expressions used must remain invariant, under the exchange of two particles. This reduced the numbers of symbols to 16+1/2 (15x16) = 136.33 A technical argument34 adjusts this to 137… And voilà! Out of admiration he had towards his old mentor, Lemaître considered it a duty to read in depth the draft version of the book. He would finish his work in June 1936 as requested by Eddington35. The latter would take into account Lemaître’s comments36, corrections37 and his work of 1931.38 Lemaître undertook a project in this field himself (1937d). In fact, he showed that one could represent the quadriquaternions in terms of the product of two algebras of quaternions, but expressed in another representation than the one he had given in 1931, with the matrices Ai and Bj. He built two “triads” Si and Dj (i and j = 1,2,3) of operators39 ob  Calling Ei and Fj (i, j = 1,…,16) the quadriquaternions generating respectively the algebras of the two particles E and F, then by computing their products, one can form 16 operators Ei Fi (indistinguishable from Fi Ei) and 15x16 operators Ei Fj (i different from j). But Ei Ej cannot be distinguished from Ej Ei, which reduce the number to 240/2 =120. 34   We refer the reader here to the beautiful book of J. Ullmo, Les idées d’Eddington sur l’interaction électrique et le nombre 137, Paris, Herman, 1934: 19-26. 35   Letter dated 23 May 1936 (AL). Eddington thanked Lemaître in his preface: vi. 36   Lemaître asked Eddington to retain a non-zero cosmological constant at the beginn­ing of the universe (cf. letter from Eddington, 23-05-1936, AL). Nevertheless, Eddington in his book (p. 279) is critical of this suggestion, and shows that his theory is not consistent with the primeval state of the universe resembling a “highly concentrated ‘atom’ ”. 37   Page 319 Eddington noticed that Lemaître had highlighted the inconsistency between equation 16.52, p. 318, and the equation 8.54, p. 128. cf. C.W. Kilmister, op. cit: 201. 38  Cf. Relativity Theory of Protons and Electrons, op. cit.: 47, where Eddington underlines the role of “triads” of the matrices Ai and Bj to construct his sedenions. 39   He shows that one can free oneself from all particular matrix representations of the operators. 33

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tained by multiplying the operators representing the matrices Ai and Bj 40. Lemaître then constructed, without calling it as such, a projector C (C2 = C)41 such that, for each quadriquaternion T, one can obtain the following results: TC = (Ψ0+Ψ1S1+Ψ2S2+Ψ3S3)C The right-hand side depends only on four numbers Ψi, and can therefore represent a spinor. Since the result above is valid for all quadriquaternions, if we multiply the left-hand side TC by another quadriquaternion T’, (T’T)C is still of the form of the right-hand side. This means thus, in algebraic terms, that the spinors can be represented as a “left ideal” of the algebra of quadriquaternions. This “ideal” can be represented as a set of matrices for which only one column is non-zero. This representation of the spinors would become one of the core themes of the algebraic theory of spinors developed by Claude Chevalley in 195442, Marcel Riesz in 195743 and that would be systematically applied to physics by David Hestenes44. Did this make Lemaître a pioneer of the algebraic theory of spinors? It would be more exact to say that he was one of the first users of this theory, which had not yet been formalized. Lemaître did not quote any source but Eddington; it was possible that he inherited from him this way of dealing with spinors, especially while talking about them in a vocabulary borrowed from the book of his professor45. In fact, according   Using the previous notation, one can write: S1 = - B2A3, S2 = - B3A1, S3 = - B1A2 and Di = - AiBi (i = 1,2,3). 41   C= ¼(1 + D1 + D2 + D3). 42   Cl. Chevalley, The Algebraic theory of Spinors, New York, Columbia University press, 1954. 43   M. Riesz, Clifford Numbers and Spinors (E.F. Bolinder, P. Lounesto, eds.) Dordrecht, Kluwer, 1993. This book involves lectures given by Riesz between October 1957 and January 1958 at the University of Maryland College Park and private lectures given by Bolinder on 9 and 11 April 1959 at Indiana University, Bloomington. 44   D. Hestenes, Space-Time Algebra, New York: Gordon and Breach, 1966. 45   One sees that he uses the terms “final” and “initial vectors” in Eddington’s Relativity Theory of Protons and Electrons, op. cit.: 18.

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to Pertti Lounesto46, a real connoisseur of the history of spinors, by 1930 Juvet47 and Sauter48 were already using a representation of spinors under the matrix form by which only one column is non-zero. Such matrices that form an ideal of the algebra of operators used for the Dirac equation, appear directly if one looks for the matrix representation of the spinors used by Lemaître. It is surprising to note that he did not attempt to integrate the knowledge acquired in Princeton while in contact with Weyl and Veblen into his own work.49 Regarding his contact with Eddington, neither was he attuned to the great theoretical current that developed the modern theory of spinors. He would join this current only later, but more in the context of personal interest. Veblen’s perspective was structural in a “Bourbakian” way, but Lemaître did not share this bent with contemporary algebraists. Eddington had occasioned Lemaître’s enormous ability to show itself in a narrow field, but nothing had impelled him to construct a more systematic theory. A detail is in order here to demonstrate the potential richness of the tool Lemaître was using in 1937. Kilmister50 and Gibbons51 pointed out, along with Eddington himself, that the triads can generate a group of automorphisms of a geometrical configuration living in the real projective space of three dimensions: the “self-dual configuration of Kummer”. The latter comprises 16 points and 16 planes with each plane containing 6 points and in a way that each point is at the   “Marcel Riesz’s work on Clifford Algebras” in M. Riesz, Clifford numbers…, op. cit: 219. 47   G. Juvet, “Opérateurs de Dirac et équations de Maxwell”, Comm. Math. Helv., t. 2, 1930: 225-235. Juvet is one of the great theorists of the Swiss School of Theoretical Physics. 48   F. Sauter, “Lösung der Diracshen Gleichungen ohne Spezialiserung der Diracschen Operatoren”, Zeitschrift für Physik, t. 63, 1930:803-814. 49   See the seminal article of R. Brauer and H. Weyl (1935): “Spinors in n-Dimension”, American Journal of Mathematics, Vol. 57, 425; and also O. Veblen and J. Von Neumann, “Geometry of Complex Domains” (mimeographed notes), 1936, Institute for Advanced Studies, in which one finds the application of the theory of spinors to general relativity. 50   Op. cit.: 119 51   Op. cit.: 46-49. 46

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intersection of the 6 planes52. One can get such a configuration by observing the nodes of a quartic which is called the “Kummer surface”53, and which had caught Eddington’s imagination54: Some years ago, I worked out the structure of this group of operators [generated by the triads] in connection with Dirac’s theory of the electron. I afterwards learned that a great deal of what I had written was to be found in a treatise on Kummer’s quartic surface. There happens to be a model of Kummer’s quartic surface in my lecture-room, at which I had sometimes glanced with curiosity, wondering what it was all about. The last thing that entered in my head was that I had written (somewhat belatedly) a paper on its structure. Perhaps the author of the treatise would have been equally surprised to learn that he was dealing with the behavior of an electron. But then, you see, we supermathematicians never do know what we are doing.

On 12 February 1938, Lemaître would have the chance to present the results of his research stimulated by the work of Eddington during the second Notre Dame symposium on mathematics by the chair of the department of mathematics, the logician Karl Menger. Surrounded by the great names of modern algebra, such as Marshall Stone, Garrett Birkhoff, Oystein Ore, Adrian Albert and John von Neumann, Lemaître, who was guest professor at this university, presented a paper entitled “The Algebraic Details of the Relativity Theory of Protons and Electrons”. The cosmologist of Louvain could have met the famous logician Kurt Gödel. The latter has been invited to the symposium where he was expected as a guest professor. Menger knew him well after having worked with him in Vienna,   If one takes the 16 base elements of the quadriquarternions algebra and assigns them the sign +1/-1, one obtains a group of 32 elements. The latter is the double cover of the group of automorphisms of the Kummer self-dual configuration. Cf. R.W.H.T. Hudson, Kummer’s Quartic Surface, Cambridge University Press, 1905. 53   Cf. H.B. Lawson, M.-L. Michelson, op. cit.: 89-90. 54   A. Eddington (1935) New Pathways in Science. Cambridge University Press, 1935: 271. 52

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before going to the United States in 1937. Nevertheless, for health reason, Gödel only went to Notre Dame in January 193955 by which time Lemaître was already back in Belgium. We recall that in 1949 Gödel would use hyper­bolic quaternions to build one solution of Einstein equations exhibit­ing the strange closed-time geodesics (i.e. the possibility to travel back in time)56, the same quaternions readily gotten from Lemaître’s matrices Ai and Bj.

3. The Fundamental Theory and the spinors of Cartan (1948) In a notebook57, which he kept from between 17 March 1947 and 15 January 1954, Lemaître wrote, on 8 June 1948: “I have studied the Cartan spinors and see more clearly the relationship between his theory and Eddington’s”. In fact, this study was occasioned by the posthumous publication by Edmund Whittaker of Eddington’s book: Fundamental Theory58, which in a manner constitutes the extension of Relativity Theory of Protons and Electrons. More especially, Lemaître had read, cover to cover and with blue and red pencils in hand, the two volumes of “Leçons sur la théorie des spineurs”59 of Élie Cartan, likely during the war or just after. The theory of spinors had been discovered by Cartan as early as 1914 in his work on the linear representation of the simple groups. Nevertheless, before the discovery of the Dirac equation, nobody had made the connection between the work of Cartan and physics. It was only after the works of Brauer, Weyl and Veblen, that Cartan had undertaken to provide his idea with a new twist. Lemaître set out to establish a detailed correspondence between his own notation and   Cf. H. Wang, Reflections on Kurt Gödel, MIT Press, 1988 (2nd printing).   K. Gödel, “An example of a New Type of Cosmological Solution of Einstein’s Field Equation of Gravitation”, Review of Modern Physics, Vol. 21, 1949, no 3: 447-450. 57   This notebook was preserved at the AL as well as the letters that are quoted below (translation from the original in French). 58   Cambridge University Press, 1948. 59   Paris, Hermann, 1937 (lessons collected and edited by André Mercier). 55 56

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that used by Eddington. He thought he had found an error in Cartan’s work60 and wrote to him on 24 May 1948 to let him know. Cartan answered Lemaître on 30 May showing that indeed there was no mistake at all; in the same letter he invited Lemaître to visit him at his home on 95 Boulevard Jourdan, Paris on 2 or 3 of June. Lemaître would go but miss Henri Cartan, who, only just having returned from five months in Harvard, had left to attend the Bourbaki Congress in Strasbourg in which André Weil was taking part. In a letter dated 17 June Élie Cartan wrote to Lemaître: “I would be hard pressed to tell you which part of mathematics Bourbaki is dealing with!” Lemaître would always hold a great admiration for the person and work of Élie Cartan. In 1956, he acquired his complete works and, from the volumes preserved at the AL, one can easily imagine that Lemaître might have read many more of his papers in the late 1950s and early 1960s. Lemaître would summarize Eddington’s Fundamental Theory in one of his notebooks, later providing a typewritten summary, and finally an unpublished text L’idée maîtresse d’Eddington (The Master Idea of Eddington)61. This text, from 1954, is important as it shows that Lemaître had read the book of Chevalley about the algebra theory of spinors. Why did he attach such importance to this kind of mathematics? Not only out of respect for his old master, but more probably because he was, as many physicists of the day, gripped by the prospect of the unification of physics. Odon Godart62 said that Lemaître sought to find the framework that would allow this unification and reconcile general relativity (which he had mastered) with quantum mechanics (which he knew only but poorly). More precisely, he believed that this fundamental theory would lead him to a theoretical foundation for the cosmological constant. This idea is still present in his conference paper entitled “L’étrangeté de l’univers” (1960a: 10-18).   Specifically a formula published in issue no 150 (pages 62-63) of Volume II of the Leçons. 61   This text is preserved at the AL (translation from the original in French). 62   Oral communication, 12 April 1996. 60

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4. The spinors: from the quantum field theory to history (1955–1957) Lemaître would use his holidays between December 1955 and January 1956 to prepare a review with the aim to “help the physicist use the theory of spinors’’.63 The title is somewhat misleading, as the article invoked quantum physics only as an original motivation. In it, on Eddington’s suggestion, Lemaître began to unify the three approaches of mathematics of the theory of the spinors: Eddington in the last chapter of RTPW64 (this last chapter throws much light on the beginning) highlights the tight connection between the theory of spinors and the Jordan-Wigner functions used in second quantization. This aspect of the theory I place in the foreground of this exposition so we might try to unify the three main works that have in common the fact that they are difficult to understand; they will be referenced by their initials of their authors: A.E. for Arthur Eddington, E.C. for Élie Cartan, C.C. for Claude Chevalley.

This text is the only one where Lemaître tried to adopt the style of Bourbaki, when he attempted to understand the Eléments in the early 1950s. One quickly sees that this style scarcely accords with his manner of thought. What is more interesting is what Lemaître studied. After his work of 1937, he integrated a number of important references: Van der Waerden, Schouten, Kähler, as well as, of course, Élie Cartan and Chevalley. The text dealt initially with Eddington’s work in the context of the Clifford algebras adopted by Chevalley. The Clifford algebras65 are associative algebras that generalize those of the qua Unpublished, 15 pp, entitled “Les spineurs et la mécanique quantique”, January 1956 (AL) 64   Relativity Theory of Protons and Electrons, the last chapter of which is entitled: “The exclusion principle”, beginning with the paragraph concerning second quantization (pp 308-329). 65   A Clifford algebra on the field of real numbers or of complex numbers, for example, is generated by adding or multiplying real or complex multiples of n generators Ai satis­ 63

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ternions. In this context, spinors are nothing more than elements belonging to spaces in which the representations of spin groups act; the latter themselves being constructed from the generators of Clifford algebras66. Interestingly, this manuscript was the only occasion when Lemaître referred to spin groups. The computing part of Lemaître’s work, where he is back in his element, consists in the construction, nowadays classical, of Clifford algebras from the Jordan and Wigner fermion creation and annihilation operators in second quantization.67 When a topic fascinated Lemaître, it invariably showed up in his classes. This is why in 1955-1956, his Masters students would enjoy playing with spinors, as along with their professor. Roger Broucke, who was doing a BA in mathematics in those years and who would later become professor in aerospace engineering at the University of Texas Austin, remembers68:

fying the following rule: AiAj = – AjAi (for i different than j) and Ai2 = gi (where gi = +1 or -1). The Clifford algebra is then of dimension 2n. The case of quaternions can be obtained by taking two generators A1 and A2 and g1 = g2 = -1. The complex quadriquaternions can be obtained by considering on the field of complex numbers four generators of square +1 or -1. For each (pseudo-Euclidean) space with a pseudo-distance: x12 + x22 + … + xp2 - y12 - y22 - … -yq2, one can naturally associate a Clifford algebra Cl(p,q) with p+q generators such that p generators have a square +1 and q generators have a square -1. The basis vectors of this space are then associated with the generators of the algebra and this association allows us to define vectors and to talk about the norms of the latter. 66   The spin group Spin(p,q) associated with the Clifford algebra Cl(p,q) is generated by exponentials having as their argument a sum of products of two generators of Cl(p,q). One can show that a map of the type f(v) = uvu-1, induced by an element u of Spin (p,q), transforms a “vector” v of Cl(p,q) into another “vector” of Cl(p,q) of the same norm. If one takes into consideration the correspondence between Cl(p,q) and the pseudo-Euclidean space Rp,q, which is associated with it, one can show that the transformation uvu-1 induces a pseudo-orthogonal group of transformations of Rp,q, denoted by SO(p,q); the spin group is thus of dimension n(n-1)/2, n=p+q. We have then uvu-1 = (-u)v(-u)-1, thus two transformations of Spin(p,q) correspond to only one element of SO(p,q). This property had already proven by Élie Cartan, in his paper of 1913. Cf. F.R. Harvey, Spinors and Calibrations, Boston, Academic Press, 1990. 67   In quantum field theory, these operators describe the production or annihilation of a particle. The construction of Clifford algebras from these operators can be found in D.H. Sattinger and O.L. Weaver, Lie Groups and Algebras with Application to Physics, Geometry, and Mechanics, Berlin, Springer-Verlag, 1986: 182-186. 68   Letter 15-01-1998 (translation from the original in French).

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I know that he often told me about spinors. I think he launched into spinors because he dreamt about a unified theory. He said that tensors were insufficient as tools […] and at one point, he said in class: “This Van der Waerden invented spinors in 1928. Strangely, Cartan also invented them in 1913. I would like for someone to try to elucidate that. That would make a nice thesis.”

This is how Roger Broucke came to write a dissertation entitled “L’invention des spineurs” (“The invention of spinors”). His dissertation adopts an historical point of view. Lemaître advised Broucke to start from Cartan in 1913.69 After a thorough exegesis, Broucke and his professor show that one can effectively say that Cartan was at that time in possession of all of the essential elements that would become the theory of spinors. But to understand his 1913 work, the cosmologist advised his student to go back to Cartan’s own 1894 Ph.D. thesis,70 which led to an interesting discovery71: We even found that in spaces of 8 or 9 dimensions, spinor groups can be found in Cartan’s thesis in 1894. We even asked ourselves why Cartan has not said (in his 1938 book) that he had discovered spinors in 1894. The reason is probably the limitation of dimensions.

Lemaître would not be satisfied for Broucke’s thesis to remain merely the result of a literature search. He would send him to ULB to consult the great mathematician, Jacques Tits72 who would become  E. Cartan, “Les groupes projectifs qui ne laissent invariante aucune multiplicité plane”, Bull. Soc. Math., Vol. 41, 1913: 53-96. In the classification of Cartan of the simple Lie algebras of finite dimensions (that serve to generate the corresponding Lie groups), one discovers four families of algebras An, Bn, Cn, Dn and five exceptional algebras E6, E7, F8, G2 and F4. The families Bn, and Dn generate rotations in complex spaces of dimensions respectively odd and even. They are thus naturally related to the spinors. 70   E. Cartan, “Sur la structure des groupes de transformations finis et continues”, Thèse, Paris, Nony, 1894 (Paris, Vuibert, 1933). 71   Excerpt of the summary of the thesis of R. Broucke, communication 15-01-1998 (translated from the original in French). 72   Lemaître had probably met Jacques Tits in the context of the Centre Belge de Recherches Mathématiques, a sort of “contact group” gathering mathematicians from 69

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later a professor at the College de France, and who was called the “successor of Élie Cartan” by Alain Valette73. Broucke would have the pleasure to learn from Jacques Tits some clarifications about the exceptional groups G2 and F4. The student and successor of Lemaître, André Deprit, also attested to his infatuation with spinors. He would produce a work, which was a synthesis and an original generalization of the algebra used by Eddington, in a Bourbaki-like language.74 Lemaître’s passion for spinors, however ended with Broucke, and would only occasionally recur in his classes75. By the end of the 1950s, his fascination returned to the classical mechanics and numerical calculations involved with the “three-body problem”. Algebra had been a sidelight to his work prior to the war and during his wartime meditations. One senses that he exhibited a certain reluctance to reopen it76 feeling that algebra had really and definitively changed. Lemaître knew in fact that some of his mathematician colleagues, fascinated by Bourbaki, considered, somewhat wrongly afterward, his work on the spinors as out of fashion. But the Canon was irrepressible, and once bellowed out to Broucke regarding his determination to preserve the ‘old’ notation of Cartan,77 “They won’t agree, but we don’t care!”

diverse Belgian universities. Jacques Tits and his wife would have the pleasure of welcoming Lemaître at their place in Berkeley in the early 1960s (oral communication, J. Tits, 30-03-1999). 73   A. Valette, “Quelques coups de projecteurs sur les travaux de Jacques Tits”, Gazette des Mathematicians, Juillet 1994, no 61: 61. 74   A. Deprit, “A.S. Eddington’s ‘E-Numbers’”, Annales de la Société Scientifique de Bruxelles, Ière série, t. 69, 22 December 1955, no 2: 50-78. 75   His students, such as J.P. Antoine or J. Weyers who later would become professors of theoretical physics at UCL, were still transcribing notes from Lemaître’s classes on spinors during the 1960s. 76   In his notebook of his spiritual retreat in August 1943, he wrote: “the course of ‘methodology’ (Note: this course was in fact a lecture of epistemology and history of mathematics) must be changed: it is not up to date concerning its algebraic part, because of the importance given to algebra in the mathematical studies now” (translation from the French). 77   R. Broucke (oral communication, 07-07-1998).

Chapter XI

From cosmology to calculation: the Størmer problem

1. The problem of the origin and nature of cosmic rays

T

he primeval atom predicted the existence high energy charged particles in the universe, the “hieroglyphs” of the first moments of the world. According to Lemaître, this fossil radiation could be the cosmic rays that started to interest several physicists of the end of the 1920’s and to which he had produced a short note as early as 1930 influenced by his reading of Millikan and Cameron’s works.1 Cosmic rays had been detected early in the twentieth century, by Elster, Geitel and Wilson. They had shown that the air in a closed vessel was being ionized, even when completely shielded by a few centimetres of lead to block radiation from terrestrial sources. This was evidence for radiation of extremely high energy, particles of more than one billion electron volts2. This result was confirmed and extended by experiments with ionization chambers carried to high altitude in balloons. There was indeed radiation, but where did it come from and what was its nature?3

  (1930a), Chapter VI.   The electron volt (eV) is a unit of energy. 1 eV is the energy acquired by one electron accelerated across a potential difference of 1 volt. 3  The reader is directed to the excellent survey paper of a student of Lemaître’s, A. Descamps, “La Radiation Cosmique”, Institut Royal Métérologique de Belgique, Miscellanées, 1943, no XIII. See also Louis Leprince-Ringuet, Les Rayons Cosmiques: Les Mésotons (preface of Maurice de Broglie), Paris, Albin Michel, 1945. 1 2

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Apart from Wilson, who held that radiation had a terrestrial origin linked to the acceleration of electrons by the intense electric fields in thunderstorms4, physicists generally regarded it as an extraterrestrial phenomenon. Millikan thought that cosmic rays were high energy photons produced by the fusion of hydrogen to helium and heavier nuclei. Jeans on the other hand, in 1925 attributed cosmic rays to the annihilation of matter. Such theories however invariably led to energies too low to have registered in the experiments with ionization detectors. Regener proposed, on his part, that cosmic radiation was linked to the total radiation emanating from the stars or from our galaxy, and which is attenuated traversing the universe to earth (in the hypothesis of the elliptical space, of course). After 1932, when Messer­schmidt discovered the isotropy of cosmic rays, several more hypotheses would be eliminated including those positing the Sun or any single galaxy as the source.5 More sophisticated experiments likewise disproved the photonic cosmic hypothesis, and showing these rays to be constituted of charged particles. In the 1930s and up until the War, the origin of cosmic rays remained a great mystery; hypotheses abounded, and in particular, that of Lemaître could not be dismissed. Several scientists opted in the late 1930s to abandon the problem of the origin of cosmic rays, lowering their ambitions to the problem of the interaction of primary cosmic rays with the atmosphere. As framed in 1945 by Louis Leprince-Ringuet:6 The origin of the cosmic rays is surely one of the most exciting problems being addressed today. Where does this radiation, that seemingly fills space isotropically within which the Earth moves, come from? […] This question was often raised over the last twenty years; and at   Pierre Auger would show that this was not possible, as at the Jungfraujoch station (3500m in the Bernese Oberland), cosmic rays were recorded with energies in the range of 1016 eV, while the electric field of storms can be estimated to be in the range of 1010eV. 5   Cosmic rays of sufficiently high energy from point sources would not lead to a homogeneous and isotropic distribution. 6   Les rayons cosmiques…, op. cit.: 306-307 (our translation from the original in French).

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the outset physicists brimmed with optimism. Unaware of the danger, and the extraordinary complexity of the problem, ignorant of the immense energies involved, and lacking precise measurements, they could afford bold hypotheses. They are now wiser and do not talk overly about the origins of radiation. We simply study it for itself, try to characterize it and estimate the highest energies of the rays, to obtain more precise indications about their nature.

Lemaître remained firmly attached to his idea deriving from the primeval atom, and with that turned to a problem within his mathematical grasp, the determination of charged particle orbits in the magnetic field of the Earth. In fact, the origin of cosmic rays is not completely understood today. Lower energy cosmic rays, mostly protons and atomic nuclei, could be produced by the explosion of supernovae, as validated by NASA’s Fermi Gamma Ray Telescope and the Very Large Telescope (VLT) of the European Southern Observatory. Nevertheless, for cosmic rays of the highest energies, up to 1020 eV, this mechanism is no longer valid. Quasars and radio-galaxies have been proposed, but also run afoul with observations. Extragalactic cosmic rays interacting with the Cosmological Microwave Background radiation restricts their energy to at most 5.7 x 1019 eV, for distances beyond 100 Megaparsecs (Mpc), the so-called Greisen-Zatsepin-Kuzmin cutoff, or “GZK effect”, as realized in 1966. Berezinsky, Birkel and Sarkar have thus proposed that such radiation may result from the decay of dark-matter particles in our Milky Way galaxy. In this picture, in the early universe, extremely massive and long-lived particles were created and aggregated to form the gravitational potentials which led to galaxies and larger structures. Their decay half-lives exceed the age of the universe, but their decay or mutual annihilation may produce very energetic protons, gamma photons and neutrons. As Michael Hillas observed in Nature in 19987, “it   M. Hillas, “Cosmic Rays without End”, Nature, Vol. 395, 3 September 1998: 15-16. I thank the late Professor Duquesne de la Vinelle who drew my attention to this paper. 7

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appears quite possible that Lemaître wasn’t far wrong”. These exotic massive particles are reminiscent of the decay products that the priestcosmologist envisioned filling the universe in its first moments “just after” the disintegration of the primeval atom. Today, the primeval atom hypothesis is simply untenable. But it is certainly plausible that the disintegration of topological defects or of other super-massive particles from the early universe may give rise to Ultra High Energy Cosmic Rays (UHECR)8 of energies greater than 1020 eV.

2. The determination of the orbits of cosmic rays: the Størmer problem During Lemaître’s trip to the United States in the first semester of the academic year 1932-1933, he stayed a long while at MIT and worked with Manuel Sandoval Vallarta9 (1899-1977) who had been appointed Associate Professor there in 1930. The latter became a great friend of Lemaître and likewise enjoyed his association with another Louvain physicist, Charles Manneback.10 Vallarta had become interested in the problem of cosmic rays in the early 1930’s when Compton’s data clearly showed that the intensity of cosmic radiation varied   Cf. K. Kotera, A.V. Olinto, “The Astrophysics of Ultra-High-Energy Cosmic Rays”, Annual Review of Astronomy and Astrophysics, 49 (2011): 119-153; Pierre Auger Collaboration, “Correlation of the highest-energy cosmic rays with the positions of nearly active galactic nuclei”, Astroparticle Physics, 29 (2008): 188-204; R. Clay, D. Bruce, Cosmic Bullets: High-Energy Particles in Astrophysics, Cambridge, MA, Perseus Books, 1997; A. Letessier-Selvon, T. Stanev, “Ultra-High-Energy Cosmic Rays”, arXiv astro-ph: 1103.0031.   9   Cf. R. Gall, “Manuel Sandoval Vallarta”, Physics Today, December 1970: 70; V.M. Lozano, “Manuel Sandoval Vallarta: Toda una Tradicion en la Ciencia”, Ciencia y Desarrollo, Mayo-Junio 1977, no 14: 6-12. 10   Manneback had nominated Vallarta as a member of the 2nd section (Physics) of the Société Scientifique de Bruxelles on 18-12-1924. In 1926, Lemaître and Manneback would propose him as a member of the 1st section (mathematics), 2nd and 6th (technical sciences) sections of this society. Archives du secrétaire general de la Société (Namur, FUNDP, University of Namur).   8

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with the geomagnetic latitude,11 confirming those of Clay performed between 1928 and 1933. Their intensity at high and low geomagnetic latitudes is about the same. However, the intensity around 50° latitude differs by about of 15%. On 14 May 1931, an important colloquium dedicated to cosmic rays12 was held at the Royal Society of London where the most recent developments of the field were discussed. Lemaître likely read the Proceedings of the Royal Society of London13 in 1931 or possibly the in-depth review by Fr. Dopp, S.J., in the Revue des Questions Scientifiques14 in July 1932 just before his departure for the United States. Lemaître was persuaded that cosmic rays could consist of charged particles, at least in part. A theory describing the interactions of charged particles with the Earth’s magnetic field had been developed by Carl Størmer, of Oslo University15, in order to understand the phenomena of the northern lights. Lemaître and Vallarta undertook to demonstrate that Størmer’s theory could also explain the latitude effect discovered by Compton and Clay.16 The cosmologist and his colleague pressed on quickly as the latitude effect was a significant unresolved issue to which Størmer’s theory would provide the key.   The magnetic field of the Earth is approximately a magnetic dipole whose axis makes an angle of 11.5º with respect to the axis of the Earth. One can define coordinates with respect to this axis, similar to geographical coordinates (latitude and longitude), termed geomagnetic coordinates. Compton had set up a network of measurements involving 69 stations where the intensity of the cosmic rays was measured by comparing the ionization caused by these rays to those produced by a calibrated source of radium. 12   Cf. L.G.H., “The nature and the Origin of Ultrapenetrating Rays”, Nature, Vol. 127, 1931: 859-861. 13   T. 132, 1931: 331-352. 14   H. H. Dopp, “Le Rayonnement Ultrapénétrant”, Revue des Questions Scientifiques, 4e série, t. XXII, 20 juillet 1932: 7-140, following the paper: “Le Rayonnement Ultrapénétrant” in the same journal, 4e Série, t. XVI, 1929: 332-357. 15   A. Egeland, W.J. Burke, Carl Størmer. Auroral Pioneer, Berlin, Springer, 2013, Astrophysics and Space Science Library 303; Brun, Viggo, “Carl Størmer in Memoriam”, Acta Mathematica, 100, 1–2 (1958): i–vii. 16   Lemaître would maintain correspondence with Jacob Clay and one of his assistants, Herman Zanstra (Cf. ‘Les Dossiers de Correspondance’ at the AL). 11

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They were not alone. The physicist Bruno Rossi was working on the same topic17 in Berlin, and in the summer of 1930 he became aware of the expedition that Bothe and Kolhöster were organizing in the North Atlantic to measure the cosmic ray intensity as a function of geomagnetic latitude. As their latitude was too high, they did not obtain any interesting results, but upon their return, Bothe drew Rossi’s attention to the Størmer problem. In fact, Bothe and Kolhöster had already referenced the theory of the Norwegian scientist, nevertheless18, “as [they] had mentioned in their paper, Størmer’s theory appeared to be so complex as to rule out the possibility of applying it to cosmicray problems”. Rossi, like Vallarta and Lemaître, was probably aware of this paper, but did not heed this warning and independently arrived to rather similar conclusions, even if the former never performed the detailed computations to the same degree as theirs. Størmer’s interest in the problem of the polar lights, northern or austral, was piqued by the experiments performed by Kristian Birkeland. As early as 1896, Birkeland hypothesized that these lights were produced by “cathode rays”19 emanating from the Sun, and are strongly curved by the terrestrial magnetic field in the vicinity of the poles, finally interacting with the atmosphere to yield their beautiful characteristic coloured veils. He conceived of an experiment where a sphere enclosing an electromagnet, playing the role of the Earth, was bombarded by cathode rays. Størmer said that20: Returning from a study trip, around Christmas in 1902, I remember that Birkeland told me about his important experiments with which he was very busy. What he said made a strong impression on my mind that oriented my future research. Indeed, as mathematician, I was cap  B. Rossi, Moment in the Life of a Scientist, Cambridge University Press, 1990: 2629. 18   B. Rossi, op. cit.: 27. 19   One would say nowadays a flux of electrons. 20  C. Størmer, De l’espace à l’atome (Trad. C. Størmer and A. Boutaric), Paris, Alcan 1929: 179 (our translation from this French version). 17

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tivated with taking on a problem of mathematical analysis: to compute the trajectories of electrons in the magnetic field of such globe, first to apply the results to Birkeland’s own experiments and afterwards to the Northern Lights in order to theoretically predict all of their characteristic features.

Størmer then remarked on something possibly known also to Lemaître: Some time before, Henri Poincaré, using mathematical analysis methods, succeeded to explain the essential features of the Birkeland experiment concerning the focusing of cathode rays by a single magnetic pole. Starting with the law describing the action of the magnetic field on the motion of the electrons, he was able to compute their trajectories, thus solving the problem. But in the case of a system with two magnetic poles and not only one, the computation of the electron trajectories was most difficult.

Between 1904 and 1907, after long calculations by hand that amounted to some 5000 hours of work, Størmer and several students succeeded in calculating 120 trajectories described by electrons in the = l where vicinity of the Earth. In his popular scientific work From the Depths is the disof Space to the Heart of the Atom, Størmer exhibited photographs tance of of the models that he had built where wire assumed the precise trajectory charged particle 21 of the electrons. at the center of A few words of explanation about Størmer’s theory are in order, the dipole and 1 which deals with the motion of a charged particle coming from infinity = (Mq/mv)1/2 ; and encountering a magnetic dipole field. The Norwegian mathematim: mass of the cian showed that the motion of such a particle can be described by two particle. v: its elementary motions that can be treated separately. The first one is a mospeed, q: the tion in the meridian plane that passes by the axis of the dipole. The point absolute value that represents the particle in this plane is then described by two nonof its charge,

r

21

  C. Størmer, De l’espace…, op. cit., 184 (fig. 59) and 186 (fig. 60).

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analytically integrable second order linear differential equations. The second is the rotational motion of the meridian plane itself, which is completely known once the motion in this meridian plane is known22. Calling θ the angle formed by the tangent to the trajectory and the meridian plane, the Størmer relation is expressed by: e sinθ = 2 γ1/rcosλ – cosλ/r2 where e has the value +1 (-1) if the charge is positive (negative), γ1 is a first integral of the motion and is related to the angular momentum of the particle at infinity and r is a parameter defined from a quantity related to the energy of the particle23; λ is the geomagnetic latitude. The Størmer theory showed that at a given point on the Earth, characterized by a geomagnetic latitude λ, particles of a given energy can only reach this point along the directions located inside a cone, having this point as its vertex, and whose axis is perpendicular to the meridian plane. The cone is directed towards the West if the particles are positively charged and towards the East if the particles are negatively charged. The opening angle of the cone is given by π-2θ where θ is calculated by the Størmer relation where one has posited that γ1 = 1. As the sine function takes its values between -1 and +1, one sees immediately that at a given geomagnetic latitude and for a value of angular momentum at infinity (γ1) initially fixed, below a  certain energy not all orbits are allowed. Intuitively, if the particles do not have sufficient energy, they “bounce” without being able to reach the Earth’s surface.   For technical details, the reader should consult first 1943a, then L. Janossy, Cosmic Rays, Oxford, Clarendon Press, 1947 or also R.C. Haymes, Introduction to Space Science: 369-401. 23   r =ρ /l where ρ is the distance of the charged particle at the center of the dipole and 1 = (Mq/mv)1/2; m: mass of the particle. v: its speed, q: the absolute value of its charge, M: the magnetic moment of the dipole, l is the radius of the circular orbit that would describe a particle of the same mass and speed on the equatorial plane. The radius l is a function of the energy of the particle. 2 g1 = (e/mlv) x (angular momentum of the particle at infinity with respect to the dipole axis). I refer here to A. Descamps, op. cit.: 10. 22

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Størmer provided a mechanical analog of the motion in the meridian plan.24 Within a certain approximation, the trajectories in this plane can be obtained as projections of trajectories of a heavy point mass sliding without friction on a particular surface25, whose shape is modified as a function of the angular momentum of the particle.26 In the case where this momentum is not too high, the surface could be described as follows. Imagine a large plain extending to infinity and gradually rises to two imposing cliffs. Between them, there is a pass.27 From the pass, one tumbles down in a basin leading to two valleys enclosing, like two horns, a peak with an ovoid base. The two extremities of the horns reach one another, behind the peak, in a point corresponding to the axis of the dipole.28 If one imagines throwing marbles with different energies down the plain, one will be able to appreciate the different types of trajectories of the Størmer problem. Certain marbles do not succeed in reaching the pass and roll back. These are the particles that never reach the Earth. Some of them stop just at the pass, i.e. have zero speed, and thus remain there. This situation corresponds to a circular orbit of a charged particle in the plane of the geomagnetic equator. Others oscillate for an infinite time in the pass, between the two cliffs. This corresponds to orbits, periodic in time, along which the charged particles oscillate from one side to the other of the equatorial plane. These trajectories can also be periodic in spatial coordinates under the condition that their period of   The reader is referred to Figure 1 of (1943a: 7) reproduced in the paper of Lucien Bossy, “Le Rayonnement Cosmique dans le Travail de Georges Lemaître”, Ciel et Terre, t. 110, juillet-août 1994: 117, or Figure 7 of A. Descamps, op. cit: 15. 25   The surface described by the height sin2q/2 of a horizontal plane. 26   More precisely, as a function of the value of g1. 27  If g1 is strictly greater than 1, there is no pass linking the plain to the basin. If g1 is negative, there is no basin at all. When g1 is situated between 0 and 1, the form of the pass and the basin is modified, but there is still a passage between the basin and the plain. 28   In the projection on the meridian plan described in coordinates (r,l), one represents the surface of the Earth by a circle, whose radius rT = (radius of the Earth)/l is changed as a function of the energy of the particle. The orbits of particles reaching the Earth correspond, in the meridian plane, to curves intersecting this circle. 24

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oscillation is commensurate with the period of rotation of the meridian plane. There are also marbles, coming from infinity, which approach more and more closely a trajectory that oscillates in the pass. One then obtains, in the case of charged particles around the Earth, what one calls orbits asymptotic to periodic orbits. For a given periodic orbit, there is in fact an infinity of orbits asymptotic to it. This “mountain” description showed both the beauty of the problem and its mathematical complexity. This complexity would not trouble Lemaître and Vallarta. The problem was well posed and they had access to the Differential Analyser, “Bush’s Machine”,29 which had just been completed in 1931 at MIT, consisting of an analog machine enabling the integration of classes of ordinary differential equations and graphically representing their solutions. Once again, Lemaître had arrived just at the right moment to obtain both good observational data (here the variation of the intensity of cosmic rays with respect to the geomagnetic latitude) and also the theoretical tools and computation needed to explain the observations, here Størmer theory and Bush’s machine. The first paper of Lemaître and Vallarta (1933a), received by the Editor of the Physical Review on 18 November 1932, provided an explanation of the latitude effect based on Størmer Theory, but hardly a simple application of it. The two scientists showed first that one can greatly simplify the problem of the intensity distribution of cosmic rays30 by the famous theorem of Liouville in classical mechanics.31 If one assumes that the in29   This machine was invented by Vannevar Bush (1890-1974). See J.A.N. Lee, Computer Pioneers, Los Alamitos, IEEE Computer Society Press, 1995, pp. 149-153. 30   The intensity of the cosmic rays in a direction is the number of particles per unit of time, per unit of surface area normal to this direction, and per unit of solid angle (cf. Janossy, op. cit: 268). 31   We assume that a conservative mechanical system is described by a Hamiltonian H that represents the energy of the system. Hamilton’s equations, derived from H, describe the system’s evolution. If we consider a volume of phase space (a space formed roughly of positions and speeds of the particles). Each point represents a possible state of the system. Liouville’s theorem states that under the evolution controlled by Hamilton’s equations, the phase space volume is an invariant. Its form can change, but its volume is invariant.

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tensity distribution of cosmic rays of a given energy is isotropic at infinity, i.e. if at great distances, the intensity of these rays is the same in all directions32, then this theorem implies that the distribution of cosmic rays that reach the Earth at a specific point remains isotropic in angle within the whole cone allowed at this point. Thus in a Størmer cone at a point on the Earth, the intensity remains the same whatever direction is considered. The total intensity of the cosmic rays of a given energy, measured at one point on the Earth, can thus be determined by the precise form of the cone of allowed directions, this intensity being roughly proportional to the cone opening. Lemaître and Vallarta would tackle the problem of finding the exact shape of these cones. What they observed was that one can determine the boundary of these cones by studying the periodic orbits as well as those asymptotic to them. The allowed directions are those corresponding to particles coming from infinity and reaching the Earth. One sees then that the periodic orbits, where the particles travel around the magnetic dipole in closed orbits, cannot represent trajectories entering the cones of all allowed directions. The trajectories asymptotic to the periodic orbits, those that closely approach but do not merge with them, determine the natural border characterizing the surface of the Størmer cone. Such considerations along with large computations on Bush’s machine, led Lemaître and Vallarta to the following. For cosmic rays of a given energy coming from infinity, there is a geomagnetic latitude λ1 such that no particle of this energy can reach the earth at a latitude between the equator and λ1 (the Størmer cone closes completely on itself). There is, on the other hand, a geomagnetic latitude λ2 over which the particles of this energy can touch the Earth in all direction (the Størmer cone open then completely and becomes a plane). Between these two limits, particles of this energy reach the Earth along a direction localized within the Størmer cone. If one remembers that there is a correspondence between the opening   As early as 1932, the work of Messerschmidt had lent credence to the hypothesis of the isotropy of the cosmic rays. 32

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of the Størmer cone and the total intensity of the cosmic rays reaching a point on the earth’s surface, one understands that Lemaître and Vallarta succeeded in explaining the Compton and Clay latitude effect. In their first paper (1933a), the intensities, or equivalently the solid angle of the allowed cones, faithfully reproduce the observed curves. These curves are constant in the very low and very high latitudes but increase dramatically at the middle latitudes. The paper also offered an explanation of the asymmetric “EastWest effect”. It was said that the positively (negatively) charged particles reach the Earth along the directions situated within a cone whose axis, perpendicular to the geomagnetic meridian plane, is directed towards the West (the East). If the radiation is composed of a quantity of particles which are mainly positive, we have therefore to detect an intensity higher towards the West than towards the East. At the end of the paper, the authors also announced that they would be able to explain another asymmetry: the “North-South effect” (1933a: 91), which will be discussed later on. Størmer’s reaction to their publication was very negative,33 even calling it “a failure”34. He may have been disappointed at being overtaken in his own field, although he could have attained the same results by pushing his own computations just a little further. But it is more probable that Størmer did not succeed because of the following reasons. His main interest was not primarily in cosmic rays, but in the Polar Lights. The hypothesis of the isotropy of cosmic rays at infinity was to him as well as Birkeland, quite remote. In the case where the distribution of the cosmic rays at infinity was not isotropic, the simplification introduced by Liouville’s theorem was of no utility to the computation. He was thus not inclined to invoke it, and additionally the Bush’s machine was not at Størmer’s disposal. But the fact remains that it was precisely the isotropy hypothesis and Liouville’s   C. Størmer, “Critical Remarks on Paper by G. Lemaître and M.S. Vallarta on Cosmic Radiation”, The Physical Review, Vol. 45, 1934: 835-838 (cf. A Deprit, “les amusoires de Mgr Lemaître”, Revue des Questions Scientifiques, t. 155, 1984: 217. 34   Cf. Letter of Lemaître to Størmer, 03-03-1934 (AL). 33

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theorem, which were the main ingredients enabling the explanation of the altitude effect. Størmer, who also implied that Lemaître and Vallarta had insufficiently recognized his own contribution, attacked them on the relevance of Liouville’s theorem. Fortunately for the two, Swann35 in the case of the motion of electrons, then Fermi and Rossi36, had also themselves independently employed the famous theorem. In a letter addressed on 3 March 1934 to Størmer, Lemaître defended himself in the following way37: In your introduction38 you seem to insinuate that the importance of your previous work for the solution of this new problem (the latitude effect) have been somewhat underestimated. You must admit at least that in regard to my work with Vallarta, we fully acknowledged the results we drew from you. We even tried to preserve your notation […]. You seem to not approve our use of Liouville’s theorem and the treatment we made of your nice work on periodic orbits.

He then drove his point home, clinching the argument: I do not know if you intend to adopt our hypothesis that the rays come uniformly from all directions or if you prefer to consider rays coming from a particular direction, from the Sun for instance. In the latter case, Liouville’s theorem would naturally be useless […] I believe it is unnecessary to return to the demonstration of this theorem as the question was discussed in detail by Swann, and Fermi and Rossi. Second, as it is sufficient at each point to determine the cone specifying where the rays come from, it is unnecessary to compute all   W.F.C. Swann, “Application of Liouville’s Theorem to the Electron’s Orbit in the Earth’s Magnetic Field”, The Physical Review, Vol. 44, 1933: 224-227. 36   Acc. Linc. Att., t. 17, 1933: 346 (cf. Janossy, op. cit.: 269). 37   A copy of the letter is preserved at the AL (our translation from the original in French). 38   Introduction to a letter sent to Lemaître by Størmer and to which he had attached a numbers of copies of his article. Lemaître found this letter after he returned from the United States at the beginning of March 1934. 35

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the trajectories, but only the ones forming the surfaces of the cones: the limited trajectories that reach infinity. This was almost solved by your own work on periodic orbits.

Størmer accepted this argument, and later maintained friendly relations with Lemaître, as witnessed by a letter he wrote him after the Second World War.39

3. The first “Lemaître’s School”: 1933–1945 Lemaître would involve his students and collaborators in the difficult task of computing orbits of the Størmer problem to determine the direction of approach of cosmic rays. One needs remember that from 1933 until the end of his life, the initial motivation of his research, linked to the primeval atom hypothesis, was given short shrift. It was as if this motivation no longer interested him anymore. Rather, one senses that he was completely in his element with the Størmer problem. He could manipulate extremely difficult power series and numerical calculations of astounding length, having found something closer to the core of his intellectual power. In February 1933, Lemaître, back from his second journey to the United States, proposed to his student Louis Bouckaert to begin a thesis on the Størmer problem. Nevertheless, he was not in a position to mentor him closely as he had to go back to the United States in September of the same year and would only return to Belgium for the second semester of the Academic Year 1933-1934. During this period, he convinced another of his students, Odon Godart, to pursue the same topic. The latter would become his technical collaborator the following year, a not very well defined status, but which consisted mostly in helping Lemaître with his computations as well as the management of his daily affairs. This was no minor task during a period where Lemaî39

  Letter dated 10-07-1946 (AL).

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tre was only occasionally in Louvain. Odon Godart would maintain this status until his departure to MIT in 1938, to replace Louis Bouckaert who was working with Vallarta.40 During the year 1935-1936, Vallarta came to spend a year in Louvain as guest professor, thanks to an advanced fellowship of the American Educational Foundation. This visit greatly stimulated the work of the group of the Collège des Prémontrés which would be joined at the beginning of the year 19361937 by Tchang Yong-Li. Lucien Bossy would join in 1939, who also contributed to the problem of the computation of Størmer orbits41. Since the key to the determination of the shapes of Størmer cones is the study of periodic orbits and their asymptotic orbits, Lemaître (1934d) and Bouckaert42 would first study trajectories arbitrarily close to a circular orbit localized within the plane of the geomagnetic equator, corresponding to the pass of the “landscape” described above. Through trial and error (1943a: 14) and various original mathematical tricks43 which were the signature of Lemaître’s handiwork, they discovered a way to categorize the periodic orbits with the help of power and trigonometric series (1934e). In his Ph.D. thesis defended in Louvain in 1938, Tchang Yong-Li would develop, in more detail, Bouckaert’s representations for the orbits located near the   Lemaître had sent Louis Bouckaert to MIT in January 1935 to work with Vallarta. Louis Bouckaert had some disagreement with Vallarta about the way to conduct one of Lemaître’s computational projects (oral communication of O. Godart, 14-06-1995). This led him to abandon the problem of the cosmic rays and to go to Princeton where he worked with Wigner before coming back as Professor of Theoretical Physics in Louvain. It was in Princeton that he befriended the mathematician André Weil (cf. A Weil, Souvenirs d’apprentissage, Basel, Birkhäuser, 1991: 138-139). 41   Lucien Bossy’s interest in the Størmer problem would continue after the War and he would be invited to submit a communication during the Study Week of the Pontifical Academy in 1962 entitled “Le problem du rayonnement cosmique dans l’espace intraplanétaire’’, organized by Vallarta. This contribution would be published as “The Motion of Particles Trapped in a Magnetic Dipole Field as a Special Case of the Størmer Problem”, Pontificiae, Academiae Scientiarum. Scripta Varia, 1963, no 25: 355-379. 42   L. Brouckaert, “Contribution à la théorie des effets de latitudes et d’asymetrie des rayons cosmiques. II. ‘Trajectoires voisines de l’équateur’”, Annales de la Société Scien­tifique de Bruxelles, série A, t. LIV: 174-193. 43   Such as the transformation of a Fourier series into a Taylor series and conversely, brilliantly described by A. Deprit in “Les amusoires…”, op. cit: 201. 40

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periodic equatorial orbit, in terms of Fourier series with variable coefficients44. In the Størmer problem, there are two families of periodic orbits: the “external” periodic orbits and the “internal” periodic orbits. As early as in their article (1933a), Lemaître and Vallarta had pointed out that there is a lower limit of g1 for which one can have two periodic orbits. Gradually Lemaître discovered that at this lower limit, the external orbits become identical to the internal orbits before they all disappear at lower values. Lemaître recognized a particular case of a beautiful theorem of Poincaré, found in his Méthodes Nouvelles de la Mécanique Céleste, which stated that when a parameter of a dynamical system was varied, a periodic orbit could not disappear alone, but should do so at the same time as another periodic orbit (1943a: 14). In the 1940s, Lemaître would also realize that the examples of the natural termination of families of periodic orbits in the Størmer problem are analogous to the fate of trajectories of a particular case of the three-body problem studied by Strömgren. We will see that this statement would play a major role in shaping his research after the war45. By studying the direction for which cosmic rays can reach the Earth, Lemaître and Vallarta observed that one cannot simply analyse the trajectories asymptotic to the external periodic trajectories, which Lemaître termed “trajectories of the first kind” (1934d: 165). In fact, they only determine a “principal cone”, for which all directions of cosmic rays coming from infinity arrive at Earth. The Størmer cone can also comprise zones where certain directions are allowed and other are forbidden. Finally, there exists a region where all directions are forbidden. Making the analogy between cosmic rays and light rays, the principal cone corresponds to the fully lit area, the forbidden zone to shadow, and the intermediate to penumbra. Such com  Tchang Yong-Li, “Contribution à la théorie des effets de latitudes et d’asymétrie des rayons cosmiques. VI. Cônes des rayons cosmiques infiniment voisins de l’équateur; VII. Trajectoires voisines de l’équateur”, Annales de la Société Scientifique de Bruxelles, série I, t. LIX: 285-345. 45   Cf. Chap. XIV, section 4. 44

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plex phenomena arise because certain allowed directions do not come from trajectories asymptotic to periodic orbits, but rather from trajectories that are tangent to the Earth (which Lemaître called “trajectories of the second kind”). If one perturbs such an orbit, one again finds trajectories that reach the observer, but it may be that the orbit must pass through the Earth before reaching the observer. This kind of orbit, for which our planet acts as a screen, generates a complex mix of allowed and forbidden directions. Mapping out this complex structure of zones in the interior of the Størmer cone would require a great deal of work and computation; several hundred curves had to be calculated by the Bush Machine, resulting in a seminal paper on allowed cones (1936c)46. Such precise knowledge of the cone’s complex structure and the “screening effect” occurring in the vicinity of the trajectories of the second kind would also enable Lemaître and Vallarta to explain why there is an excess of the intensity of cosmic rays in the South (1935a, 1936a). When Thomas Johnson of the Franklin Institute, who was familiar with their work47, carried out a campaign of measurements in Mexico48, Vallarta’s homeland, he succeeded in observing the effect as the two had predicted in 1932. At the close of the 1930s, Lemaître and Vallarta would further improve the method of the representation of orbits asymptotic to periodic orbits (1936d) and provide an explanation of the ‘longitude effect’ by which the intensity of cosmic rays at the same geomagnetic latitude vary with the geomagnetic longitude (1937c), this variation being approximately 8% at the equator. This phenomenon is well-described using Størmer cones and by assuming that the centre of the dipole is approximately 300 km away from the centre of the Earth.   In his paper, there is also found an explanation of the energy distribution of cosmic rays. At any point on the Earth, there is a minimal energy required for a particle to arrive. All particles of a higher energy follow a direction allowed by the Størmer cones. 47  T. Johnson, ‘North-South Asymmetry of the Cosmic Radiation In Mexico’, The Physical Review, Vol. 47, 1935: 91-92 and 326. 48   The measurements were carried out at two stations; one near Mexico City at 2280 m and the other at the top of a volcano in the State of Mexico, the Nevado de Toluca, at 4300 m. 46

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Lemaître also invited Lucien Bossy to study trajectories that he had not yet considered and which oscillate in the basin of the “landscape” around a singular curve passing near the axis of the dipole49. One can observe a gradual shift in Lemaître’s research with Odon Godart concerning Størmer orbits, which became very clear after the War. Following the Canon’s suggestion Godart would adapt methods of solving an equation of Hill’s theory of the Moon50 and apply the theory of characteristic exponents of Poincaré, in order to understand the properties of instability of periodic orbits.51 The War would put an end to the work of the group of the Collège des Prémontrés that one could call the first school of Lemaître.52 Sustained by their fruitful interaction and deep friendship, the group of Lemaître, Vallarta, Bouckaert, Godart and Tchang Yong-Li published seven papers in that period, which later appeared as a whole under the title: “Contribution à la théorie des effets de latitude et d’asymétrie des rayons cosmiques” (“Contributions to the theory of cosmic rays latitude and asymmetry effects”).53

  This work would lead to a publication (1945k).   Hill’s theory of the Moon leads to the problem of orbital perturbations. The Keplerian orbit of the Earth-Moon system is perturbed by the Sun and massive planets. 51   O. Godart, “Contributions à la théorie des effets de latitude et d’asymétrie des rayons cosmiques. V. Determination des exposants caractéristiques des trajectories périod­ iques”, Annales de la Société Scientifiques de Bruxelles, série I, t. LVIII: 27-41. 52  Alphonse Descamps, whose excellent article has been mentioned and who started his BA dissertation in 1940-1941, must also be associated with this “first school” of Lemaître. His works would be published after the War: “Contributions à la théorie des effets de latitude et d’asymétrie des rayons cosmiques. VIII. Détermination de l’angle h des trajectories asymptotiques en leur point d’intersection avec l’axe l”, Institut royal de métérologie de Belgique, Miscellanées, 1945, no XV. 53   One must add to these publications that of Alphonse Descamps and a last one from René de Vogelaere (“Contributions à la théorie des effets de latitude et d’asymétrie des rayons cosmiques. IX. La pénombre au voisinage de l’équateur”, Annales de la Société scientifiques de Bruxelles, t. 64, 1950: 115-223. 49 50

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4. The Størmer problem after 1945 Lemaître read Poincaré’s Méthodes Nouvelles de la Mécanique Céleste (New Methods of Celestial Mechanics) during the War 19401945, and he also knew well the Analytical Dynamics of Whittaker, who had used techniques inspired by Delaunay’s theory of the Moon in some problems of dynamics. This inspired Lemaître to introduce some new methods in the study of the Størmer problem. In August 1948, his meeting with W.W. Heinrich from the University of Prague would convince him that it would be fruitful to apply Delaunay’s ideas to problems of analytical mechanics54. The theory of Charles-Eugène Delaunay (1814-1872) describes the complex motion of the Moon55 that does not rigorously follow a Keplerian orbit due to various perturbations affecting it, notably from its interaction with the Sun. The originality of this theory derives from a technique by which, representing the orbit in terms of Fourier and power series, the perturbation terms are progressively eliminated.56 The French astronomer begins with the equations of motion written in Hamiltonian form. A canonical transformation, i.e. one that does not change the form of Hamilton’s equations, then eliminates the constant term and the first order pertubative term in the series. But this transformation modifies the higher order terms of the series. However by performing further canonical transformations in the same way, those higher order terms are sequentially eliminated as well.

  Research notebook 1947-1953 (AL). An entry of 9 October 1948, clearly states that the meeting with Heinrich aroused new ideas on the manner of tackling the Størmer problem. 55   From the applications of the Hill theory by Godart after 1938, and during the War, with the thesis of Dr. Wang on the theory of the Moon’s libration, Canon Lemaître became increasingly interested in the theory of the perturbation of the lunar orbit. 56  For the technical details: W. Neutsch, K. Scherer, Celestial Mechanics. An Introduction to Classical and Contemporary Method, Mannheim, B.I. Wissenschaftsverlag, 1992: 564-597. I thank the “groupe de mécanique céleste” of the FUNDP (University of Namur) and more especially V. Dentant, for having drawn my attention to this work. 54

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Lemaître would adapt Delaunay’s theory57 to the Størmer problem to describe orbits that oscillate periodically in the neighbourhood of the circular equatorial orbit. These orbits could be represented with the help of the Fourier series of variable coefficients, as has been established by Bouckaert and Tchang Yong-Li. Lemaître’s ideas was then to eliminate, by a series of canonical transformations “à la Delaunay”, the first terms of these series, to reduce the complex problem of the oscillatory motion of a particle to the problem of a plane periodic orbit pertubated by the higher order terms. The crux of this method is finding a translation of the Størmer problem into a suitable Hamiltonian formalism. The Canon would succeed in expressing the problem’s Hamiltonian in a form of a trigonometric series58 with variable coefficients, with the help of two methods: one elementary, the second involving the elliptic functions of Jacobi59, whose Fundamenta Nova Theoriae Functionum Ellipticarum Lemaître had studied during the World War60. One should note the original and innovative aspects of Lemaître’s works. It could even be said that Lemaître was thirty or forty years ahead of his time in terms of the history of mathematics. While the greatest mathematicians of the day such as André Weil, together with their schools, had embarked on the Bourbakian style61, Lemaître was working “à la mode de Poincaré”, on dynamical systems, perform  Delaunay’s method considers trigonometric expansions with the same number of arguments as there are degrees of freedom in the system. In the Størmer problem, as in the works of Poincaré and in the use of these works by E.W. Brown and C.A. Shook who adapted the theory of Delaunay, one uses expansions that use only one argument (oscillation period in Lemaître’s work, mean longitude of the stars in others). 58   A series comprising sine and cosine functions includes as an argument the oscillation period of the cosmic particles, while in celestial mechanics, one uses the star’s celestial mean longitude. 59   The trigonometric terms of the series came from an expansion of the Jacobi elliptic function cn(x). Cf. D.F. Lawden, Elliptic Functions and Applications, Berlin, SpringerVerlag, 1989: 24-49. 60   The construction of the Hamiltonian formalism of Lemaître involved, since he considered periodic orbits, the famous “action-angles” variable. Cf. (1949c: 85-86). 61   This school was characterized by its disdain for explicit numerical calculation and an immoderate taste for abstraction and overgeneralization. 57

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ing numerical simulations such as became common in the 1970s and 1980s. Since then, raw computational power has allowed us to visualize many wonderful mathematical objects that held no secret to the Canon. As previously mentioned in the algebraic theory of spinors, Lemaître often displayed a knack for making surprising progress in fields that afterwards were recognized as being very subtle and profound. More recent astrophysical questions could have profited from Lemaître’s expertise in cosmic rays, for example the Earth’s radiation belts studied by Van Allen and Alfvén62. But according to Lucien Bossy63 “such works never awakened his curiosity”, probably because at the very moment in 1958 when the Van Allen belts were discovered, he was engrossed in the problem of galactic clusters. For Lemaître, a new scientific passion must necessarily drive out the old, even one that had absorbed his cerebral energy for a long time.64 Be that as it may, it was not Lemaître and his collaborators that were to profit from his analysis of the Størmer orbits for astrophysical or space science applications. The first fruits fell to others. For example, in the Space Sciences section of the nuclear research centre of the CEA (Commissariat à l’Energie Atomique) in Saclay, created in 1967 and directed by Dr Lydie Koch-Miramond, the results of Vallarta and Lemaître were put to good use for the determination of the orbits of charged particles in the neighbourhood of the Earth. Interestingly, the first parallel computer bought by the CEA, under the direction of Messiah, was first tested and used to compute the orbits of the Størmer problem according to Lemaître’s methods65.

  Cf. R.C. Haymes, Introduction to Space Science, New York, Wiley, 1971: 166-194.   “Le rayonnement cosmique…”, op. cit.: 118. 64   Lemaître categorically refused a research contract that was proposed to him by the U.S. Air Force for the study of the Van Allen belts. 65   I am grateful to Mrs. Lydie Koch-Miramond for her hospitality at the CEA and for this valuable information (11-5-1999). Cf. L. Koch-Miramond, ‘’Cosmic Ray Sources and Confinement in the Galaxy” in The Big Bang and Georges Lemaître…, op. cit.: 315-325. 62 63

Chapter XII

A time of war (1940–1944)

1. Exodus

I

n 1939 a number of the friends and colleagues of Lemaître were mobilized. Such was the case of Abbé Reyntens of the Collège SainteGertrude of Nivelles and Canon Renoirte. The latter joined the Signal Corps, as an officer of the engineering reserve corps responsible for the pigeons still used for communication, just as in the trenches of 1914-1918. Louvain’s academic year 1939-1940 was spent in an unusual environment where the cassock and the academic regalia of some professors were substituted by military uniforms, as remembered by Jean Ladrière1: Several professors who were mobilized had the opportunity to return and give their classes in Louvain; this was the case with Canon Renoirte. Those who were at the Institute (Institut Supérieur de Philo­ sophie) in 1939-1940 remembered this momentous year of juxtaposed activity, that would characterize the entire wartime: there was the time of major events, where one was waiting for the invasion – and then, there was a sort of eternity, where one was meditating on the texts of the De spiritualibus creatoris or on reasoning in terms of fact in Husserlian logic. The presence at the Institute of a professor who was  “Monsieur le chanoine Fernand Renoirte, professeur à la Faculté des sciences et à l’Institut Supérieur de Philosophie. 1894-1958. Éloge académique prononcé aux Halles universitaires le 16 mars 1959, par Jean Ladrière, chargé de cours, à la Faculté des sciences”, Annuaire de l’Université catholique de Louvain, t. 1957-1959: 104. 1

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teaching us hylomorphic theory in the uniform of an engineering officer epitomized this strange duality.

As a non-commissioned officer, Lemaître had passed the aged of being mobilized. He looked wistfully at his friends and colleagues leaving for a war that everyone thought imminent. Among his friends, there was the pianist Henri Janssens who, through his letters, would keep him up to date about the atmosphere that reigned among the garrisons as they waited for the offensive. Shortly after the invasion of Belgium, Lemaître joined his family, while Louvain was being deserted by a large fraction of its inhabitants who had been terrorized by the air bombing of 10 May. As with many Belgians who retained traumatic memories of the depredations committed by the German troops in 1914-1918, he prepared himself for the exodus. His plan was to take part of his family to England. As early as 13 May, if one believes the photo album of the Canon’s mother, he reached Charleroi. From a little notebook of the journey in which he recorded where he had travelled and whom he had met, it is possible to retrace his exodus in detail. On 15 May, the day of Netherlands’ capitulation, he left Marcinelle with two Ford cars and a trailer. The Canon took with him 22 people, including his uncle and godfather, the doctor Édouard Lemaître aged seventy-eight, one of his sister-in-laws and her four children, two of his cousins, and household servants2. Having passed  More precisely the group comprised doctor Édouard Lemaître (b. 1861; resident of Charleroi) and his daughter; Marthe Gallez-Lemaître (b. 1890; resident of Charleroi, widow of Louis Gallez and cousin of the Canon); Mrs. Maurice LemaîtreDegen* (b. 1903; resident of Marcinelle and sister-in-law); her four children: Henry (b. 1928) Jeannine (b. 1930), Francis (b. 1932) and Gilbert (b. 1934), accompanied by a household servant of Italian origin, Mrs. Ziller* as well as her three children: Constant (b. 1924), Adolphe* (b. 1926) and Olga* (b. 1928); Mrs. Laure Schlick (b. 1914 and resident of Marcinelle, a niece of doctor E. Lemaître); Miss Anne-Marie Lemaître* (b. 1895 and cousin of Georges Lemaître); Mr. and Mrs. A. Laurent* and their daughter* (b. 1912) accompanied by their chauffeur Mr. Adhémar Lejeune* (b. 1904) and his spouse* born Berger as well as their two children: Marie* (b. 1928) and Maurice* (b. 1934). The asterisks refer to those who would not enter France with Canon Lemaître 2

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Binche and Mons, they arrived in Stambruges that evening around 5:30 and decided to pass the night near the church. The day after, on the advice of the parish priest of the place, Lemaître led the group to Péruwelz, in two successive trips and from there, they scouted ahead around Wiers near the French border. He then joined the group that stayed in Péruwelz and had the chance to spend the night of 18 May in the house of Mr. Pierre Fabri, director of the local branch of the Banque Nationale (National Bank)3. But difficulties would soon beset the group. First, he had to take care of the hospitalization of his sick sister-in-law4, then one of the two cars broke down5. They finally resigned themselves to abandoning part of their luggage in the caves on the bank of Péruwelz. Of the 22 persons, only ten, all related to the Canon, would be allowed to pass the French border with him. After having fulfilled all formalities, the latter entered France through Bon-Secours on 18 May. The group being smaller and the car having a trailer, the family of Lemaître made relatively rapid progress until Douai where they spent the night, accommodated by the family Butrille. The day after, they arrived at Labuissière, near de Bruay-enArtois, and spent the night at the mine hospice. On 20 May, slowed down by the columns of refugees, they reached Saint-Venant, south of the Nieppe forest, but their car fell into the ditch. Having rescued the car, they progressed until Montreuil not far from Le Touquet. The hope of Lemaître was, if possible, to head to Boulogne and find a boat that could take them to England. On 22 May, Lemaître drove back north and reached Samer. Having more and more problems driving on the road, they had to jettison the trailer that same day. The advance of the tanks that had created a breach on the front at Sedan, had progressed through Saint-Quentin, Amiens and Abbeville to complete the on 18 May 1940. This list was established after the document dated 17 May 1940 written by Georges Lemaître to obtain the authorization of passage in France (AL). 3   The latter being absent, they were probably taken in by M. Homerin, the collector of Mr. Fabri (Letter of P. Fabri to G. Lemaître dated 29 August 1940, AL). 4   The Canon would fortunately benefit from the help of a nurse of Bon-Secours: C. Lusein (letter of the latter to Lemaître dated 20-01-1941, AL) 5   It was probably that of Mr. and Mrs. Laurent.

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encirclement of the French and Belgian Armies, as well as of the expeditionary unit of Lord John Gort. As with refugees and allied soldiers alike, the Lemaître family had been caught in their pincers. Their adventure on the roads of the north came to an end when a German motorcyclist forced them to stop.6 It was around 27 May 1940, ‘Operation Dynamo’ had just begun, the plan by which Lord Gort would attempt to re-embark with his expeditionary unit on the beaches of Dunkerque, and during which two French divisions were captured. Father Lemaître had to abandon his planned escape and, for the time being, he tried to organize the provisioning of his family and its accommodation in the region of Boulogne. His journey notebook records their travels along the road, helped by the parish priests of the villages that they were crossing and that he often had to cope with makeshift solutions for the feeding of his relatives. At the beginning, the members of the family could live on the food that they had brought with them, but from 25 May onward, they had to kill whatever chicken they caught, or they benefited from the generosity of the French and the distribution of bread organized for refugees. Around 14 June, while the German army continued to progress through the South and the French government took refuge in Bordeaux, the Canon ensconced his family in a villa, Stella Matutina, not far from of a farm situated near Boulogne. On 18 June, the entire family took the road back towards Belgium and Georges Lemaître, having accomplished in an exemplary way his role of pater familias joined his father and mother in Brussels.

2. A time for solidarity On 19 March 1940, Msgr. Honoré Van Waeyenbergh, Vice-Rector of UCL since 1936, succeeded Msgr. Ladeuze as the head of this University. From the very outset of the War, he was courageously deter Recollection of Gilbert Lemaître, who took part in the attempted exodus (21-051999). 6

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mined to return to academic life, refusing any kind of collaboration with the enemy.7 On 8 July, classes were able to resume despite the absence of some professors. The academic year 1940-1941 began on 12 November 1940, just a month late. Lemaître came back to Louvain at the end of June 1940 where he started teaching his normal classes to which was added the class ‘Introduction to Philosophy’ for first year engineering students8. That had been the class of Msgr. de Strijcker, rector of the American College of Louvain, who had left for the United States with some of his seminarians at the end of May. Life in Louvain during the War was especially hard because of the housing problems caused by the destruction of May 1940, and the supply and communications difficulties. The students were touched by the great consideration of the Canon in adapting to their needs of their very existence on a day by day basis.9 Fearing that the Germans would appropriate them, Lemaître moved a series of Mercedes mechanical computing machines to his apartment on 7 Place Foch from the Collège of Prémontrés. He generously opened his place to students of mathematics and physics who needed to perform calculations. This was the case with Sr. Émilie Fraipont, an Ursuline Sister who remembered that the door of the apartment of Lemaître was always open. The Canon also allowed students to come even during his absence. When he was there, he was closely interested in their work, even if they were not doing their thesis with him. Understanding, for instance, that Sr. Émilie Fraipont had to solve some numerically rather intricate equations for her BA in physics with Manneback, he taught her the computation method   This opposition to all forms of collaboration had consequences. On 19 March 1943, Msgr. Van Waeyenbergh on behalf of the UCL and of the two State Universities (ULB having already been closed by the occupying force), refused to deliver to the Germans, the list of first year students who were destined for the “S.T.O.” (German obligatory work service). This refusal earned the Rector Magnificus a jail sentence at the prison of Saint-Gilles in Brussels. 8   The content of this class, of Lemaître which had left notes, will be discussed later. 9   Oral communication of Sister Émilie Fraipont (25-06-98). 7

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that he himself was learning during these years, the “rational iteration method”. When the students were working at his place, Lemaître came from time to time to bring them a cup of hot chocolate that he had prepared, and also sometimes he came to ensure that their use of the Mercedes was not being disturbed by the sound of the piano that he played with uncommon energy. The attention of Lemaître for his students also manifested itself in 1941 on the occasion of an event that had great consequences for Belgian inter-university relations. That year, the occupiers decided to close the Université Libre de Bruxelles. Msgr. van Waeyenbergh did not hesitate to welcome the ULB students to his Alma Mater. This courageous initiative was far from commonplace at that time. The two universities were radically diverging philosophically and religiously, and certain classes, as well as the internal discipline of UCL would have appeared incompatible with the deep-rooted philosophy of the University of Brussels. Lemaître had acquired, thanks to the contact with the Anglo-Saxon world and his Chinese students, a capacity to transcend philosophical and confessional barriers. Moreover, he had very good contacts with the members of the Université Libre de Bruxelles, including De Donder and Cox. He understood that fostering the “Bruxellois” could only be carried out respecting their own convictions. He approached both Msgr. van Waeyenbergh, and Msgr. Suenens, then Vice-Rector, in order to exempt the ULB students from religious classes. This reception posed not only ideological problems but also practical ones (the student population grew from less than 5000 in 1940 to 7000 in 1944), but opened up opportunities for Lemaître and for all those who had the privilege to meet him.10 After the war, he retained the familiarity and ease of contact with certain students and 10   There is a photograph taken with Lemaître's camera showing the “seconde candidature” (2nd year Bachelor) in physics on 26 May 1942 at the last floor of the “Collège of the Prémontrés”: of 8 students supervised by Abbé Gillon (future rector of Lovanium, in Congo) and Lemaître. 6 came from the ULB. (copy of Mme André Chalet-Jacquemain provided by Professor L. Henriet).

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colleagues of ULB, Papy for instance, in regard to research on the pedagogy of calculations, and Jacques Tits to whom he would send Roger Broucke for his study of spinor theory. Lemaître was not only devoted to his students, he also tried to comfort his friends. He approached Queen Élisabeth in order to ask her to intercede on behalf of his pianist friend Henri Janssens, who was a prisoner in Germany. Janssens would later become Lemaître’s music teacher. According to information available in the archives of the Royal Palace in Brussels, Lemaître was never received in a private audience by King Albert or by Queen Élisabeth, nor by King Leopold III, from whom he received the Francqui Prize. The only sovereign that would grant him this honour would be King Baudouin11, whose passion for astronomy and his general interest in science are well known. Lemaître was however invited to a private meeting with Queen Élisabeth, around September 194312. The Queen had long wished to meet the cosmologist, whose name certainly came up regularly in her conversations13 with Einstein. According to the account provided by Lemaître of the Queen’s maid of honour, Mrs. Carton de Wiart, the Queen had intended to invite Lemaître to discuss his cosmological theories. However, it has not been established if such a discussion ever took place.

  The archives of the Royal Palace (Brussels) prove that King Baudoin had given a private audience with Lemaître on 24 January 1952. I am grateful to Mr. Gustave Janssens, archivist of the Palace, for providing me with this information, as well as Colonel Thierry de Maere for his kind mediation. 12   This information is provided in a letter dated 23 September 1943, sent to Lemaître by a close relation of the Queen, Baroness Carton de Wiart (AL). 13   Nevertheless, his name did not come up in the important correspondence that Queen Élisabeth maintained with Einstein between 1929 and 1955 (cf. “Archives du Palais Royal. Archives du secrétariat privé de la Reine”, dossier AE 680). 11

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3. The time of isolation and reading Cut off from his international contacts, Lemaître adapted to the rhythm of Belgian scientific life, thanks to the Classe des Sciences meetings of the Royal Academy of Belgium, of which he became a titular member on 14 December 1940, and the Royal Belgian Society of Astronomy, Meteorology and Earth Physics, of which he was elected VicePresident for three years, on 13 January of the same year. From Lemaître’s notebooks14, one can see that beginning around 1943 he undertook a program of reading in order to enrich his class of mechanics. He immersed himself in the Leçons sur les invariants intégraux of Elie Cartan15 and Poincaré’s Méthodes nouvelles de la mécanique céleste. The thread linking these readings would constitute a central theme in the class and in his mathematical thought. Specifically, it is the notion of an integral invariant. The latter appeared as early as 1899 in the third volume of the Méthodes nouvelles de la mécanique céleste of Poincaré16, but would also appear later in several publications of De Donder17, widely quoted by Élie Cartan in his aforementioned book and that constituted a course he taught at the Sorbonne in 192118. These invariants associated with a system of equations, are mathematical expressions defined on sets of points and expressed with the help of integrals, which do not change when one moves these points along the curves which are solutions of these equations. If these equations describe the motion of a body in mechanics, one can appreciate   There is one notebook, probably written during his spiritual retreat in Schilde in August 1943, comprising projects of readings, BA theses and personal research. 15   E. Cartan, Leçons sur les invariants intégraux. Paris, Herman, 1922. 16   H. Poincaré, Méthodes nouvelles de la mécanique céleste. III, Paris, Gauthier-Villars, 1899. [translation of the book of Poincaré, H. (1899), New Methods of Celestial Mechanics. Vol. III., Berlin, Springer.] 17   The first scientific publication of Lemaître (1923a), which is quoted in the book of De Donder, Théorie invariante du calcul des variations, Paris, Gauthier-Villars, 1935, is linked to this context. 18  E. Cartan, “Théories des Invariants Intégraux et Mécaniques” in Notice sur les Travaux Scientifiques, Paris, Gauthier-Villars, 1974: 104-107. 14

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the interest of such invariants as they represent mathematical quantities which are preserved along the trajectories or even bundles of trajectories. Such invariants are highly useful, for example, in studying the whole ensemble of closed trajectories describing the periodic motion of particles oscillating around a circular orbit. This clearly interested Lemaître who tried to characterize the behaviour of the families of charged particle trajectories in the neighbourhood of the periodic orbits of the Størmer problem. Fortuitously, the study of these periodic orbits was completely analogous to those of the periodic orbits which appeared in a particular case of the threebody problem studied by Strömgren19. Lemaître would find in Cartan’s Leçons a unified theoretical framework that allowed him to link together the two fields of celestial mechanics and the Størmer problem. These readings would prove transformational for the next phase of Lemaître’s life. In fact, from the late 1940s until his death, the three-body problem and the Størmer problem, intimately connected to the context of the Cartan’s integral invariants would never be far from his mind or classes. The reading of Lagrange’s Mécanique, which he planned to be the reference text for the class of the seconde candidature (second year of the Bachelor’s program), would reveal a few surprises. Lemaître found a passage showing that the latter “has discovered the existence of differential forms enclosing several kinds of variations and that remain invariant when one takes the derivative d/dt in conformity to the Lagrangian equations […], an essential step to the discovery of the integral invariant”,20 a discovery he would discuss with De Donder at the Belgian Royal Academy.   The three-body problem seeks to determine the trajectories of three masses under their mutual Newtonian attraction. The special case here considers two masses in a circular orbit around their center of gravity. A third mass moves in the plane of the other two under their combined attraction, but not perturbing their motion. Strömgren had succeeded at the Copenhagen Observatory, to calculate some families of such periodic orbits. 20   Cf. Letter of De Donder to Lemaître dated 03-11-1943 (translation from the original in French). 19

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Lemaître also took advantage of his isolation in Louvain to read the works of Jacobi. He deepened his knowledge of the elliptic functions that would constitute another powerful computational tool in his arsenal which helped unify a great number of his works. The volume of iconic mathematical works that Lemaître had read in the original was nothing short of stunning, and reflected the salutory research habits he inherited from his Jesuit teacher, Fr. Bosmans. In 1942 for example, he began to read Gauss, particularly the Theoria Motus in which the “Prince of Mathematics” described a method to compute the orbit of a planet from three observations.21 Lemaître generalized this method and derived the concept of rational iteration (1942a)22, enabling the solution of numerical equations of the type x = f(x),23 as well as differential equations of the kind dx/dt = f(x,t) (1942d). Lemaître used this rational iteration method to solve the differential equation dx/dt = 2x2 (x-t), using his Mercedes computing machines. Following the drift of his research, one can see in retrospect that he did not envisage any further studies on cosmological models. From the beginning of the 1930s, he had opted for a model of a ‘hesitating’, finite and boundless universe, and to which he remained committed until the end of his life. He continued to ponder his computations on models of galaxies and clusters of galaxies, and he outlined the research that he would begin in the late 1940s.24 If he did not work   Cf. K.F. Gauss, Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections. Theoria Motus (trans. by Ch. Davis), New York, Dover, 1963: 161233. 22   In this paper, p. 350, one can find the Aitken acceleration method discovered by the latter in 1926, but rediscovered here independently by Lemaître (I thank Professor Michel Deville of the EPFL (CH) for this observation). 23   The idea of the method is the following. If one knows an approximation x1 of the solution, one can then calculate x2 = f(x1) and x3 = f(x2). One can prove that a new approximation is given by x = (x1x3-x22)/(x1-2x2+x3). 24   In August 1943 he imagined three types of behaviour of particles in “spherical condensations” (galaxies or clusters): “a first with a unique speed in each direction, a second with all speeds exclusively radial […] the third one with all possible speeds in all directions equally distributed in phase space” (“carnet” already quoted, AL; our translation from the original in French). 21

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anymore during the War in the field of cosmology or on models of formation of large-scale structure, he did not stop reading works and papers dedicated to cosmology in general, e.g. the book of Heckman (1944a) or the publications sent him by Edward Arthur Milne25. The latter had an important influence on British cosmologists, beginning in 193326. This is where one finds, for the first time, an explication of the cosmological principle requiring the homogeneity and isotropy of the universe. Milne had developed a rather original cosmological theory of his own.27 For him, the universe could be described from two points of view. The first is that of ideal observers that observe the motion of galaxies independently of the gravitational forces between them. For these observers, the cosmological principle is valid. The universe is a space-time that is infinite and flat, a Minkowski universe as in special relativity, undergoing expansion from time zero, with the relative distance between two points being linearly proportional to the time. This time t of the ideal observers is called “kinematical time”.28 If however, one considers the point of view of observers fixed to the galaxies, it is possible to give another description of the universe. Here, the universe possesses a hyperbolic geometry, but is no longer expanding. It is characterized by a “dynamical time” t logarithmically related to the “kinematical time” t. With dynamical time, the time t = 0 is situated in the infinite past and there is no more beginning of the universe. One of the consequences of the “heretical” cosmology of Milne is that the laws of nature must change; the gravitational constant, for example, varying with time.   The AL has preserved a copy of the article “World Structure and the Expansion of the Universe”, Zeitschrift für Astrophysik, Vol. 6, 1933: 1-95, dedicated by Milne to Lemaître. 26   Cf. H. Kragh, Cosmology and Controversy. The Historical Development of Two Theories of the Universe, Princeton University Press, 1966: 61-67. 27   For a popular presentation, I refer to P. Javet, Les Figures de l’Univers. Cosmogonies Modernes (Preface of G. Thiercy), Neufchatel, Éditions du Griffon, 1947: 151-190. 28   It is called kinematical, as it can be defined from the motion of the galaxies independently of the forces are exerted on them. If one takes into account these forces, one departs the realm of kinetics for that of dynamics. 25

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This description, incompatible with general relativity29, presented a further difficulty pointed out by Lemaître. After a detailed reading of Milne’s works30, Lemaître showed that the description of certain physical phenomena cannot be entirely done either referring only to the kinematical point of view or only to the dynamical point of view. The first often implies the second and the schema of Milne is rendered inconsistent (1945e: 4-5). There was in fact no criterion according to which one should adopt one or another description of the universe. Neither was Lemaître sympathetic to the assumption of a Euclidean infinite universe, and had renounced de Sitter’s universe for the same reason. Thus for the Canon, the universe could not be infinite. Lemaître would encounter Milne again on 10 September 1947, on the occasion of the first symposium organized in Brussels by the International Academy of Philosophy of Sciences, founded by the Belgian Dominican, Fr. Stanislas Dockx,31 and held at the Palais des Académies. In an interesting discussion with Hermann Weyl and Théophile De Donder, Lemaître showed that his opposition to the theory of Milne did not come from its mathematical formulation, which he respected, but from its physics.32 For the Canon, what was important is the verifiable character of the predictions of a cosmology. Lemaî  In general relativity a homogeneous and isotropic universe has a metric defined by ds2 = dt2 – R(t)2 da2 where da is the element of length of the Euclidean, spherical or hyperbolic geometries. By the change of variables Rdt = dt, one obtains a metric defined by by ds2 = R2 (dt2-da2). If one introduces this in the equations of Einstein without the cosmological constant and if one considers a universe empty of matter, then the element da corresponds necessarily to a hyperbolic geometry and R(t) = bt where b is a constant. To obtain his static space (dynamical description), Milne describes his metric ds’2 = dt2 – da2. 30   Lemaître would cull interesting elements from Milne for his classes, for example his elementary description of the Cayley-Klein model of the hyperbolic geometry of Lobachevsky. 31   L’Académie Internationale de Philosophie des Sciences (1947-1987), Bruxelles, 1989 (presentations, history, colloquia, etc.). The author is thankful to Fr. J.-M. Van Cangh and Mrs. Cambier for information on this topic. 32   Problemes de Philosophie des Science (Premier Symposium-Bruxelles 1947). III. Théories Nouvelles de Relativité, Paris, Hermann, 1949, Archives de l’Institut international des science théoriques, série A, Bulletin de l’Académie internationale de philosophie des sciences 3: 57-69. 29

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tre, invoking once again his defence of a finite and non-Euclidean universe, opted for the proper time of general relativity, which is the basis of the explanation of phenomena such as redshift. Milne’s rather vapid defense was little more than trying to attribute the Canon’s critique of his theory simply to being so comfortable with general relativity that he could no longer see the advantages of another theoretical construct! Milne did not consider his own descriptions as representations of physical reality. Along with Poincaré, he simply considered them as conventions which made it possible to ‘save’ the results of measurements. However, he believed that these views on the universe could be coupled with a theological approach, and later wrote a book on this topic.33 Very likely this disturbed Lemaître, but in the short review he wrote for this book (1950f), he did even not bother to reiterate his position regarding the purely natural beginning of the universe. Apparently he did not see the point to attack positions that seemed to him indefensible, preferring to ignore them completely. Neither did he take the trouble to point out the strange aspect of the materialist interpretation that the English biologist Haldane made of Milne’s theory. While the latter considered his cosmology as compatible with the idea of a Creator, as there is a beginning of time34 (t=0) in the kinematical representation, Haldane, on the contrary, was delighted that the dynamical approach excluded any “creation”. For Haldane, Milne’s cosmology was even more interesting, as the variation of the laws of physics was in harmony with the dialectic of Engels.35 As a result, curiously Haldane’s position drew even closer to Lemaître’s views concerning the primeval atom. In the representation of the expanding universe, the age of the universe t provides an upper limit for   E. A. Milne, Modern Cosmology and the Christian Idea of God (Edward Cadbury Lectures in the University of Birmingham for 1950), Oxford, Clarendon press, 1952. 34   “I do most fervently believe that this universe was created by Almighty God” (Modern Cosmology…, op. cit.: 160) 35   J.B.S. Haldane, The Marxist Philosophy and the Sciences, London, Allen & Unwin, 1938: 62 et seq. 33

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the wavelength of the photons, ct, which is the distance travelled by light during the time t. If one goes backward in time, the wavelength decreases, and thus the frequency and energy increase. As observed by Helge Kragh,36 at t=10-92 sec, a photon could have the energy corresponding to the mass energy of a galaxy and “without mentioning Lemaître, Haldane pictured the universe as originating from one or a few such super-photons of almost infinite energy and sketched from this assumption the entire evolutionary history of matter and life”. Lemaître never made any comment on this topic. During the War, Lemaître not only devoted himself to scientific readings, but also immersed himself into one author who would never leave him for the rest of his life,37 the Flemish mystic Ruysbroeck (1293-1381, whose name is also written Ruusbroeck). With the persuasion of the Amis de Jésus, and particularly Canon Allaer38, Lemaître was encouraged to read this author at the origin of a famous current of spirituality, called the devotio moderna, and whose principle characteristic was the insistence on personal meditation to reach an intimate union with God. Lemaître, who has pronounced his votum immolationis, this vow of total offering of his person to the Christ, on 12 August 1942 in Schilde, developed a strong interest in this author, to the point of deepening his study of Middle Dutch.39 Just after   H. Kragh, Cosmology and Controversy, op. cit: 65.   In the middle of a 1960 notebook about Pascal, Laplace, Eddington, Clifford, Lagrange and Louis de Broglie, one finds 10 pages of translation and summary extracts of Ruysbroeck. Two independent testimonies confirm that Lemaître read and treasured his works (Christiane Houyet-Lemaître, 3-7-1995, and Albert Caupain, 23-03-1995). 38   Ruysbroeck became in fact, under the influence of Canon Allaer (= J.A.), a main reference for the Amis de Jésus: “Pensées pour chaque jour du Bienheureux Ruusbroeck” Apostolus, 1939, no 148: 23-24; J.A., “Connaissez-vous Ruusbroeck?”, Apostolus, 1949, no 23: 53-56; J. A., “Vie active, vie intérieure, vie contemplative chez Ruusbroeck”, Apostolus, 1946, no 7 (Supplentum IV); J. Allaer, Ruysbroeck l’Admirable. Le Tabernacle Spiritual (Paragraphes XIX to XLVII), 1950, internal document of the Amis de Jésus (AFSAI). A retreat preached by Canon Allaer from 31-07 to 09-08-1949 in Schilde, would be dedicated entirely to the “The Spiritual Espousals” of Ruysbroeck (Apostolus, 1949, no 26: 161-165). After this retreat, Allaer would request that the Amis study Ruysbroeck’s books in their local groups. 39   It should be mentioned that Lemaître was studying the language of Ruysbroeck and not the current Flemish that he could have practiced in Louvain. The latter would always, in 36 37

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having written some his research projects on galactic clusters and on the determination of families of orbits asymptotic to the periodic orbits of the Størmer problem, the Canon carefully copied a passage of the L’anneau ou la pierre brûlante of Ruysbroeck. Herein lay a fruitful window into the personality and spirituality of the priest-cosmologist. His fidelity to the retreats in Schilde and to his long daily prayers, his retreat notebooks and his study of Ruysbroeck emphasizing personal meditation, all attest to a deep interior life. The amiable Canon with the resounding laugh and extroverted and overflowing personality, possessed simultaneously a passion for spiritual meditation and intellectual reflection, two deep confluent streams manifested by the regular alternation of scientific and religious pages that can be found in his notebooks.

4. A time of reprimand and trials Life in Louvain during the war was extremely bleak, especially for someone who had been a global figure for a quarter century. Lemaître relaxed by playing tennis at “sportkot”. He considered physical activity very important, and during the 1930s, he encouraged the students of his university to take part in competitions.40 It is remarkable to compare, during international conferences for example, the external appearance of the most venerable scientists representing countries where sport holds a place of honour and those where it doesn’t (…) If we forget (our body) it will take its revenge on our superb intellect. Five minutes of morning exercises every day are able to transform a man! fact, present problems of comprehension for him. In the 1960s, he was obliged to have the help of others to speak with the Flemish sacristan of the Saint-Pierre church where he was celebrating daily Mass (Oral communication, Abbé Smeyers, 03-03-1999). 40   G. Lemaître, Annuaire de l’étudiant 1936-1937 quoted from Petite Gazette des Archives, UCL, automne 2002, no 7: 1.

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Lemaître also relaxed by playing the piano, and his passion for music led him to concerts in the theatre of Louvain. Attending such spectacles was not permitted for ecclesiastics at that time and Lemaître was reported to the Vice Rector, Msgr. Suenens. Lemaître tried to justify himself by noting that during the concert, the curtains were closed behind the pianist, and thus this event could not be considered a spectacle in the usual sense of the world. Nevertheless, the ecclesiastical authority feared that priests from Louvain would take advantage of Lemaître’s fame to take the liberty of attending such events themselves. On 29 February 1944, Lemaître would receive a letter from Cardinal Van Roey requesting him to respect the diocesan norms in this matter, which he did.41 This was not the last time he had some problems with authority. He was reprimanded for having removed his cassock during the class of gymnastics that he attended at the sportkot. With all his peregrinations in Anglo-Saxon countries he had become somewhat casual in regard to wearing the cassock, to the extent that he was often seen without the customary sash for priests. During the 1950s, he excused himself completely from the wearing this ecclesiastic cloth42. As soon as priests could shed their cassock in the Archdiocese of Melechen, he adopted the clothing of a clergyman, regarding the outfit to be “more decent”43. To Lemaître, such details did not signify that he was questioning authority44. It was his own accommodation with the rules by which he knew to make sense of things, distinguishing the essential from the merely accessory. The war years were ones of devotion to his students, but also a time of physical and moral difficulties for Lemaître. On 7 November 1942, he lost his father, who died in a tram travelling on Rue de la Loi in Brussels while he was returning home after work. With him,  AL.   Testimony of Abbé Albert Caupain. (23-03-1995). 43   He made this declaration publically during one of the first meetings of the ACAPSUL (oral communication of Professor A. Meesen, September 1998). 44   He was bound by a special vow of obedience to Cardinal Van Roey due to his affiliation with the Fraternity of the Amis de Jésus. 41 42

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he lost a father but also a confidante who had advised him in the discernment of his priestly vocation and who had endowed him with his taste for literature, and walking. In the spring of 1944, another trial would affect the Canon.  Allied aircraft flew missions to bombard the Belgian and French railway installations to isolate the Reich. Louvain was a strategic node in the rail system and thus, on Wednesday 26 April and Monday 1 May, daytime bombings were carried out on the university campus by American planes. The locals were not overly worried, thinking that the Allies would only bomb the train station. However, on 11 May, just before midnight, reconnaissance planes flew over the city to mark out the targets. Unfortunately, due to a mix-up, the Allied airmen would drop their bombs not on the the railway, but along the axis of the Rue de Namur, destroying the Collège du Saint-Esprit, the Collège de la Sainte-Trinité, the newest section of the Collège of the Prémontrés and a part of the Halles Universitaires.45 Georges Lemaître was in his apartment on Place Foch during the night of 11-12 May. Hearing the air raid sirens, he fortunately took refuge in his basement; his building was along the bombing run and the façade of the house was fractured by the bomb blasts. The building did not catch fire, but his apartment was damaged by shrapnel that riddled his piano.46 A short while afterwards, one of his students ran to Place Foch to enquire about him. The Canon was there in front of the building and showed him a relatively small passageway in the rubble from which he was able to escape from the basement.47 Lemaître was not injured, but was in a state of massive shock, seeing his university in flames and his house now uninhabitable. Several professors who stayed in Louvain that night,

  Apparently the airmen interrupted their bombing when they saw Place Foch in flames (oral communication, Ch. Courtoy). 46   The piano remarkably survived the ordeal, and still sounds under the fingers of the Canon’s godson, Gilbert Lemaître. 47   Testimony of Marcel Nève, student in physics during the war, who had heard this account from the student who had encountered Lemaître (oral communication 12-101997). 45

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such as Canon Jozef Bittremieux, Professor of the Faculty of Theology, would never recover from this painful experience48. Lemaître moved some of the things in his office of the Collège of the Prémontrés, with the help of his students, among them Albert Caupain49, Jacques Peters and a priest from the Diocese of Liège50. In fact only the newest wing consisting only of classrooms had been damaged by the bombs. The spectroscopy laboratory of de Hemptinne, as well as the professors’ office situated on the side of Rue de Namur beside the Collège d’Arras had miraculously escaped obliteration. Lemaître kept a souvenir of these disastrous days in his office for a long time, a piece of a blackboard that had been shattered by the explosion. It was reported that the day following the bombing, he went to play the piano in what remained of his apartment, but he never reestablished his flat in Louvain. He preferred to join his mother in her house at 9 Rue de Braeckleer in Brussels. On 3 September 1944, one day before the liberation of Louvain, Lemaître, at the end of his Mass celebrated in one of the side chapels of the Saint-Henri church, heard of the liberation of Brussels, in a most unusual way. During his Mass served by Hubert Durt, future assistant of Msgr. Lamotte51, a café on the church square had begun to broadcast the anthem The Internationale as loudly as possible, which the Canon found amusing.52 Shortly before Christmas of that year, while von Rundstedt launched his counter-offensive in the Ardennes, Lemaître welcome his brother Jacques’ family into their parents’ house. Following the German advance, the family had been evacuated from Dinant by the Gendarmerie, along with the gold of the bank where Jacques was director.53  Cf. the obituary of J. Bittremieux written by J. Coppens in the Annuaire de l’Université Catholique of Louvain, 1950-54, XCVII-CXXXVIII. 49   Oral communication, A. Caupain (23-03-1995). 50   Oral communication, Professor J. Peters (03-03-1999) 51   I am grateful to J.-B. Sepulchre, Mr. and Mrs. Daniel Sepulchre, and Mrs. A.-M. Moors-De Coninck for the information on Msgr. Lamotte. 52   A recollection of Professor H. Durt living in the parish Saint-Henri (24-03-1999) at that time. I am grateful to the mother of Professor Durt, as well as his nephew, Professor Thomas Durt, and to the VUB for having made the contact with H. Durt possible. 53   Oral communication, O. Delenne-Lemaître (28-11-1997). 48

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In May 1945, Lemaître reflected on the previous years of oppression and murderous madness (1945m: 238): Here is discarded finally and definitively the foolish dream of the German, who wanted to paint the whole globe in an uniform grey; here is finally reestablished the human right to collectivity, the respect of human dignity, the freedom of mind and belief, all that finds its symbol in the democratic ideal of all our great Allies.

During this time, while the means of transport remained very uncertain in a free Belgium, Lemaître would live partially out of his office in the Collège des Prémontrés. When communication would be fully reestablished and he would be able to commute between Brussels and Louvain, the Canon would establish his home in their parental house.

5. Back to science Lemaître, cut off from his English and American colleagues during the war, got back in touch with the international scientific community a few days after the liberation of Brussels, thanks to the unexpected visit of an Indian Jesuit, Lurdu Yeddanappalli. The latter has studied chemistry in India and went to Louvain around 1937-1938 to prepare his Ph.D. on problems in catalysis. Taking advantage of the stay of Hugh Taylor, he wrote a paper with him on the dehydrogenation of cyclohexane54. At novitiate, this Jesuit knew an uncle of Hubert Durt that had gone to India around 1920 to pursue his formation in the Society of Jesus. During his time in Louvain, Yeddanappali, who was staying at the Faculty of Philosophy and Theology of the Jesuits in  H.M. Taylor, L.M. Yedanappalli, “Déshydrogénation catalytique du cyclohexane en présence des oxydes de chrome et de vanadium”, Bulletin de la Société Chimique Belge, t. 47 (1938): 162. 54

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Eegenhoven, often came to visit Durt in Brussels. On 11 May 1940, being a British subject, he had to escape Belgium and took a boat in Antwerp that brought him to the United States, establishing himself at Princeton, where he would follow closely the works of Taylor who taught there. It was Taylor who would be responsible in 1943–1945 during the Manhattan Project, for supervising the production and testing of membranes used in the gaseous diffusion process for enrichment of uranium 235 from uranium hexafluoride. The Indian Jesuit also had the chance to make contact with Albert Einstein. In September 1945, Yeddanappali arrived to finish his Ph.D., installing himself at Durt’s house. One of his first requests was to organize a meeting with Lemaître. Hubert Durt, who served the Canon’s Mass every morning, was at that time entrusted with directing the Jesuits at 9 Rue de Braeckeleer. It is probable that the Jesuit was bearing messages from Einstein and Taylor, and Lemaître found their discussions stimulating. He was reestablishing the fertile contacts that had been his scientific lifeblood during the 1930s. Nevertheless, Fr. Yeddanappalli confided to Durt his astonishment with Lemaître’s reaction to scientific news. The Jesuit who had immersed himself in the remarkable progress made in nuclear physics in the United States during the war had the odd impression that the war years had created an enormous chasm between the Canon’s science and the state of physics in 1945. Lemaître, who had no appreciation for particle physics, seemed uninterested in the ‘new physics’. Lemaître also admitted to him that he was not convinced of the reality of the nuclear explosions of Hiroshima and Nagasaki of August 1945; as with most of the preeminent German physicists held captive by the Allies, he dismissed the news as war-time propaganda. Lemaître had been left behind by nuclear and particle physics, but his readings of Poincaré, Cartan, Jacobi and Gauss would open for him another line of research. He abandoned modern developments in cosmology related to nuclear physics, but the war had led him back to his fixed points, classical mechanics joined with numerical computa-

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tion, heralding an era that would flourish long after his death – computational studies of dynamical systems. Just one year after the liberation of Brussels, in September 1945, Lemaître was once again expounding his primeval atom hypothesis, this time to the Société Helvétique des Sciences Naturelles in Fribourg (Switzerland). This conference would catalyze the project, following the suggestion of the Swiss philosopher Ferdinand Gonseth, of the book that would make the works of Lemaître known to the general public: L’hypothèse de l’Atome primitif (1946a & b). Einstein would be apprised of the content of Lemaître’s talk by his faithful friend Michele Besso55: Some weeks ago, I attended a conference of Abbé Lemaître in Fribourg, during the annual assembly of the Société Helvétique des Sciences Naturelles. Do you remember the one in Lucerne, where Anna especially took part? Abbé Lemaître does not reject the cosmological term that, in his view, is absolutely fundamental; his conclusions are based entirely on that, as it was in the past for you and de Sitter. Unflappable, he extrapolates from the primeval atom that generates the expanding space, in which all charges are balanced, as if it were an isotope of the neutron…

  Our English translation from the French edition: Albert Einstein. Correspondance avec Michele Besso. 1903-1955 (translation, notes and introduction of Pierre Speziali), Paris, Hermann, 1972 (1979 edition): 221. 55

Chapter XIII

Lemaître the master. A portrait of his pedagogy (1940–1944)

1. Teaching and research, a seamless cloth

A

comprehensive picture of Lemaître requires examining his role as an educator, both as the classroom lecturer, and as the research director forming his intellectual progeny one by one. The priest-scientist was very much current with the phenomenon of the close integration of the ‘blackboard’ and the ‘laboratory’, which has become the hallmark of all modern great research universities. Lemaître began his teaching career in 1925-1926, where he took on the courses of history and methodology of mathematics designed by Charles de la Vallée Poussin and by inaugurating a course on relativity1 created especially for him in the first year of the Masters in mathematical and physical sciences2. At the same time, he substituted for Simonart for lectures in classical mechanics for physicists, mathematicians and engineers, and was entrusted with the engineers for their classes in mathematical analysis. During the year 1932-1933, following the death of his former professor Alliaume, he took over the class and exercises of astronomy, the class of celestial mechanics and the class on probability theory along with the theory of observational   Notes from the course on relativity taken by Maurice Biot in 1927-1928, courtesy of his spouse. From these notes, it would seem Lemaître did not allude to any contemporary developments in cosmology, of which he was one of the major protagonists. 2   The list of classes given by Lemaître can be found in various directories and course programs, in the archives of UCL, and edited between 1925 and 1964. 1

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errors. Following the departure of Maurice Biot for the United States in 1937, his teaching load expanded with new responsibilities for classes on analytical mechanics for the candidatures (students in the first two years of the Bachelor) in physical and mathematical sciences, and engineering. During the War, he would be entrusted with the class of philosophy and religion for engineers, replacing Msgr. De Strijker3. Afterwards, the Canon was relieved from his classes of astronomy, and the exercises designed for Odon Godart. He ceded his class of probability theory to Ballieu in 1947, and in the late 1950s, began to turn over his classes on mechanics to André Deprit. Until the end, he kept the class on the relativity theory for himself, and would only give up his class on methodology in his last year of professorship, in 1963-64. It is nearly impossible to get a clear idea of the structure or content of his classes before the Second World War, as neither Lemaître’s notes or those of his students have been found. In all likelihood, according to various testimonies, he taught relativity in a manner reflecting his papers of 19274 and 1933,5 and his approach did not markedly deviate throughout his career. It should be noted that Lemaître’s classes also covered his own scientific contributions, but without the slightest reference to himself; one would think there was nothing beyond Friedmann’s work on those topics. It is significant also that in Lemaître’s treatment of cosmology, there was not the slightest trace of philosophical or religious allusions when approaching the problem of the initial singularity;6 it was simply one mathematical solution among many. Before WW II, Lemaître did not have the luxury of extensive editing of his classes due to his long trips to the US. Lemaître’s natural amiability had been reciprocated by his colleagues who quite happily offered to substitute for him7 in his absence, along with the trust bestowed in him by Msgr. Ladeuze.   More detail concerning Msgr. De Strijker will be provided later in this book.  (1927c). 5  (1933e). 6  Oral communication, Jean Ladrière, 26-10-1994. 7   In a letter dated 04-08-1932 addressed to Msgr. Ladeuze by Canon Lemaître (AL), one learns that, during the academic year 1932-33, Charles Manneback replaced Lemaître for the October exams on probability and astronomy, and de la Vallée Pous3 4

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For methodology and history8, he relied on Euclid’s works, Greek arithmogeometry and the sources of non-Euclidean geometries. After the War, the class of methodology would be enriched by his studies of the works of Jacobi, Lagrange, Poncelet and Desargue, all these authors being more or less closely linked to his research. The history of mathematics was crucial for Lemaître, but he did not approach the subject as an historian of science. Lemaître was not interested in reconstructing a work within its context, only to replace it after critical analysis. Rather he brought ancient texts to life by injecting their substance directly into contemporary research. This relationship to history is characteristic of the great mathematicians, such as Gauss and his Disquitiones Arithmeticae, in which he rereads Fermat and Euler, or André Weil, who studied Klein and Riemann. This relationship is also characteristic of the typical conception of the history of “Bourbaki” that one can discover reading the famous ”Eléments d’histoire des mathématiques”9. Lemaître had attended the courses of history and methodology of mathematics of Charles de la Vallée Poussin, who enjoyed a reputation for meticulous detail and excellent pedagogical style10. The cosmologist took inspiration from these courses during his first years of teaching as, according to various testimonies, his classes bore clear similarities of approach to those of the “Prince of Analysis of Louvain”, sin replaced him in methodology and history of mathematics. Van Hove agreed to shift his own class of astronomy for engineers in order to let Lemaître deliver his course on probability theory in the second semester. 8   This class of history ceased after the Second World War. 9   Paris, Masson. This is a conception of history shaped by searches for conceptual sequences, and cast in contemporary language. 10   Course notes of de la Vallée Poussin during the Second World War courtesy of the author’s professor and friend. Br. Robert Graas (Maxime-Léon), who donated them to the Archives de la Vallée-Poussin in Louvain-la-Neuve. The course content had not significantly evolved since Lemaître’s time as a student. Occasionally, Br. Graas relied on the notes of Br. Nicolas-Joseph Schons, whose own famous mathematics texbooks have been used for generations in Catholic schools. Born in 1884, Schons had attended the class of de la Vallée Poussin before World War I; cf. R. Graas, “Trois géants de la pédagogie en mathématiques”, Humanités chrétiennes, 30ème année, juin-août 19861987, no 4 (manuscript without pagination).

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for instance, the detailed elaboration of certain Greek mathematicians, notably Euclid11, and of non-Euclidean geometries12. There were points of departure as well, as Lemaître’s lectures never included number theory,13 which he eschewed, or algebra14 which he abandoned after the War.15 Lemaître likewise charted his own course in his methodology class in the late 1940s with his attempt at the reformation of the education system of arithmetic with his “new figures”, which will be discussed later. Part of the curriculum of history of mathematics of de la Vallée Poussin was dedicated to the famous problem of trisection of the angle going back to the Greeks,16 namely finding a method to divide a given angle in three equal angles by ‘construction’, i.e. with only a ruler and compass. This problem in fact has no solution, as these two instruments are described by just first- and second-degree functions, i.e. a straight line and circle, whereas the trisection of an angle requests a fourth degree curve called the “conchoid of Nicomedes”, belonging to the family of the so-called “conchoids of line”17. Lemaître was well acquainted with this problem, likely in part due to Fr. Bosmans, but certainly due to de la Vallée Poussin. It was also the subject of a lecture by d’Ocagne18 on 9 May 1935 at the Société Scien­tifique   De la Vallée Poussin, Histoire des Mathématiques (course notes of R. Graas), Ch. II.   De la Vallée Poussin, Méthodologie (course notes of R. Graas), Ch. II, Part 3, “Les trois espèces de géométries”; Ch. IV, “Quel est le système de géométrie réalisé dans la nature?” 13   De la Vallée Poussin, Méthodologie (course notes of R. Grass), Part 1. 14   De la Vallée Poussin, Méthodologie (course notes of R. Graas), Part 2, “Questions méthodologiques”. 15   The topic was not fashionable, in any case, after the “revolution” of Modern Algebra (cf. retreat notebook, August 1943, AL). 16   Histoire des mathématiques, Part 1: Histoire des mathématiques anciennes, Ch. 1, “Époque pré-euclidienne ou hellène”, § III, “Mathématiques en dehors de l’école de Pytagore”, II, “trisection de l’angle”” (course notes of R. Graas). 17   A conchoid of a given curve (line, circle, etc.) is obtained in the following manner. Draw a straight line through the origin O and any arbitrary point on the curve. Mark the two points, each of equal length “d” measured on either side of where the straight line intersects the curve. The ensemble of all such points represents the conchoid. 18   “À propos the trisection of the angle”, Annales de la Société Scientifique de Bruxelles, Série A, t. 555, 12 juillet 1935, no 2: 37-38. 11

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de Bruxelles19. When he was invited for the second semester of the academic year 1937-1938 as a visiting professor at Notre Dame University, he attended a seminar of Karl Menger on the three famous geometrical problems of the Greeks: squaring of the circle, the trisection of the angle and the duplication of the cube.20 During the seminar itself, Menger asked a student, Bernard J. Topel, to demonstrate the approximate trisection of an angle discovered by the German, Kopf, by construction, i.e. solely with a ruler and a compass, and whose precision was extraordinarily good. When Topel had finished demonstrating Kopf’s method21, Lemaître explained the fundamental reason for its great precision, namely the fact that the circle used in the drawing closely approximates a fourth degree curve, called the “Limaçon of Pascal”, which is nothing other than a conchoid of circle22. Lemaître proposed a modification of Kopf’s solution which was likely to further improve the approximation’s precision. Topel was dumbfounded and later published a note related to the Kopf-Lemaître solution.23 Lemaître’s intuition which helped him assess the geometrical content of any problem, led him from the conchoids of line he learned from de la Vallée Poussin to the conchoids of circle24, to which the “Limaçon of Pascal” belongs,25 in real time!   This was during this time that Lemaître himself was in the United States.   André Deprit was the first who quoted this work refering to information given to him by Karl Menger, through an intermediary, Doctor Howland (letter, K. Menger to A. Deprit, 11-10-1983, related by A. Deprit and preserved at AL). 21   This solution was published by O. Perron, “Eine Neue Winkeldreiteilung des Schnei­ dermeisters Kopf”, Sitzungber, d. Bayerischen Akad. d. Wissensch., München, 1933. 22   In this case of the “Limaçon of Pascal”, the fixed point O, with respect to which the conchoid is defined, is situated on the circumference of the considered circle. 23   B. J. Topel., “Concerning a remark of Canon Lemaître about Kopf’s trisection of the Angle”, Reports of a Mathematical Colloquium, 2nd Series, 1939, no 1: 49-52 (it concerns the proceedings of the seminar edited by Menger). 24   The polar equation of the conchoids of line is r = (a/cosq) ±b; the polar equation of the “Limaçon of Pascal” (conchoid of circle) is r = a cosq + b. 25   The conchoids are evoked (but not in details) in the part of the class where de la Vallée Poussin spoke of Pascal (Partie II), “Histoire des mathématiques au temps modernes”, chapitre II, “De Descartes à Hughens (1637-1675)””; lectures notes taken by R. Graas. 19 20

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The course on probability26 played a special role in Lemaître’s career. He inherited this class with the death of Alliaume, although Lemaître was not interested in probability theory as such. His operative conception of probability, i.e. the ratio of the number of cases satisfying the event criterion to the total number of possible outcomes, all possible outcomes being equiprobable, involves a certain philosophical circularity, and would ultimately be replaced by Kolmogorov’s more axiomatic formalism. But Lemaître’s approach and style of teaching and research was ultimately very pragmatic, focusing on the essentials; he had no patience for such formalistic or philosophical fineries. Any semblance of a systematic structuring of the material beginning with definitions and theorems went out the window; the master and students marched with aplomb right in to the classical game problems (games of patience, St. Petersburg paradox, etc.) or the famous geometrical probability problems (Buffon’s problem27, rain drops problem28, etc.) as one might find in the works of Borel and Deltheil.29 Perhaps the problem most elaborated in detail during his wartime classes concerns cosmic rays. Lemaître showed his students how to calculate the probability that at least one cosmic ray triggers a detector during a certain time. Probability distributions were also illustrated by astronomical examples, e.g. the random distribution of stars in the sky. In the second part of his class, the cosmologist took up observational error theory, developing the least squares method drawing inspiration from a presentation of Eddington and showing   Notes of Lemaître’s class (27 pp) taken by Br. Robert Graas during the year 19411942. In 1943 Lemaître thought to edit the class notes, but ultimately never did so. 27   If one drops a needle randomly on the floor, and the width of the floorboards is greater than the length of the needle, what is the probability that the needle falls on a crack? 28   A series of points is distributed randomly on a surface. Picking one at random, what is the probability that the distance to its closest neighboring point is between r and r + dr? Lemaître began this exercise by drawing a parallel with the problem of surviving an bombardment of randomly distributed falling artillery shells, a problem he was all too personally familiar with from his service in World War I. 29   E. Borel, R. Deltheil, Probabilités et erreurs, Paris, Armand Colin, 1934 (1954, 9e édition). This book is one of the references used in the class of Lemaître (cf. page 58-88 for the continuous probabilities and pages 149-192 for observational error theory). 26

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how the methods of Goedseels and Alliaume were hardly applicable. The finale of the course was an introduction to Fourier transforms and their application to probability distributions. But it was by far his classes of mechanics that showed the most pedagogical originality and mirrored his own research after 1938. His mechanics class during the Second World War was almost entirely thematic around the Størmer problem, and the liberal dose of elliptic integrals and their computation by the Landen transformation clearly reflected his own scholarship of the late 1940s (1947b). His treatment of the pendulum likewise draws from his work on elliptic functions30 and to his interaction with Professor W.W. Heinrich of Prague, at the International Astronomical Union Congress in Zurich, 11-18 July 1948. Through Heinrich’s own papers, Lemaître discovered the methods of Sommerfeld, Epstein and Born from the beginning of quantum mechanics, and which he used to advantage in pendular motion. He even discovered new techniques from Legendre’s letters to Jacobi31. If Lemaître’s teaching benefitted from his research interests, there is also at least one example where his pedagogy resulted in a publication. The final work of Lemaître’s career (1967d) was a popular article on his ideas that matured while he was delivering his famous lectures on the pendulum, specifically the ideas connected to a well-known theorem of Poncelet32. His courses on celestial   The solutions of the pendulum equation involve elliptic functions.   “[The meeting in Zurich] led me to study a previous work of Heinrich on the introduction of normal coordinates and in general on the practical manner of performing the variation of constants in Delaunay’s way. The demonstration appeared obscure to me or at least involved assumptions that I was not very familiar with. But the author refers to the methods developed by Sommerfeld, Epstein, Born, etc. from the beginnings of quantum mechanics […] when one applies this method to pendular motion, one obtains that the conjugate variable to the argument of the elliptic functions is a simple function of the modulus […] there is thus a possibility to set to music the program of variation of the elliptic elements following the suggestion made by Legendre in one of his last letters to Jacobi” (notebook 1947-1953, AL, dated 09 October 1948; our translation from the original in French). 32   (1967e). For the relationship between the pendulum, Poncelet’s theorem and elliptic functions cf. J. Snape, Applications of Elliptic Functions in Classical and Algebraic Geometry, Master’s Dissertation, University of Durham, 2004. 30 31

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mechanics similarly profited from his own scholarship. Thus, his lectures on Delaunay’s theory of lunar motion were given precisely during his intense study of Poincaré’s works concerning canonical variables in Keplerian motion (1945i). He revisited this topic during his meeting with Heinrich33, where he realized that he could apply Delaunay’s techniques for the Moon’s orbit, to compute orbits of the Størmer problem (1949c).34 His interest in machines also figured into his teaching. His classes were supported by numerical manipulations on the mechanical computing machine Mercedes, before the War, and until the late 1940’s. Near the end of his career, he taught courses on the ALGOL programming language.35 Incorrigible to the end, on the very first day of class, he had his students work through the last problem in the textbook!36 His passion for computing prompted introducing exercises for students, and later the establishment of a full course on numerical analysis. This course would later be given by Odon Godart in the “interstellar vacuum”, the whimsical name given by Lemaître’s students to a room on the uppermost floor of the Collège des Prémontrés, which afterwards became the office of Charles Manneback.37

2. Attending a class and passing exams with the Canon All personal testimonies concur that Lemaître’s teaching style could be unsettling for his students. He rarely proceeded in a linear and systematic fashion, and his delivery was not always in tune with his audience. His approach to teaching is understandable against the backdrop of his approach to research. He was much less interested in systematic   Cf. (1949c: 84).   Discussed in more detail in the following chapter. 35   Cf. (1965a, b). 36   Oral communication, R. Weverbergh. 37   Oral communication, Odon Godart. 33 34

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enquiry than by the resolution of problems and enigmas, or by numerical simulations of real problems, ‘where something happens’. His classroom performance reflected the same instinct for the jugular that guided his research. He began by framing a problem that he would take from a book in front of him. He then probed for the solution by trial and error, while students marveled at the spectacle of his juggling with formulas that did not always give the anticipated results. He would occasionally leave the classroom in irritation, deferring the solution to a problem to the next class or to a reference book, or even to better times where the technology of machines would be more advanced! It must be said that class preparation was not the highest priority for the cosmologist. His retreat notebooks reveal that he struggled with his unceasing torrent of ideas which interrupted his class preparation. In his retreat notes of September 1927, we find38 “…what have I done for one year? My class on relativity and the class of history have been prepared from day to day. This is the same for the exercises that lack an overall plan.” He then made the following resolution: “I could take as a main project, the editing of my class on the theory of relativity”. Twenty-six years later, with the project still unfulfilled he noted again39 “the class of relativity theory should not be modified, and could be written’’. In fact, the course would never take shape as a book. He also wondered about his notes on probabilities and astronomy, which likewise remained inchoate. Only his notes on classical mechanics and an introduction to vectors and tensors would be edited;40 even here his assistants and students would often be called   Notebook from his September, 1927 retreat at the seminary of Mechelen (AL).   Notebook from his August 1943 retreat (AL). 40   Among the reproductions of his class notes, one can find: La Mécanique Analytique. Cinématique-Statique. Dynamique du Point, Louvain, Imprimerie H. Dewallens, 1940, 116 pp.; Cinématiques-Statique. Dynamique du Point, Louvain (not dated, probably from the 1950s), Imprimerie H. Dewallens, 162 pp.; Mécanique Analytique. Cinématique-Statique. Dynamique du Point. IIe partie, Louvain (not dated), Imprimerie H. Dewallens (containing the second part of the previous course: 73-162); Mécanique Analytique. Équations de Lagrange. Dynamique du Solide. Équations Canoniques. Intégrales Elliptiques, Louvain (not dated), Imprimerie H. Dewallens, 85 pp.; Leçons de Mécanique. Le Pendule, Louvain, Service d’impression des cours, 1955-1956 and 1956-1957 38 39

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upon to complete these publications. Lemaître was clearly aware of his pedagogical weaknesses41, but despite all his efforts, he could not restrain the personal demons in his research life from hijacking his class. It has also been observed that his course content was not always well matched to the level of his students, although this was only strictly true of his courses for the Bachelors in engineering sciences. It is most certainly the case that his theoretical interests led him to overly emphasize the pendulum problem, the computation of elliptic integrals, and later the Størmer problem, to the detriment of solid mechanics. The improvisation that reigned in the class of the famous cosmologist occasionally elicited a real uproar,42 but more often was limited to a good-natured chiding and complaint. If Lemaître did not appreciate the former43, he took a certain delight in the latter case and enjoyed the reactions that his performance had on the students44. How were these classes received by his students? For several, time cast a golden hue over their recollections of his classes: the waltz of the formulas on the blackboard, the laugh of the professor, the background noise of the audience…. The famous Revue (a student variety shows) organized by the engineers were particularly revealing of the impres(definitive version), 53 pages; Leçons de Mécanique. Vecteurs et tenseurs, Louvain, Service d’impression des cours, 1955-1956, 43 pages. There are also typewritten versions of the class of “seconde candidature” (second year of the Bachelor): Mécanique Analytique. Les systèmes matériels. Théoremes généraux (not dated) and some notes of supplementary material for the mechanics class provided in the BA program and concerning the problem of two-body problem, the problem of the two centres, the geodesics of the ellipsoid and the Størmer problem. 41   To compensate, he would, for example, introduce a lecture with a reprise the previous class of much greater clarity than the first attempt (communication, Fr. Ch. Courtoy, student of Lemaître during the Second World War, June 1999). 42   Cf. A. Lederer, “Un chahut chez Msgr. Lemaître”, Ciel et Terre, t. 110, juillet-août 1994, no 4: 92. 43   Testimony of O. Godart (16-03-1995) 44   Upon being appointed prelate, he entered the amphitheatre girded for the first time with the imposing red sash. This entrance was greeted by a loud reaction from students, to which he responded, laughing “By coming here, I wanted to know the effect it would have on the audience!” Lemaître rarely wore it thereafter. (Oral communication, J. Lizin, 18-03-1998).  

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sion Lemaître left on the minds of those who would later command important positions in industry. The amusing caricatures of Xavier de Callataÿ that illustrated the programs of these Revues, spoke volumes of the place that the Canon occupied in their minds, as did the song “Duo des integrals nébuleuses”45 by a student playing the role of Lemaître during the students’ show of 1952-53,46 where faculty were affectionately roasted: Qui c’est qui fait d’l’analytique,

Who’s doing the analytics,

Qui c’est qui cherche des géodésiques,

Who’s looking for the geodesics,

Qui ne prends jamais la plume,

Who never takes that pen,

Et surtout pas quand j’ai un rhume,

And especially not when I have a cold,

Qui te sourient gentiment

Who smiles at you kindly

Quand tu me mens gauchement,

When to me you lie awkwardly,

Qui c’est qui fait de la musique

Who’s playing music

Tout en faisant de l’astrophysique,

While performing astrophysics,

Qui se chauffe aux rayons cosmiques

Who’s warming himself with cosmic rays

Dans un paysage électronique?

In an electronic landscape?

....

....

Qu’est-ce qui se trouve être aux anges

Who is in the seventh heaven

Quand on parle du grand Lagrange?

When one speaks of the great Lagrange?

The answer is of course was the Canon himself, whose slogan “the vector is to scalar, what poetry is to prose” tickled the students to no end. Lemaître’s idiosynchrasies provided endless fodder for the students ‘variety shows’ of the 1950s. The students tried to figure out what kind of gift he got from the Holy Spirit. The immediate answer

  “Duo of the nebulous (misty) integrals”: the French language play of the fact that ‘nébuleuses’ can both refer as a noun to ‘nebulae’, and as an adjective to ‘nebulous’ or obscure (note of the translator). 46   Program of the “Revue” of 12 December 1952, edited by the Cercle Industriel (engineering students’ club). The author is grateful to the Denoiseux-Paternostre family for enabling him to consult the complete collection of the programs of the student variety shows (1952-53 to 1957-58). 45

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was: “the intelligence”. How do they find his class?47 “Misty”. Where did they imagine Lemaître was spending the weekend?48 “At the observatory”. If the Canon had to have a small lunch, what would he take?49 “Everything”, which explained why his favourite radio program was50: “la minute gastronomique” (the gastronomic minute) and his cardinal sin was, according to the students, “overindulgence”. But the Canon did not seem to be overly offended, telling his 195657 students51: “several things prohibited on Earth, are allowed in heaven!” What was the favorite bedside book of the professor?52 “In Praise of Laziness”, which was in fact, according to Lemaître a quality of the great mathematicians who “always reflect a lot before not computing”53. Which film most appealed to him? “La route semée d’étoiles”,54 and the fable he could have written “The child and the Schoolmaster” since he often said: “Research is a game and who does not like to play, should not do it”. What is revealing about these Revues, is that no matter how obscure the classes, Lemaître was treated gently and affectionately – unlike some of his colleagues. He had the figure of a good-natured and pleasant person, whose only minor fault was being a gourmand. In fact very few students were able to follow Lemaître’s lectures completely fruifully. The subtle analysis of the pendulum’s motion, the mechanical interpretation of the Størmer problem in the Bachelors program, or even the integral invariants of Cartan in the Masters program, could be profitably assimilated only by a tiny minority of the class; what the most gifted derived from his lectures was an understanding of and ambition for real research. His courses were more  “Revue”, 11-12-1953.   Ibid. 49  “Revue”, 28-11-1958. 50  “Revue”, 1956-1957. 51  Ibid. 52  “Revue”, 28-11-1958. 53   Communication of J. Lizin, 18-03-1998. 54   French translation of the film “Going My Way” of Leo McCarey, 1944 (note of the translator). 47 48

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of a live performance of one of the great masters of twentieth century cosmology in the act of discovery; what could be better to motivate the next generation? From time to time, such unscripted theatre would predictably take unpredictable turns. Leaving for his astronomy class of the seconde candidature (second year of the Bachelors program) one day, Lemaître hastily picked up a series of slides to project for his students. But to everyone’s surprise, including his own, rather than a galaxy appearing on the screen, there was the Canon having a picnic with his colleagues during one of his trips to the United States. Recovering gracefully, he commented on the importance of friendly discussions in the research process!55 Lemaître was a passionate devotee of photography. Both his natural family as well as his sacerdotal fraternity, the “Amis de Jésus” have preserved a large collection of his photos from his trips and meetings; although the majority of these pictures were never annotated56. The Canon was especially determined to take pictures of his Master students, prevailing on his students with the argument “So, if there is among you a Nobel Prize, I would at least have a picture of him”.57 The candidates were none the wiser that he more than occasionally failed to put film in the camera! What is certain is that one of the most stimulating aspects of his teaching style was putting his students into direct contact with the original texts, a custom he learned from Fr. Bosmans. In his class of methodology he commented on translations of Euclid with the Greek text in hand; nor did he hesitate to quote the works of Gauss or Jaco­bi in the original Latin. One of his closest collaborators, Jacques Masset, put it best: Lemaître “was not teaching a subject, but an approach, a way of doing research”.58 Such a teaching style was only conceivable in a framework where academic freedom really meant something, and   Oral communication, G. Thill, 25-06-1997.   Owing to the diligence of Canon J. Goeyvaerts, of happy memory, the author was able to identify all the characters in Lemaître’s album related to the “Amis de Jésus”. 57   Oral communication, Sr. Émilie Fraipont (10-10-1997, 25-06-1998). 58   Oral communication, 15-12-1997. 55 56

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in an era prior to students’ reflexive criticism so prevalent after May 1968. Today, personalities as remarkable and original as Lemaître would have little chance to be accepted by an academic establishment where pedagogy is judged by rigid standardized criteria, and where scientific productivity is measured by the number of publications produced in the right journals. Unquestionably Lemaître’s teaching legacy was one of great strengths and great weaknesses. But it was a rare student who had not learned something vital and important alongside the Canon on their mutual journey into uncharted scientific territory. Lemaître’s exams were likewise ‘original’, but moderate;59 he was aware that too rigorous an exam would be unfair given his evident foibles. Thus he would propose that each student evaluate himself before beginning the exam, and with that self-evaluation fixed the upper limit of the points he could obtain. He then gave each student a question proportionate to their ability. Sometimes he gave the exam questions and left them by themselves for the hour. Other times, he distributed notes but forgot to provide exams! One July afternoon he forgot to administer an exam entirely. Coming back from his favourite restaurant, “Majestic” quite late, and seeing a queue of mystified students in front of his office, he realized his omission and bellowed out “13 for everyone!” The students left happy, especially those who had not studied or understood the class of the Canon. His style of examination was so famous in Louvain that it became the theme of a student song in 195860:

  On one occasion, he quipped to Sr. Émilie Fraipont: “I am always clement!’’ (Oral communication, 25-06-1998). 60   “Ambiance d’examen (Air: actualité)” in Plastic en stock ou les profs en stuc, “Revue”, 28-11-1958. 59

XIII. Lemaître the master. A portrait of his pedagogy (1940–1944) Le soleil luit sur le toit du bâtiment

The sun is shining on the roof

Dans la cour, dix étudiants,

In the courtyard, ten students

S’épongent en travaillant

Wiping their sweat while working

Ballieu sourit en lisant des feuilles à l’envers

Ballieu smiles while reading upside down sheets,

Derrière son tapis vert

Behind his green carpet

Simonart est en colère

Simonart is furious

...

...

Tout là-bas pourtant un espoir vient de renaître:

Over there, hope is revived:

Un type sort de chez Lemaître

A guy leaves from Lemaître

Réussissant sans rien connaître.

Succeeding without knowing anything.

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Chapter XIV

From mechanics to calculators and back again (1940–1944)

1. Mechanics and cosmology: the nebulae and their clusters

F

ollowing the Second World War, Lemaître was increasinging captivated by mathematical methods associated with classical mechanics and with numerical analysis. His immersion into the works of Poincaré and Gauss during the war, coupled with his early training, reoriented his scientific career along new paths for the final third of his life. Cosmology was not totally abandoned, but research in relativity theory was increasingly relegated to a secondary position relative to problems of classical mechanics. What interested him now was to develop his intuitions from 1932-1933 regarding models of the formation of galaxies that he still called nebulae1. He had already demonstrated that the solution of Einstein’s equations corresponding to the gravitational field of a sphere filled with an inhomogeneous fluid, gives rise to condensation of matter in a globally expanding universe. These condensations, he held, could be the nebulae themselves. (In fact, in 1932, Lemaître opined that the stars were formed prior to the nebulae, and their condensation gave rise to the nebulae.) But such  For the problem of the formation and evolution of galaxies: cf. W. H. Waller, P.W. Hodge, Galaxies and the Cosmic Frontier, Harvard University Press, 2003: 76-86. 1

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a process posed a conundrum for him,2 namely “how the nebulae could [have] lost as much energy to be as dense as they are?” and further “this difficulty, perceived but unresolved, forced me to be prudent in the editing of an important dissertation”.3 Stymied, Lemaître abandoned the condensation problem for a long time, returning to it only in the early 1940s. Reflecting on the implications of his primeval atom hypothesis, and the cosmic ray problem which he worked on since the early 1930s, he at last saw a shaft of light opening up toward the problem of the formation of nebulae and their clusters. As he confided it to Gonseth in 1945:4 It is only during these last years that I have returned to the problem of the great speeds in the clusters, whose interpretation had provided me with the keys to the formation of the gaseous clouds from the radiation issuing from the primeval atom.

To understand the mechanism of the formation of nebulae, in Lemaître’s view, one must remember that the disintegration of the primeval atom produced gaseous clouds of massive particles moving at great speeds.5 When the hesitating universe arrives at the state where its radius hardly varies, there exist density fluctuations of the gas which can act as seeds for growth. The clouds tend to concentrate there, initiating the condensation which is the beginning of a nebula. During this condensation process, the clouds collide inelastically and dissipate their energy to form strongly condensed centres which are   Letter to F. Gonseth, 21-01-1945, AL (our translation from the original in French).  (1933e). 4   Letter of the 21-01-1945, op. cit. 5   In his review (1958a: 479), he explained how these clouds form. Some particles emitted by the disintegration of the primeval atom are charged (he did not, however explain why). Their motion creates regions where powerful magnetic fields trap other particles. Elastic scattering between them particles naturally leads to a Maxwellian distribution of the particles; one may then speak of a “gas cloud” of particles. It is important to remember however that not all flows of charged particles constitute a “gas”. 2 3

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the nebulae. These inelastic collisions also give rise to the stars, at the same time as the nebulae6. Lemaître thus believed he had solved the problem of the formation of cosmological large scale structures, the problem he had laid aside in 19337. Inelastic collisions between clouds represented the energy dissipation mechanism, and the understanding of nebular condensation. The great speeds observed among nebulae could also plainly be accounted for by the speed of the clouds from which they condensed. By 1945, he had a schematic picture of the first stages of the formation of galaxies, which he developed over the next sixteen years to fully understand their structure, evolution and clustering. His methods in classical mechanics harken back to those of Eddington in his study of the dynamics of globular clusters, as Lemaître himself acknowledged (1961e: 604). He assumed that the gaseous clouds in the galaxies, and galaxies within their own cluster, are moving in the gravitational field, produced by the clouds and galaxies themselves, and described by the Poisson equation8. He made use of Liouville’s theorem, that he had applied to the Størmer problem, to ensure that the distribution of the clouds and galaxies remains invariant in phase space. With the help of R. Keil, he first studied the model of spherical galaxies (1946f),9 although this model was inappropriate, as it lacks a strong central nucleus, as most galaxies possess. He next pro  Cf. “[…the stars] did form as a result of inelastic collisions, in regions where attraction dominated over repulsion, regions that became galaxies” (1950c: 49-50; our translation from the original in French). 7   One of the limitations of the papers (1993c, d) is the fact that they do not take into account the proper speeds of the clouds that condense to produce a galaxy. These papers posited the condensations as concentric layers of different densities, in the inhomogeneous model. However, due to their proper speeds, one cannot truly ascertain whether the galaxies are indeed “independent concentric cells” (cf. 1946e: 27). 8   In classical mechanics, this equation describes the gravitational potential given a density source term, and derives from general relativity in the weak field limit. Lemaître modified this equation slightly to take into account the effects of the cosmological constant. 9   The distribution of the clouds is assumed to be static, with a uniform distribution of speed (i.e. there are clouds of all speeds, from zero to the escape velocity). 6

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posed a model with spherical symmetry where the gaseous clouds undergo radial oscillations (1948j). The computations performed with R. Vander Borg, one of his former students working at Natal University College, for this problem led to a satisfactory description of the collapse of the center of the clouds. Their results, for the case of such models with radial oscillations, were in accord with the observations of elliptic galaxies made by Hubble in 1930,10 and would be confirmed by the work of Belzer, Gamow and Keller on the dynamics of the stars and spherical galaxies in 195111. In 1948, Lemaître published his first work on galactic clusters (1948h), with the goal to confirm the existence of clusters populated with high velocity galaxies. Such a problem had not even been envisioned when considering the ‘hesitating model’ at first. During his quasi-static period, there is equilibrium between the gravitational attraction due to masses and the repulsion described by the cosmological constant. Consequently, if there are clusters of galaxies of great speed, they can take advantage of this equilibrium to escape. But to maintain equilibrium, clusters can only exist if the galaxies that emerge can be replaced by others in the neighborhood. This first work of Lemaître led to solutions corresponding to clusters that remained stationary in an Einsteinian static universe. Lemaître would describe them at the 11th Solvay Conference in 1958, in Brussels, and again during the Study Week on the Problem of Stellar Populations of the Pontifical Academy of Sciences, as “stationary waves occurring in the assemblage of moving galaxies”12. A second contribution, whose calculations were carried out by Abbé Van Hoebroeck, who assisted the Canon between 1948 and 195013, studied condensation on the small  E. Hubble, “Distribution of Luminosity in Ellipsoidal Nebulae”, Astrophysical Journal, Vol. LXXI, 1930, p.231. This article is quoted in 1948j: 123. 11   J. Belzer, G. Gamow, G. Keller, “On the Stellar Dynamics of the Spherical Galaxies”, Astrophysical Journal, Vol. 113, 1951: 166-180; quoted by Lemaître in 1958a: 486. 12   (1958a: 484) and (1958f: 19). 13   Abbé Van Hoebroeck would be appointed Chaplain near Jurbise in 1950 (letter to Lemaître, 22-08-1950, AL). 10

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est scales as a function of time14. This led Lemaître to analyze the way in which the clusters behave during the third epoch of the hesitating universe, corresponding to the global accelerating expansion of the universe15. To see if a cluster would disintegrate uniformly or only from its edges, Lemaître realized that it was important to specify the conditions at the boundary of the cluster (1952a)16 and to take into account the effect of all the other clusters on it.17 The computations involved in the resumption of expansion are relatively intricate. In 1958, Lemaître and Andrée Bartholomé would use the Burroughs E101 computer that had just arrived at the Collège des Prémontrés to study precisely this aspect (1958h). In fact, Lemaître was never able to definitively answer whether clusters disassemble or remain intact during the final expansion of the universe. In a lecture at the symposium Hypothesis of Instability of Systems of Galaxies: Its Implications and Evidence For and Against, held at the University of California Santa Barbara, 8-9 August 1961. Msgr. Lemaître unveiled plans for a grand computational project that ultimately he would be unable to accomplish. With that failure went his hopes for confirming his hypothesis by which clusters trade galaxies and dissipate only around their edges (1961e: 606).

  This paper presents the hypothesis of “quasi-isotropy”, i.e. the assumption that one can separate the radial motion of galaxies from motion along other coordinates, although this hypothesis would prove incompatible with realistic cluster boundary conditions. 15   In his research notebook 1947-1953 (AL), he describes in an entry dated 16-021952: “[…] in the contribution of 48, we have studied a strong static condensation in an Einsteinian universe. One could examine what happens to this condensation in an expanding universe.” (Our translation from the original in French) 16   The considerations of boundary conditions were presented by Lemaître during the 50th anniversary of the South African Association for the Advancement of Science, in Cape Town, 7-12 July 1952. 17   Lemaître would only become aware of the importance of this effect in September 1951: “In regard to these nebular clusters, it seems that I have missed one important point so far. I have treated the problem as if there was only one condensation…” (Research notebook 1947-1953, AL, 15-09-1951; our translation from the original in French). 14

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How should we assess nowadays his studies of the formation of galaxies and clusters? The ideas of cluster formation by specific fluctuations of matter density18 is still a very fertile hypothesis that serves as a guideline to research, as pointed out by the great Princeton cosmologist, P.J.E. Peebles:19 We are left with Lemaître’s program: try to find the character of density fluctuations in the early universe that would develop into the irregularities we observe.

Nevertheless, these ideas of Lemaître did not attract much of a following during his life, for two reasons. First, he had used an inhomogeneous model to describe the development of condensation in the universe. But most cosmologists were strongly attached to the cosmological assumption of a homogeneous and isotropic universe. Lemaître’s adherence to a non-zero cosmological constant did not help the situation either, particularly as Einstein and others assumed it to be zero. But there was more. In 1946, Lifshitz,20 studying the linear perturbations within the Friedmann-Lemaître models, had shown that the gravitational instability could not generate the formation of distinct galaxies through a process of matter condensation as Lemaître had envisioned. Assuming some fluctuations of the density or the velocity of the original matter, he had demonstrated that these fluctuations should be damped, or at least should not grow. He was able to show that certain fluctuations could nevertheless be amplified, but such fluctuations could not grow sufficiently to form structures such as galaxies in cosmological time.

  This program merely reprises, in a relativistic cosmological context, the work of Jeans on the growth of density fluctuations due to the gravitational instability of a fluid filled static universe (cf. P. Coles, F. Luccin, Cosmology. The Origin and the Evolution of Cosmic Structure, New York, Wiley, 1995: 190-219). 19  P.J. E. Peebles, The Large-Scale Structure of the Universe, Princeton University Press, 1980: 35. 20   E.M. Lifshitz, J. U.S.S.R. Acad. Sc., Vol. 10: 116. 18

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W.B. Bonnor21 would show in 1956 that the Lifshitz analysis needed to be reevaluated as it did not take into account the nonlinearity of the field equations that could lead eventually to an acceleration of accretion. But Bonnor ultimately arrived to the same negative conclusion as Lifshitz22: My conclusions are that although there can indeed be a speeding up not predicted in the linear approximation, and although condensations certainly can eventually form in the models, [the isothermal fluctuations in density] are much too small to have produced nebulae or stars by the present time. Put another way, this means that the formation of nebulae is a tremendously improbable occurrence in these models if ordinary statistical theory is used.

A section of Bonnor’s paper showed, more precisely, that statistical isothermal density fluctuations cannot lead to the formation of galaxies in Lemaître’s hesitating universe, and indeed many astrophysicists adopted the position of Lifshitz and Bonnor until the beginning of the 1960s. In fact, an unusual situation prevailed in the late 1950s in the astrophysical community whereby everyone’s intellectual position was clearly defined but no there was no real dialog between scientists of opposing viewpoints. As Peebles observed23, the Solvay Conference in 1958 on the structure and evolution of the universe24 was emblematic of this phenomenon. Lemaître quoted Bonnor, but without alluding to the difficulties that he had encountered with his hypothesis (1958f: 18). E. Schücking and O. Heckmann dedicated one paragraph to inhomogeneous models without mentioning

  W.B. Bonnor, “The Formation of the Nebulae”, Zeitschrift für Astrophysik, Vol. 39, 1956: 143-159. 22   W.B. Bonnor, op. cit.: 145. 23   P.J.E. Peebles, op. cit.: 23. 24   La structure et l’évolution de l’univers. Rapports et discussions du onzième Conseil de Physique tenu à l'Université de Bruxelles du 9 au 13 juin 1958 (Institut international de physique Solvay), Brussels, R. Stoops, 1958. 21

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Lemaître’s name.25 In discussions of the contribution of these two scientists, the Canon didn’t even intervene26. Everyone’s position was solidly entrenched.27 The objections of Bonnor and others were interesting; nevertheless, they did not deliver a fatal blow to the relevance of Lemaître’s idea. These objections were based on a hypothesis concerning fluctuations at the beginning of the universe. But no one had a completely accurate theory of the structure of these fluctuations and fine details of their growth. It was thus impossible to discredit Lemaître’s ideas on the basis of the presumed rate of fluctuation growth leading to large scale structures28. Only one idea of Lemaître proved not to be well grounded, namely the preservation of the form of the clusters through a continual interchange of galaxies with the surrounding universe.29 The mechanical models of galaxies and clusters would require more and more refined numerical methods to integrate Poisson’s equation characterizing the gravitational field. All the computing machines at Lemaître’s disposal would be commited to this gigantic project. In the second part of his career, beginning in 1945, the problem of galactic clusters, along with the Størmer problem, represented the driving elements for the Canon’s creativity in the domain of the numerical analysis and computer science.   “World Models” in La structure et l’évolution…., op. cit.: 155.   Op. Cit: 159. Lemaître had several contacts with astronomers of the International Astronomical Union, most especially his friend Pol Swing from the Institut d’astrophysique of the University of Liège situated in the park of Cointe (the two scientists carried on a correspondence between 1934 and 1961). Nevertheless, Lemaître rarely discussed his ideas on galaxies and clusters with other astronomers, except with Van Albada (letter, 26 October 1960 of the latter to Lemaître and (1961e: 606)). 27   To have an idea of the state of the theory of the formation of galaxies ten years after the death of Lemaître, see B.J.T. Jones, “The Origin of the Galaxies: A Review of Recent Theoretical Development and their Confrontation with Observation”, Review of Modern Physics, Vol. 48, 1976, no 1: 107-148. 28   The study of the stationary waves leading to the formation of galaxies was also a fertile idea as one can gauge from today’s massive simulations; see the paper of François Combes, “L’histoire mouvementée des formes galactiques. Des anneaux et des barres emboités comme des poupées russes”, La Recherche, t. 305, 1998: 63-65. 29   P.J.E. Peebles, op. cit.: 23. 25 26

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2. Numerical calculation Lemaître was the ultimate mathematical pragmatist. He was solely interested in answers, preferring explicit computation of particular solutions of differential equations, to abstract theorems and existence proofs. Numerical computation was his passion, and filling out a table of numerical values of a function was one of life’s greatest pleasures. A part of his work would always be dedicated to the development of numerical techniques related to the computation required for modelling clusters of nebulae or finding Størmer problem orbits. As seen previously, during the Second World War, Lemaître developed the technique of rational iteration (1942a) drawing on a method used by Gauss to determine a planet’s orbit from only three observations. In fact he had achieved greater precision than Gauss himself, showing that the method could be used to numerically solve differential equations (1942d), in particular the ones involved in his model of nebulae with radial velocities. After the War, he would use the well-known Runge-Kutta method to numerically integrate a certain class of differential equations (1947a), his motivation coming from the calculation of nebular clusters (1946f)30. The method of rational iteration did not produce entirely satisfactory results, so he resorted to the Runge-Kutta method he modified to generate an interpolation formula, which provided solutions of greater precision than the original Runge-Kutta method.31 Applying it to a particular case of the Størmer problem that he had tackled with Lucien Bossy (1945k)32 confirmed its superiority. His re  Lemaître’s explanation is found in his research notebook (AL), 17 March 1947.   Lemaître used the Runge-Kutta method of the fourth order (cf. J. D. Lambert, Computational Method in Ordinary Differential Equations, London, Wiley, 1973: 114-161). He established with this method another formula accurate “if one is satisfied with the results of the third-order solution, but with half of the increment” (1947a: 106); our translation from the original in French. 32   Research notebook 1947-1953, Monday 17-03-1947 (AL). In this notebook, Lemaître talks of the “limit orbit” i.e. an orbit infinitely close to the Earth’s magnetic field lines. 30 31

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search notebook33 in 1948 showed that he was still “considering some new variants of the Runge-Kutta method”, while admitting that “the question is quite confused for the moment”. His confusion faded over the years and in 1961, Msgr. Lemaître came back to the numerical methods of integration of differential equation during a colloquium of the Centre Belge de Recherche Mathématiques held in Mons (1961a). After having explained how one can modify the methods of Adams and Størmer used for the integration of differential equations of the first and the second order respectively, Lemaître proposed a conjecture for the Runge-Kutta methods of the fifth and sixth order34. Lemaître’s unique style emerges here that one could characterize as “experimental mathematics”, where intuition is given free rein to drive the development of numerical methods, and to which abstract synthesis and demonstrative rigour takes a back seat.35 Lemaître likewise made important contributions to the integration of differential equations by means of harmonic analysis36. This also arose from the Størmer problem and guided him to this fertile field of contemporary mathematics. The determination of orbits arbitrarily close to the equator, performed by Lemaître from 193437, implic  Dated 8 June 1948 (AL).   The conjecture of Lemaître concerns the existence of a Runge-Kutta method of the fifth or sixth order with exactly five or six pivots, respectively. 35   Lemaître’s style situates itself squarely in the context of the debate initiated by the article of Arthur Jaffe and Franck Quinn, “ ‘Theoretical Mathematics’. Toward a Cultural Synthesis of Mathematics and Theoretical Physics” (Bulletin of the American Mathematical Society, Vol. 29, July 1993, no 1:1-13. Armand Borel likewise could well have had Lemaître in mind with his famous observation, “I have often maintained, and even committed to paper on some occasions, the view that mathematics is a science, which, in analogy with physics, has an experimental and a theoretical side, but operates in an intellectual world of objects, concepts and tools. Roughly speaking, the experimental side is the investigation of special cases, either because they are of interest in themselves or because one hopes to get a clue to general phenomena, and the theoretical side is the search of general theorems” (“responses to ‘Theoretical Mathematics…’”, Bulletin of the American Mathematical Society, Vol. 30, 1994: 180). 36   Harmonic analysis finds its origin in the works of Fourier by which periodic functions, the ‘signals’, are represented by sums of the elementary sines and cosines as the basis functions (the ‘Fourier series’). 37  (1934d). 33 34

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itly involves the equation that had been studied by Hill around 18771878, in the context of his theory on the lunar perigee motion38. The cosmologist only realized this in the 1930s, at the time he was working with Odon Godart on the study of the stability of periodic orbits39. The Hill equation has the form d2y/dx2 + f(x) y = 0 where f is a periodic function of the variable x. Lemaître showed in 1938 how one can generalize Hill’s method of solving the equation40 to a system of n equations (1938a). After the War, he taught his students how to integrate equations generalizing the Hill equation of the form L(y) = z(y,x) where L is a linear operator of y and its derivatives with respect to a variable x, and where y and z are periodic functions of x. Lemaître’s method was based on a harmonic analysis of y and z, i.e. based on their expansion as Fourier series. This research would lead to only one publication (1956a), whose numerical computations would be performed in collaboration with the assistant and secretary of the Canon, Miss Andrée Bartholomé41. Nevertheless, this paper was just the tip of an iceberg. What Lemaître had in fact done was   Lemaître was aware of this equation from the book of E.T. Whittaker and G.N. Watson, A Course of Modern Analysis, Cambridge University Press, 1902 (Fourth Edition, 1927, re-edited nine times until 1996): 413-417. A survey of the Hill theory about the motion of the perigee of the Moon can be found in W. Neutsch, K. Scherer, Celestial Mechanics. An Introduction to Classical and Contemporary Methods, Mannheim, B.I. Wissenschaftverlag, 1992: 564-585. 39   O. Godart, “Contribution à la théorie des effets de latitude et d’asymétrie des rayons cosmiques. V. Déterminations des exposants caratéristiques des trajectoires périod­ iques”, Annales de la Société scientifique de Bruxelles, série I, t. LVIII: 27-41. The theory of the characteristic exponents, which Lemaître and Godart had learned in Poincaré’s Méthodes nouvelles de la mécanique céleste (t. I, Paris, Gauthier-Villars, 1899: 162), permits the study of what happens when one disturbs a periodic orbit. 40   Hill has shown that one of the solutions could be written y = exp(mxi) z(x) where z is a periodic function and m is an integer. By developing the periodic function in Fourier series and by substituting them in the equation, one shows that the determination of m leads to a determinant of infinite dimension called the “Hill determinant” (Cf. E.T. Whitaker, G.N. Watson, op. cit: 415-417). 41   Lemaître took for example L(y)=d2y/dx2 and z(x) = - 4 sin(y). It is the equation of motion of a simple pendulum that could be integrated by using the elliptic functions (Lemaître compared the numerical results coming from his method by harmonic analysis with those that can be obtained directly by computing the solution with the Jacobi series expressing elliptical functions (1956a: 122)). 38

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to develop his own personal techniques to numerically compute harmonic analyses and syntheses of periodic signals42, as well as their derivatives and integrals. In fact, in the early 1950s, the Canon taught his students that these operations could be carried out by simple matrix multiplications. One of Lemaître’s students, René de Vogelaere43 would systematize this theory and rigorously introduce the concept of “Lemaître’s matrix”44 in a class at the Centre of Numerical Analysis at Notre Dame University in 195545. He applied Lemaître’s techniques to study a particular case of the non-linear equation of Duffing,46 which was extremely interesting, as André Deprit47 pointed out, the theoretical framework being precisely that of the Fast Fourier Transform (FFT). The algorithm is generally attributed to James W. Cooley and John W. Tukey48, but it would seem Lemaître deserves to be credited in part for its development. His inspiration was drawn from his wartime readings of Gauss, whose seminal work prepared for the FFT’s discovery49.   The analysis is the decomposition of the signal in a Fourier series. The synthesis is the reconstitution of the signal from the knowledge of its harmonics. 43   It should be noticed here that the latter has studied in depth the Hill equation in relation with the Størmer problem: R. de Vogelaere, “Équation de Hill et problème de Størmer”, Canadian Journal of Mathématics, t. II, 1950, no 4: 440-456. 44   These matrices are linked to the matrix of Toeplitz, whose columns are obtained from the first one by circular permutation of its elements. 45   R. de Vogelaere, Fourier Series, Sums and Expressions. Lecture 2, December 1955, Center of Numerical Analysis, University of Notre Dame. “The practical computation of harmonic analysis and synthesis was taught to us by Professor G. Lemaître of Catholic University of Louvain” (page 25). 46   R. de Vogelaere, Solutions of Differential Equations using Fourier Expression. Report 3, December 1955, Center of Numerical Analysis, University of Notre Dame, me 1.3 and 5.2. A particular case of the Duffing equation is d2y/dx2 + y + by3 = m cos(wx). The theory of Lemaître only applies directly to the case b = 0. From the Duffing equation, one can obtain a Mathieu equation (d2y/dx2 + (a + bcosx)y = 0) which is a particular case of the Hill equation (cf. D.W. Jordan, P. Smith, Nonlinear Ordinary Differential Equations, Oxford, Clarendon, 1987: 251-262). 47   “Les amusoires de Mgr Lemaître”, Revues des Questions Scientifiques, 155, 1984, no 2: 223. 48   Cf. James W. Cooley and John W. Tukey, “An algorithm for the machine calculation of complex Fourier series”, Math. Comput. 19 (1965): 297–301. H.J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms, Berlin, Springer, 1981. 49   C. F. Gauss, “Nachlass: Theoria interpolationis methodo nova tractata”, Werke band 3: 265–327 (Königliche Gesellschaft der Wissenschaften, Göttingen, 1866); M. T. Hei42

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Characteristically, Lemaître had independently developed the technique and used it without trying to create a rigorous theory or fully develop all its potential. The solution of Einstein’s equations in cosmology50, the study of the Størmer problem51 and his classes of mechanics often led Lemaître to elliptic integrals and the elliptic functions related to them52. Lemaître was familiar with them from the teaching of Alliaume and de la Vallée Poussin. Alliaume had made significant contributions to the geometrical interpretation of the elliptic functions of Jacobi53. A major part of the course of analysis of de la Vallée Poussin was dedicated to these questions54. This course would influence Lemaître and one can find traces of this influence in his lecture notes on mechanics55, and even in his very last publication (1967a). This publication, as well as his class dedicated to the pendulum refer to the Poncelet polygons, i.e. those which are inscribed in one conical and circumscribed to another. These polygons are connected to the theory of the motion of the simple pendulum and thus to elliptic functions56. One can show for exdeman, D. H. Johnson, and C. S. Burrus, “Gauss and the History of the Fast Fourier Transform”, IEEE ASSP Magazine, 1, no 4 (1984): 14–21. 50   Cf. for example (1933e: 24-27) where Lemaître integrates the Friedmann equation using the elliptic functions of Weierstrass. 51   Cf. (1949c: 84). 52  Cf. D.F. Lawden, Elliptic Functions and Applications, Berlin, Springler-Verlag, 1989. The elliptic integrals are integrals that contain the square root of a fourth-degree polynomial. Legendre showed that this integral can be reduced to three canonical forms called integrals of the first, second and third kind. 53   M. Alliaume, “Représentation géométrique simulatanée des trois premières functions elliptiques de Jacobi”, Annales de la Société scientifique de Bruxelles, t. XLIV, 1925: 307-312. 54   See the handwritten notes of the course of analysis of de la Vallée Poussin taken by R. Graas (Br. Maxime-Léon), preserved in Louvain-la-Neuve. Two documents are dedicated to elliptic functions, one of 91 pages ending with an historical survey, and another of 77 pages. 55   Cf. “Calculs des integrals elliptiques” in Mécanique Analytique. Équations de Lagrange, Dynamique du Solide. Équations Canoniques. Intégrales Elliptiques, Louvain, Imprimerie H. Dewallens (undated): 82-83. 56   The solution of the equation for the simple pendulum involves elliptic functions: J. Snape, Applications of Elliptic Functions in Classical and Algebraic Geometry, Master’s Dissertation, University of Durham, 2004 (available on the web): 37-44.

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ample, that two points, describing pendular motion of the same total energy on a given circle, are linked by a line segment that remains, at all time, tangent to another circle. This kind of segment can serve to generate a polygon that remains always inscribed in the first circle and circumscribed to the second57. All this geometrical interpretation can be found explicitly in the course of de la Vallée Poussin58. The originality of Lemaître, in the field of elliptic functions however, did not lie there, but rather in the extension of methods known in his time for numerical computations of elliptic integrals. Through his lectures during the war, Lemaître knew Gauss’ work on the computation of secular perturbations caused by a planet on the orbit of another, involving certain elliptic integrals59. One of them60, written J(A,B) is, up to a factor, the integral of 1/(A2cos2a+B2sin2a)1/2 with respect to a. In 1818, Gauss and independently John Landen (1719-1790), discovered a technique that greatly simplified the computation of J(A,B)61. They observed that J is unchanged if one replaces A by A1 = ½(A+B) and B by B1 = (AB)1/2, in other words, if one replaces A and B by their arithmetic and geometric means, respectively. By repeating this operation several times, one obtains two series of numbers (An) and (Bn) that converge toward a same limit: L = L(A, B), which Gauss termed the arithmetic–geometric mean. One has, therefore, J(A,B) = J(A1,B1) = … = J(L,L). But, the latter is nothing but the integral of a constant that can be written 1/L. This computation technique, called “Landen transformation” possesses   Poncelet showed that if one succeeds in constructing such a polygon, inscribed and circumscribed to two conics, then there exists an infinity of such polygons (cf. M. Berger, Geometry II, Berlin, Springer-Verlag, 1987: 198-199). In the case of the pendulum’s motion, this infinity of polygons can be generated by rotating one of them in a way that it remains always inscribed in the first circle; this rotation of the polygon vertices corresponds precisely to the overall pendulum motion of the points. 58   Lecture notes of analysis 1942-1943 (taken by R. Graas), op. cit., “Les fonctions elliptiques”, Ch. II, § 15 “Équation d’Euler. Polygones de Poncelet”: 17-27. 59   More precisely, the acceleration of the perturbative motion of the orbit can be expressed by elliptic integrals of the first and second kind. 60   One of the complete integrals of the first kind. 61   W. Neutsch, K. Scherer, op. cit.: 278-291, and D.F. Lawden, op. cit.: 17-18 and 77-81. 57

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some beautiful geometrical62 and mechanical63 interpretations, and is particularly well adapted to the numerical computation that Lemaître performed on the Mercedes calculators. Having read an article of Bartky that generalized the Gauss-Landen technique64, in 1947 Lemaître extended this technique to a case not treated by Bartky: the incomplete integral. This method allowed him to compute all the elliptic integrals that he needed, without having to use their expressions in terms of infinite series, i.e. by means of Jacobi’s theta function. Once again, everything in Lemaître’s work is driven by the requirements of the computations he is doing and their implementation on a machine. The computer is thus linked to all of Lemaître’s calculations, as will be discussed in the next section.

3. Mesmerized by machines Georges Lemaître always loved calculators. As noted by his nephew Gilbert Lemaître65, he collected adding machines of the ADDIATOR type, which consisted in a rectangular case on which one could perform the operations (addition and subtraction) by dropping or raising some slides with the help of a stylet located in the parallel grooves. With time, the Canon acquired more performing machines, first manual and later electronic. The interest of Lemaître in calculating machines was largely stimulated by his interactions with Vallarta. Many of his computa  The Landen transformation corresponds to the doubling of the fundamental domain of the network of the periods of elliptic functions (which Lemaître had not foreseen). 63   Lemaître showed that the Landen transformation enables passing from one simple pendulum motion to another: (1947b) and Leçons de mécanique. Le pendule, Louvain, Service d’impression des cours, 1956-1957: 14-16. 64   Bartky dealt with the case of the complete elliptic integrals of the third kind while Gauss concentrated on the integrals of the first and second kind. Cf. (1947b: 200). One speaks of a complete integral when one evaluates the integral over specific limits. The integral is incomplete when one leaves the upper limit of integration as a parameter. 65   Gilbert Lemaître, “Monseigneur Lemaître et les machines à calculer”, Ciel et Terre, t. 110, July-August 1994, no 4: 119-121. 62

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tions, e.g. the trajectories of cosmic rays, had been performed using the differential analyser of Vannevar Bush,66 an analog device67 for integrating ordinary differential equations and plotting their solutions68. Lemaître had followed the development of the construction of this machine that began at MIT in the second half of the 1920s. Two members of Lemaître’s Ph.D. thesis committee at MIT, Vallarta and Norbert Wiener, were passionate about the project, that the idea of which would strongly influence Wiener’s development of cybernetics.69 Vannevar Bush generously made his differential analyzer available to Vallarta and Lemaître in 193270. There is no evidence that Lemaître himself had programmed Bush’s machine, but rather the actual work had been done by a whole team of assistants directed by professor Samuel H. Caldwell (1936a: 726). Interestingly, another Belgian was interested in Bush’s machine in the late 1930s, namely Professor Ledoux of the University of Liège, who came to study the radial oscillation of stars71 in 1939-1940, working on a model of the differential analyser built at the University of Oslo’s Institute of Astrophysics under Svein Rosseland72.   V. Bush, “The Differential Analyser”, Journal of the Franklin Institute, Vol. 212, 1931: 447. 67   In an analog computer, numbers are represented by physically measurable quantities varying quasi-continuously like the intensity of a current or an angle of rotation as was the case for Bush’s machine. The simplest example of an analog computer is the slide rule. 68   The machine could even receive data directly in the form of curves. 69   P.R. Masani, Norbert Wiener. 1894-1964, Basel, Birkhäuser, 1990: 160-163. Wiener became a friend of Lemaître as noticed by Masani. 70   Lucien Bossy confirms that Lemaître had already benefited from the Bush’s machine during his early trips to MIT. (“Le rayonnement cosmique dans l’oeuvre de Georges Lemaître”, Ciel et Terre, t. 110, 1994: 118). Explicit references to this machine appear only in Lemaître's work in (1935a), then in (1936c). 71   P. Ledoux, “Sur la théorie des oscillations radiales d’une étoile”, Astrophys. Norvegica, t. 3, 1939. P. Ledoux described Bush’s machine in Ciel et Terre, 1939, no 11: 393-401. 72   Størmer was part of this institute during the same period. Nevertheless, he never used the machine built under the direction of Rosseland (letter, Rolf Brahde to A. Deprit, 16-02-1984, AL). In 1946, he expressed the hope to compute on such a machine (Letter, Størmer to Lemaître, 10-07-1946, AL), but this never happened. 66

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Lemaître acquired several Mercedes electromechanical machines in 1933 both for his research and to induct his students into the deep secrets of numerical methods. These machines, which had seven memories and which could multiply and divide, were installed on the top floor of the Collège des Prémontrés. He moved them to his apartment at Place Foch during the war, apparently surviving the bombing of 1944 as Lemaître and his students73 used them until the mid1950s74. While living at 9 Rue Braeckeleer between 1945 and 1956, Lemaître had the opportunity to buy an electromechanical calculator from a bank that could be programmed and print the results – the Moen Hopkins. Gilbert Lemaître paints a remarkably different and romantic picture of programming in that era75: Yet, the most astonishing thing was the programming. On the trolley one could screw on a long ruler on which little mechanical blocks were grabbed and moved freely. On each little block, one could screw on several little wedges, for which each one had a function depending on its position and height. One could engage motions to the right and to the left, order operations, change registers or impressions, paper feeding and manipulation, etc. My uncle mastered all these intricacies. With a watchmaker’s precision, he would place dozens of little wedges next to each other and programmed very complex calculations.

This affinity for technical detail would dispose Lemaître towards programming in ‘machine language’ and to delve down to the lowest level of detail to understand what the calculator was doing. That was the case for the Moen Hopkins, which, from computations of bank interest,   In the context of exercises of numerical analysis given in “licence en mathématiques” (Master in mathematics) by Odon Godart. 74  Van Hoebroeck used these machines to perform computations related to galactic clusters (1951a). For some idea about numerical computations on this kind of mechanical machine, see D.R. Hartree, Numerical Analysis (Oxford, Clarendon, 1952: 11-26), used by O. Godart in his exercises of numerical analysis conducted under Lemaître’s direction. 75   Ibid, p.120. 73

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was modified for rational iteration and Runge-Kutta methods, to integrate differential equations determining the shape of nebular clusters or Størmer orbits. It was with the Mercedes machines, soon to be complemented with the Burroughs76, that Lemaître would start, in 1952, his Laboratory of Numerical Research, renaming and reorganizing the activities going on in some of the rooms on the last floor of the Collège des Prémontrés77 since the 1930s, with a view to obtaining external funding from his alma mater. This organization, whose scientific council included the Canon and professors Ballieu and Bouckaert had benefited from the support of the Centre Belge de Recherches Mathématiques78 and from the FNRS. From the laboratory’s outset, Lemaître would benefit from a competent collaborator, Miss Andrée Bartholomé, a former student of his, who would support him not only in the computations, but also in the day-to-day management the cosmologist was incapable of providing. If the Canon did not have any interest in management, he was, on the other hand, a visionary that instinctively followed the most promising paths of research. By founding this laboratory in the lofts of the Collège des Prémontrés, he set UCL on a trajectory toward what would become in the future information technology. In fact, thanks to Lemaître, his alma mater played a pioneering role in the field. As early as 1952, it became one of the first Belgian universities to make concrete proposals on how to distribute official funding among universities aimed to promote the creation and the development of laboratories for numerical computations79. More precisely, Lemaître was not totally alone at UCL in studying what   Specifically, the Burroughs Calculator 7282.   These rooms included the office of the Canon, a  room where the Mercedes was installed, a room where the Burroughs E101 would be installed and a seminar roomlibrary where his assistant also prepared tea (communication of J. Valembois, 19-121997). 78   It seems that certain machines used by Lemaître were already being subsidized by the CBRM before the creation of the Laboratory, (letter, 04-01-1951, preserved at the AL), and FNRS assisted with the maintenance of the Burroughs Calculator Model 7207222. 79   Letter, Jean Willems, Director of the FNRS to Lemaître (31-03-1952; AL). 76 77

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was needed to perform computations of the kind going on across the Atlantic. As early as 1947, his colleague Charles Manneback, in collaboration with Léon Brillouin, his professor at the Collège of France and Harvard University, had written a detailed report entitled “Mathematical Machines in the United States”80, in which he recommended a strategic thrust in numerical calculation. But it was clearly Lemaître who was the first to promote such ideas in Louvain, along the lines of his professor and colleague Maurice Alliaume, who wanted UCL to create an “Office of Astronomical and Numerical Calculations”81. In 1958 at the Brussels World’s Fair (Expo 58), he fell in love with another calculator used in banks, the Burroughs E101. It was not a binary computer, but an electronic machine whose readout consisted of a series of lamps displaying numbers, the value determined by the transmission of a string of pulses.82 The memory of this imposing machine could hold a mere 220 numbers of 12 digits. There were two ways to program the machine. One of them consisted of placing needles in holes, each hole corresponding to an elementary operation. The computation of a series representing an elementary mathematical function, resulted in a particular configuration of the needles, the precise position of which could be saved by marking the holes in a piece of cardboard. The second method consisted in feeding the machine with a perforated tape prepared on a keypunch machine. Later that year, Lemaître succeeded in acquiring an E101, and contributed to part of its financing. He announced one day to a Bachelor of Arts student of mathematics and physics, “I will bring a computer and I need arms, because UCL does not give me resources.”83 A certain number of students, including his future assistant, Jacques Masset, were consequently pressed into service transporting the machine to the top of the Collège des Prémontrés. Lemaître also benefited from the helpful assistance of some technicians from the Faculty   Typewritten Report, Archives Dockx, Namur, FUNDP (University of Namur)   Cf. Chapter 3. 82   The number 8 for instance corresponds to a train of 8 pulses. 83   Oral communication, J. Masset, 15-12-1997. 80 81

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of Science who loaned him a winch to move the E101 up the ancient staircase of the Collège. During a short ceremony later on, the machine was blessed by the rector, Msgr. Van Waeyenbergh. The place where the machine resided was baptised the ‘Computing Room’, in English to avoid all linguistic frictions between Flemishs and Walloons. It was not ideal, as the lamps of the E101 emitted a great deal of heat and the room only had small windows which needed to be opened from time to time for cooling. Despite all the problems, Lemaître succeeded in obtaining from this contraption a whole series of eagerly awaited results. With it, Andrée Bartholomé and the Canon succeeded in predicting the behaviour of the clusters of galaxies during the last expanding phase of the hesitating universe (1958h). Lemaître thus described the gymnastics required for the computation of the “radius r1 of the limiting sphere of a cluster of galaxies”84: The computation was performed with the help of a Burrough E101 machine with a memory of 220 numbers, and punched tapes. By taking care to systematically use space in the memory as soon as it became available, it was possible to compute the 424 numbers involved in the equations describing the rebound behaviour. These numbers were registered on a punched tape. The checks were facilitated by providing the partial sums in the calculations. The computations could have been minimized if the machine had benefited from an output mechanism that could have registered the computed numbers on the tape directly. In the second part of the computation, during which the tape was providing the coefficients already computed, the capacity of the machine allowed for every value of r1 tried to compute the coefficients of the systems of ten equations with ten unknowns and to provide the solution as well as the residue obtained carrying it in the first equation. Each attempt took about 45 minutes.   (1958h: 101). Galaxies that leave the cluster are replaced by others that come from the surrounding field. Mathematically, this is equivalent to the scenario where galaxies are reflected, or “rebound” on the limit sphere. 84

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In the early 1960s, the E101 was moved to the Arenberg campus in Heverlee, in the Institute of Nuclear Physics directed by Marc de Hemptinne. There it completed its duty to the Louvain community by occasionally serving as a computation tool for the doctoral students, in spite of its limitations. It was sold around 1962 to the Saint– Luc School in Tournai, where it was used for teaching and as a supply of spare parts for a similar machine. In the 1980s it was sent to the Lemaître Archives in Louvain-la-Neuve. Beginning in the 1960s, André Deprit85 and Andrée Bartholomé, who later married, would play a key role in researching and advising Lemaître on the acquisition of calculators86. In 1961, they succeeded in obtaining, for the Laboratory of Numerical Research two hours of calculation on the Remington Rand machine that was made available to UCL every month. This facilitated the characterization of certain orbits of the three-body problem studied by Deprit and his student André Délie.87 In 1962, Lemaître’s Laboratory bought a NCR-Elliott 802 machine, consisting of a binary computer with lamps and transistors, with a memory of 1024 33-bit words. As usual, Lemaître began programming it directly in machine language. His bent for efficiency pushed him to learn assembly languages.88 With his nephew Gilbert Lemaître, he developed a new language, AUTOCODE; and in 1965, he published two reprints related to symbolic machine code designed  After a stay of three years in Cambridge and two years of teaching in Lovanium (Belgian Congo), Deprit returned to Louvain at the request of Lemaître himself, the latter having made some proposals to the Rector of UCL in order to ensure that his student would succeed him in mechanics (“première candidature”: Bachelor 1) and in astronomy (“deuxième candidature”: Bachelor 2). Cf. Letter, A. Deprit to G. Lemaître, 28-05-1958. 86   Letter, 16-02-1960 of A. Deprit to G. Lemaître concerning a visit to the Computing Unit of the University of London, and to the National Physical Laboratory. 87   Letter of A. Deprit to G. Lemaître, 29-04-1961. 88   Assembly language enables replacing binary instructions for the machine with symbolic mnemonic codes, which are more easily manipulable. Assembly language falls in between machine language and high-level languages, in Lemaître's day being ALGOL, FORTRAN and COBOL. 85

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for the Elliot 802 (1965a,b). Msgr. Lemaître’s liking for machine and assembly languages did not lead him to completely disdain the new higher level languages. While he never studied FORTRAN, or the kind of BASIC that Gilbert Lemaître developed, VELOCODE, he did study ALGOL, and predicted a bright future for it.89 According to André Deprit90, his interest in ALGOL came from meeting Adriaan Wijngaarden (1916-1987)91 in Berkeley in the early 1960s, a guest professor like himself. Lemaître’s love for machines was always subordinated to his interest numerical computation. The machine was for him only a tool for research. From the 1930s until his death, these almost always concerned calculations of classical orbits. Computational power would play a major role once more during his career, when he turned his attention to the three-body problem.

4. The apotheosis: the three-body problem During the war, reading Poincaré’s Méthodes Nouvelles de la Mécanique Céleste92 and Élie Cartan’s Leçons sur les Invariants Intégraux93 had led Lemaître to become interested in the intricate problem of computing orbits of the three-body problem,94 namely determining   Oral communication of R. Dejaiffe (30-10-1997). ALGOL is discussed in a correspondence between Lemaître and Manneback (letter, 26-02-1960, AL). 90   “Monsieur Georges Lemaître” in The Big Bang and Georges Lemaître, op. cit.: 286387. 91   Director of the Amsterdam Mathematisch Centrum and an important member of the International Federation for Information Processing. He developed ALGOL 60. Cf. J.A.N. Lee, Computer Pioneers, Washington, IEEE Computer Society Press, 1995: 681-682. 92   Especially the third volume (Paris, Gauthier-Villars, 1899). 93   Paris, Hermann, 1922: 172-185; concerning the three-body problem, 177-185. 94   One can detect a trace of this interest in his retreat notebook of August 1943 where he alluded (in the context of the thesis of Scohier) to the relevance of a comparison between the problems of periodic and asymptotic orbits of the Størmer problem and a specific case of the three-body problem analyzed by Thiele and later by E. Strömgren and his Copenhagen school, namely the problem of the gravitational interaction between a point mass and two centres of rotation. 89

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the trajectories of three point masses under their mutual gravitational attraction. Poincaré had shown that this problem, contrary to that of Kepler95, is not integrable. In other words, there is no closed-form analytical representation of the orbits. This is due to their being intrinsically mathematically ‘chaotic’.96 But there was another element that led Lemaître to be deeply interested in this iconic problem of mechanics. The study of the families of periodic trajectories of the Størmer problem led him to assert that the latter exhibited behaviour similar to those encountered in a particular case of the three-body problem.97 The difficulty of the three-body problem does not come only from the absence of an analytical formula allowing the computation of the orbits; it also comes from the singularity introduced by the collisions between the bodies. When two point objects approach one another, the force between them increases, becoming infinite at zero separation; the equations of motion then lose all their significance. This kind of singularity, i.e. the appearance of infinite values, poses a serious problem to the numerical computation of the three-body problem. One is led to search for appropriate coordinate transformations that eliminate this kind of singularity, what is called a “regularization” of the problem. This type of problem was not new by the time of Lemaître.98 Already in the 18th century, Euler had become interested in the regu  The Kepler problem concerns the orbits of two bodies that attract each other under Newton’s law of gravity. This problem leads to the famous Kepler’s laws governing the motion of a planet around the Sun. In this case, the problem is completely integrable and the orbits (conics) can be expressed by means of a simple formula. 96   Chaotic behavior means the extreme sensitivity to a change of initial conditions. If one changes the position or the speed of a body a tiny amount, it can result in huge change of its trajectory, preventing any reliable computation of the system’s evolution in the future. 97  “The Størmer problem thus provides an example of natural termination of a family of periodic orbits, analogous to the famous example studied by Strömgren in the restricted three-body problem” (1943a: 15). 98   R.J. Dejaiffe, “Les contributions de Lemaître au problème général des trois corps”, Hervelé-Louvain, Institut d’astronomie et de géophysique Georges Lemaître, publication no 2, 1967. 95

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larization of a particular case of the three-body problem, in which one body is attracted by two other point masses which are fixed in space. Lemaître was well aware of the regularization procedure of Lagrange99. Technically, it consisted of a change of coordinates, determining a conformal transformation, and transforming the parabolic trajectories possessing very strong curvature in the vicinity of the scattering centre with an almost straight trajectory. This regularization technique was further developed by Thiele, in a particular case of the three-body problem, and numerical studies were conducted by the Strömgren school in Copenhagen. Levi-Civita100 had also introduced a regularization technique for the problem of three bodies whose motions are restricted to the same plane. Finally, in 1912 Sundman had provided a regularization of the general three-body problem by eliminating the singularities related to close collisions. Lemaître, who knew of this work through his lecture on Whittaker’s Analytical Dynamics101, was struck by the limits of this regularization when one tries to compute the orbits numerically: “[…] nobody has been able to apply Sundman’s theory to an actual numerical problem” (1955i: 207). Lemaître’s work on the three-body problem was prompted in part by reflecting on the limitation of Sundman’s procedure. The regularization in fact requires two distinct steps. The first one is, as in Lagrange’s case, a geometrical transformation that changes the trajectories in the vicinity of the singularities introduced by the collisions. But this is insufficient. It is also necessary to perform a transformation of the time variable to avoid the appearance of infinite velocities on the regularized trajectories, e.g. the straight lines in the case   Lemaître had read the original work of Lagrange (1963b: 1), but he was already familiar with it from studying the book of E.T. Whittaker, Analytical Dynamics, Cambridge University press, 1937; cf. (1955i: 2008). 100   Cf. E.T. Whittaker, op. cit.: 424 (quoted by Lemaître in 1955i: 208). 101   As early as 1925 (reading notes, AL), one can see that Lemaître had read E.T. Whittaker, A Treatise on Analytical Dynamics of Particles and Rigid Bodies, with an Introduction to the Problem of Three Bodies, Cambridge University Press, 1904. He was surely aware of the paper by the same author: “Report on the Progress of the Solution of the Problem of Three Bodies”, British Association Report, 1899: 121-159. 99

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of the Lagrange regularization102. Levi-Civita’s work took both into account; nevertheless, as Lemaître saw in 1954103, the work of Sundman considered the regularization of trajectories as secondary to time regularization. And this is where the method falls short (1955i: 209): [Sundman’s regularization] has found no practical use in numerical computations. This may be due to the fact that, while Sundman accounted for the required rescaling of time, he completely neglected the secondary aspects of Levi-Civita’s regularization i.e. the geometrical simplification of the trajectories in the neighbourhood of the singularity.

The second starting point of Lemaître’s work came from his meeting with Heinrich at the seventh general assembly of the International Astronomical Union held in Zurich 11-18 August 1948. The latter had stimulated the curiosity of the Canon by giving him a copy of a paper concerning an extension of methods of celestial mechanics in the case of the computations of orbits, which are particularly complicated. By studying the works of Heinrich, Lemaître found new ideas concerning the problem, treated by Thiele, concerning the two cen  Consider the simple example of the Kepler problem with one dimension perturbed by a force deriving from a potential V(x). The equation of motion is written d2x/dt2+a/ x2 = - dV/dx (a, constant). The equation is singular at x = 0 (collision with the attractive center). One can obtain the regularization by putting x = um (geometric transformation) and dt = unds (temporal rescaling) and by choosing m and n in such a way that the equation of motion in u and s is not anymore singular. The equation is thus: 2 d2u/ds2 = (V+E) u +1/2 u2 dV/du (E is the energy, a constant); cf. W. Neutsch, K. Scherer, op. cit.: 391-393. 103  On the last page of his research notebook (1947-1953), AL, dated 15-01-1954, Lemaître noticed: “the regularization comprises two aspects 1) the time of regularization […] particularly considered by Sundman. 2) A geometric transformation, transformation of Levi-Civita or something analogous. Sundman has only considered the first aspect and has a theoretical proof of regularization, unfortunately impracticable.” One sees Lemaître following a geometrical intuition. Thus he added: “…would it not be appropriate to try the opposite point of view, to consider only a geometrical regularization?” 102

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tres in rotation. In October 1948, he declares104: “This leads me to a very simple idea of how to treat the three-body problem.” In fact, this idea concerned a particular choice of coordinates that allows one to express the formulas occuring in the general three-body problem in an elegant way. But during this period, Lemaître did not talk about the “regularization of the problem”. During the academic year 19481949, the Canon applies his new “symmetrical coordinates” to a particular case of three bodies, that of three equal masses. This allows him to state that his symmetrical coordinates led him to perform the regularization of the problem, which he accomplished probably before 12 April 1949105. This success would encourage the Canon to involve his collaborator on the numerical study of orbits of certain particular cases of the three-body problem106. As for the case of the Størmer problem, Lemaître drew the periodic orbits and empirically tested their stability. Clearly his intuition had revealed to him a profound linkage between the three-body problem and the study of cosmic rays trajectories107. In 1951, he found a way of translating the problem of the three equal masses located on a plane into one of characterizing the motion of a point moving in a force field described by a scalar and a vector potential such as found in electromagnetism108. In 1951-1952 he succeeded in extending the aforementioned techniques   Research Notebook 1947-1953 (AL); our translation from the original in French.   Research Notebook 1947-1953 (AL). 106   A. Deprit, “Les amusoires de Monseigneur Lemaître”, op. cit.: 222 (note 45) for a list of the contributions made by Lemaître’s students on this topic. Among them, it is worth mentioning C. Cauwe (1957), H. Vilz (1957), and E. De Vijlder (1958). Cf. S. Batteux, Problème général des trois corps et regularisation de Georges Lemaître, Masters Dissertation in Physics, FUNDP (University of Namur), June 2001, unpublished. 107   His Research Notebook 1947-1953 clearly reveals the intertwining of the two subjects whose theoretical unity is crystallized in the techniques of celestial mechanics of the kind used by Poincaré and Delaunay. Thus Lemaître in 1951 outlined three main axes of his research: clusters of nebulae, the application of Delaunay's theory of the motion of the Moon to the Størmer problem, and the calculation of periodic orbits in the three body problem; AL 05-03-1951. 108   Research Notebook 1947-1953 (AL), 11-07-1951. For such potentials see (1952b: 584). 104 105

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to the general three-body problem and to achieve, in this context, the regularization of binary collisions109. The regularization technique fully reveals Lemaître’s genius.110 The Canon possessed an unusual capacity to envision the coordinate changes that would simplify a problem and to interpret results geometrically. A few words are in order about Lemaître’s regularization method which could still bear fruit today along with other techniques such as the Kustaanheimo-Stiefel transformation111. The success of the technique is based on two tricks. The first one relies on the critical choice of symmetrized coordinates. In essence, all singularities associated with binary collisions are restricted to lie on three semi-infinite line segments. The second is the discovery of a geometrical transformation, which, like the conformal transformation of Levi-Civita, eliminates the sharp corner and cusp that appear due to the binary collision singularity. Finally, time regularization is carried out similarly to Sundman. In 1954, Lemaître would come up with an equivalent, but simpler, version of his regularization method (1954d) in a work of a rare mathematical beauty (1955) very clearly in line with the work of Levi-Civita. There is an interesting detail here. The LeviCivita regularization was based on a transformation of the type w = z2 where z is a complex variable112. If one considers complex numbers z of unit norm (z thus lying a circle of unit radius), this conformal transformation maps a circle onto a circle. It is possible to generalize this Levi-Civita transformation by using quaternions instead of complex numbers.113 One then obtains a way to generate a map of   These results are published in (1952b, e).   V. Szebehely, Theory of Orbits. The Restricted Problem of Three Bodies, New York, Academic Press, 1967: 105-107 (§ 3.7. Lemaître’s regularization). 111  P. Kustaanheimo, E. Stiefel, “Perturbation Theory of Kepler Motion based on Spinor Regularization”, J. Reine Angnew. Math., Vol. 218, 1965: 204-219. Cf. A. Deprit, A. Elipe, S. Ferrer, “Linearization: Laplace vs. Stiefel”, Celestial Mechanics and Dynamical Astronomy, Vol. 58, 1994: 151-201. 112   If one writes z = x + iy and w = a + ib (i2 = -1; x, y, a, b, real numbers), one obtains: a = x2-y2 and b = 2xy. The Levi-Civita transformation can be written f(x,y) = (x2-y2, 2xy) and one may check that if x2+y2 = 1 then a2+b2 = 1 (i.e. one circle maps onto another). 113   A quaternion can always be written q = z1 + j z2 (zk is a complex number and j2 = -1). 109 110

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a three-dimensional sphere (that represents the set of quaternions of unit norm, which is nothing more than the elliptic space of Lemaître’s cosmology), to the usual two-dimensional sphere. This map, which was found in 1931 by Hopf114, is indeed the foundation of the Kustaanheimo and Stiefel transformation that provides another regularization method. As mentioned before,115 Lemaître was aware of this map, called the “Hopf fibration”, as far back as 1957. His knowledge of the elliptic space and quaternions could have led him to discover the Kustaanheimo and Stiefel regularization (KS). Nevertheless, as observed by André Deprit116, Lemaître stayed out of the movement that led to KS. His mindset did not lend itself to perform the kind of algebraic generalization that would have been necessary to pass from Levi-Civita to KS. His fundamental works (1952b,e) bore the traces of the influence of the Leçons sur les Invariants Intégraux of Élie Cartan.117 In his very last scientific work, edited in 1963 when he was a guest of the Space Sciences Laboratory of the University of California in Berkeley118, Lemaître linked his contribution explicitly to that of Cartan119 who proposed a general geometrical interpretation of the equations of the n-body problem. In fact, Lemaître’s work can be thought of as a specific realization of the abstract program outlined by Cartan in One generalizes the transformation of Levi-Civita by writing: F(z1, z2) = (z1z1*-z2z2*, 2z1z2*), where * refer to the complex conjugate. 114   It is interesting that this was also the very year Dirac discovered his theory of the magnetic monopole, whose geometrical foundations are based on the existence of this Hopf fibration. Moreover, it was also in 1931 that Lemaître published his first work related to quaternions (1931c). All these works were independent. The motivation of Hopf was the search for examples of homotopically non-trivial maps between spheres. 115   Cf. Chapter 10. 116   E-mail of 01-07-99. 117   See in particular his introduction of the differential forms (1952b: 590) 118   During the 11th general assembly of the International Astronomical Union in Berkeley, Lemaître had presented on 16 August 1961, at the request of Dirk Brouwer of Yale, president of the commission of celestial mechanics of the Union, a communication on the regularization of the three-body problem whose redaction constituted the basis of his 1963 work. 119   (1963b: 29-34).

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his Leçons. The famous geometer showed that it was possible to reduce120 the phase space 121 of the three-body problem and to work on a reduced manifold, but without giving any clue how to do so122. The last work of Msgr. Lemaître, circulated only as a preprint, drew from computations performed by Carl Burrau in 1913, on an unusual rendition of the three-body problem. In Burrau’s problem, each body begins at rest from the vertex of a triangle, and each one possesses a mass proportional to the distance between the other two. For the Canon, Burrau’s problem offered an ideal context to demonstrate the potential of his symmetrical coordinates. On 15 February 1965, Msgr. Lemaître would undertake drafting a treatise summarizing his study of the Burrau problem123. It was the last technical manuscript that he would ever write. One could legitimately claim that his work on the regularization of the binary collisions ranks among the most beautiful and fruitful of Lemaître’s career. His works in the 1920s and 1930s did not give rise to a cosmological “school”. The first school of Lemaître, his students and colleagues who worked on the Størmer problem, would not perdure in the end. Nevertheless, as observed by Jacques Henrard, an “implicit school”, that could be called the “second school of Lemaître”, indeed emerged in the 1960s, in the wake of his works on celestial mechanics.124 Independent of Lemaître, but very much in his tra  Here lies the whole philosophy of Cartan, that undertakes to show that one can use mathematical objects that remain invariant, the “integral invariants”, the “first integrals”, to simplify the problem by diminishing the number of degrees of freedom. 121   Let us recall that phase space is an abstract space built with the positions and the velocities of the bodies. A point of this space represents the state of the motion of all these bodies at a given moment. 122   Cf. A. Deprit, “Dynamics of Orbiting Dust under Radiation Pressure” in The Big Bang and Georges Lemaître. Proceeding of a  Symposium in Honor of G. Lemaître, Fifty years after his Initiation of Big Bang Cosmology. Louvain-la-Neuve, 10-13 October 1983 (Berger, ed.), Dordrecht, Reidel, 1984: 151-153. 123   “Le problème de Burrau”, unpublished manuscript preserved at the AL. The interest of Lemaître for this problem was important; he advised R. Dejaiffe to preserve the problem of Burrau as a Ph.D. topic (oral communication, 30-10-1997). 124   J. Henrard, “Monseigneur et les trois corps”, Ciel et Terre, Vol. 110, juillet-août 1994, no 4: 98-99. 120

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dition, an important group of collaborators and students would make significant contributions to celestial mechanics in general and to the three-body problem in particular125. Lemaître never sought widespread acceptance, but he left a legacy of students and colleagues in classical mechanics who knew how to assimilate and develop what the Canon often abandoned in draft form. Paradoxically, the field in which he is best known, relativistic cosmology, never gave rise to the creation of any true school. This is a significant clue revealing Lemaître’s decided preference for classical mechanics and numerical calculations which had preempted, by the end of the 1930s, his interest in the mathematics involved in general relativity: Riemannian geometry, tensor calculus, etc. It is interesting to note that these latter works were completed by the Canon when he was between 55 and 69 years old. According to Jean Dieudonné, one must conclude that Lemaître was one of those ‘few mathematicians beloved by the gods’ or loved by God, which he would perhaps prefer. In fact, the famous mathematician said the following126: It is true that several major discoveries have been made by mathematicians whose age did not exceed thirty. Yet, for many among the greatest like Poincaré, Hilbert or H. Weyl, their creative period was prolonged, fruitful until the age of fifty to fifty-five; while other like Killing, Emmy Noether, Hardy […] or more recently Zariski and Chevalley, were at their best in their forties. Finally some mathematicians, those who were beloved by the gods, like Kronecker, Élie Cartan, Siegel, A. Weil, J. Leray or I. Gelfand, were still able to prove beautiful theorems into their sixties.

  For example, A. Deprit, A. Delie, “Regularization of the three-body problem”, Archives for Rational Mechanics and Analysis, Vol. 12, 1963, no 4:325-353. Cf. A. Deprit. “Les amusoires…”, op cit.: 222 (note 46). 126   J. Dieudonné, Pour l’honneur de l’esprit humain. Les mathématiques aujourd’hui, Paris, Hachette, 1987: 18-19; our translation. 125

Chapter XV

Faith and science: the Un’Ora problem (1951–1952)

1. From Deus Absconditus to the natural beginning of the universe

I

n the 1930s Lemaître formulated a clear-cut distinction between two paths, one leading to the knowledge of nature and scientific truths, and the other to the knowledge of theological truths1. A consequence of this approach is that the relationship of God to the World cannot be demonstrated through means used by the natural sciences. From the Mechelen Catholic Congress in 1936, Lemaître would increasingly refer to the idea of the “hidden God” explicitly linking it to the affirmation of Isaiah: “Vere tu es Deus absconditus Deus Israel salvator”2. If God remains hidden, it is not because he does not exist, but simply because he does not identify himself purely and simply with the World and because he respects its autonomy (1936b: 69): [The Christian seeker] knows that everything that has been done has been done by God, but he knows also that God does not supplant his creation. The omnipresent divine activity is essentially hidden everywhere. It can never be a question of reducing the Supreme Being to the rank of a scientific hypothesis.

  D. Lambert: “Monseigneur Georges Lemaître et le débat entre la cosmologie et la foi”, Revue théologique de Louvain, t. 1997: 28-53 and 227-243. 2   Is. 45, 15 (Vulgate). 1

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The notion of Deus absconditus is one of the most constant, if implicit, themes of Lemaître’s theology. In the final passage of his paper for Nature (1931d), which he chose not to publish, one could find already this expression3 “God is essentially hidden”. In 1958, when he spoke in front of the 11th Solvay Council, he returned to this theme of the hidden God to repeat that his hypothesis of the primeval atom was not related to any philosophical or religious conception (1958f: 7). As far as I can see, such a theory [of the primeval atom] remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being. He may maintain the same mental position for the beginning of space-time as he has adopted for non-singular events. For the believer, it removes any attempts to familiarity with God, as were Laplace’s chiquenaude or Jeans’ finger. It is consonant with Isaias speaking of the “hidden God”, hidden even at the beginning of creation.

The idea of a discreet God shunning any ostentatious manifestation of his power was so strongly rooted in him that he believed he had the responsibility to warn Cardinal Van Roey, on 4 September 1947, to avoid involving the University of Louvain with a popular demonstration organized on the occasion of the stay in Belgium of a statue of Our Lady of Fatima. Some people had in fact asked Lemaître, as a professor of astronomy, to express his opinions on the astonishing signs related by persons who were in Fatima on 13 October 1917, specifically the abnormal motion of the Sun that appeared to be dancing in the sky. Lemaître chose to be circumspect in front of a series of prodigious events that seemed to constitute a partial revocation of the essentially hidden character of God’s transcendence. By writing to the Cardinal, the goal of Lemaître was to correct the general public belief in some sort of “astronomic proof” of the existence of God. He was right, and we shall see below that his intervention with the   Draft of the paper preserved in the AL.

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Vatican would be similarly motivated. Nevertheless, he could have considered these “signs” as being part of a spiritual experience lived by each person during the occasion of the apparitions of Fatima, this experience de facto evading strict experimental control. In his letter to the Primate of Belgium, he gave no quarter to this possibility and he asked the Primate to “express his skepticism” in public, since for him the events of Fatima were an example of unbridled credulity4: It seems clear that on 13 October 1917 the Sun did not move more than any other day, no one has remarked on anything at the Coimbra Observatory; the 50,000 people who saw it dancing were misled by some meteorological or psychological phenomena.

However, one begins to probe of the limits of Lemaître’s ‘prudence’. Indeed, if the stories of the people present in Fatima described, in fact, not an observation of a physical phenomenon, but an authentic spiritual experience, then there would be no sense in asking the advice of the Coimbra astronomers. Doing so would constitute falling into some sort of concordism that Lemaître had attempted to combat with reason. Curiously, the prudence of the Canon of Louvain led him to formulate an argument that contradicts his ‘two paths to truth’ theory, because one cannot demonstrate the non-existence of a spiritual experience or of a transcendent reality by scientific methods. In any case, the position of Lemaître showed clearly that his faith was not blind fideism as a good dose of skepticism would always accompany the intense convictions of this “Ami de Jésus”. By writing to Cardinal Van Roey, Lemaître knew that he would be listened to. Indeed, before 1950, the Cardinal was not completely in favour of acknowledging the reality of the appari  This sharp language is reinforced by a troubling and ironical reflection: “What a misfortune that those things are spread outside the countries they were intended for, these countries where the crucifix is moving naturally.” Letter, 04-09-1947, whose draft is preserved in the AL and whose original version is preserved in the archives of the Archbishopric of Mechelen-Brussels; our translation from the original in French. 4

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tions of the Blessed Virgin in Belgium.5 Moreover, in a letter dated 27 February 1947, he had advised Msgr. Kerkhofs, Bishop of Liège, to be prudent regarding this approval6. Not without a touch of irony, Lemaître concluded with the following advice to the Cardinal: “If Fatima must come to Louvain, wouldn’t be better during the holidays?” The concept of the “two paths” of knowledge, and the Deus Absconditus together codify his position concerning the purely natural beginning of the universe. Admitting the possibility of a description of a purely natural beginning of the universe thus respects the transcendence of God and correlatively, the autonomy of the World. This is why, as Lemaître would not cease to repeat (1960b: 13; our translation from the original in French): As far as I am concerned, I prefer this natural beginning to the flick evoked by Pascal before Laplace and for which God would have had to intervene to put the World in motion. I prefer to think of the hidden God of Isaiah: Deus Israel salvator, to the supreme and inaccessible God. “No one has known God”, said Saint John, to the God hidden even in the beginning of the World.

According to Lemaître, it was simply out of the question to confuse the ex nihilo creatio, in the theological sense, with the beginning of the universe such as it was described by his primeval atom hypothesis. In a text written for the Japanese Catholic Encyclopaedia, which was writ  Another anecdote further exemplifies how charged these questions were at the time. After a dinner following the consecration of the Bishop of Namur, Msgr. Charue in 1942, Cardinal van Roey made some critical remarks concerning the apparitions of Banneux. Perturbed by these comments, the Bishop of Liège, Msgr. Kerkhofs who was working on the acknowledgment approval of these apparitions, abruptly left the room!. (Dossier de Beauraing 2. André-Marie Charue 27e évêque de Namur reconnaît les apparitions. Documents (presented by C.-J. Joset), Beauraing/Namur, Pro Maria/ Recherches Universitaires, 1981: 31. 6   The official recognition of the reality of the apparitions of Beauraing and Banneux was dated 1949. In this letter the Cardinal wrote: “[…] I believe that it would be seriously imprudent, despite your personal conviction, to pronounce yourself in favor of the divine origin of these events” (archives of Fr. Scheuer, S.J., FUNDP, University of Namur). I am thankful of Fr. L. Wuillaume, S.J., for having related this information. 5

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ten some time before the Second World War, but which would remain at the manuscript stage7, Lemaître insisted on this point (1985a: 47): What happened before that? Before that we have to face the zero value of the radius (of the universe). We have discussed how far it had to be taken as strictly zero, and we have seen that it means a very trifling quantity, let us say few light-hours. We may speak of this as of a beginning. I do not say a creation. Physically it is a beginning in the sense that if something had happened before it, it has no observable influence on the behaviour of our universe, as any feature of matter before this beginning has been completely lost by the extreme contraction at the theoretical zero. A preexistence of the universe has a metaphysical character. Physically everything happens as if the theoretical zero was really a beginning. The question is if it was really a beginning or rather a creation: something starting from nothing, is a philosophical question that cannot be settled by physical or astronomical considerations.

Between 1933 and 1950, Lemaître never ceased to repeat this claim. Curiously, he did not seem to be listened to. From the materialist side, one continues to believe that the hypothesis of the primeval atom was a strategy of a scientist Catholic priest to accredit the theology of the creation. The historian Helge Kragh highlights a passage which is as significant as it is virulent by the communist ideologist Andrei Zhdanov who, in 1947, declared8: The reactionary scientists Lemaître, Milne and others made use of the “red shift” in order to strengthen religious views on the structure of the universe… Falsifiers of science want to revive the fairy tale of the origin of the world from nothing…

  It would be published later by O. Godart and M. Heller (1985a).  H. Kragh, Cosmology and Controversy. The historical development of two theories of the universe, Princeton University Press, 1996: 260. 7 8

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In fact, at the end of the 1940s, opposition to the cosmology of Lemaître was particularly easy since there was not any convincing observational test permitting it to be validated. Yet, during that period, there was another rival theory that seemed promising and did not involve any “beginning”. It was the “steady state” theory of Hermann Bondi, Fred Hoyle and Thomas Gold9. This theory, developed at the end of the 1940s, was based on the “perfect cosmological principle”, according to which the universe should remain the same whatever the position of an observer is within the space, but also whatever the moment is when this observer makes his observations10. The universe would thus be homogeneous and isotropic in space and time. As is, such a steady state cosmology could not account for the expansion of the universe that had already been observationally well confirmed. But if the universe is expanding, the number of galaxies per unit of volume must decrease, and therefore the universe would not be static. To satisfy the perfect cosmological principle, and to ensure that the density of galaxies remains constant in spite of the expansion of the universe, it is necessary to assume that there is a process of continuous creation of matter. Paradoxically then, this theory that tries to avoid a “beginning” of the universe – and which satisfies the materialists who saw in the latter a “creation” in a theological sense – leads one to assume, in a purely ad hoc way, the creation of matter everywhere and at all times. The theory would finally be discredited in the late 1960s when it became clear that it could not account for cosmological background radiation11. The defenders of this theory competed virulently and critically with the cosmologists supporting the idea of an initial singularity, an “initial Big Boom”, or a “Big Bang”.   Cf. H. Kragh, op. cit: 142-201.   The metric describing the universe of Bondi-Hoyle-Gold is formally identical to that of de Sitter written in the form that Lemaître had used in 1925. Today, one can interpret this metric like that of an inflating universe. The exponential describing this inflation of space depends on a scalar field that couples with the gravitational field to drive the inflation. 11   Cf. Hoyle, “An Assessment of the Evidence against the Steady State Theory” in Modern Cosmology in Retrospect (B. Bertotti, R. Balbinot, S. Bergia, A. Messina, Eds). Cambridge University Press, 1990: 221-231.   9 10

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This expression was used for the first time by Fred Hoyle in 19491950 to disparage Lemaître’s cosmology12. In the early 1960s, while he was attending a conference in California, Odon Godart, seated not far from Fred Hoyle, would once more hear the latter mockingly quip to a colleague: “Look, there’s the Big Bang man!” while Lemaître made his entrance13. Paradoxically, Lemaître’s thesis, on the independence of the idea of the natural beginning of the universe from the theology of creation would not be accepted even by some Catholics. This became eminently clear on the occasion of the famous discourse of Pius XII.

2. The Un’Ora discourse On 22 November 1951, Pius XII in front of the members of the Pontifical Academy of Sciences who had gathered for a study week on micro­seismicity, delivered a discourse in Italian entitled “Un’Ora”14 and whose theme concerned the proof of God’s existence in light of natural sciences. Pius XII, who had developed an interest in the scien­ces15 and had a passion for astronomy16, wanted to suggest that   Cf. H. Kragh, op. cit.: 191-192.   Oral communication of O. Godart (14-06-1995). 14   Pius XII, “Discorso per la Sessione plenaria e per la Settimana di studio sul problema dei microsismi” in Discorsi dei Papi alla Pontificia Academia delle Scienze (19361993), Cità del Vaticano, Pontificia Academia scientiarum, 1994: 81-94. (“The Proofs for the Existence of God in the Light of Modern Natural Science. Address to the Plenary Session and to the Study Week on the subject: ‘The Question of Microseismicity’”) in Papal Addresses to the Pontifical Academy of Sciences 1917-2002 and to the Pontifical Academy of Social Sciences 1994-2002 (Preface by Prof. N. Cabibbo; Introduction by H.E. Msgr. M. Sanchez-Sorondo), Scripta Varia, 100, Pontifical Academy of Sciences, 2003: 130-142. 15  Cf. J Chelini, L’Église sous Pie XII. L’après-guerre (1945-1958), Paris, Fayard, 1983: 162-169. 16   Pius XII performed astronomical observations himself when he was in Castel Gandolfo at the Vatican Observatory in the presence of its director, F. O’Connell and a brother in charge of the preparation of the instruments (oral communication, M. Heller of the Pontifical Academy that recorded his testimony, 17-10-1994). Cf. also: R. Ladous, Des Nobel au Vatican. La foundation de l’Académie pontificale des sciences, Paris, Cerf, 1994: 136. 12 13

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contemporary physics was useful in enriching the empirical basis on which the Thomistic “ways” could be rooted (these “five ways”, the quinque viae proposed by Thomas Aquinas, aimed to establish the existence of the philosophers’ God). But, the Pope also intended to suggest that astrophysics gives credit to the doctrine of ex nihilo creation, at the beginning of time17: With the same clear and critical gaze with which he examines and judges facts, he also catches sight of and recognises the work of the omnipotent Creator, whose power aroused by the mighty ‘fiat’ pronounced billions of years ago by the Creative Spirit, unfolded itself in the universe and, with a gesture of generous love, called into existence matter, fraught with energy. Indeed, it seems that the science of today by going back in one leap millions of centuries, has succeeded in being a witness to that primordial Fiat Lux, when out of nothing, there burst forth along with matter a sea of light and radiation, while the particles of chemical elements split and reunited in millions of galaxies.

In fact, Pius XII was under no illusion that there was an astrophysical proof of the reality of creation and of the beginning of time, which would be at variance with Thomas Aquinas who, in a famous passage of the Summa Theologiae claimed that18: “By faith alone do we hold, and by no demonstration can it be proved, that the world did not always exist […].” Pius XII himself claimed as much19: “The facts verified up to now are not arguments of absolute proof of creation in time as are those drawn from metaphysics and revelation”. According to the Pope, the arguments leading to the statement of an ex nihilo creation remains “outside the sphere of the natural sciences”. Despite these qualifications, the Holy Father ventured in his use of expressions that implicitly suggested that contemporary astrophys  Papal Addresses to the Pontifical Academy of Sciences 1917-2002, op. cit: 139.   Question 46, Article 2 (Translation by Fathers of the English Dominican Province, Benziger Brothers edition, 1947. Retrieved from http://www.ccel.org/). 19   Papal Addresses to the Pontifical Academy of Sciences 1917-2002, op. cit: 139. 17 18

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ics could lead quite naturally to the field of Revelation20: “Although these figures [the estimates of the age of the universe] are astonishing, nevertheless, even the simplest believer would not take them as unheard of and differing from those derived from the first words of Genesis, ‘In the beginning…’ which signify the beginning of things in time. These words take on a concrete and almost mathematical expression…” Such a statement is clearly in diametric opposition to the thesis that claims that materialism is the only philosophy compatible with the data of physics and in particular of astronomy21: […] it is worth noting that modern exponents of the natural sciences consider the idea of the creation of the universe entirely reconciliable with their scientific conception, and indeed they are led spontaneously to it through their research, though only a few decades ago such a “hypothesis” was rejected as absolutely irreconciliable with the present status of science.

It seems plausible that one motivation for this discourse was to take a stand against the materialistic interpretation that went hand in hand with the steady state cosmology, that had significant currency at that time, a theory which assumed a continuous creation of matter but without any Creator! Yet, this is precisely the title of a paper written, in September 1951, by Fr. Giovanni Stein (1871-1951), S.J., Director of the Vatican Observatory: “Creazione senza creatore?”22. This paper quoted Lemaître (1948a) and registered its strong opposition to the “Nuova Cosmogonia” of Fred Hoyle. Fr. Stein was a Jesuit who met Pius XII often, and who had certainly influenced him in writing the ‘Un’Ora’ discourse.

  Ibid: 138.   Ibid.: 140. 22   Ricerche Astronomiche, 2, no 14, Settembre 1951, Specola Vaticana: 345-354. 20 21

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3. Lemaître’s reaction Lemaître was present among the 26 pontifical academicians when Pius XII pronounce his “Un’Ora” speech. All testimonies from that day accord that the cosmologist was not enthusiastic with the discourse. One can easily understand this, first and foremost in light of his conception of the relationship between faith and science. Science can only see in the disintegration of the primeval atom a natural beginning, and this has nothing to do with theology, but rather with quantum mechanics and general relativity. According to Lemaître, the cause of this decay was of the same nature as the cause of the decay of an atomic nucleus, and could only be understood in a probabilistic manner. Pius XII’s discourse totally neglected Lemaître’s reflections concerning the natural beginning and the distinction between science and theology, codified in his “two paths to truth”. Further, Pius XII used the expression “Initial, primitive state of the universe”23, which was clearly evocative of the primeval atom hypothesis. Moreover, the Pope impugned the steady state theory by categorizing it as a gratuitous hypothesis without mentioning explicitly the names of Bondi, Hoyle and Gold.24 This would only aggravate the opponents of Lemaître’s hypothesis, especially as the Pope seemed partial to a theoretical framework for which no one had absolutely decisive observational validation. Lemaître had thus been thrust into an awkward position as it reinforced the idea, that he had always distanced himself from, that his hypothesis of the primeval atom was part of the Church’s apologetic agenda. What was Lemaître’s reaction to all this? It is certain that he never criticized Pius XII; to the contrary, he had a great veneration and re “E quale era lo stato iniziale, primitive dell’universo?” (“And what was the initial, primitive state of the universe?” in Papal Addresses to the Pontifical Academy of Sciences 1917-2002, op. cit.: 137). 24   Papal Addresses to the Pontifical Academy of Sciences 1917-2002, op. cit.: 136. The influence of Fr. Stein’s paper is clearly seen here. 23

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spect for the Roman Pontiff. Even when Pius XII was dead and a wind of conciliar freedom was blowing through the Church, he still declared25: On the Supreme Pontiff’s view, it clearly finds its place in its own field and has no relation with the theories of Eddington or of mine. My name is not, in this regard, mentioned in the Pope’s discourse.

Lemaître’s name was in fact not mentioned by Pius XII. An important source of the Pope’s discourse was the work of Edmund Taylor Whittaker (1973-1956)26: Space and Spirit, and subtitled: Theories of the Universe and the Arguments for the Existence of God27. Whittaker was a mathematician of the first rank who converted to Catholicism in 1930 and had been chosen in the same year as Lemaître to become a member of the Pontifical Academy. Whittaker’s book gathered together the conferences he had given at Trinity College Dublin in June 1946 and made no allusion to Lemaître.28 This book sowed even more confusion between the notion of creation and the notion of the beginning of the universe. The mathematician declared for example that29: there was an epoch about 109 or 1010 years ago, on the further side of which the cosmos, if it existed at all, existed in some form totally un-

 “Univers et atome”, conference given 23-06-1963 in Namur (unpublished manuscript preserved at the library Moretus-Plantin of the FUNDP): 2; edited in D. Lambert, L’itinéraire spirituel de Georges Lemaître, op. cit.: 200. 26   G. Temple, “Edmund Taylor Whittaker”, Bibliographical Memoirs of Fellows of the Royal Science Society, Vol. 2, November 1956: 299-325. 27   London, Thomas Nelson and Sons, 1946. 28   Even when he wrote about the theory of the expansion of the Universe, Whittaker referred to Eddington: p. 80. In 1942, in a conference paper given in Newcastle, he talked about the beginning of the universe and about the original state of the matter without any allusion to the work of Lemaître. 29   Space and Spirit, op. cit: 118. One can identify several examples of this confusion between the creation and the beginning of the universe (initial singularity of the physics, limit of the validity of spatio-temporal descriptions: pages 116-117 and 131). 25

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like anything known to us: so that it represents the ultimate limit of science. We may perhaps without impropriety refer to it as the Creation.

This confusion was roundly criticized by a number of authors30. While Lemaître respected much of the mathematical work of Whittaker, and recommended it to his students31, it was clear that he did not appreciate his approach to the relationship between science and faith, particularly perhaps as he failed to acknowledge Lemaître’s own work, especially as Whittaker was his colleague in the Pontifical Academy32. But he did not hold Whittaker directly responsible for the discourse that he considered problematic. Lemaître’s position in regard to Pius XII and Whittaker can be gauged in the second book of Canon Van Steenberghen, entitled significantly: “Dieu caché” (Hidden God)33 written in 1961, whose primary theme was the problem of the proof of the existence of God. Lemaître belonged to the same group of the “Amis de Jésus” as Van Steenberghen from 1925 to 1945 and again from 1956 to 1966, and thus they saw one another on a regular basis. It would be most unlikely that the two had not discussed the topic of the book, and even its title. One can say that Lemaître is both absent and present in this work. Absent, because his colleague did not cite him even once; nevertheless, he is implicitly present as Van Steenberghen employed the term “primeval atom” several times to designate the original state of matter alluded to by Pius XII34, but who himself never used this ex  For instance: E.L. Mascall, Christian Theology and Natural Science. Some Questions on their Relations (Hampton Lecture, 1956), London, Longmans, Greek and Co., 1956: 138-155 (this book does not contain any reference to Lemaître either) and F. Van Steenberghen, Dieu caché. Comment savons-nous que Dieu existe? Louvain/Paris, Publications universitaires de Louvain/Nauwelaerts, 1961: 97-124. 31   Communication of P. Macq. 32   A review of the book of Whittaker by Lemaître (1955g) indeed shows that the two scientists were not on the same wavelength. 33   Hidden God. How Do We Know that God Exists? (translation by Th. Crowley), Louvain/Saint Louis, Publications Universitaires de Louvain/ B. Herder Book, 1966. 34   Op. cit.: 112-113 (French original edition: 132-133). The English translation uses the term: “primitive atom”. 30

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pression. Moreover, Van Steenberghen embraced a natural evolution of matter that fit perfectly with the notion of the “natural beginning” of the world, a central idea for Lemaître. The fact that Lemaître is not quoted may have been due to his own request as one cannot reasonably imagine that Van Steenberghen had not considered citing his fellow scholar while referring to his theories. Following Lemaître, Van Steenberghen did not criticize Pius XII in any way, but adopted a measured and prudent tone:35 However, the reader will have noticed, every time his admiration for the discoveries of science tempts him to make imprudent statements, he pauses to add the necessary reservations and nuances. Taken alone, he says, science cannot prove the existence of God.

On the other hand, regarding Whittaker, van Steenberghen is more critical, underscoring the problem that arises when one try to find support in scientific data, which may later need to be revised, to establish a metaphysical proof of God’s existence. Van Steenberghen’s primary criticism of Whittaker is that he has made the paths of philosophy and science interfere unduly. It would later be quipped that Lemaître would spend much time researching who is the second author that might be hidden “beneath” the work of Molière. It is interesting to observe here that, “beneath” the content and the title of Canon Van Steenberghen’s book, there appears to be another author, Lemaître himself. To this day, the single document offering the clearest insight to Lemaître’s reaction to the “Un’Ora” discourse is a letter sent 24 December 1951 by one of his friends, Abbé Herman Heyters, to the Benedictine Sister Madeleine Delmer.36 Father Heyters, a doctor in philosophy and theology, had been ordained in Mechelen at the same   Hidden God, op. cit.: 111.   The author is grateful to Sr. Delmer for having provided this letter (our translation from the original in French). 35 36

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time as Lemaître, and also belonged to the Amis de Jésus. Moreover, when he was a teacher at the Collège Sainte-Gertrude in Nivelles, between 1927 and 1936, he was a colleague of an intimate friend of Lemaître, Abbé Louis Reyntens. According to Sister Delmer, it is likely that Abbé Heyters was Lemaître’s spiritual director, and also his assistant. This requires some explanation. From 1946, all of the Amis were accompanied by a priest of the Fraternity, called an ‘assistant’, who was responsible for advising the observance of the specific statutes of the Amis37. The letter of Abbé Heyters reveals that Lemaître attributed the initial draft of the speech “Un’Ora”, not entirely to Pius XII, but rather to his staff: [Canon Lemaître] was in Rome and heard this speech. His impression? A discourse composed by two scribes: The first one having written in the sense: “science brings new proofs of the existence of God”, the second, which the Pope himself had corrected by introducing some text clarifying that it did not consist in new proofs; the only true proofs being of a metaphysical nature (evidently a scientific hypothesis supposing that the world had begun, suggests in a manner more adapted to human psychology, the idea that Someone had been at the origin of this beginning and this is the advantage that the Pope probably welcomed).

Such an interpretation is not readily dismissed38. Fr. Giovanni Stein, Director of the Vatican Observatory, in all probably played a role in the preparation, providing the Holy Father with some references. Nevertheless, it is quite difficult to believe that Pius XII, on a subject that was of utmost importance for him, namely astronomy, would have contented himself with making only a few additions. It is well known that the Pope personally prepared his addresses with great   J.A. (= Jules Allaer), “Discipline et fidélité”, Apostolus, mars 1946, no 5: 65-66; “Nos assistants-directeurs”, Apostolus, mai 1949, no 5: 65-69. 38   Working alongside Pius XII, there were several German Jesuits (acting as secretaries and librarians); yet curiously, besides Whittaker, the only contemporary scientist mentioned in the speech is A. Unsoeld, the director of the observatory in Kiel. 37

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thoroughness. When science, medicine or technology was concerned, he made it a point to steep himself in the literature and master both the concepts and vocabulary39. What is somewhat surprising is that Lemaître’s name is not quoted in this papal address; Pius XII knew Lemaître personally, and when he served as the Secretary of State of Pius XI, he was in charge with implementing consultations regarding the constitution of the Pontifical Academy. He was himself a member of the Academy40 and as Pope, asked Lemaître to give the funeral oration for Ernest Lord Rutherford. He knew certainly also Lemaître’s paper, published three years before in the Acta of the Pontifical Academy: “L’Hypothèse de l’atome primitif ” (1948a) quoted in Fr. Stein’s 1951 paper. Why then did the Holy Father not quote Lemaître’s name? To shield him against some reactions from his opponents, the defenders of the steady state cosmology? Perhaps, but there could be another reason explaining Pius XII’s omission. One should not forget the context in which the discourse was written. Pius XII had just published the previous year, the encyclical Humani Generis41. While opening up new some perspectives, the document was largely received and interpreted as severely constricting new trends and contemporary frames of thought in rethinking Catholic theology. Against this backdrop, any deviation regarding “Thomistic orthodoxy” could be considered as suspect. Canon Van Steenberghen had paid the consequences himself during the third International Thomistic Congress in September 1950. He was sharply rebuked for simply wishing to underline certain difficulties inherent in Saint Thomas “five ways” towards the existence of God42. One can   Cf. Chelini, L’Église sous Pie XII, op. cit: 157-160.   Cardinal Pacelli was nominated as “Honorary Academician” on 19 March 1936 (Annual Report, Pontificia Academia Scientiarium, Vatican City, January 1994: 111). 41   Pius XII, encyclical “Human Generis. Concerning Some False Opinions Threatening to Undermine the Foundations of Catholic Doctrine”. Available at http://www. vatican.va/. 42  Cf. Hidden God. How do we know that God exists? (trans. By Th. Crowley), Louvain/Saint Louis, Publications Universitaires de Louvain, B. Herder Book, 1966. (In the original French version: Dieu caché, op. cit: 167). 39 40

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readily imagine the reaction to Lemaître’s 1948 paper concerning the primeval atom hypothesis. It surely struck a nerve in some defenders of “Thomistic orthodoxy” as Lemaître strongly defended the concept of a natural beginning of the universe remaining outside any metaphysical investigation. And he did so adopting modes of reasoning diametrically opposed to thomistic realism. Very likely, Pius XII and his Jesuit collaborators, did not appreciate the “unrealistic” or “conventionalist” twist Lemaître had given to his primeval atom hypothesis as it undercut the ontological consistency of the argument of the Un’Ora discourse. Indeed, according to Lemaître, his primeval atom hypothesis consisted in a “history” by which the scientist tries to trace its past, but without endowing it with physical reality. It is merely a model that works and that produces certain observational results (1948a: 25, 40): One of the portraits that came to us of the philosopher and mathematician René Descartes is accompanied with the motto that seems appropriate for the beginning of this talk: mundus est fabula. The world uncovers a beautiful history, which each generation endeavours to enhance. The whirlwinds of Descartes did not survive the progress of science; however, perhaps something remains from that mindset that made Descartes declare his mundus est fabula and that Poincaré would later call the cosmogonic hypotheses for which man cannot avoid trying to tell the story of the universe and reconstituting its past evolution […] By concluding I cannot do better than to remind you the words of René Descartes I used in my introduction and which can be applied to the primeval atom: Mundus est fabula.

To the end of the pontificate of Pius XII, Lemaître was never an object of critical remarks from the authorities of the Curia. Nevertheless, why the Pope had not consulted him in the writing of the discourse, an issue in which he was personally concerned, was unmistakably clear. The episode is a kind of ironic inversion of the Galileo

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affair here. Galileo would never have been condemned if he would have accepted the advice of his friend Cardinal Bellarmine, to represent his heliocentric cosmology only as a model “saving the phenomena” and not a series of statements concerning reality. Here it was just the opposite. Lemaître’s 1948 work was in all probability dismissed because it represented itself not as a description of reality as such, but as a “history” that allowed modern scientists to save observational results.

4. A small detour to Rome: the intervention of 1952 The discourse of Pius XII was unfavourably received or misunderstood all around. In Marxist circles, authors like Jean Dienne in La Nouvelle Critique or Paul Labérenne in La Pensée interpreted it as a misappropriation of science in favour of faith.43 What Marxists could not accept was Pius XII embracing a cosmology where the universe has a finite age and size44. Curiously, the Marxists and Pius XII shared the same presupposition in opposition to Lemaître’s thought: some models of the universe would necessarily imply specific metaphysical options. But according to Lemaître, the distinction between science and metaphysics is such that a Marxist could adopt his primeval atom hypothesis just as well as a believer could espouse a model without a natural beginning (as in the case of his own 1927 exponentional model without beginning or end). The French and Belgian press, as well as the general public, interpreted the discourse of the Pope as a defence of the Lemaître’s hypothesis. The Canon was put in an uncomfortable position, as he confided to Abbé Heyters upon his return to Belgium. Heyters’ report to

  F. Russo, “Marxisme and Cosmology”, Études, t. 273, 1952: 387-392.   Cf. On this topic: J.B.S. Haldane, “Mathematics and Cosmology” in Marxist Philosophy and the Science, Random House, 1939: Chapter 3; H. Kragh, Cosmology and Controversy, op. cit: 256-268. 43 44

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Sister Madeleine Delmer spoke volumes about the role played the media in the “Un’Ora problem”45: […] the review of La Libre Belgique (as well as the one of Match46) seemed to imply that the Pope would have somehow confused the metaphysical and scientific fields. And Lemaître had the same impression while listening to the discourse. Unfortunately the text didn’t make it very clear. Returning from Rome, G. Lemaître passed through Paris. Match tried to interview him: the magazine intended to publish, side by side, the picture of the Pope and that of Lemaître. Our man had enough common sense to be wary of American-style journalists, and managed to dodge the situation. Sympathetic to Lemaître, Match was content with quoting him and snidely mentioning that the Pope saw a proof of the existence of God in the cosmology of the “very religious” Canon, while the Canon demurred from drawing any such conclusion from his hypothesis, even if wholly confirmed. This was the summary of my conversations with Lemaître on the topic.

In September 1952, the eighth assembly of the International Astronomical Union was planned to be held in Rome, with the Pope giving the inaugural lecture. This was clearly problematic for the Marxist astronomers who could not countenance the prospect of another speech along the lines of “Un’Ora”. This was an evident diplomatic risk for the Union. Absent an actual document, one cannot say what kind of discourse Pius XII had in mind for his inaugural allocution; oral testimonies47 reveal however, that Lemaître attempted to inter  Letter 24-12-1951. Personal archives of Sr. M. Delmer; our translation from the original in French. 46   Ph. De Baleine, “Réconciliant la science et la foi, le Pape explique aux chrétiens comment Dieu a crée le Monde”, Paris Match, no 143, 15 December 1951: 18-19. 47   The first writing concerning this intervention is that of André Deprit, “Les amusoires de Mgr Lemaître”, Revue des Questions Scientifiques, t. 155, 1984: 207-208, based on Lemaître’s own recollections. J. Turek in “Georges Lemaître and the Pontifical Academy of Sciences”, Vatican Observatory Publications, Vol. 2, 1989, no 13, claims that 45

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vene with the Vatican. According to Joseph Turek, Lemaître made a stop in Rome en route to a conference in Cape Town at the beginning of July 1952. The evidence is that he spoke with Fr. O’ Connell, and possibly Msgr. Angelo Dell’Acqua48 of the papal Secretariat of State, both of whom had easy access to Msgr. Tardini.49 The latter, one of the closest collaborators of Pius XII, was Deputy for Extraordinary Affairs and as such, helped draft the addresses of the Holy Father50. A credible interpolation of known facts is that Lemaître had emphasized the risk, for the credibility of the papal message, of a unilateral defence of a cosmology that had not yet been unanimously accepted by the astronomical community. Ever the diplomat for the cause of science, Pius XII was agreeable to excise anything from his text that could have unsettled some of the audience as had his previous address. It was one of his well-known traits to change, right up to the last instant, some nuance of his discourse in order to, as he said himself “to sweeten the pill”. Here once again, with the document already in hand, he removed some parts of sentences which he deemed a bit harsh, and replaced them with a more palatable phraseoloLemaître contacted O’Connell and the Secretary of State in July 1952, but provides no confirmatory details (moreover by this date the position of Secretary of State did not exist anymore; there were only two deputies for ordinary and extraordinary ecclesiastical affairs: Msgr. Montini and Msgr. Tardini). All other authors that discuss this topic quote these two sources. Note that the paper of O. Godart and M. Heller, “Les relations entre la science et la foi chez Georges Lemaître”, Commentarii Pontificiae Academiae Scientiarium, t. III, no 21:1-12, was presented by O’Connell himself at the plenary session of the Pontifical Academy of Sciences on 12-10-1978, and did not mention this intervention. 48   The letter of Mgsr. Lemaître to Msgr. Dell’Acqua (AL) dated 27-01-1966 from Louvain leads one to believe that the cosmologist was a welcome visitor at the Secretariat of State thanks to Mgsr. Dell’Acqua: “In closing, let me express the regret that your high occupations did not allow you to receive me as previously during the meetings of the Academy. The advice and support you provided me were more than useful and I remember the way in which you deigned to welcome me and resolve the difficulty of the moment with such an understanding”. This was confirmed by the oral testimony of André Deprit (8-07-1998). 49   The hypothesis of R. Ladous in Des Nobel au Vatican, op. cit: 150. 50   From the leaflet of Cardinal Domenico Tardini, Pius XII (translation E. De Pirey), Paris, Éditions Fleurus, no date: 55-56.

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gy.51 Contrary to what is sometime claimed, the discourse pronounced at Castel Gandolfo on 7 September 1952 relied on a conception of the relationship between faith and science not essentially different from the “Un’Ora” discourse.52 While here was no allusion to the notion of the primeval state of the universe, the Pope continued to assert53: In its intrepid audacity, the human mind does not qualm in front of the most formidable cataclysms of a nova or supernova, it measures the incredible speeds of gases released and seeks to discover its causes. It darts towards the traces of galaxies fleeing in space, thinking back over the course that they have followed over billion of years in the past, and in this regard become the spectator of the cosmic processes that occurred in the early morning of the creation.

And in the same sense as in 1951, he indicated a way that goes from physics to metaphysics: […] it is impossible that even the most gifted researcher could succeed in knowing, much less resolve, all of the enigmas enclosed in the physical universe. They postulate and point to the existence of an infinitely superior Spirit, of the divine Spirit that creates, conserves, governs, and consequently scrutinizes with a supreme intuition, everything that exists, today just as at the break of creation’s first day.

  Cardinal D. Tardini, Pius XII, op. cit.: 60. Cf. Also J. Chelini, L’Église sous Pie XII. La tourmente 1939-1945, Paris, Fayard, 1983: 92-94 (in order to understand the details on the method of work of Pius XII). 52   This kind of conception was part of the “core” of the thought of Pius XII. On 15 June 1952, he returned once again to the contents of the discourse ‘Un’Ora’ in an address to the university youth of Rome: “We have reported in our discourse at the Pontifical Academy of Sciences that today one sees among scientists an increasing movement of coming back to the idea of creation.” (La documentation catholique, 13 July, no 1125: 838); our translation. 53   “Le discours du Souverain Pontife au congrès mondial d’astronomie”, La documentation catholique, 5 October 1952, no 1131: 1222 (both passages are on the same page); our translation. 51

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Indeed, all subsequent commentators linked this discourse to “Un’Ora”54. These events were very trying for Lemaître. While he generally was a man of great discretion on everything concerning religious issues, he mentioned this issue to several people in the Fraternity of the Amis de Jésus, Abbé Heyters, the retreatants at Schilde 12–27 August 195255, as well as his collaborators Odon Godart and André Deprit56. The determination of Lemaître to demonstrate the autonomy of physical cosmology from theological doctrine as well as anti-theological options, contributed to liberating research in this discipline from strong taboos. Yet the trail he blazed is no longer quite as clear today. Some, and not among the least, still imagine that any model with an initial singularity involves metaphysical or creationist positions and it is not unusual to see agnostic or atheistic authors developing models without a ‘Big Bang’, believing that they are being more coherent in their philosophical options. They would do well to follow the example of the ‘very religious Canon’ who did not see any difficulty in claiming that his own “hypothesis of the primeval atom is the antithesis of the natural creation of the world”57.

 Cf. For instance, F. Alessandini, “Les voies de la science”, La documentation catholique, 5 October 1952, no 1131: 1223-1224. 55  According Canon Goeyvaert, Lemaître would have asked Canon Allaer, who was responsible for the Fraternity, for advice on how to respond to the situation (oral communication, 02-10-95). 56   Oral communication (07-07-98) 57  “Univers et Atome”, manuscript, op. cit.: 35; edited in L’itinéraire spirituel de Georges Lemaître, op. cit: 213. 54

Chapter XVI

Monsignor Lemaître (1956–1964)

1. A little out of breath

O

n 25 March 1956, Marguerite Lemaître died in her house in Brussels. Immediately, the Canon celebrated Mass1 in her room for the repose of the soul of the one who had always considered him a hero and avidly followed his “adventure” by creating albums of photographs and clippings. He had not only lost a mother, but also a confidante. His great love for her was marked by a respectful distance, but did not exclude a little teasing, never failing to greet her at night with a theatrical ‘Good evening Mother!’. Their respect was mutual; Marguerite never forgot that her son was a Canon, and at table, she was always served him first in recognition of this. After the events of 1944, Lemaître had taken up residence at 9 Rue de Braeckeleer. On the ground floor there were three rooms in a row. The piano which had been saved from the bombing was ensconced in the hall, which had a view onto the street. Then came the dining room, whose cupboards were from time to time cluttered with some   Lemaître benefited from an Indult of Rome allowing him to celebrate the Mass at home only for its occupants, rights which was not automatic prior to the Second Vatican Council, except for some prelates who had the right to possess a private chapel. This privileged “domestic altar” Lemaître had requested of the Vatican, through the intermediary of the Apostolic Nuncio in 1947, allowing him to celebrate Mass daily for his mother. At de Braeckeleer street, there was no particular chapel and thus Lemaître celebrated Mass on an altar stone which lay on the small desk of his mother. One significant detail, a long time before the Council, was that he asked his niece Christiane to serve his Mass and, contrary to the custom of the time, he read the Canon aloud, enunciating deeply and clearly every Latin sentence. 1

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of the Canon’s calculators. Finally, on the garden side, was Lemaître’s office with a Mercedes machine, and the famous Moen-Hopkins that had gradually forgotten its banking career. The other rooms of the cosmologist were on the second floor. He had a bedroom, and another room used as photographic laboratory. Between 1944-1945 and 1956, he frequented Louvain only two or three days a week to take lunch at the Majestic, a restaurant located Avenue des Alliés (Bondgenotenlaan), as did many professors who were single or did not live in Louvain. One could find not only Msgr. Massaux, Charles Moeller, professor at the Faculty of Theology, and Odon Godart, but also, from time to time, the economist R. Rousseaux, a professor of French lite­ rature, Charles de Trooz, and occasionally some young researchers invited by their masters 2. The isolation and the trials of the war, especially the loss of his apartment of Place Foch had certainly shaken Lemaître. He found some tranquility in the atmosphere of the family house in Brussels. The death of his mother would test him once more as Lemaître was a ‘loner who does not like to be alone’. He appreciated time for reflection and silent meditation, but he did not enjoy being deprived of companionship for a long time. He needed company to expound his ideas and inspirations about some new computations, and to stimulate his creativity. His interlocutors were well remunerated by a veritable cataract of ideas, good words and his shattering laugh3. The year that followed his mother’s death, the Canon would not publish anything. The emotional upheaval may explain in part this   For example, Abbé Adolphe Gesché was invited by Msgr. Moeller (oral communication, 18-12-1997) and M. Louis Duquesne de la Vinelle was invited by Professor Rousseaux (oral communication, 02-12-1998); both were thus able to talk with Msgr. Lemaître. 3   Several testimonies concur that during the years 1950 and 1960, Lemaître often invited students, collaborators, colleagues to a restaurant around the “rue de Namur” (Naamsestraat). At table, he was irrepressible. If his interlocutor was in the slightest bit a mathematician, he would witness a volcano of ideas ending in formulae written on tablecloths, which Lemaître took with him after having, of course, paid the owner for them (testimony of R. Dejaiffe, 30-10-1997, who met Lemaître between 1963 and 1965). 2

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drop in scientific productivity, which was not age-related, as Lemaître would write a first-class paper at 69 years of age. Nevertheless, this is only a partial exploration. In reality, Lemaître needed some external stimulation for his work. This is not to diminish the role of his originality and genius, as André Deprit observed, Lemaître conducted research as he played tennis, with a brilliant backhand stroke – but that requires a partner to play! Since the War, he had no partner as his peer, or more precisely nobody that played him at the game he enjoyed. The war and his disinterest in elementary particle physics left him on the fringes of the great movement in astrophysics. On their side, the mathematicians of note spoke the language of Bourbaki which he was only beginning to speak falteringly. Their circles had but little interest in the long numerical computations that Lemaître loved. All this contributed to Lemaître’s lethargy, but from which his international contacts would extricate him periodically. By this time the Canon, having renounced his legacy due to his vow of poverty, again took up his quarters in Louvain in an apartment situated at 5 Avenue du Roi Albert, not so far from the Collégiale Saint-Pierre and the Place Foch.

2. The Presidency of the Pontifical Academy On 19 March 1960, Canon Lemaître was appointed “Domestic Prelate of His Holiness”4 and on 27 March 1960, the public learned from the front page of the Osservatore Romano that Msgr. Lemaître had been chosen by Pope John XXIII as President of the Pontifical Academy5, succeeding Fr. Gemelli. Georges Lemaître was very happy and

 Cf. Acta Apostolicae Sedis 1960: 541. A purely honorific distinction awarded by the Pope to certain ecclesiastics occupying positions of high responsibility. At that time, in the hierarchy of the honorific prelacy, the “domestic prelate” came in third place after the patriarchs, archbishops, bishops “assistant to the papal throne” and the “protonotaries ad instar participantium”. The bearer of this title was called Monsignor and whose garb was similar to that of bishops with the exception of the pectoral cross and the ring. 5   He was named president at the same time as being appointed prelate (19-03-1960). 4

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honoured by this recognition.6 His laboratory, at the Collège des Prémontrés organized a small celebration in his honour during which he was offered a writing case with the pontifical coat of arms. Nevertheless, it seems that he was disappointed with the relative indifference of the official authorities of his university regarding his new promotion in contrast with the enthusiasm of his alma mater in 1934 on the occasion of the Francqui Prize7. As documented by Regis Ladous8, the presidency of Lemaître was marked by a distinct broadening of the scope of the pontifical academy, both in ecumenical and geographical terms. Under the aegis of Lemaître, the Academy also opened its doors to many Nobel laureates; during the first two years at the head of this prestigious institution, Msgr. Lemaître welcomed no fewer than seven, among them Dirac and Raman in physics and John Eccles in physiology. Lemaître had at last found a place to his measure, and which provided him with intellectual stimulation after a long period of isolation. Msgr. Lemaître initiated “study weeks”, small gatherings of specialists from various fields, in the rich surroundings of the Casina of Pius IV, home of the Academy. These “weeks” afforded him the opportunity to meet the greatest figures in science, many of whom were unfamiliar to him. The topics included molecular biology in 1961 (study week: “Macromolecules of Biological Interest”), econometrics in 1963, and neurophysiology in 1964 (study week: “Brain and Conscious Experience”). In 1962, Lemaître presided over a study week in physics in place of Nobelist Victor François Hess, for a topic which was close to his heart and which was organized by his friend Vallarta:9 “The problem of cosmic rays in interplanetary space”. Lucien Bossy,   One could be tempted to confuse the humility of Lemaître with a kind of indifference as regards ecclesiastic dignity. Even if he made an occasion jest concerning authority and discipline, it was clear he attached great importance to the ecclesiastic state and dignity. 7   Testimony of André Deprit, who was among those who offered the present to the new prelate (oral communication 10-11-1995), 8  R. Ladous, Des Nobel Au Vatican. La Fondation de L’Académie Pontificale des Scien­ces, Paris, Cerf, 1994: 170-171. 9   Vallarta was himself appointed to the Pontifical Academy in 1961. 6

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then working at the Royal Meteorological Institute of Brussels, presented a contribution on the Størmer problem that week.10 Presiding over the Academy was satisfying, but not always simple. Under the pontificate of Paul VI, who succeeded John XXIII in June 1963, Lemaître was tasked with a project to reduce the numbers of academies existing in the Vatican and placing them under the direct control of the Curia. This ran contrary to his sensibilities, as he strongly subscribed to the concept of the Academy of Pius XI and Fr. Gemelli, according to which the Academy should not depend on the Curia or on the Church as such, but only on the person of the Holy Father,11 an opinion he freely shared with Msgr. Angelo Dell’Acqua, Deputy Secretariat of State. According to Lemaître himself12, it appeared that a “certain administrative commission” of the Vatican had prevailed “to completely substitute his authority with that of the President of the Academic Council” in imposing its requirements on the Academy. These were not limited just to the practical problem of the financing of the study week “Brain and Conscious Experience” organized by Eccles, but touched on the core principle of the Academy’s very autonomy. According to a letter of Msgr. Lemaître to Msgr. Dell’Acqua, persons outside the Academy had wanted to add to the documents of the study week, some “Roman sheets” to be published by a scientific publishing house, outlining the rules of the Academy and the Pope’s discourse pronounced at the official opening session. Faithful to his philosophy of the “two paths to truth”, Msgr. Lemaître judged it inappropriate that a text dedicated to scientists included a passage mixing science and theology. He wrote then to Msgr. Dell’Acqua13:

  “The Motion of Particles Trapped in Magnetic Dipole Field as a Special Case of the Størmer Problem”, Pontificiae Scientiarum. Scripta Varia, MCMLXIII, no 25. 11   Copy of the letter of Msgr. Lemaître to Msgr. Dell’Acqua dated January 1966: 3, (AL): “The Pontifical Academy of Sciences has received from Pius XI the privilege of depending only upon the Holy Father” (our translation from the original in French). 12   Letter to Msgr. Dell’Acqua, op. cit.: 1. 13   Letter to Msgr. Dell’Acqua: ibid. (our translation from the original in French). 10

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The “Roman sheets” are clearly essential to the official publication of the Academy. But to what purpose are they essential to the broad dissemination among the scientific world? Doesn’t it suffice that the title or the jacket-cover appropriately mentions that the published work constitutes a week organized by the Pontifical Academy?

If one examines the discourse pronounced by Paul VI on 3 October 1964 at the close of the “Brain and Conscious Experience” study week, one will appreciate why the cosmologist, along with the defenders of the “mind-matter” dualism and the materialists, each for their own reasons, would have been offended by the following statments14: To be sure, when you speak of ‘consciousness’, you do not refer to the moral conscience: the very rigour of your methods ensures that you do not depart from strictly scientific domain belonging to you. What you have in mind exclusively is the faculty of perceiving and reacting to perception, that is to say the psycho-physiological concept that constitutes one of the accepted meanings of the word conscience. But who does not see the close connection between the cerebral mechanisms, appearing from the results of experimentation, and the higher processes concerning the strictly spiritual activity of the soul?

Paul VI in fact posed a problem that is crucial in the context of Christian anthropology: the need for a theological understanding, and an articulation of the brain, thought and the soul. Nevertheless, Lemaître’s perspective on the relationship between faith and sciences did not admit of any building of connections, any articulation between these domains, but only inclined him to defend the epistemological autonomy of a purely natural approach to human thought. It is most   “Address to the Plenary Session and to the Study Week on the Subject ‘Brain and Conscious Experience’” in Papal Addresses to the Pontifical Academy of Sciences, op. cit.: 184. 14

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likely that just as he would have adhered to the natural beginning of the universe, that he would equally have defended the idea that, “at the level of science as such, the biological analysis of the brain activity has nothing to do with the theology of the soul”. Paul VI did not confuse the scientific and religious fields, but he viewed man from a unified perspective that could not admit an absolute separation between body and mind. The Pope could not but refuse to give science a complete autonomy by which it would evolve independently without any social control15: The scientific world, which in the past adopted a position of autonomy and self-confidence, from which flowed an attitude of distrust, if not of contempt, for spiritual and religious values, is today, on the contrary, impressed by the complexity of the problems of the world and mankind, and senses a sort of insecurity and fear when faced with the possible evolution of a science left, without any control, to follow its own driving force. Thus the fine self-confidence of the early days has for many given place to a healthy disquiet, so that the soul of the scientist today is more easily open to religious values, and glimpses, beyond the prodigious achievements of science in the material domain, the mysteries of the spiritual world and the glints of divine transcendence.

Msgr. Lemaître knew that this discourse troubled some scientists present at the study week. Nevertheless, it should not be concluded that the cosmologist defended the idea of a science beyond social control, dominated only by its own internal logic or by its financial sources. It is well known that he refused an important contract proposed to him by a delegate of the U.S. Air Force Office for Scientific Research. This contract concerned the possibility to perform analysis, by techniques used in the Størmer problem, of data gathered in 1958

15

  Ibid.: 184-185.

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by the Explorer I and Pioneer III satellites, on the Van Allen Belt that had recently been discovered16. This contract could have transformed his numerical research laboratory into a prestigious centre and could have brought important financial resources to Louvain to support research. Yet Lemaître preferred autonomy, freedom and the total control of his own research to money and prestige. In this he was in complete alignment with Paul VI and also with Pius XII. In the summer of 1961, he would have another occasion to prove it when he used his status of President of the Academy to oppose another proposal from the U.S. Air Force, the West Ford Project. The U.S. Air Force envisioned spreading some 350 million small metallic needles in the upper atmosphere to serve as a microwave reflector for a new mode of global communication. Msgr. Lemaître, as a number of important persons before him, viewed it as a significant risk for astronomical research. He made it a point of pride to write to the White House in order to express his disapproval. To Dr. Jerome K. Wiesner, the White House Science Advisor, he wrote17: “[There is] a real danger of contamination of the upper atmosphere [which] might jeopardise the development of radio astronomy and even optical astronomy.” Msgr. Lemaître considered science was a game: “those who don’t want to play, should not do science” as he would say – but his deep conviction always prohibited him from “playing dangerous games”. Paul VI esteemed Msgr. Lemaître, in who he saw18 “the worthy successor of the late lamented and unforgettable Fr. Gemelli”. When he was yet Archbishop in Milan, Msgr. Montini had the opportunity to observe Gemelli closely as Rector of the Cattolica. Paul VI’s de  Cf. A. Deprit, “Monsignor Georges Lemaître” in The Big Bang and Georges Lemaître (A. Berger, ed.), Dordrecht, Reidel, 1984: 385. 17   Letter of 6 July 1961 (AL). 18   “Address to the Plenary Session and to the Study Week on the subject: ‘The Econometric Approach to Development planning’ ” (13 October 1963) in Papal Addresses to the Pontifical Academy of Sciences,…, op. cit.: 180. 16

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sire to involve Lemaître in the thorny issues of the conciliar debates was a testimony of the same kind of trust in him as he had invested in Gemelli. It was under the presidency of Msgr. Lemaître that the two volumes of the Miscellanea Galileiana would be edited. Lemaître had them sent to Paul VI who made a reference to them in his speech of 3 October 196419. Significantly, these volumes are cited in the famous conciliar Constitution “Gaudium et Spes” promulgated on 7 December 196520. In 1964-1965, with the exception of the most official occasions such as opening sessions or the closing of the study weeks, Msgr. Lemaître did not have the chance to meet with the Holy Father, nor with Msgr. Dell’Acqua on their mutual business. During this time, the number and duration of the Pope’s audiences were strictly monitored by the Council. As Lemaître felt that age and illness did not allow him to bear his responsibility alone, modestly he proposed to Msgr. Dell’Acqua21: I would not find it unusual if the Holy Father replaced me now as Presi­ dent of the Academy; the primary consideration must be the rejuvenation of the Academy. In other academies, we usually had a younger President for a fixed period. I occupied an analogous position at the Royal Academy of Belgium some thirty years ago.

The Holy Father did not dismiss him from his function, and even after his death, he would wait until 15 January 1968 to assign his friend and fellow astronomer, Fr. O’Connell as President.

  Op. Cit., p. 125.   Gaudium et Spes, 3, no 36, note 7 (text available on the Vatican Website ). 21   Letter of the 27-01-1966, op. cit., our translation from the original in French. 19 20

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3. A mathematician in the spirit of Vatican II Shortly after his nomination as the head of the Pontifical Academy, Msgr. Lemaître was received in audience by John XXIII together with other academicians. The Pope, who was busy with the preparation of the Council, asked Lemaître what could the Academy could contri­ bute to the conciliar debates. The cosmologist was quite taken aback and did not respond. As he confided to a prelate, probably once more Msgr. Dell’Acqua22: When His Holiness asked me how the Pontifical Academy of Scien­ ces could make a contribution to the Council, I was totally caught off guard.

Msgr. Lemaître could have proposed integrating academicians in the preparatory commission or to insist that there be an important representation of academicians as auditors at the Council. He did nothing of the sort. He rather sought to maintain the Academy’s autonomous status with respect to the Church, adhering to his own philosophy of the “two paths to truth”. In any case, he was not interested that scientists would take a large part in the conciliar debate or in its commissions. In retrospect, this appears to have been a missed opportunity as the discourse around the famous Schema XIII and notably of the future Constitution Gaudium et Spes concerning the Church in the contemporary world offered the perfect place for scientists, believers or not, to have expressed themselves. The address to “men of thought and science” at the end of the Council (8 December 1965) would have maybe received a wider audience if it has been supported by a more important number of scientific personnalities. As it was, Lemaître   Letter, 1-11-1960, sent from Louvain by Lemaître to a prelate (AL) (our translation from the original in French). The letter bears no name or address of the correspondent, but from context the addressee worked in the apostolic palace, and was not a cardinal. Knowing the contacts and affairs linking Lemaître to Msgr. Dell’Acqua, second person of the Secretariat of State, this hypothesis seems well-founded. 22

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could not have been pleased with how it turned out, nor could one image the reflections being to Gemelli’s liking either. Preserving the autonomy of the Academy certainly required a certain prudence and particular status, but didn’t the wind of change that was entering in the Church by the windows opened by the ‘good Pope John’ justify some audacity? In any case, Msgr. Lemaître did not take up the offer of John XXIII and contented himself with this surprising proposal23: There is something that concerns certain scientific circles, namely how the date of Easter is fixed. The announcement of the Council has given rise to the hope that this issue, so often postponed, would finally find a solution, for instance that Easter would be celebrated on the first Sunday of April. If such a project would be of interest to His Holy Father, the Pontifical Academy of Sciences would be glad to assist in carrying it out. It would be pleased to affirm its devotion and to contri­ bute to the success of the great enterprise of the Council.

The Council would hold a second surprise for Lemaître. On 27 April 1963, John XXXIII created a commission charged with examining the issues related to conjugal morality24. The commission met in this matter beginning in October 1963 in Louvain, a time when Paul VI had already succeeded John XXIII. Paul VI thought highly of Lemaître and decided to add him, as the President of the Academy, to the pontifical commission that was, among other things, in charge of studying the problem of birth control, to be debated in October 1964 during the third session of the Council. Since June 1964, it was known that the Pope had withdrawn these sensitive issues from the competence of the Council and counted on the new commission to enlighten him. By assigning Lemaître to this commission, Paul VI was likely hoping to benefit from the lights of all the Academy’s members.   Letter (1-11-1960), op. cit., our translation from the original in French.  I refer here to the paper of the F. de Locht, “Au Concile. La morale conjugale à l’épreuve de la foi vécue” in Vatican II et la Belgique (under the direction of Cl. Soetens), Louvain-la-Neuve, Quorum, 1996: 269-284. 23 24

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According to the testimony of Canon Pierre de Locht25, who was an active member of the commission, Msgr. Lemaître himself never participated. Why? In part because he could not travel easily to Rome following the heart attack he suffered on 8 December 196426, but also for a very understandable reason that he explained to Fr. Henri de Riedmatten, a Dominican of the Angelicum in Rome in charge of leading the “Study Group on Population”27: I have already expressed my surprise at having been made a member of the commission that you are leading, and I am keenly aware of the danger for a mathematician who dares to venture beyond his area of expertise.

Nevertheless, even if he did not attend the meetings of the commission, Msgr. Lemaître felt, in his conscience, the duty to help: “If I were made a member of a commission, I perhaps have the duty, whatever the risk, to remain silent”. The prelate then sent a note in triplicate, giving the Dominican consent to make use of it as he wanted and asking him modestly to inform him if he was completely off the mark! This note concerned, in fact, the regulation of births. Msgr. Lemaître did not question the most fundamental teachings of the Church in this field. Nevertheless, he surmised that one key difficulty about birth control if one wants to respect these teachings is related to the fact that28 “the means that allow one to discern natural infecundity do not always offer physiological certainty”. In order to ensure that this certainty of infecundity could be assertained, Msgr. Lemaître hypothetically envisioned that the Church could justify the   Letter from F. de Locht (29-10-1995). I am grateful to him for this information.   He mentioned it in his letter to Msgr. Dell’Acqua dated 27-01-1996. It was after his return from Rome, where he had attended the famous study week “Brain and Conscious Experience”, that Lemaître had his heart attack. 27   The name of the pontifical commission. The quote comes from a  letter sent from Louvain on 29 June 1965 (AL); our translation from the original in French. 28   “Note pour le Groupe sur l’étude sur la Population” (29 June 1965); our translation from the original in French. 25 26

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use of contraception, but only when the contraceptive means were “used during a period of natural infecundity”. Putting a sharper point on it, he introduced the following distinction in moral theology: Wouldn’t it be of interest that specialists state precisely the conditions following which, one could have a moral certitude of infecundity? Couldn’t the Church then link its injunctions to such a moral certitude, rather than a physiological certitude that is often impossible to reach?

And he then concluded: If it were possible to give a precise sense to the notion of moral fecundity, by linking it to some criteria easily applicable, it would become possible for the Church to mitigate its discipline even regarding certain radical means; those would remain prohibited only outside of the case of moral infecundity. This is perhaps, an element of a solution to the problem we are trying to solve that would allow us to respect the Moral with great rectitude and security.

It must be reiterated that this proposition was based on a simple research hypothesis destined to make the members of the commission think and which Msgr. Lemaître was ready to retract if Fr. de Riedmatten judged it to be objectionable. We do not know the Dominican’s response; nevertheless, it is clear that this hypothesis had little chance of going over well29. Whatever one’s perspective, Msgr. Lemaître’s note had the merit of showing the tension between on one hand, a resolute will to stay inside the traditional teachings of the Church and, on the other, a desire to listen to the concrete problems of Catholic couples. Lemaître followed the progress of the conciliar debates in discussions over dinners at the Majestic with certain members of the   Indeed, it is not compatible with the foundation of the argumentation developed later in the Encyclical Humanae Vitae, promulgated on 25 July 1968. 29

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Faculty of Theology of his alma mater. Msgr. Lemaître particularly confided in Msgr. Charles Moeller, assistant of Msgr. Philips, another professor from Louvain who was a member both of the theological preparatory commission and of the doctrinal commission of Vatican II. Msgr. Lemaître applauded the aggiornamento, and indeed had already relaxed some aspects of ecclesiastical discipline in his own person that were not essentially related to the core of the faith. That having been said, he did wistfully regret the introduction of the vernacular language in the liturgy. Not only did he appreciate Latin, but the great traveller loved the facility afforded by Latin language, in terms of being able to celebrate Mass or to attend it in every country, without linguistic barriers. In this too, Lemaître did not fail to surprise, juxtaposing in his person values both from the old and new world!

Chapter XVII

Mundus est fabula The philosophy of a  cosmologist

1. Lemaître and the philosophers

A

fter his studies at the Institut Supérieur de Philosophie until the mid-1930s, Lemaître had completely abandoned the study of philosophy. But in 1935, a particular event would give him the opportunity to renew his acquaintance with philosophical circles. On Tuesday and Wednesday, 24-25 September, the Société Philoso­phique de Louvain jointly organized with the Société Thomiste of Paris, a study day devoted to mathematics and physics1. Lemaître was invited together with de la Vallée Poussin and Manneback. The discussions2 that followed the talks of Canon Renoirte and Fr. Salman, O.P., professor of the Dominican Faculty of Philosophy and Theology of Le Saulchoir,   The program is available through the Revue néoscolastique de philosophie, Vol. 38, 1935, 398-403. On Tuesday 24-09-1935, A. Mansion and Fr. Salman, O.P., delivered a paper on the Aristotelian and Scholastic notion of physics, and Renoirte and Yves Simon from Paris discussed the question of modern natural science and philosophy. On Wednesday, Ferdinand Gonseth and the Fr. Guérard des Lauriers, O.P., discussed the notion of necessity in mathematics while Michotte and Fauville spoke on experimental psychology. Responsible for the organization was Canon Harmignies, Secretary of the Institut that was also part of the same local group of the Amis de Jésus as Lemaître (cf. AFSAJ, letters of Willockx to Lemaître dated 7-11-1925 and 8-02-1926). 2   The texts of the contributions are found in the Revue néoscolastique de philosophie, Vol. 39, 1936: 5-77. The proceedings are published in ‘Discussion des rapports présentés aux journées d’études de Louvain”, Revue néoscolastique de philosophie, t. 39: 411-458. 1

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located at Kain (near Tournai), were animated to say the least, perhaps even responsible for the breaking off of the friendship between Renoirte and Lemaître. As shown by the contribution of Charles Manneback, the neo-Scholastic philosophers were developing a conception of the world that did not take into account recent advances of the “infra-atomic” physics and, in particular, quantum indeterminacy.3 Lemaître4 interjected to criticize, in a sense similar to that of Salman, the notion of a material body as conceived by the Scholastics and which did not seem able, in his view, to withstand the critique of contemporary physics. Needless to say, this intervention disturbed a number of philosophers who had come to listen to the debates, in particular Dopp who reproached him for not having understood the significance of the specific philosophical method5. One of the high points of those days was the meeting between Lemaître and Ferdinand Gonseth, whose influence ultimately inspired the publication of L’Hypothèse de l’atome primitif (1945g) and who would provide the book’s preface. The Swiss philosopher-mathematician and the Louvain cosmologist quickly found themselves on the same wavelength. Lemaître defended, as Gonseth, a philosophy continually open to the discoveries of empirical science, without fitting them into a Procrustean bed of some a priori philosophical ideas. From his essay “La physique d’Einstein” (1922a), one can see clearly in Lemaître’s thought an openness to the changing paradigms catalyzed by experiment and observations underpinning the “relativistic revolution”. This does not mean to imply that Lemaître gave short shrift to the theoretical dimension, particularly given the profound influence both Einstein and Eddington exerted on his life. But the latter would never be overestimated. In Lemaître’s work, theory and empirical advances are intertwined, with neither outpacing the other as a way to knowledge. This philosophical conception he shared with Gonseth. The title of the   “Discussion des rapports…”, op. cit.: 426-427.   “Discussion des rapports…”, op. cit.: 430-434. 5   Letter of Dopp to Lemaître, 18-12-1935 (AL). 3 4

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great work of Lemaître is revealing. It does not consist in a theory of the primeval atom, but simply of a hypothesis that, as underscored by Gonseth in his preface (1946e: 16) constitutes a real inductive synthesis anchored in observational data. As a hypothesis, it is necessarily revisable. Which of the two men, Gonseth or Lemaître, conceived of the title of the book? The Swiss philosopher may have proposed this title, which would accord with his “open philosophy”6. Even if it was not the case, the title suggested a strong philosophical bond between the two men. The two likewise held a common perspective on the nature of mathematics. Opposing all Platonism, formalism or purely empirical philosophy, Lemaître considered that mathematics contained both formal elements and linkages to experience and intuition. For Gonseth, as for Lemaître, the axiomatic played a secondary role of ‘formatting’. The cosmologist seconded the position of his colleague in a laudatory review that he made of Gonseth’s book: Les fondements des mathematiques (1927a: 196) citing the following passage7: Mathematics can only artificially, can only in appearance be detached from its intuitive foundations and its extension to the real. The axiomatic...is only in fact a method…there is no field, however small as it would be, where the axiomatic would be self-sufficient.

Lemaître had not studied all of Gonseth’s works deeply; he was not attracted by philosophy as such. One could say that through his contact with Gonseth, Lemaître probably identified the outlines of a philosophy of science that best suited him. Through the Institut Supérieur de Philosophie, Lemaître had been formed in the Thomistic realism that predisposed him to be open to empirical data. His stay with   F. Gonseth, Philosophie néo-scolastique and philosophie ouverte, Lausanne, L’âge d’homme, 1973 (ref. to Lemaître: 61); La métaphysique et l’ouverture à l’expérience. Second entretiens de Rome (under the direction of F. Gonseth), Paris, P.U.F., 1960. 7   F. Gonseth, Les fondements des mathématiques. De la géometrie d’Euclide à la Relativité générale et à l’intuitionnisme (préface de J. Hadamard), Paris, Blanchard, 1926 (1974): 13. Our translation. 6

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Eddington exposed him to a more idealistic perspective. Through his “open philosophy”, combining in a dialectical process both theoretical aspects and openness to experiments, Gonseth offered Lemaître a locus situated between the realism of his initial formation and the idealism of Eddington8. In the last chapter of his book, Gonseth began by defusing any possible opposition between Eddington’s idealism and Weyl’s realism in the context of general relativity9. An unpublished text reveals how closely parallel ran the thought of Lemaître and Gonseth. In an introduction to a class on mathematical physics for engineers, Lemaître (perhaps substituting for Charles Manneback) begins by trying to circumscribe the objective of physics10: The aim of physics is to know the matter and then succeed in using it, according to our needs or interests. To understand and know something, one needs to make a mental representation for oneself and evaluate the correspondance between this representation and the reality. In this way, it is possible, to an extent, to capture a given reality, making it ours, and getting an overall snapshot of it.

Yet, for Lemaître, as for Gonseth, our knowledge will always be imperfect, limited and perfectible; thus, “the mental representations would never be adequate to the prodigious complexity of any phenomenon”. Lemaître then points out the dialectic link existing between formalism and experience: Mathematics, that develops these mental representations and experiments that validate them are both necessary for physics […]. Neither mathematical nor experimental physics, are by themselves a science   On the Kantian influence on Eddington’s thought, cf. C.W. Kilmister, Eddington’s Search for a Fundamental Theory, Cambridge University Press, 1994: 49.   9   F. Gonseth, Les fondements des mathématiques, op. cit., 185. 10  The introduction, preserved in the AL, includes neither title nor date. Lemaître states explicitly in the text that it consists of an introduction to the elements of mathematical physics for engineers. Our translation from the original in French.   8

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as neither of them can make us know anything without the help of the other. They intertwine and complete each other, as the experimentalist cannot avoid simple mathematical expressions to interpret his findings and the theorist builds his mathematical constructs in order to interpret facts gathered by the experimentalist.

The cosmologist ends his introduction by demonstrating, following the example of the Swiss philosopher, the impossibility of completely isolating mathematics from all contact with the emprirical world and by stating his opposition to the famous maxim of Bertrand Russell: “Mathematics is the only science where one never knows what one is talking about nor whether what is said is true”! At the end of the 1940s, Fr. Stanislas Dockx, a Dominican, had just founded, with the encouragement of Gonseth and de Bernays, the International Academy for Philosophy of Science, and organized at the Academy Palace of Brussels an important symposium entitled Problèmes de philosophie des sciences that gathered luminaries such as Louis de Broglie and Hermann Weyl in physics, and Brouwer, Heyting, Nikodym in mathematics. Lemaître immediately jumped into the debate concerning Milne’s cosmology. He also took part in the discussion that followed the presentation of Jean-Louis Destouches on Determinism and indeterminism in modern physics11. Lemaître did not hesitate to defend the “dialectization process” advocated by Ferdinand Gonseth12. According to Gonseth, the notion of reality can truly be affected by quantum physics; nevertheless, this does not at all mean that reality has no more sense. In the process of the development of the sciences, something related to the concept of reality endures and it is by analyzing this dialectical process that one can come closer to a fuller meaning of what reality is. Lemaître made  In Problèmes de philosophie des sciences (premier symposium-Bruxelles 1947). IV. Problèmes de connaissance en physique moderne, Paris Hermann, 1949, archives de l’Institut International des sciences théoriques, série A, Bulletin de l’Académie internationale de philosophie des sciences 4: 7-42. 12   Problèmes de connaissance en physique moderne, op. cit.: 52-53 and 55. 11

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use of this idea by applying it to the notion of quantum states; states here having a very different meaning than in classical physics. But this notion preserves a dialectical sense that opens it to a more ample meaning, as the “state” in quantum physics describes a whole set of potential realities. In another discussion prompted by this symposium, Lemaître set up a distinction between the notion of an observer that enters in the theoretical schema of quantum mechanics and the notion of the real observer: the knowing macroscopic subject. According to the cosmologist13: In quantum phenomena, it makes a profound difference if one is at the macroscopic or the microscopic level. My instinct is that the analysis of the usual macroscopic observer and the theoretical observer can be taken quite far, and one can move easily from one to the other. However, the transition, from a theoretical observer to a physical observer, remains. And when one addresses this philosophical problem, one wonders about the reality of these knowing subjects. One runs the risk of confusing one with the other. This is what I wanted to emphasize. It is the macroscopic observer, the one who is in the common sense, who confirms the far-reaching consequences of the results of measurements by observing the theoretical observer.

If one analyzes Lemaître’s contribution in detail, one notices that his interpretation of quantum mechanics has erected a high wall between the quantum world, with its Heisenberg uncertainty relationships and observed by idealized theoretical observers, and the world of real corporeal human subjects, that seemingly evade quantum mechanics. Lemaître solicited Weyl’s view on this question, who would recount his answer thus14:   Problèmes de philosophie des sciences (premier symposium-Bruxelles 1947). II. Les sciences et le réel, Paris Hermann, 1948, archives de l’Institut international des scien­ ces théoriques, série A, Bulletin de l’Académie internationale de philosophie des sciences, 2: 88. 14   Ibid.: 85-86. 13

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I think it is dangerous to denature the observer, of whom quantum theory speaks, into an idealized fiction. The problem seems to lie in the mental sphere altogether and has to do with the fact that our mind is capable of self-reflection. Thus I am inclined to side on this question with Dubarle rather than Lemaître. With Niels Bohr one may even expect that there holds, for the mental process of self-observation, an indeterminacy principle of a much wider range than the Heisenberg indeterminacy principle of quantum physics.

Whereas, according to Lemaître’s implicit philosophy, quantum mechanics does not apply to the whole universe and certainly not to the human sphere. It is noteworthy that, in Louvain in 1935 or in Brussels in 1947, Lemaître never intervened in any substantive discussion on mathematics, even when his friend Gonseth spoke15. Philosophical questions did not seem to concern the mathematics that, for Lemaître, remained a kind of game with numbers and formulas, but without deep ontological implications. Lemaître’s contributions to philosophical meetings clearly revealed that he never tried to propose a philosophical vision that would buttress his own scientific work. Lemaître worked on particular scientific problems. General speculative thought, and the philosophy of nature in particular, were not his cup of tea.

2. Lemaître: philosophy teacher The classes of methodology and history of mathematics could be taken as an option by BA students or by doctoral students at the Institut Supérieur de Philosophie. But strictly speaking, Lemaître did not teach philosophy before the beginning of World War II. In 1940,   F. Gonseth, “Les conceptions mathématiques et le réel” in Les sciences et le réel, op. cit., 31-49; discussion: 50-60. 15

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he replaced Msgr. de Strijker in his class which consisted, in fact, of an introduction to philosophy and religion designed for undergraduate student engineers. Some of his preparatory class notes, the last of which took place around September 1944, have been preserved. What was Lemaître talking about during these classes? Certainly he did not intend to give a class about the history of philosophy, but restricted himself to a series of problems he judged important. Examples include the problem of the life after death, the development of Western civilization or the evolution of the human race. To undertake anthropological questions with his students in engineering sciences, Lemaître thought it important to present some elements of physiology, which led him to talk about the sense organs and of the link between intelligence and sense. As an example of the awakening of intelligence via the senses Lemaître drew upon the discovery of the satellites of Jupiter! Elementary mathematics is also dependent on sensory experience. Lemaître would then talk of metric or projective geometry, or of topology, but pointing out that these notions demonstrated that human thought had developed to such a point that it had completely outrun the sense experience that prompted them. This provided the Canon with his beachhead to refute the “materialism that reduces thought to sensation”, and the “idealism that gives to the idea an origin independent from the sensation”. These refutations opened a way to a defence of the spiritual that sought an answer to the questions of the transcendence of the human being, his thought and even the existence of a life after death. According to students’ testimonies16, this class was more a succession of brief reflections, without a clear systematic plan. It combined some philosophical concepts with religious considerations, and then quickly segued into mathematics. The Canon undertook the task with good will, but his teaching and research activities did not prepare him for philosophy, at least that which was supposed to be taught in 16

  Oral communications of R. Graas (18-10-1995) and Ch. Courtoy (17-10-1995).

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the first university year. If the cosmologist was not a born philosophy teacher, he nevertheless had an implicit philosophy that will be further explored in the following section.

3. An intelligible, non-deterministic and strange universe. In “La physique d’Einstein” (1922a), Lemaître took the view that the universe might be intelligible. The human being is then not lost in a world unfamiliar to him. The Louvain cosmologist thus took the position opposite to Blaise Pascal who famously affirmed17: Let man, having returned to himself, consider what he is in comparison with all that is; let him see himself as if thrown out of the district of Nature; and, from this little prison cell in which he finds his lodging, I mean the universe, let him learn to judge the earth, its kingdoms, its villages, and himself with a proper estimation. What is man in the infinite? […] What is man in nature? He is nothing in comparison with the infinite, and everything in comparison with nothingness, a middle term between all and nothing. Failing to contemplate these infinities, men have recklessly taken it on themselves to study nature, as if it had the same proportions as they did. It is a mighty strange thing that they wished to comprehend the principles of things, and to arrive from there at a knowledge of everything, with a presumption as infinite as their object. For doubtless no one could devise such a plan without a presumption or capacity as infinite as nature’s.

  Original from the French, Blaise Pascal, Pensées, Paris, Garnier-Flammarion, 1976: 65-66. Translation from The History Guide: Lecture on Modern European Intellectual History, Steven Kreis (2000), last revised 13 May 2004. http://www.historyguide.org/. 17

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Lemaître would explicitly oppose such tenets from 192918 to 196319 by claiming, for example (1929a: 200; our translation):

The thinking reed of Pascal dominates the cliff that crushes it, because it knows it; if we dominated the skies, whose harmony is known by us, wouldn’t we be able to overcome the universe only in part and should our mind admit that it is powerless to understand the world in its entirety? I still must tell you how we can avoid this pessimistic conclusion and conceive an intelligible form of the whole world.

In the conclusion of a talk given at the Catholic University of Paris on 17 February 1950 where he was introduced by Paul Claudel, Lemaître asserted in the same vein (1978a; our translation): I hope to have shown you that the universe is not out of reach for humans. This is Eden, this garden that has been put at the disposal of humans in order for them to cultivate it, to look after it. The universe is not too big for human beings, it does not exceed the possibilities of science, nor the capacity of the human mind.

This intelligibility of the world as a whole traditionally conflicted with the antinomies of Kant20, who had demonstrated that intelligence could not countenance the temporal beginning or spatial limits of

 (1929a).  “Univers et atome”, unpublished conference given in Namur on 23 June 1963. Edited in D. Lambert, L’itinéraire spirituel de Georges Lemaître, op. cit. Note the conference given by Lemaître on 8 April 1960 in Italy (1960a) also contains a critique of Pascalian arguments: 14-15. 20   J. Ladrière, “La portée philosophique de l’Hypothèse de l’atome primitive” in Mgr Georges Lemaître, savant et croyant, Louvain-la-Neuve, 1986, Reminiscience 3: 57-80. 18 19

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the universe without encountering contradictions.21 In his preface to “L’hypothèse de l’atome primitif ”, Gonseth showed how Lemaître’s cosmology would constitute a framework for overcoming these antinomies22 (1946e: 19-23). Lemaître would allude to this statement23, but never develop the question in depth. More fundamental in Lemaître however is the idea that the intelligibility of the universe does not at all imply that it must fit our expectations, our a priori representations. The universe can be apprehended by human intelligence, but what this intelligence apprehends will often surprise; the universe may be both intelligible and strange at the same time.24 This has deep philosophical consequences. Indeed, according to the cosmologist, “the discovery of the strangeness of the world is opposed to a certain form of simple idealism” (1960a: 14; our translation) that would only be found in our thought, according to its own constitutive principles25. One can find, in Lemaître’s implicit philosophy, a welcoming stance towards the wealth and complexity of reality. The strangeness of the universe, its constantly surprising character indicates a kind of continual overflowing of reality on its representation which remains always partial: “Doesn’t the strangeness of the actual description of the atomic world come from our at  For example, we envision the idea of a beginning of time. If one supposes that the world has begun, there is a first instant. As with any instant, this first instant must be a position on timeline. If so then, there was time ‘before’ the first instant, which is impossible. If on the contrary, we make the assumption that the world never began, our present has been preceded by an infinity of events, which is impossible to conceive phenomenologically. One can then conclude that it is impossible to decide if the universe has begun or not. According to Kant, this question is deprived of phenomenal content. 22   One can understand the beginning of time as the disintegration of the primeval atom. There is no instant ‘before’ the beginning of time, as time loses its meaning when the universe as a whole is reduced to the primeval quantum. 23   Cf. (1946e: 7) and (1960: 14-15). 24   I refer here to the conference of Lemaître significantly entitled: “L’étrangeté de l’univers” (1960a) [The Strangeness of the Universe] 25   Lemaître did not adhere completely to the philosophy of Eddington as developed in The Philosophy of Physical Science (Cambridge University Press, 1939). Nevertheless, Lemaître inherited the idealism of his professor, a certain trust in the theoretical “moment” of scientific activity. 21

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tempt to put inside the narrow space of our sensible intuition a universe, with a notably greater number of dimensions?” (1960a: 18; our translation). The epistemological position of Lemaître then consisted of seeking a continually unstable equilibrium between the impetus of thought and the fidelity to what reality offers through experience (1960a: 7-8; our translation): Any idea comes somehow from empirical reality, according to the saying “Nihil est in intellectu nisi prius fuerit in sensu”. For sure, the idea arising from the fact must overtake it and follow the natural impetus of thought, the basic activity of the intellect. Nevertheless, perhaps one of the most important lessons brought by the strangeness of physics is that this impetus must be controlled; it should not lose contact with the facts, but rather be conditioned by them. One should find, as in many other fields, a happy medium between the dreamy idealism that wanders off and a narrow positivism that remains sterile. […] Perhaps we are starting to find that the strangeness of the world is a welcome thing. If the world of science would be exactly what we expected, would it teach us anything?

It has been seen previously that Lemaître considered that the representations offered by mathematical physics are always imperfect and subject to revision. They do not describe the reality in a completely satisfying way. Is it related to the fact that nature is always richer than what we believe about it? Or rather is it rooted in the fact that science is, in principle, unable to provide adequate descriptions? Does science have an ontological value or is it only a system of conventions allowing us to incorporate in a concise way a set of experimental results? Lemaître leaned towards the second thesis. Influenced by Poincaré, he had a tendency to give his scientific practice a conventionalist twist. The intelligibility of the world then means that it is possible to find coherent systems of convention which ‘save’ the experimental and observational data that one possesses at one moment and that can change at any time by surprising us with their strange-

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ness. This ‘conventionalism’ appears in the following (1948: 25; our translation)26: The world is a beautiful story that each generation tries to improve. The whirlwind of Descartes did not survive the progress of the sciences; however, it remains perhaps something of the mental attitude that made Descartes say “Mundus est fabula” in what Poincaré later to call the cosmogenic hypothesis through which man cannot avoid trying to tell the history of the universe and to reconstitute its past evolution.

It is perhaps this kind of conventionalism that led Lemaître to hold the ontological value of the description of the origin of the universe as purely relative, and which would explain, in part at least, the absence of any reference to Lemaître in the 1951 address “Un’Ora”. This dimension combined with a ‘scientific utilitarianism’ (i.e. which defines the relevance of physical quantities only according to their usefulness for measurements) was in fact noticed by the philosophical world. Specifically, they were analyzed by Carlton W. Berenda, a philosopher at the University of Oklahoma27. He demonstrated that it was precisely Lemaître’s operationalism in regard to cosmology that allowed him to remain on the side of physics without straying into theological questions. But Berenda further observed that this operationalism also risked undermining the scope of Lemaître’s cosmological representation, as no one possessed any theory or measurements related to the primeval atom and thus to the natural beginning of the   We could situate this passage alongside another one: “When Lorentz explained the theory of Maxwell, he was referring to a physical intuition, talking of ether, of small gearings,..he gave the impression of talking about something known, but he was imagining them; they were no more real than the p and q of an equation” (discussion after a presentation of E.W. Beth, “La cosmologie dite naturelle et les sciences mathématiques de la nature” in Problèmes de philosophie des sciences (premier symposium, Bruxelles 1947). I. Les methodes de la connaissance, Paris: Hermann, 1948: 30. 27   C. W. Berenda, “Comments and Criticism. Notes on Lemaître’s Cosmology”, Journal of Philosophy, Vol. XLVIII, 10 May 1951, no 10: 338-341. This paper was written in the wake of the translation of “L’hypothèse de l’atome primitif ” (1950e). 26

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universe itself. This is what enabled Lemaître to say that the concepts of space and time were not applicable to the beginning of the universe and that, following Kant’s advice, one should not speculate on this beginning using concepts rooted in our usual understanding of the macroscopic world. Lemaître thus also avoided a certain number of aporias arising when one tries to apply the frame of our usual perception to fields far from our macroscopic scale. Nevertheless, this position unquestionably reduced the cosmological representation to a “fabula” and to limit its scope, as well as that of science as such. Lemaître was conscious of this fact, and which surely had not escaped the attention of Pius XII’s advisers nor of the university philosophers. A last facet of the natural philosophy of Lemaître concerned his insistence on the non-deterministic character of the universe. The world continuously produces something new owing to quantum indeterminism. Lemaître, while liking Laplace’s celestial mechanics28 remained a strong “anti-Laplacian” at the philosophical level (1967b: 161; our translation). In Laplacian determinism, everything is written, evolution is similar to the implacable rotation of a recorded magnetic tape or the engraved spiral of a phonograph disc. Everything that would be heard would have been read from the tape or the disc. It is quite another story with the advent of modern physics and, according to the present theory these concepts should also apply to the universe, at least to the beginning of its evolution. This beginning is perfectly simple, indivisible, indifferentiable, “atomic” in the Greek sense of this world. The world differentiates as it evolves; it does not consist in the spinning out, the decoding of a recording. Rather it consists in a song, each note of which is new and unpredictable. The world made itself and made itself randomly.

28

  Cf. (1950d).

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Lemaître’s option for indeterminism reflects in part the philosophical orientation of his mentor, Eddington29, for whom indeterminism was not an effect of ignorance or of human limits, but a fundamental characteristic of the universe that makes its future unpredictable in detail30. Nevertheless, neither of them would have ever attempted to explain human consciousness or free will by the indeterminism intrinsic to physical law. The implicit philosophy of Lemaître is in some manner a middle course between Eddington’s idealism, the conventionalism of Poincaré and a form of empiricism. What is striking is the character of this philosophy that made it so closed to the intuitions of Gonseth: an openness to something entirely other, which is always strange, always new, upsetting to our mental representations: the world is, according to Lemaître, a song which is always new and unpredictable.

4. Teilhard listening to Lemaître The cosmological ideas of Lemaître were widely diffused and assimilated in the Catholic intellectual world between 1930 and 1950. The Catholic Center of French Intellectuals (Centre Catholique des Intellectuels Français) had played a large role in popularizing the Belgian cosmologist by inviting him to conferences in Toulouse, Carcassonne, Nîmes, Avignon, Grenoble and finally Paris in 194831. As early as 1945, Fr. Sertillanges, O.P., had mentioned Lemaître in his famous book: L’idée de la création et ses retentissements en philosophie32, where following St. Thomas Aquinas, he clearly made the distinction   Cf. A.S. Eddington, The Philosophy of Physical Science, op. cit: 179-184. Concerning Gonseth’s interest in these questions: Déterminisme et libre arbitre (interviews with F. Gonseth, collected and edited by H.-S. Gagnebin), Neuchatel, Édition du Griffon, 1944 (1947). 30   Cf. A.S. Eddington, “The End of the World: From the Standpoint of Mathematical Physics”, Supplement to Nature, 21 March 1931, no 3203: 452. 31   Cf. The files about these conferences are preserved in the AL. 32   Paris, Aubier, 1945: 38. 29

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between the beginning of the universe and creation, understood in the theological sense. In 1954, Grison, professor at the Saint-Sulpice Seminary, devoted part of his book related to the problem of the origin of the universe to the description of Lemaître’s cosmology by reproducing the graph of his hesitating universe33. His thought was also referenced in several popular books such as that of the Belgian Jesuit, Boigelot.34 In the US, the ideas of Lemaître benefited from an even greater recognition than in Europe among the general public and in Catholic circles in particular35, partially as a result of the media coverage of his meetings with Einstein, and the fact that journalists were astonished that this priest had reached the peak of the scientific world. By the Second World War, after L’Hypothèse de l’atome primitif had been widely disseminated, one could truly say that Lemaître’s cosmological ideas were in the mainstream of Catholic intellectual culture. It is no coincidence then to find these ideas in Teilhard de Chardin. One cannot establish with certitude that Lemaître had not read some texts of Teilhard. Nevertheless, the library of Lemaître, or rather what remains of it, contains no trace of Teilhard’s work;36 the cosmologist’s interests lay elsewhere. Moreover, in Louvain, as in many other Catholic centres in the 1940s and 1950s, significant obstacles impeded the acceptance of Teilhard’s ideas.37 This is not to say that   M. Grison, Problèmes d’origine. L’univers – Les vivants – L’homme, Paris, Letouzey et Ané, 1954 (1959): 31-51; the graph can be found on page 46. 34   R. Boigelot, L’homme et l’univers: leur origine, leur destin. I. L’origine de l’univers, Bruxelles, Action familiale, coll. Pro Fide, no 1: 26-27. The ideas of Lemaître are sometimes exploited in a concordist manner, likely contributing to the distortion of the understanding of the scope that the cosmologist attributed to his thesis concerning the beginning of the universe (cf. for instance, H. Bon, La création, vérité scientifique au XXe siècle, Paris, Nouvelles editions latines, 1954: 28-31-33). 35  F. G. Gevasco, “The Universe and Abbé Lemaître”, The Catholic World, Vol. 173, 1951: 184-188. 36   The library does not contain, in fact, any book of biology with the exception of a small one related to statistics applied to life sciences. 37   Jacques Leclerc said in this regard: “The prestige of a man like P. Teilhard de Chardin comes from the fact that he tried to make a Christian synthesis in relation with the advances of the science of his time…One could expect that in Louvain, which is proud of being the greatest Catholic university in the world, there would be a collective tendency to go in this direction, but the general mindset of the University went in the 33

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Lemaître was opposed to the French paleontologist’s ideas. As underlined by Professor Armand Panier38, who had the opportunity to discuss the topic with him, the cosmologist was open to an evolution of the kind advocated by Teilhard and he was saddened about the disciplinary measures he encountered for them. Lemaître had likely not read Teilhard, but Teilhard had read Lemaître.39 In the first pages of his book entitled Man’s Place in Nature: The Human Zoological Group40, completed in Paris on 4 August 1949, he stated41: “Do not scientists now speak of a universe that has been in process of explosive expansion ever since time and space were compressed in some sort of absolute zero, in a kind of primitive ‘atom’?”

This short excerpt indicates that he had read the contribution published by Lemaître (1948a) the previous year, in which he used the allegory of “throttling” for the first time (étranglement in French)42. The opposite way. And if an isolated professor or another has this kind of concern, he would not be well accepted” (private diary 1938-1962, unpublished, made available thanks to the kindness of Jean Ladrière and Fr. Pierre Sauvage). 38   Oral communication (7-2-1996). Professor Panier hosted a social circle at the Facul­ tés Universitaires N.-D. de la Paix in Namur (now University of Namur), where the students, thanks to the mediation of Fr. Boné, discussed the thesis of Teilhard. Lemaître was interested in this circle and invited Armand Panier, as well as some students who participated to come several times to meet him in Louvain. 39   Doctor J.-P. Dumoulin, from the Fondation Teilhard de Chardin, has informed the author that there is a loose sheet written by P. Teilhard de Chardin dated 1949 containing a list of 13 references, Schrödinger, Huxley and Zundel etc., and whose eleventh title is L’hypothèse de l’atome primitif. The author is grateful to J.-P. Demoulin, as well as the Fondation for this information. 40   Oeuvre de Pierre de Chardin. 8. La place de l’homme dans la nature. Le groupe zoologique humain (preface de J. Piveteau), Paris: Seuil, 1977 (Paris: Albin Michel, 1956). [English translation: Teilhard de Chardin, Man’s Place In Nature: The Human Zoological Group (translated by Rene Hague), Collins: Fontana Books (http://www. pdfarchive.info/Te/)]. 41   P. Teilhard de Chardin, La place de l'homme dans la nature, op. cit. p. 45 ( P. Teilhard de Chardin, Man's Place in Nature, op. cit. p. 32). 42   “The space throttles time and impedes its extension beyond the bottom of spacetime” (1948a:40; our translation). In October 1949, Teilhard came to Rome for the first

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influence of Lemaître on the Jesuit paleontologist goes beyond simple name-dropping. The primeval atom contributed to his idea of the Omega point. For Teilhard, the evolutionary process is accompanied of an increase in both complexity and consciousness, as well as a deep movement towards unity and interiority of the noosphere under the attraction of an ascendant pole, of a final cause, the “Omega point” that assembles, recapitulates and gives its ultimate consistency to reality as a whole. As such, this “point” does not belong to the spatiotemporal manifold, but nevertheless plays the role of a causa causarum, that explains the carrying out and the convergence of the evolutionary process that takes place in the space-time. This “point” is, in this regard, a counterpoint to the primeval atom, which, similarly, does not belong to the space-time manifold, but remains its deep initial (material and efficient) cause, since the latter only appears as a consequence of the disintegration of the primeval atom. This primeval atom produces the spatiotemporal multiplicity that, according to Teilhard, would be unified under the attraction of Omega. The fact that all the stuff of space-time comes from a single primordial atom endows a character of deep unity to the physical reality, which was already underlined by Teilhard in Le phénomène humain written between 1938 and 1940, and revised and completed in 1947-194843. Meditating on the Primeval Atom, Teilhard attributed to the temporal evolution of the world an image, not the image of a cone, whose summit would be occupied by the Omega point, but rather the image of a spindle, whose both time where he completed his book The Phenomenon of Man. It is not surprising, in this regard, that he was informed about the communication entitled “The Hypothesis of the Primeval Atom”, delivered by Lemaître to the Pontifical Academy on 8 February of this year and that would be published in (1948a). 43  “Considered in its physical, concrete reality, the state of the universe cannot divide itself but, as a kind of gigantic ‘atom’, it forms in its totality (apart from thought on which it is centred and concentrated at the other end) the only real indivisible. (…) the cosmos in which man finds himself caught up constitutes, by reason of the unimpeachable wholeness of its whole, a system, a totum and a quantum: a system by its plurality, a totum by its unity, a quantum by its energy …”, P. Teilhard de Chardin, Phenomenon of Man, translation by Bernard Wall, London, 1958, Harper Perennial: 43. (http://www. pdfarchive.info/Te/).

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extremities are occupied by the Omega point and the Primeval atom of Lemaître44: As things now stand, modern astronomers have no hesitation in envisioning the existence of a sort of primitive atom in which the entire mass of the sidereal world, if we took it back several thousands of millions of years, would be found to be included. In a way, biology mirrors this primordial physical unit; is it not odd that if biology is extrapolated to its extreme point (and this time ahead of us) it leads us to an analogous hypothesis: the hypothesis of a universal focus (I have called it Omega), no longer one of physical expansion and exteriorisation, but of psychic interiorisation—and it is in that direction that the terrestrial noosphere in a process of concentration (through complexi­ fication) seems to be destined, over the course of millions of years, to reach its term. A remarkable picture indeed—a spindle-shaped universe, closed at each end (both back and front) by two peaks of diametrically opposite character.

And Teilhard went further by explicitly quoting the cosmologist of Louvain, for the first time: Resembling in this respect Lemaître’s primitive atom, the Omega point so defined, lies, strictly speaking, outside the scientifically observable process to which it provides the conclusion: the reason being, that to attain Omega (by the very act, indeed, of attaining it) we step outside space and time. At the same time, this transcendence does not prevent it from appearing to our scientific thought as necessarily endowed with certain expressible properties.

It was in October 1948 that Teilhard wrote a memo for the Superior General of the Jesuits, the Belgian Jean-Baptiste Janssens (1889  Teilhard de Chardin, Man’s Place In Nature: The Human Zoological Group, op. cit.: 115-116, retrieved from (http://www.pdfarchive.info/Te/). 44

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1964) in order to defend himself from his critics, who were upset by his evolutionary thinking. No sooner had he been appointed in 1947, Fr. Janssens informed Teilhard that he was not allowed to publish any work of a philosophical or theological nature. According to GérardHenri Baudry45, the attitude of the Superior General was understandable, as he regarded evolution as only a passing “scientific fad”, and he was unwilling to risk the reputation of the Society of Jesus by allowing the public think that he was defending this fad. It is interesting to note that the argumentation proposed by Teilhard to Fr. Janssens is quite similar to that used by Lemaître in the 1930s to defend the “natural” character of the notion of the beginning of the universe46. According to Teilhard, there is a purely “phenomenological” way of talking about evolution and the human being that does not interfere with philosophy and theology, in the same way that, according to Lemaître, there is a completely “natural” way of talking about the beginning of the universe that does not involve taking any position in regard to creation understood theologically. As the paleontologist remarked to the Superior General:47 Nobody dreams of blaming Canon Lemaître for speaking of an ‘expanding Universe’ (spatially). For my part, I am doing no more than putting forward the complementary picture of a Universe ‘that folds in   Anthology of the correspondence of Teilhard de Chardin (from the collection of his published letters), Lille, edited by the author, Boulevard Vauban 60, 1974. This dictionary substantiates that there was no correspondence between Lemaître and Teilhard. 46   Teilhard understood perfectly the meaning of the purely “natural beginning” of the universe. In his journal (unpublished, Fondation Teilhard de Chardin) he observed on 09-11-1949: “Canon Lemaître: by approaching of the Atom O, 1) one goes out of the T Space, 2) one goes out of the large numbers. The physics shuts up” and on 19-031950: “the atom of Lemaître only represents a natural zero and would not betray therefore the ‘creation’: the universe fading (emerging) backward…” The author thanks Doctor Jean-Pierre Demoulin for having drawn his attention to these excerpts of the Journal and, more generally, to the impact of Lemaître on Teilhard. 47   P. Teilhard de Chardin, “À la base de mon attitude” in Oeuvres de Pierre Teilhard de Chardin. 13. Le Coeur de la matière, Paris, Seuil, 1976: 182. (“The Basis of My Attitude” in The Heart of Matter, translated by René Hague, San Diego/New York/London, 1978, A Harvest Book: 138). 45

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upon itself (organically, that is physico-chemically and psychically)’. Neither of us introduces philosophy or theology. But what we have here, as Péguy would have said, is a “porch” which for many of our contemporaries, I believe, provides a way into the Church.

The relevance of the life and work of Teilhard to the study of Lemaître becomes clear, putting together three elements. First, there is a complementary nature and symmetry between the representations of the world of Teilhard and Lemaître; between the Omega and the Primeval atom. Second, there is in both scientists, a parallel between the manner of defending the relevance of a purely “natural” status of the evolution of the biosphere for the first one, and of the physical cosmos for the second. Third, this parallel was presented in black and white terms to the Superior General of the Jesuits, Fr. Janssen. But among the closest advisers of Pius XII, one could find many Jesuits: Father Robert Leiber (1887-1967)48, his secretary (who was also professor of Church History at the Gregorian University49) and Fr. Wilhelm Hentrich.50 All of them were in close contact with Fr. Janssens. Consider  Sister Pascalina Lehnert (1894-1983) commented: “[…] in 30 years, the faithful and selfless assiduousness of Fr. Leiber never wavered. I could see and feel closely the extent Pius XII also knew that and how he regarded Fr. Leiber. Even when his Chair in the Gregorian occupied him later, the Holy Father always looked for fresh opportunities to show him that he had all his trust and his affection. How many times did Pius XII go down the stairs that led to the floor below, to the office of Fr. Leiber to show him a work or to listen an advice or a point of view…” (Pius XII. Mon privilège fut de le “servir” [translation to French, J. Pottier], Paris, Tecqui, 1985 [1982]: 37); our translation from the French version. 49   The testimony of the physician of Pius XII, Dr. Riccardo Galeazzi-Lisi (Dans l’ombre et la lumière de Pie XII, Paris, Flammarion, 1960: 147-148): “There were in the immediate surroundings of the Pope two Jesuits that collaborated with his secretariat; Fr. Robert Leiber, professor at the Gregorian University, and Fr. Wilhelm Hentrich, advisor to the Supreme Congregation of the Holy Office. In their free time, they dedicated themselves to the ordering of the vast private library of His Holiness, and provided him with some documentation for his studies and discourse”; translation from the French version. 50   “Father Robert Leiber, Professor at the Gregorian University, was part of the small circle of intimate friends (of Pius XII). Until his death in 1967, this Jesuit was the righthand man of the Pope on all delicate topics, his personal secretary, while another member of the Society of Jesus, Hentrich, provided him with the documentation requested to prepare his speeches”. (R. Serrou, Pius XII. Le pape-roi, Paris, Perrin, 1992: 261). 48

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ing these three elements sheds some light on the “Un’Ora problem” and supports the hypothesis according to which Pius XII, and those who were participating in the writing of the speech “Un’Ora” would have avoided quoting Lemaître because they were conscious of a certain intellectual proximity between the cosmology of the Canon and the “natural philosophy” of Teilhard which was judged, during this period, highly problematic. On the other hand, barring this hypothesis, the absence of any explicit reference to Lemaître’s work is not easy to comprehend. One must explain why Pius XII, who invoked the primeval state of matter clearly in his discourse, and who could not have ignored the talk Lemaître had delivered on the primeval atom at the Pontifical Academy (1948a), had made no allusion to the Canon. A subtle but logical link relates the interdictions that weighed on the work of Teilhard and the “Un’Ora problem”. While Lemaître’s scientific contributions were held in high regard by Pius XII, it is also certain that the Holy Father could be distrustful of Lemaître’s implicit philosophy that insistently defended a purely natural state of the beginning of the universe and that was close, in a manner, to Teilhard’s phenomenology. The Pope’s advisers could not have helped but contribute to reinforcing this mistrust.

Chapter XVIII

A “pair of Molière” and the “Nim-Pythagoras” fight

1. A double star: Molière

F

rom the late 1940s to the late 1960s1, to the astonishment of his colleagues, Georges Lemaître developed a profound interest in – Molière!2 No one is quite sure why, but we know that Lemaître had a deep interest in literature, witness his study of Ruysbroeck’s writings. Lemaître inherited a taste for literature from his father, and acquired an instinct to go back to original texts with a critical eye from Fr. Bosman. Moreover, we know that Lemaître liked to solve little enigmas he discovered through his readings and meetings. He was, for example, captivated by the so-called “travelling words”, i.e. those which travel from one language to another, transforming themselves in contact with other linguistic worlds3.   On 16-03-1960, he bought at the Fonteyn Bookshop, 13 Place Foch in Louvain, an edition of the complete works of Molière. At the same time, he purchased “La vie du petit Saint-Placide” of Geneviève Gallois (sales slip preserved at the AL). 2   In the files of the AL, one can find among detailed bibliographical notes on the literature concerning Molière, two typewritten texts: Une étoile double (7 pages) and Mélicerte. Pastorale des atributs royaux (2 pages), two manuscripts corresponding to the conferences entitled Une étoile double: Molière (37 pages); a manuscript of 18 pages on Le Tartuffe and one manuscript concerning Les Plaideurs of Racine. All these texts refer most probably to the preparation of conferences given by Lemaître. An edition of these texts with an introduction can be found in: G. Lemaître. Une paire de Molière(s) (introduction et commentaires de D. Lambert et J.-F. Viot), Bruxelles, SAMSA, Académie royale de langue et litterature françaises, 2014. 3   Oral communication of Pierre Lemaître, 08-11-1997. 1

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Molière occupied a central place in the Canon’s life. In the early 1950s, he discovered interesting papers about Molière written by G. Lenotre and M. Garçon, through an issue of the French review Historia4. Garçon, a great Parisian jurist, had tried to establish that there was a second author who wrote certain passages of the works of Molière. Initially, Lemaître became interested in the works of Molière as he was stimulated by the new studies of Molière’s texts following the ideas of Garçon. He did not undertake any research on the writings of Jean-Baptiste Poquelin, but he had become sufficiently fascinated to carry out a more systematic study, leaving his primary interests aside for a while. Garçon’s thesis, that Louis XIV was the hidden author beside Molière, immediately drew in Lemaître, who begin to deepen his knowledge of Poquelin’s works in search of stylistic differences, vocabulary, etc. He would share his findings during some evening meetings at La Petite Rotonde (a central lecture room in Louvain), perhaps at the invitation of the Cercle Pédagogique of UCL that brought together alumni of the Faculty of Philosophy and Letters, or perhaps his personal friend Charles de Trooz, professor of this faculty. He was also invited, in 1959, to speak about The Pair of Molière in the Cercle de Droit (the law students’ club). His talks were given amusing titles, often puns: Une Paire de Molières, with a unofficial subtitle: Le petit Garçon n’avait pas tort [the small Boy (Garçon) wasn’t wrong] and, ever the astronomer, Molière une étoile double [Molière: a double star]5. The latter title is a thinly veiled allusion to the resolution of a double star, in which   G. Lenotre, “Louis XIV était-il Molière?”, Historia, June 1951; M. Garçon, “Postface”, Historia, March 1953. 5   Lemaître said: “I have dreamt that when Molière was put to the test in Paris, in the Salle des Gardes of the Louvre Palace before the King, and surprised him with a small play after the main program: le Docteur Amoureux, he played the comedy…the King knew very well who was the ‘Docteur Amoureux’. In fact, he had invited Molière to Paris only to attend this play, for which he was the author. A dream of an astronomer: If there were two authors in Molière, he was like a double star” (J.K., “Portrait. Le chanoine Lemaître. Du cosmos aux précieuses ridicules”, La libre Belgique, 23 janvier 1960: 2). 4

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one establishes the existence of two stars from an apparently single luminous source. At the beginning of Une paire de Molières, he emphasizes that Garçon did not always defend the same positions in regard to Molière, and compared his shift of position with Einstein’s on the cosmological constant! In the end, what interested him was not an analysis of a man of letters’s thesis, but the simple hypothesis6 “that does not belong anymore to its author, provoking the irritation of some, the enthusiasm of others, and perhaps the indifference of a few”. In this literary field, Lemaître was conscious of his limits: “[…] I am not qualified through studies or my training to undertake this research, my excuse is that the competent people seem not to have possessed the curiosity to undertake it…” And he ended his cycle of talks in a modest style that remained coloured by the influence of astronomy7: I think that resolving the double star prompted a double admiration for each of the incomparable stars whose flashes have been often confused. I do not flatter myself thus for having done anything definitive, for having proven anything. I only wanted to show what can happen if an astronomer starts reading Molière and imagines that there is in literature something like there is in the sky: double stars.

His colleagues’ reactions were mixed at best. Charles de Trooz was not convinced by the argumentation of Lemaître. Odette Delenne-Lemaître, one of his nieces, who contributed to the archival record of her uncle on his writing about Molière, penned him a brief if revealing note “Doctor Hénusse seemed both skeptical and very interested”. The Dr. Hénusse was a friend of Lemaître’s parents as well as   “Une paire de Molière. Le petit Garçon n’avait peut-être pas tort”: 2-3(AL).   “Molière une étoile double”, 20 handwritten pages in French (AL), 20; our translation. Lemaître's manuscripts about Molière are edited in Une paire de Molière(s) (edition and introduction by D. Lambert and J.-F. Viot), Bruxelles, SAMSA, Académie Royale de Langue et de Littérature Françaises, 2013; Collection Histoire Littéraire. 6 7

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a great specialist of Molière’s works. His scientist colleagues, for their part, did not really understand Lemaître’s obsession with Molière. After Lemaître’s demise, Louis Bouckaert and Odon Godart opined that this interlude should be relegated to marginalia at best in his bio­ graphy. But could one overlook a decade-long consuming interest, and was there any serious risk of diminishing his scientific stature? After all, Schrödinger, one of the founders of quantum mechanics, immersed himself in Greek, becoming such a specialist as to contribute to an academic debate among the most prestigious philologists8. André Weil, one of the greatest mathematicians of the 20th century, studied Sanskrit9 and the great Fourier was an Egyptologist of no small fame, who directed Champollion towards his famous discovery. Lemaître’s literary avocation showed that he was hardly a narrow scientist incapable of putting aside his equations. Rather, this interest underlines the cosmologist’s turn of mind and his weakness for small but stimulating enigmas. In the late 1950s, he was also interested in Racine and especially to Les Plaideurs (The Litigants), whose writing would also reveal several literary “stars”10. His passion for the “literary double stars” was such that Lemaître talked about it to everyone around him: among his family of course, but also to those who were invited to share his table at the Majestic. Adolphe Gesché11, later the famous theologian, remembered that when he was invited to table by Msgr. Charles Moel­ ler, the cosmologist spent the whole meal convincing his fellows of the relevance of his thesis of the double Molières! But his infectious enthusiasm was hardly limited to the world of letters.

  Cf. E. Schrodinger, The Nature and The Greek, Cambridge University Press.   A. Weil, Souvenir d’apprentissage, Basel, Birkhäuser, 1991: 40-41. 10   Lemaître carefully preserved an article from Le Monde, 03-12-1959 authored by Pierre de Grosclaude entitled “Un document nouveau sur les Plaideurs. L’avocat Bonnaventure de Fourcroy, collaborateur de Racine”. 11   Oral communication, 18-12-1997.   8   9

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2. Let us calculate without fatigue! After the Second Word War Lemaître became interested in the teaching of elementary arithmetic12. Between 1945 and 1953, the Canon had already worked in this area with Adrian Demeure, son of his colleague Charles Demeure13. During several visits to La Prévôté, the castle of the Demeure family in Sirault, in the Belgian province of Hainaut, George Lemaître and Adrien Demeure produced a manuscript regarding a new system of numbers.14 It seems however, according to his unpublished notes, that it was only in the early 1950s, and more specifically around 1954, that he started to work on the project of the “reform of elementary arithmetic” that would ultimately lead to the publication of a book, Calculons sans fatigue (1954a) [“Let us calculate without fatigue”]. Undoubtedly this project was rooted in Lemaître’s infatuation with mechanical calculating machines; he collected ADDIATOR calculating machines like others collected stamps. In analogy with the mechanical operation of a slide rule, Lemaître observed (1955b: 379): In the use of modest machines, the only ones for which I have some experience, the subject enters in some way into the operation of the machine, whose nature can reasonably qualify as mechanical. It consists of the execution of simple operations, of repeated gestures, capable of being learned and repeated in an entirely automatic fashion, and does not require any active participation from the operator, other than a state of attentive concentration, an absence of distraction towards this strange object.   Émilie Fraipont, the Ursuline Sister, confirmed that Lemaître was already talking of his new numbers in his class of “Methodology of Mathematics” in 1943 (oral communication, 25-06-1998). 13   A mine engineer and professor working in what would become the Faculty of Applied Science. He had been assigned to UCL in the same year as Lemaître, and had benefited, as the latter, from a study-travel grant to the US from the CRB. 14   The author is indebted to Charles-Bertrand Demeure, son of professor Demeure and former assistant of the Higher Institute of Philosophy, as well as the intervention of Guy Boodts and Manuela Nève de Mévergnies. 12

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Eventually, all these manual operations and their associated muscular fatigue would disappear with electronic machines, which even obviated the need for any long- or short-term memory (1955: 380381; our translation): Elementary computation calls for resources that have been etched in the memory by prolonged exercise. When the operator has in front of him two numbers, 7 and 8 for example, his brain has to figure out the numbers 15 or 56 depending whether an addition or a multiplication has taken place. The operator has to know addition and multiplication tables. He must learn them ‘by heart’. There is still another type of activity that is involved in elementary computation, and which has no equivalent in mechanical work: the operator enters some numbers and must remember others. This requires another kind of memory, not a long-term memory, as needed for basic tables, but a short-term memory that could perhaps be compared with that of a student before an exam; the latter needs at least a few seconds to remember a partial sum until calling into help the other memory, he then adds it up to the number in front of him and writes the final sum.

Lemaître then conjured up an entirely new mechanical way of computing that did not require memorization of the so-called Pythagorean tables of multiplication or addition. Lemaître’s research focused on a technique that reduced the thought component in elementary arithmetical operations as much as they possible. This required two conditions however. One must change the system of Arabic numerals that we use, and secondly change the way we perform the operations. According to the Canon, the first condition stems from the fact that Arabic numerals do not represent what they signify. Looking at the numeral 3, one does not immediately recognize it as a symbol representing three units, while with the Roman notation III or the Chinese notation (three stacked bars) that Lemaître knew well, the meaning of the numerical symbols is immediately evident. The notation of numerals thus involve, in the Arabic numeration system, a supplemen-

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tary call to the memory (in order to remember the symbols) that could be reduced by an appropriate notation showing directly what it represents. The second condition then arises from fact that how we structure written calculations follows a reverse logic with respect to how we write in English. We perform additions, for example, by adding a column of numerals from right to left while we are writing an English sentence from left to right. In order to ensure that arithmetical operations are performed in with a manner consonant with French or English writing, Lemaître developed algorithms for the preparation of operations (1955b; 384386), that allow one to calculate from left to right. (One could reasonably wonder if this would really be easy for a first or second year student in primary school to master!) Lemaître gave the following sum as an example, that we cannot resist reproducing (1955b: 385): 4376 9367 8256 + 3278 3654 0462. To prepare the operation one places (from right to left!) “+” and “-” signs according to the following rule: below the figures of the sum, one writes “-” if the sum is larger than 9. This “-” is the “entry delay”; one writes “+” as soon as the sum of the figures returns to a number less than 9. After this preliminary operation, one performs the addition from left to right respecting the following rule: upon encountering the “-” sign, one adds modulo 10 (i.e. drop the first digit of the number). Between the “+” and the “-”, one does the same thing, but adding 1, in other cases, one adds as usual. This gives: 4376

9367

8256

3278

3654

0462

+ 7655

3021

+8718

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Lemaître did not persist with the “simplification” he proposed15. Nonetheless, he spent a lot of time developing new symbols to replace Arabic numerals. In fact, Lemaître was 40 years ahead of a development which logicians would nowadays term, following Newton Da Costa, “semiography” i.e. the study of constructive symbolic configurations16 which Msgr. Lemaître called in 1962, the “stenomatic” (1962: 7). Lemaître proposed two versions of his new notation of numerals that visually expressed what they signified. One conformed to the constraints of a typewriter and is reminiscent of, as Professor Peter Lipnik observed, the basic units of the quaternions. The other was inspired in part by stenographical writing in loop and lines, but even more by musical notation. His first system of numerical representation used four symbols representing the first four powers of 2: 20=1, 21=2, 22=4, and 23=8. These symbols are i, j, k, l. Zero is denoted by an empty case or by “_”. The numbers are then formed by concatenating the written symbols from left to right. Thus the numerals 3, 5, 6, 7, 9 are denoted ij, ik, jk, and il. In fact, in 196217, instead of i, j, k, l, Lemaître used what Peter Lipnik18 called the “tetrads”: (1000), (0100) (0010) and (0001). Addition is then easily performed: ijk is written (1110). A few extra additional rules are needed, e.g. i+i equals j, or in tetrads, (1000) + (1000) = (0100); j+j equals k, or (0100) + (0100) = (0010), etc. The upshot of this was to group the binary digits four by four, which was not entirely novel. In fact, for Lemaître the decimal system had advantages that should not be forsaken lightly. What he developed was   In the early 1930s, Lemaître already performed addition left to right, to the amazement of his class (oral communication, Th. Cornet d’Elzius de Peissant, 28-08-99). 16   Cf. N.C.A. Da Costa, Logiques classiques et non classiques. Essai sur les fondements de la logique, Paris: Masson, 1997: 146. 17   (1962a: 7). 18   P. Lipnik, “Les nouveaux chiffres de Mgr Lemaître”, Ciel et Terre, t. 110, juilletaoût 1994, no 4: 124-125; “Architecture de Mgr Lemaître en arithmétique”, Revue des Questions Scientifiques, t. 168, 1997, no 2: 161-178. P. Lipnik was the first to carry out a detailed analysis of the numeral systems of Msgr. Lemaître. 15

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some kind of hybrid binary-decimal system, where each numeral in decimal notation is expressed through a binary tetrad. Thus by reversing the usual direction for reading decimal numerals, 10 = 6 + 4 is represented as follows: (0000) (1000) = _i = (0110) + (0010) = (0101). In the same way, 16 is denoted (0110) (1000) or (jk) i = _i + jk. To pass from the binary notation to the binary-decimal notation, one must perform what Lemaître called a “reduction of supernumerary numerals” (1954a: 11): this is what was done for 10 by passing from the form jl = (0101) to the form _i=(0000) (1000). This can be performed mechanically as in computation; (0101) is equivalent to (0000) (1000). For this reason, Lemaître used the following trick. To perform this reduction, forget for a moment that one is using decimals. One adds 6 = (0110) to the number to be normalized, (0101), and then make the addition as in the usual binary calculus. One then gets 00001. Interpreting this in the binary-decimal notation, one obtains (0000) (1000), the expected result. To normalize, it suffices then to add a six mechanically.19 This hybrid representation where the numerals of the decimal numbers are encoded in binary notation would be used years later to store data in computers. Once again, Lemaître was ahead of his time. The other notation, largely developed by Lemaître in his book “Calculons sans fatigue” (1954a), is a series of symbols looking like horizontal eighth-notes on a lonely line of a stave20 or resembling the “Duployé” stenographic system in some way, even if their representation of numerals did not follow the logic of Lemaître’s “new numbers”. From the Canon’s notebooks, the notation of these new   This stemmed from the link that exists between the numeral system of Lemaître and the base 16 number system. Cf. (1955b: 395). 20   “This procedure is used by musicians who write their signs of a stave that ensure its positioning” (unpublished manuscript from the AL entitled: “Emploi de la numération binaire”; without date; our translation from the original in French). 19

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numerals was by no means fixed once and for all21; he proposed several schemes, and in 1955 admitted that the “musico-stenographical” notations are only one example among others (1955b: 398). Finally in 1960, he expressed his hope that whatever system would be adopted would not deviate too much from it (1961b: 25-26; our translation): I would like to express the hope however, that the authors who will contribute to the diverse developments involved in these new techniques, will not deviate from the notations that I have introduced without cause. It would be a pity that in 10 years one must convene a congress in order to unify the diverse systems of notations that it would be easier to invent. In any event, the characters that I use are at everyone’s disposal. They can be provided at the cost of lead at the Ceuterik Printing House in Louvain where the originals are preserved. Indeed, the Monotype Company that made them has reserved for itself all rights to reproduce them.

In the 1960s, the notebooks of Lemaître were covered with these ‘new numerals’ and he talked about it with everybody. His nephew and nieces, as assistants, were invited to test the advantages of computing “without mental pain, but not without muscular ache and the expenditure of paper”! According to Jean Valembois22, his assistant until 1962, Msgr. Lemaître systematically sought volunteers to test the speed at which one could perform computations using his notation. The prelate was so convinced that his system could transform elementary arithmetics that he sought to disseminate it as broadly as possible. To this end, he contacted Professor van der Essen, from the Faculté de Philosophie et Lettres at Louvain, but who also occupied a function at the Ministry of Foreign Affairs in order to en  There is also a notation based on balls and arrows; a slash for the zero, a ball under the slash for the 1, a down arrowed slash for 2, a up arrowed slash for 4 and finally a slash surmounted by a ball for 8. This system would quickly be forgotten. 22   Oral communication 19-12-1997. 21

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sure the spread of Calculons sans fatigue across the network of Belgian embassies.23 The arithmetical system of Lemaître is based on the decomposition of numbers using only zero and the symbols for 1, 2, 4 or 8. This decomposition, according to the cosmologist, has practical advantages, even if one did not adopt his “new numerals”. He had proved that one can “simplify” the operations by decomposing the numbers in a sum of numbers generated by using only zero and 1,2,4 or 8. For instance, if one must compute 357 x 727, by manual addition, but without resorting to the Pythagoras tables, it is useful to decompose the operation as follows (1955b: 390-391): 357 = 111 + 202 + 44. One computes then by successive additions the following results: 727 x 1 = 727, 727 x 2 = 1454, 727 x 4 = 2908. One has then: 727 x 357 = 727 x 111 + 727 x 202 + 727 x 44 = (727 + 7270 + 72700) + (1454 + 145400) + (2908 + 29080) Lemaître was very happy to show that the decomposition of the numbers that he had used was linked to the game of Nim24. The latter is a Chinese game in which one starts with a certain number of piles of chips. The players take turns picking a certain number of these chips, but only from one pile. The winner is the player who picks the last chip. One can prove that it is possible to find a strategy in which   Oral communication 18-12-1997.   Lemaître even invented a checkerboard where one added up numbers represented by chips placed on it, and built a model of this checkerboard. This is explained in an unpublished handwritten text entitled: “Calculons en jouant” (“Let’s calculate by playing”) (AL). 23 24

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one wins every time25. This strategy was based on what Lemaître called ‘good combinations’ related to the particular decomposition of the numbers. For example, let a game of Nim begin with 3 piles of 3, 5 and 7 chips respectively. Consider the number 357 and the decomposition exhibited above. Observe that one of the terms of the sum contains an odd number of non-zero figures, namely 111. Such a combination is “bad”. Any similar combination, where at least one of the numbers resulting from the decomposition of its associated number contains an odd number of non-zero figures, is called “bad”. If the decomposition is comprised only of an even number of nonzero figures, the associated combination of chips is called “good”. Thus the initial combination of a game of Nim that starts with three piles of chips with 3, 5 and 6 chips respectively is good because 356 = 110 + 202 + 44. Lemaître showed that if a player succeeded to make a ‘good combination’, he would always be able to win. In some handwritten and published texts, Lemaître presented his new figures as a struggle between the Chinese Nim and the Greek Pythagoras (1962a). Lemaître’s interest in the new numerals was not only theoretical, but he seriously thought it would be helpful for pupils (1961b: 26; our translation): Rather that inventing new symbols, I hope to strike up a useful collaboration among those that understand that there is more than a mathematical game here and that it’s possible to do away with the mass of prejudices inherited from Pythagoras. One would not only save children from fruitless efforts and tiredness, but also liberate our civilization from totally unnecessary obstacles. I know that some will answer that the study of multiplication tables is an excellent exercise for memory training. But there are so many other ways to ob-

  A description of this strategy can be found in the book of G. Godefroy, L’aventure des nombres, Paris: Odile Jacob, 1997: 188-191. 25

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tain the same results, notably by learning the dynasties of pharaohs by heart.

He would in fact have the opportunity to meet specialists in pedagogy who could develop and apply his ideas as he had hoped. His first success was with a team of the Cours Charlemagne. In 1963, Mr. Le Bon, a psychologist, along with one of his former students, Mrs. Marthe Mahieux, founded a primary school where the pedagogy was based on principles of inventiveness and creativity26. One of the teachers’ ideas was to make children learn numbers in several bases, i.e. binary, decimal, etc. The children of Gilbert Lemaître, the nephew of Msgr. Lemaître, attended this school, and he proposed putting the teachers in contact with his uncle so they could use his ‘new numerals’. Msgr. Lemaître received the teachers in 1964 in his apartment in Louvain. He was enthused with the prospect of finally putting his new pedagogy of arithmetic to the test in a real school environment. However, as recounted by Peter Lipnik who was the first to document this experiment, after four weeks, Lemaître agreed to desist using the ‘new numerals’, which did not prove helpful to the students’ understanding of arithmetic. The second experiment was conducted by Georges Papy and Frédérique Papy-Lenger, two great Belgian specialists of what was called at that time, the “modern mathematics”. Lemaître and Papy had known one another for a long time and met quite regularly27. After Lemaître’s death, Georges Papy, in collaboration with his wife Frédérique, wrote a book entitled Minicomputer that was one of the most beautiful tributes to Lemaître.28 Papy used Lemaître’s numerals in their “musical” notation, but organized the symbols following a vertical axis as opposed to Lemaître’s horizontal depiction. Papy then showed that this representation   Oral communications from D. Le Bon and M. Mahieux (October 1997).   Oral communication of P. Lipnik, 29-09-1997. 28   Copyright 1968, Papy & IVAC. His book begins with a short biography of Lemaître. 26 27

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was equivalent to placing checkers on a checkerboard of four squares, each one representing a power of two. One can easily make elementary arithmetic operations on this checkerboard following Lemaître’s philosophy; thus the term Minicomputer is fitting indeed. In the 1970s, Frédérique would use the “Papy version” of Lemaître’s numerals in her book Les enfants et la mathématique (Children and Mathematics)29, explaining her approach as follows30: Until now, children have not made any manual or mental calculations. The method used to initiate the child in this new cognitive approach exploits the decisive advantage of the binary system over all other systems while making allowances for the decimal context in which one is immersed. It was possible to attain this result thanks to the MINICOMPUTER of Papy. Inspired by the work of Msgr. Lemaître, this kind of two-dimensional abacus harmoniously uses the binary within decimally prearranged plates.

And so it happened that Lemaître earned a place in the pantheon of modern mathematics pedagogy, with which he only had a passing encounter. Some would equate this interlude with his interest in solving the puzzle of the “pair of Molière”; a mere diversion of no enduring impact. The author does not share this point of view, and in fact rejects it strenuously. Lemaître was a visionary, and beneath the apparently trivial exercise of basic arithmetic, he saw and apprehended problems of great difficulty. It is interesting that some of the great names of neurophysiology, such as Stanislas Dehaene, became involved in research concerning the biological basis of calculational ability. And these luminaries fall in with Lemaître’s instincts, in particular that it is unnecessary from a pedagogical point of view to make pupils memorize the Pythagorean tables, nor should pupils be led to   Frédérique Papy-Lenger, Les enfants et la mathématique. Tome 1, 2 and 3, Bruxelles/ Montréal/ Paris: Marcel Didier, 1970, 1971, 1972. 30   Les enfants et la mathématique. 1, op. cit., p. XI (our translation). Allusions to Lemaître are found in Vol. 2: 4 and Vol. 3: 4. 29

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believe that computation involving a long sequence of memory-taxing operations, is to be considered a natural process. Stanislas Dehaene observes for example31: […] memorizing the multiplication table, executing the subtraction algorithm, and dealing with carryovers are purely formal operations, without any counterpart in a primate’s life. Evolution can hardly have prepared us for them. The Homo sapiens brain is to formal calculation what the wing of the prehistoric bird Archeopteryx was to flying: a clumsy organ, functional but far from optimal. To comply with the requirements of mental arithmetic, our brain has to tinker with whatever circuits it has, even if that implies memorizing a sequence of operations that we do not understand. We cannot hope to alter the architecture of our brain, but we can perhaps adapt our teaching methods to the constraints of our biology.  

The neurophysiologist’s conclusion would have pleased Lemaître: […] there are alternatives to the rote learning of arithmetic. (Forcing a child’s brain to absorb arithmetical algorithms little adapted to this use is perhaps not the best way to form future mathematicians or instruct engineers).

The intuition of Lemaître on the suitability of calculating from left to right can be based on the same arguments. Dehaene showed, for example, that a prodigious calculator, Scott Flansburg owes his speed to an algorithm that in fact performs computations from left to right, minimizing as it does the memory usage during the computation32.   S. Dehaene, The Number Sense. How the Mind Creates Mathematics, Oxford University Press, 2011, revised and expanded edition: 119 (La bosse des maths. Quinze ans après, Paris, Odile Jacob, 2010: 150). The second extract quoted can be found in page 120 (La bosse des maths, op. cit.: 151; the quotation in brackets exists only in the French version; our translation). 32   S. Dehaene, The Number Sense, op. cit.: 152. 31

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Lemaître’s ideas about educational reform find much support in contemporary neurophysiology and cognitive psychology; ironically however, the modern tradition of these fields discredit in part one of his primary theses, namely that numerals express what they mean. Recognition of the structure of a symbol (e.g. the number of vertical bars of the first Roman numerals, or the counting of balls and quavers of Lemaître’s “new figures”) involving more than five elements takes more time and effort than the recognition of abstract symbols. Perhaps Arabic numerals are not so far afield from our cerebral system after all33: This numeration tool, with its ten easily discernible digits, tightly fits the human visual and cognitive systems.

What was considered in the 1950s and even in the 1960s as an amusement, or even an eccentricity34 by Lemaître’ students, was in retrospect highly fertile from the viewpoint of cognitive psychology and contemporary neurophysiology. Msgr. Lemaître knew nothing of those fields, but his familiarity with the practice and art of computing endowed him with critical insight into the scope and the limits of our cognitive abilities.

33 34

  Ibid.: 87.   Oral communication, Jacques Masset, 15-12-1997.

Chapter XIX

The last years (1962–1966)

1. Last works

L

emaître’s passion for mechanics continued unabated to the end of his life; he produced a remarkable theoretical work on the threebody problem even in 1963. In one of his last notebooks, dated March 1966, three months before his death, one still sees remarks on a “nonoscillating orbit of the Størmer problem”. In his final years, while he tried to start a groundswell on the “new figures”, what really interested him above all were computers. Msgr. Lemaître spent much time inventing algorithms for elementary functions and translating them into machine language, wanting to understand every detail of the operations. The development of these algorithms greatly amused him and he would never think to consult the literature to see if there were simpler versions. In the early 1960s for example, he spent a considerable amount of time testing an algorithm to calculate the arctangent function on the E101 with his assistant Jean Valembois1, who told him that he could have saved a great deal of time if he had consulted the available literature produced by teams dedicated to numerical calculations for computers2. Lemaître   The latter succeeded Miss André Bartholomé who became Mrs. Deprit. He would remain the assistant of Lemaître until 1962, when he would join the famous glass manufacturing company Glaverbel, for whom he performed calculations on the E101 from time to time (Oral communication, 19-12-1997). 2   When he arrived in Glaverbel, Jean Valembois would discover a book of C. Hasting, Approximations for Digital Computers (Princeton University Press, 1955) which contained an algorithm that would have saved Lemaître a great deal of time. 1

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developed “Louvain-style” algorithms to compute trigonometric functions with the help of Chebyshev polynomials, always faithful to his principle “that it is easier to solve a problem by oneself than to check in the literature if it has already been solved”! He was similarly captivated by the “logarithm of addition” and for which a 1965 notebook contains a brief mention.3 His goal was to find algorithms to compute the logarithm of a sum of several terms as a function of the logarithms of these terms. Among the cataract of ideas from the last years of his remarkable life, one must include the “super-numerals”, i.e. how to computationally represent extraordinary high number – at least exceeding the technical abilities which the machine’s manufacturer specified. In wresting capabilities from a computer that it was not designed for, Lemaître was the undisputed champion. In a notebook he penned an essay entitled “Géometrie et calcul”4 dedicated to the study of projective geometry with the help of a tracing flatbed plotter connected to the Elliott 802 computer. Msgr. Lemaître provided an interesting justification for this piece (our translation): Computing machines have organs which are able to draw. It should be possible for them to make geometrical figures or, better yet, complete working drawings. It is said that when he was a student, Henri Poincaré computed the coordinates of the points of the figures that he would draw. What he was simply doing was recording them on drawing paper. Probably he was not the only one to have done that.

It seems that Lemaître himself did the same thing when he was a student. In “Géometrie et calcul”, he represented figures of projective geometry associated with the usual two-dimensional space within a disk used as a model of a bi-dimensional elliptic geometry. He could   The author is grateful to Roger Weverbergh for this information and Jean Valembois for making him aware of Msgr. Lemaître’s love for numerical calculation. 4   Found in 1999 in the archives of O. Godart and transferred to the AL. 3

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then calculate and visualize on the border the points at infinity and all the interesting configurations of that projective geometry. The program written by Msgr. Lemaître was tested on the theory of conics and the prelate took great satisfaction in making machines calculate and represent the conic passing through five points given a priori. He concluded his work thinking once more about his favourite cosmological model: “Likewise, if this representation of the projective space in the elliptic space were generalized, one should be able to familiarize oneself with the properties of the elliptic space. This would be especially important in three dimensions.” In his last years, Lemaître seemed to go in a number of directions all at the same time. He would ask his collaborators to perform some particular computation at the end of the day. The next day, he would barely glance at the results before leading his team off with the same frenzy in another direction. He was so irrepressible, that his daily arrival at the Laboratory of Numerical Research in the year 196263, was described by his assistant Jacques Masset5 as a “hurricane”. Prone to fits of anger when things did not go as expected, Lemaître once performed a memorable exit recounted by André Deprit, having become furious at not having at his disposal a machine up to the task of computations of the theory of the Moon of Delaunay6. Jean Valembois7 likewise recalled a spectacular quarrel between Lemaître and his lifelong friend Charles Manneback regarding a disagreement about the best method to use in order to compute the eigenmodes of a certain molecule, but which was just as quickly defused by his joviality and bonhomie. Not surprisingly, the Canon’s mercurial interests and unpredictable cataract of ideas was unnerving, and his schedule was often out of   Masset succeeded Jean Valembois between 10-09-1962 and 31-08-1963.   “Les Amusoires de Mgr Lemaître” in Discours pronouncés lors de la ceremonies d’ouverture du symposium international organize en l’honneur de Lemaître cinquante ans après l’initiation de sa cosmologie du Big Bang (Louvain-la-neuve, 10-13 October 1983), Revue des Questions Scientifiques, t. 155, 1984: 213. 7   Oral communication, 19-12-1997. 5 6

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phase with those of his colleagues and students. When he did not have class, Lemaître would generally celebrate daily Mass in Saint-Pierre church very early, but arrived at the “attic” of the Collège des Prémontrés only around 10:30 or 11, greeting his collaborators with his resounding “Bonjour, Messieurs les calculateurs!” New ideas were the order of business until noon; little time was dedicated to correspondence, which he did not answer on a regular basis anyway, but relegated to the faultless devotion of his collaborator, Mrs. Andrée Bartholomé, and later to Odon Godart8 and his assistant. At noon, he joined the famous table at the Majestic for a meal followed by his ritual walk, returning around 3pm. At 5pm, Lemaître was ready for another ritual: teatime. Miss Bartholomé, later assisted by Jean Valembois, prepared the tea and a plate piled high with pastries. This moment was a tradition of the Collège des Prémontrés that would be exported to the campus at Héverlee where the Laboratory of Numerical Research moved in 1960. Lemaître’s colleagues joined him periodically, and his assistants would drink in these unforgettable conversations with Manneback, de Hemptinne, Delfosse, Ballieu and others. After this respite, reminiscent of those pre-War teas at the “De Belva” cake shop, Lemaître worked until 7pm and sometimes later. Jacques Masset9 observed that Lemaître was not always mindful of the impact of his timetable and demands on the personal lives of his young collaborators. When tactfully reminded however, he tried to remedy the situation, but it was clear, according to Jean Valembois, that he himself continued to work late into the night. Msgr. Lemaître liked being surrounded by a small number of devoted collaborators, but he was not the type of person to coordinate big research teams as were beginning to develop in science after the War. This would have required him to dedicate part of his time to administrative work and management that he disliked. It would have also   At the end of the 1950s, when Odon Godart returned to Louvain after a career in the Belgian Air Force. 9   Oral communication, 15-12-1997. 8

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required him to modify his schedule, but most of all he would have been obliged to work on projects he wasn’t necessarily interested in. Lemaître needed a space for intellectual freedom where he could explore whatever ideas he had in mind. His nephew and godson Gilbert Lemaître captured it succinctly10: “[…] my uncle was very adventurous but not disciplined enough for many people. This caused some troubles”. Therefore, when the creation of a computation centre in Louvain to support the needs of a growing number of scientists was being studied, some voices advised the bureaucracy to leave Msgr. Lemaître’s Laboratory for Numerical Research of out of the picture. This was a rather sad turn of events, if understandable in light of Msgr. Lemaître’s admitted lack of interest and skill in administrative affairs. But with a minimum of tact and diplomacy, the matter could have been handled much better, without wounding the person who had introduced the first computer in Louvain; at the least the powers that be could have conferred on him an honorific title and position within the new structure. But this is not what transpired,11 and he was ousted from the Collège des Prémontrés and welcomed along with his faithful friend Professor Godart into the Institute of Nuclear Physics by Professor de Hemptinne. An entire floor was put at his disposal, at the Institute located in the beautiful park of Arenberg in Héverlee, a suburb of Louvain. The E101 was moved there as was an Elliott 802 sold by NCR shortly thereafter. In reality, while Msgr. Lemaître was sentimentally attached to the Collège des Prémontrés, several of his group were delighted to move from the old attic on the Rue de Namur, where the E101 was located, a room without window, lighted with projectors and where the door had to be open to avoid overheating of the machine. The move resulted in a noticeable change in the working environment of the Laboratory for Numerical Research owing to the proximity of the teams of researchers who had important needs for numeri  G. Lemaître, “Monseigneur Georges Lemaître et les machines à calculer, Ciel et Terre, t.110, Juillet-août, no 4: 121. 11   Ibid. 10

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cal calculation. Jacques Masset who was present during the moving attested that12 “After one month the atmosphere is different, one can see a crowd of people performing computations. Priority is always given to Msgr. Lemaître, but during the dead time, physicists come to run their programs. Some of them even put up with being locked in the building during the night to use the machine”. The distance between Héverlee and the centre of Louvain, where he lived, explains why Lemaître began to be less present in his laboratory, which was being run by a technician, an assistant and Gilbert Lemaître, who was being drawn into computer science. He was responsible for driving his uncle between Louvain and Arenberg Park. Between 1963 and 1965, when the Canon came to Héverlee, something was recaptured of the old atmosphere of the Collège des Prémontrés, at the table of the cafeteria of the Institute of Nuclear Physics, in the company of de Hemptinne, Godart and assistants, and later of the one who became his successor in Louvain-la-Neuve, David Speiser. Msgr. Lemaître would help him compose a 26 page report in 1964-65 entitled Sur l’utilité d’une grande calculatrice en Belgique13 showing by his experience at MIT, ETH Zurich, etc., the necessity and great advantage of large computing facilities for the needs of fundamental and applied research. In the final two years of his life, his visits to Heverlee gradually trailed off. For health reasons, he was living in his apartment at 5 Ave­nue du Roi-Albert (now Dirk Boutslaan). Yet he continued to compute and to write programs for his machines. Gilbert Lemaître or Roger Weverbergh were in charge of bringing him the output of his programs every day. Visitors still came to meet with him in Louvain, among them Hubert Reeves in 1964. Reeves gave lectures that fall on stellar evolu  Oral communication, 15-12-1997.   One copy of this report (originally written in English) can be found at the AL. F. Cerulus, F. Buckens, J. Meinguet and J. Peters also provided information for his publication. R. Gastmans, A Verbeure and J. Weyers took care of the translation into Dutch and J.-P. Antoine translated into French. 12 13

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tion and nucleosynthesis at the Fondation Universitaire in Brussels at the invitation of Marcel Demeur, and took the opportunity to talk with Lemaître about the topics as well as Fred Hoyle’s cosmology. Lemaître was very kind but told him that he had never had any interest in nuclear physics. At the end of the visit, the Canon invited Reeves to listen to him playing Chopin on his piano.14

2. To oppose “The sin against the Holy Spirit”: the ACAPSUL George Lemaître had an unbounded attachment to his University, but also for his city of Louvain. They were, for him, inseparable and should remain so. Understandably, he looked askance both at the Flemish separatists as well as the “movers”, a group of French-speaking professors campaigning for the departure from Louvain. From Lemaître’s cosmopolitan world-view, he could not accept that in such a small country as Belgium, the two linguistic communities could not get along. Moreover, he could not understand the dissensions existing between Catholics and even between Belgian bishops. Lemaître was not insensitive to the Flemish claims. During his youth, he had campaigned in the late 1920s as a leader of a local group of the Amis de Jésus in Louvain for the complete integration of Flemish priests and to allow them to use their language15. During the First   H. Reeves, Je n’aurai pas le temps. Mémoires, Paris, Seuil: 160-163; the lectures “Evolution stellaire et nucléosynthèse” were edited, with the help of M. Crétin, G. Reidemeister and R. Vanden Borre (ULB) as a preprint, IISN, OCDE, Bruxelles, 1964. 15  Letter of Lemaître to Canon Fernand Willockx, general secretary of the “Amis de Jésus” dated 13-06-1929 (AFSAJ. Secrétariat I. Correspondance du secrétaire general avec les members II.): “It would be necessary to have a Flemish member who would have authority over all Flemish groups, exert real control on the bulletin in Flemish and would give directives following the Flemish spirit. It would be necessary that this leader of the Flemish groups be found. That would prove to the Flemish people who got into the Fraternity that they would have a direction consonant with their spirit and that they could feel at ease…It would be desirable that the directives open to the Flemish cause were given to the French speaking ‘Amis de Jésus’, for instance, the rigorous observation of the rule of languages using during the seminar, a sincere effort to learn Flemish….” (our translation). 14

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World War, he had a good friend strongly committed to the movement supporting the Flemish claims (the so-called Frontbeweging). But with time, he lost interest in this issue and was convinced that the coexistence of the two communities in Louvain would be best served by the “Verriest Model”, named after one of his fellow algebraist. This in fact was the model until the breakup of UCL: one university situated in Louvain, partitioned by language but with the faculty teaching in both sections. Nothing could be more ideal for a young Belgian than a large campus where he could experience the coexistence of two communities and develop a reciprocal open-mindedness to the other’s language and historical or cultural perspectives. Many generations already had experienced that richness. However, politics is rarely logical and one could not change history as one might change the hypothesis of a calculation. With his long history of international travel and his immersion in his own research, Lemaître could hardly be prepared to grasp all the dimensions of the local linguistic problem. In contrast to Jacques Leclerc, the other giant of UCL, Lemaître was not a political analyst. He had lived at the margin of public affairs and by the early 1960s had some difficulty understanding them precisely. Solely on the official declaration, made in the early 1960s by the bishops and politicians, who could have foreseen the dynamics that would determine the future of his alma mater16? With a certain naivety, to his credit, he could not have imagined that one could attack such a good example of national unity with a five hundred year history, nor take seriously those who already thought the cause to be lost, and who already saw the future of the institution elsewhere. In order to defend his university, on 13 February 1962, he consented to become the inaugural president of ACAPSUL17 (Association du Corps Académique et du Personnel Scientifique de l’Université de   See, for example, Christian Laporte, L’affaire de Louvain 1960-1968, Paris-Bruxelles, De Boeck Université. 1999, POL-HIS. 17  Among the most important members of ACAPSUL were two mathematician colleagues of Lemaître: Ballieu and Deprit (its secretary). Also included were his longtime friends Canon Jardin and his fellow Ami de Jésus, Canon Van Steenberghen. 16

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Louvain), the acronym being a pun in French, “CAPSULE” meaning a seal. This group in fact was independent of the institutional structures of UCL; its goal was the defence of the interests of the Frenchspeaking section of the University. Over the course of his presidency, his fits of temper became more frequent; UCL was a part of his soul and the separatists’ intent was for him a “sin against the Holy Spirit”, according to an expression later used by his friend Msgr. Massaux18. Everything opposing his struggles within ACAPSUL appeared to him treasonous, as was the Francophone initiative emerging independently of the Association. Pierre Arty, a great man of the theatre, his friend and that of his brother Maurice, had to countenance the prelate’s anger19. All he did was to suggest that Lemaître consider the possibility of the French-speaking professors to negotiate the departure of their section from Louvain, for which he was branded as a “dangerous man”. Lemaître’s rejoinder was simply “We have been in Louvain for five hundred years, we shall stay here for five hundred more years!” At its root, his fulminations were the symptom of a deep sadness, which he confided several times to his friend Fr. O’Connell and who would later relate it to Odon Godart20. To the defenders of the Walen buiten (“Wallons go away”), Msgr. Lemaître appeared more and more like the figurehead of a University which was already history to them. During a demonstration on the night of 28 February 1962, some extremists broke the windows on the first floor of the house where his apartment was21. He received   “This is the first time in world history that a university sacked another one, and this was done between Christians: This is for me was the great scandal; this is the sin against the Holy Spirit, the one that the Gospel says won’t be forgiven”, Msgr. E. Massaux, Pour l’université catholique de Louvain. Le “recteur de fer”. Dialogue avec Omer Marchal, Bruxelles, Didier Hatier, 1987: 33; our translation. 19   Oral communication, 31-05-1999. 20   Letter of Fr. O’Connell to Odon Godart dated 28-03-1968, preserved at the AL. 21   I refer here to Ch. Laporte, op. cit.: 100: “[…] the Flemish demonstrators were invited to go to the house of Msgr. Georges Lemaître, the President of ACAPSUL. Objective: to break the windows as a warning. Anecdotally, the damage was indeed done, but the stone throwers were mistaken and targeted the windows of the…. Flemish owners of the first floor and causing 3000 Francs (at that time!) of damage” (our translation). 18

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expressions of sympathy from both Belgian22 and foreign colleagues. He left a few days later for Mexico23 and the United States. Welcoming him in Berkeley with De Vogelaere, Jacques Peters would hear Msgr. Lemaître express his relief at escaping, for a while the Louvain atmosphere that was increasingly burdensome for him24. Msgr. Lemaître even hoped that someone would offer him a visiting professorship at Berkeley in order to escape the “Louvain problem”. The members of ACAPSUL never withdrew their confidence in Msgr. Lemaître. In the year he became Professor Emeritus, while Paul VI confirmed a fourth year mandate as the head of the Pontifical Academy on him, the ACAPSUL re-elected him unanimously as President25. This confidence did not relieve him from the heavy sadness that he harbored and that darkened the last years of his life. Nothing was as before, the “University of Verriest” was living its last moments. As Fr. O’Connell would remark in 1968, it was good that Msgr. Lemaître did not live to see what would happen later.

3. At the end of the “two paths" Apart from a hospitalization, “for a non-life threatening operation”26 and subsequent convalescence27, Lemaître had rarely needed a doctor. Nevertheless, on 8 December 196428, in his first year of becoming Pro  Cf. for example the postcard from P. Swings of the University of Liège, 14 May 1963. 23   He visited Vallarta in Mexico in March 1962 in order to work on the study week of the Pontifical Academy related to the cosmic rays. From there he went to Berkeley and later to Montréal in June. 24   Oral communication, 03-03-1999. 25   Cf. La libre Belgique, 21-06-1966. 26   Letter of Lemaître to Fr. Dockx, 24-12-1947 (Archives of the Académie Internationale de Philosophie). 27   In his notebook 1947-1953 (AL), 8 June 1949 is found this entry: “I was to some extent prevented from working on these various problems (galaxies clusters) by my trip to the clinic and long convalescence”. 28   Letter to Msgr. Dell’ Acqua, 27-01-1966 (AL). 22

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fessor Emeritus, he suffered a heart attack after his return from Rome, where he had attended the study week of the Pontifical Academy entitled “The Brain and Conscious Experience”. His recovery was slow. In 1965, his health improved a little29 but in order to avoid further heart complications, he was advised to follow a draconian food regimen30. In 1966, Lemaître was diagnosed with leukemia. On 9 June 1966, Msgr. Lemaître was transported to the Saint-Pierre university hospital in Louvain “after a heart attack combined with a blood illness”31. On Thursday the 16th or Friday the 17th, Odon Godart came to visit him with the news of the discovery of the Cosmic Microwave Background Radiation (CMB) by Penzias and Wilson32, the fossil radiation confirming the validity of the theory of an explosive beginning of the universe. Msgr. Lemaître finally had his “hieroglyphs” that bore witness to the initial state of the universe, just as he had predicted in 1931 (1931: 406). However, they were not the cosmic rays he had spent so much of his career studying.33 With emotion, Odon Godart recounted this final conversation with his friend one year after his death34: […] we had an hour long discussion on the most recent astronomical discoveries and their consequences for cosmological theories. Despite being very sick, he lucidly expressed his satisfaction regarding the discovery of a type of cosmic microwave radiation that seemed to confirm the idea of an explosive origin of the universe.

  Letter to Fr. de Riedmatten, 19-01-1966 (AL)   Testimony of J. Peters and L. Henriet, 03-03-1999. 31  Cf. La libre Belgique, 21-06-1966. 32   Cf. R.W. Wilson, “Discovery of the Cosmic Microwave Background” in Modern Cosmology in Retrospect (B. Bertotti, R. Balbinot, S. Bergia, A. Messina, eds.), Cambridge University Press, 1990: 291-307. 33  From the early 1960’s, Lemaître became deeply interested in space research, as attested to by several newspapers clippings that he had saved (AL). He was hoping that some satellite like Lunik could carry some detectors designed for his research on cosmic rays. The irony that a Soviet Lunik might one day confirm the theory of a Canon greatly amused him! 34   O. Godart, “Monseigneur Lemaître et son oeuvre”, Ciel et Terre, t. LXXXIII, MarchApril 1967, no 3-4: 57-86; our translation. 29 30

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On Sunday 19 of June, Charles Manneback came to visit him for the last time and a little while after, Msgr. Lemaître fell into a coma. Immediately, someone tried to inform the nearby French-speaking university parish, so a priest could give him the last rites. Msgr. Goosens, the parish priest was out at this moment and it was one of his assistants, Fr. Lemaire, a Jesuit, who was called to the bedside of the prelate35. By this time, the apostolic Nuncio, Msgr. Oddi had been informed, and came from Brussels, giving him the last rites and a special blessing from the Sovereign Pontiff. After having watched over him for several hours, Gilbert Lemaître witnessed the death of his uncle sometime in the night of Sunday to Monday 20 June. The funeral of Msgr. Lemaître would take place Friday 24 June at the “église de l’Annonciation” (Church of the Annunciation), seat of the French-speaking university parish. Owing to the traffic in Louvain that day, the coffin was brought to the church in the morning and Roger Weverbergh was assigned to stay at his side. Around 10:15, a professorial cortege led by the two vice-rectors of Louvain, Msgr. Massaux and Msgr. De Raeymaker, entered the church of the Annunciation preceded by two ushers. The Rector Magnificus, Msgr. Descamps, hospitalized that day, could not join the ceremony. Among the ecclesiastic personalities present one could note, among others, Msgr. Oddi (who took his place on a prie-dieu in the choir of the church) and the vicar-general of the diocese of Tournai. Nevertheless, no Belgian bishop made the trip. No document at our disposal explains this omission. It was clear that during this awkward period of the “Louvain problem”, the bishops might have considered that it was more diplomatic not to make a public appearance in this city.36 It is also likely that some bishops had not understood or got over the fact that the cosmologist had accepted the presidency of the ACAPSUL.   Oral communication of Fr. Lemaire, 04-10-1997.   One should also not forget the tension existing between the Flemish students and the bishops springing from the decisions concerning the University of Louvain in the early 1960s. The crisis of Louvain reached its peak in the years 1966-68. 35 36

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In the Church of the Annunciation where the family of the prelate were praying, several of his colleagues from UCL were present, notably Professors Dupriez, the new President of the ACAPSUL, and Bruylants, Dean of the faculty of sciences and who would pronounce the funeral oration. The Belgian press37 would also note the presence of the principal private secretary of the Minister of National Education, of the President of the University Foundation, as well as Professor Nicholson, representative of McGill University in Montreal (who had honoured Lemaître with the Ph.D. honoris causa), and the rector of the Facultés Notre-Dame de la Paix (Namur University) Fr. Boné. It was Msgr. Goosens, assisted by a deacon, who celebrated the funeral Mass on a small provisional altar in the choir of the church, in the modest liturgy of the post-conciliar renewal. Then, the funeral cortege took the direction of the “Pays Noir”, and after the celebration of the absolutions of death at 13:30 in the Church of Marcinelle, the body of Msgr. Lemaître was led to the cemetery of Marcinelle-Haies where his tomb is still prominent today. Monsignor had definitively rejoined the land of his ancestors and his birth. Perhaps it was also at this point where the ‘two paths’ that he had followed would finally intersect.

37

  Cf. for example the report in Le Soir, 25-06-1966.

Chapter XX

Msgr. Georges Lemaître: a  star that was without a  double (1962–1966)

I

f one approaches the life and work of Msgr. Lemaître or attempts a biography relying on isolated testimonies from reliable sources in contact with him in scientific circles at one moment of his career, one could be tempted to think that Lemaître was, like ‘his’ Molière, a double star. This does not mean to imply that behind the work of Lemaître, there would be found another author, even if the thought of Lemaître often emerged explicitly as an answer, a complement or in opposition to ‘another’ (Eddington, Silberstein, Hubble, Størmer, Heinrich,…). It simply means that the unique character of his work seems to manifest aspects so disparate that one could have the impression of a split personality, of the coexistence of two persons or two minds in one. Lemaître might then be a double star in two ways: at the level of his personal life with his religious convictions hermetically sealed off from his scientific activity, and at the level of this scientific work itself, in which his monumental cosmological research would be opposed to others which seemed more incidental or even frivolous. This biography strenuously argues that neither is the case. There was about the prelate of Louvain a deep unity between his personal life and his scientific work, which evidence and reflection will support.

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1. Unity of life There were not two Lemaîtres, one being the pious Amis de Jésus living from blind faith and the other one being the scientist indifferent to the religious questions as soon as he entered the door of his computer room of the Collège des Prémontrés. A superficial examination of his life might suggest he had problems with the ecclesiastical authorities or that he distanced himself somewhat from ecclesial institutions. In fact however, Lemaître was doing no more than showing a healthy freedom of spirit characteristic of scientists, and besides, all these ‘controversies’ concerned at most secondary aspects of ecclesiastical rules of discipline, which in any case have been long since been abrogated. Some may bring up the “Un’Ora problem”, which was certainly of a more fundamental nature. But this must be put into context of the atmosphere of questioning which existed at the time within some theological circles and the Curia itself after the publication of Humani Generis. Nevertheless, at no time did Lemaître’s esteem for the Holy Father weaken. His affection for the See of Peter was well known, particularly for the two successors of Pius XII: John XXIII and even more Paul VI. Never did he violate his special vow of obedience to his bishop he pronounced as one of the Amis de Jésus. Nevertheless, a healthy understanding of obedience does not mean subservience, but first listening intelligently and respectfully, involving one’s critical faculties and having a sense of humour. Lemaître was fully conscious of this, and explains why he could criticize the position of certain Belgian bishops regarding the “Louvain problem”, or poke fun of certain ecclesiastical publications, while never failing in his duties to the bishop, the pope or to his own priestly dignity. What is often missed is that Lemaître respected the differences of language between science and theology. Far from the concordist compromises that sought to derive the truths of faith from scientific results or denying the relevance of faith by an overconfidence in science, Lemaître insisted that science, and world it describes, have

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their own autonomy. He had experienced that concordism could only lead to a negation of the real transcendence of God or to an obscurantism blocking the exercise of reason. By defending the autonomy of science and cosmology in particular, he was defending the demythologization of the cosmos, consonant with the ad extra character of the universe expounded by Thomas Aquinas. In doing this, he was protecting the intellectual domain where astrophysicists of all philosophical and religious convictions could meet and exchange ideas, as envisioned by Pius XI and Fr. Gemelli in establishing the Pontifical Academy of Sciences. One can have a rational discussion on the merits and limits of Lemaître’s position, whether it adequately articulates the relationship between science and theology or not. But by no means is his position schizophrenic. The unity of professional and spiritual life cannot be situated on the level of ideas, but on the plane of action. Lemaître did not create a speculative theology demonstrating that science and faith harmonize. His actions spoke for themselves; he made no attempt to convince or compel anybone. He showed by his life, his state and his ecclesiastical garb that one can participate at the highest level to the advancement of science, to the search for truth of the physical world, without apologies “to make oneself the heart of a small child entering the kingdom of Heaven” (1936b: 70; our translation). But Lemaître’s discretion, so consonant with his idea concerning the Deus Absconditus of Isaiah, should not allow us forget the explicit apostolic component of his life. His activity on behalf of the ‘Chinese home’ for students in the 1920s, and in the Academic Committee for Chinese Students in the 1950s, prove that he never abandoned his humanist and religious commitments toward foreign students. Between computations on the inhomogeneous spherically symmetric universe, he would help them move into the Chinese house on the Rue des Joyeuses-Entrées. By his conviviality, solidarity and action he showed it was possible to build bridges between science and the faith, and live a unity of a life fully sacerdotal and scientific.

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2. Unity of work If Lemaître lived a unity of life, moreso did he live a unity of work. Here again there were not two Lemaîtres, the meteoric youth setting the agenda in the premier questions of all cosmology, and the other post-war veteran, puttering around in numerical diversions. The experience of the War clearly explains much of his isolation, his readings and tastes afterwards, but it would be erroneous to think that his work after 1945 was fruitless or disconnected from everything he had done before. To understand the work of Lemaître and its unity, one should analyze the manner in which the three pillars of his scientific thought – classical mechanics, general relativity and numerical analysis – are related to and mutually support one another. Before the Second World War, general relativity would play the dominant role in the elaboration of his cosmology. After the War, classical mechanics would take over; these two career epochs would never lose their grip on him, and would fuel his interest in numeral computation. We now consider the framework that gave unity to all his work. His study of general relativity would require him to analyze in depth, following Silberstein, the singularity that appears in some representations of de Sitter’s universe; this in turn would lead Lemaître to develop under Eddington’s inspiration, his model of a universe with spherical symmetry for his Ph.D. thesis at MIT. This model would be the root and starting point of Lemaître’s cosmology, encompassing the static universe of Einstein and the empty universe of de Sitter as special cases. It was only natural for him to seek a non-static universe as an interpolation between them. In the context of this universe with exponential growth, later called the Eddington-Lemaître universe having neither beginning nor end, Lemaître derived a Hubble’s Law concerning redshift that he had already dealt with in de Sitter space. What could be called today the “Hubble-Lemaître law” remains the central point of the (1927c) paper. His choice of universes with spherical symmetry was a fixed point of his work in cosmology. The three-dimen-

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sional sphere and elliptic geometries were good frameworks for his description of a space which was finite but boundless, fully intelligible to the mind. To more fully understand these geometrical models required that he delve deeply into the quaternions of Hamilton and Clifford parallelism. Indeed, the three dimensional sphere can be viewed as the set of unit norm quaternions. His interest for quaternions strengthened when interest picked up in the mathematics used in Eddington’s generalization of the famous Dirac equation: the quadriquaternions and the algebraic spinors. This in turn led to his study of the theory of Cartan’s spinors just after the Second World War. Lemaître’s model of the universe was already there in germinant form in his MIT thesis which would be published in part in his second fundamental paper (1933e). This would come to be called the “Lemaître-Tolman model” and has as particular cases the “internal” and “external” solutions of Schwarzs­ child. The elimination of the singularity of the de Sitter solution, by an insightful change of coordinates, led to the proof that the solution arising in the “exterior” field of Schwarzschild is only fictitious. This was the root of the theory of horizons that masks the true gravitational singularities existing at the centre of black holes. This was also Eddington’s idea, concerning what he called the “repugnant” concept of the origin of the universe, but which prompted the primeval atom hypothesis. This “atom universe” is described by Lemaître as the fundamental state from which the “hesitating spherical universe” expands, after a mysterious initial disintegration. In the beginning, the universe was an ‘atom’ and the unity of the world comes from that fact. The description of this universe that underwent a long quasi-static phase (resembling temporarily the static and instable universe of Einstein), requires a non-zero cosmological constant, which Lemaître would defend to Einstein until the end of his life, as an essential ingredient of relativity. Two lines of research would develop as a consequence of the primeval atom cosmology and of the hesitating universe, already identified by Lemaître between 1931 and 1933, but systematically developed from 1945 to 1963. One concerned cosmic rays and the other, the formation of galaxies and clusters.

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Lemaître believed that cosmic rays were the ‘hieroglyphics’ which encoded the history of the early universe following the disintegration of the primeval atom. Along with many scientists in the early 1930s, Lemaître made no real headway in understanding cosmic rays, his only paper on the subject being an attempt to explain the abundance of hydrogen from cosmic rays and which did not prove successful. Lemaître in fact was far afield from his area of expertise, and which would require a knowledge of quantum field theory and elementary particles physics that he would never possess. But if he did not deepen in his understanding of the nature of cosmic rays, he excelled however in the determination of their trajectories through the Størmer problem. This determination was not an interest of a purely theoretical nature. Here Lemaître was spectacularly successful in understanding the puzzling inhomogeneities in their distribution; his knowledge of classical mechanics and numerical methods, fed by Poincaré’s “Méthodes nouvelles de la mécanique céleste” did not fail him here. Cosmology was put aside, replaced by a research program where Lemaître revealed himself as a pioneer: the study of dynamical systems that would be only fully developed twenty or thirty years later. The study of the Størmer orbits and the “Leçons sur les invariants intégraux” of Cartan guided him through the analysis of the trajectories of the threebody problem, regularizing the binary collisions with a choice of coordinates that demonstrated his keen geometrical intuition. The second path related to Lemaître’s cosmology, was the study of galaxy and cluster formation, beginning again with the inhomogeneous model and spherical symmetry. Before the War, Lemaître would arrive at the possibility of spherical condensations made from the ashes of the primeval atom and constituting the seeds of galaxies and their clusters. After the War, he would study mechanistic models of galaxies and clusters, opening what Peebles has called the “Lemaître program” to explain large-scale cosmological structures from initial fluctuations, a program still current today. Lemaître’s study of cosmic ray orbits, the birth of galaxies or clusters, and his thesis research characterizing the variations of the

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central pressure in a sphere of constant invariant density, all involved enormous numerical computations. This led Lemaître to use and to program mechanical, electrical and electronic machines and also to invent new techniques of numerical analysis, such as the precursor of the Fast Fourier Transform. One of Lemaître’s mathematical warhorses, from his teachers Alliaume and de la Vallée Poussin, as well as his study of Gauss and Jacobi, were the elliptic functions. These appear in the solution of the Lemaître-Tolman equation, again in the Størmer problem and yet again in his research on clusters. His passion for computation, especially for mechanized calculation, led the Canon to the audacious idea of reforming arithmetic. Far from a mere diversion of a mathematician at the end of his career, his ideas proved strikingly resonant with the more recent studies in cognitive science and in neurophysiology, concerning the foundations of human computational ability. One thus sees all the dots connected from his early cosmology, even as he left general relativity behind for classical dynamical systems. The isolation of the War was an accidental circumstance, not a cause of this evolution. Lemaître would never be deflected from his model of hesitating universe, although general relativity would no longer prove useful to him, whereas classical mechanics emerged as the essential tool for his work on the Størmer trajectories. The isolation of the War and the opportunities for deep reading and reflection would only reinforce this reorientation of his efforts, which put him on the trajectory he followed to the end of his career. The great step in the Canon’s thought proceeded from a few powerful intuitions, among them the primeval atom hypothesis and its decay products. Nevertheless, as observed by Teilhard de Chardin, the primeval atom itself is banished from the field of physics1. It is   At least according to the physics of that time, because now we can conceive a primeval state of the universe that would be not described by space-time concepts, this primeval state being logically anterior to space and time (cf. S.-T. Yau, S. Nadis, The Shape of Inner Space. String Theory and the Geometry of the Universe’s Hidden Dimensions, New York, Basic Books, 2010: 307-320 chapter 14, “The end of geometry”). 1

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logically anterior to space-time and no method developed by Lemaître could characterize it. This explains the ‘fluctuations’ of his thought concerning the nature of this ‘primeval state’: singularity, ‘polyproton’, ‘polyneutron’, sphere of a certain radius… As in all great cosmological representations, such as those of Galileo or Laplace, the imagination underlying the theory went far beyond the mathematics capable of embodying it. Could this mental image fade away completely, leaving only a formal skeleton, without entirely eviscerating the whole impetus for the research? Mundus est fabula was the mantra of his cosmology, but one should not misinterpret this mantra: the fable is full of sense and the myth powerful in term of inspiration, in the same manner as Plato’s Timaeus, which stimulated the thought of Kepler, Galileo and even Heisenberg. It may be impossible to reach a rigorous description of nature without, at some point, ‘telling a story’, just as it is impossible to be completely serious by never laughing, as Alphonse Allais would have said. Lemaître perfectly embodied this. More than anyone he had the capacity to tell a story in order to make things understandable and the propensity to laugh in a booming and unforgettable manner, even facing the most serious and daunting questions. If one can discover a unity in the content of Lemaître’s work, one can also observe a unity of the form, something from Lemaître’s unique style. One could characterize it by saying that in his work ‘the numerical experience’ or the ‘manipulation of formulas’ in particular cases where ‘something happens’ preceded the rigorous, structural and synthetic textual editing. This was congruent with his pragmatic relationship to mathematics and his manner of teaching. The Canon relished solving small problems, analyzing them from all angles, pushing them to their limits, precisely where the ordinary prudence of the mathematician would not venture beyond. The resoluTeilhard considered the primeval atom along with his Omega point as “meta-empirical” concepts. Lemaître had always considered his primeval atom as a purely physical state and he would be not surprised today by a “physics without space and time”.

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tion of the literary enigma of the “pair of Molières” must be situated in the same vein. But if this method has proven fruitful in Lemaître’s case, it is because he combined it with a phenomenal gift for arithmetic and algebra, and an exceptional geometrical intuition that allowed him to discern well in advance which would be the fruitful paths and to avoid those which would lead nowhere. Lemaître’s style was fruitful only because he was Lemaître, and his research style did not always carry over well into his pedagogy. Nevertheless, what is more fruitful than to forge a young mind in the ways of research, seeing in real time a mind in progress, in activity? From this angle, his style certainly helped provoke many scientific vocations, though his students in the classroom often tore their hair out. One can then see that this ‘star’ was not at all binary, yet have we been able to adequately compass it? The aim of this work would be complete if, at the end of these pages, other budding astronomers, forgetting these lines, would decide to turn their telescopes toward this ‘star’ to draw some new and stimulating ideas for their research, their reflections, their life…

Postscript

ATV-5, the Georges Lemaître

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uring the night of 29 July 2014 (23:44 GMT), the Automated Transfer Vehicle 5 (ATV-5), the Georges Lemaître, was launched from the Guiana Space Centre in Kourou, French Guiana, on behalf of the European Space Agency. The 6.6-tonne craft, lifted 420 km into orbit by an Ariane 5ES rocket, was the 5th and final ATV launched by ESA to provision the International Space Station with fuel, water, air and cargo. The spectacular nighttime launch came off flawlessly, and the Georges Lemaître executed a perfect docking with the ISS on 12 August 2014, a fitting tribute to the hapless artillery adjutant who was once disciplined by his Commanding Officer during the First World War over a question of ballistics! Even more fittingly, Lemaître joined the ranks of the other transcendent “stars” of European and world science after whom the first four ATV’s were named, in order: Jules Verne, Johannes Kepler, Edoardo Amaldi, and Albert Einstein. In particular, the conjunction of ATV-4, the Albert Einstein, launched on 5 June 2013, and ATV-5 the Georges Lemaître would have met with approval of both cosmologists who had happily traveled around the world together once before, some 80 years earlier.

Michael Heller Vatican Observatory Pontifical Academy of Sciences

Afterword

When should one stop doing cosmology and turn to calculations?

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fter reading Dominique Lambert’s book, it is hard to add something substantial to his account of Lemaître’s cosmological views, scientific legacy, or philosophical and theological ideas, nor is this my aim in writing these final remarks. I would rather like to share with the reader some reflections concerning the way in which cosmology should be conducted and which has been inspired by Lemaître himself. Today Lemaître is commonly acknowledged as the father of the Big Bang theory of the universe. Helge Kragh, the renowned historian of cosmology, admits that this is justified by the number of similarities between Lemaître’s “audacious hypothesis that the entire universe had come into being a finite time ago in a cataclysmic explosion” and the contemporary vision of the beginning of the present phase of cosmic evolution. However – he continues – “this does not imply that our present conception of the universe can be traced back to his work in some direct way”.1 Kragh remarks that if we do not read the history of cosmology backwards by adapting it to our present standards but rather place ourselves in the context of Lemaître’s epoch, then we could see that his work had a relatively small impact on further develop­ments in   See, H. Kragh, “‛The Wildest Speculation of All’: Lemaître and the Primeval-Atom Universe”, in: Georges Lemaître: Life, Science and Legacy, ed. by R.D. Holder, S. Milton, Springer, Heidelberg – New York – Dordrecht – London, 2012, pp. 23-38. 1

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cosmology. In Kragh’s view, “this was basically justified, simply because Lemaître’s theory was not scientifically convincing in its original formulation”.2 If this is so, the question can be asked: is it not purely a matter of chance that our present image of cosmic evolution, in its general lines, coincides with Lemaître’s speculations? We should agree with Kragh that Lemaître’s Primeval Atom hypothesis has had no direct influence on research in cosmology, but this is not true as far as his other theoretical works are concerned. For instance, the result of his paper in which he demonstrated that the de Sitter solution describes empty and expanding space-time by introducing suitable coordinates, soon became standard; his 1927 paper discussing the logarithmic solution to Einstein’s equations (which helped him to deduce Hubble’s eponymous law before he did) suggested to Eddington the proof that the Einstein static solution was unstable; and the fact that the now standard cosmological solutions are called Friedman-Lemaître solutions (sometimes Friedman-LemaîtreRobertson-Walker solutions) is telling in itself. It is true that some of Lemaître’s results were later, but independently, obtained by others and only afterwards ascribed also to him, but we should not forget that in this pioneering period something similar quite often happened to other scientists as well. Lemaître himself was partially responsible for the fact that his Primeval Atom hypothesis, after initially arousing interest amongst a general audience (more so in the United States than in Europe), played rather marginal role in the scientific milieu. In the second part of his active life, he isolated himself in Louvain, having rather sporadic contact with other fellow cosmologists. He never created his own research group and had no students who would continue and develop the work of their master. He refused to get in touch with the Gamow group in order to confront his conceptions with the rapidly developing particle physics. Finally, when the steady-state model began to gain popularity, he completely cut off his contact with mainstream cosmology. 2

  Ibid., p. 24.

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All of these facts cannot be denied and should be taken into account when evaluating Lemaître’s achievements from the historical point of view. I think, however, that his real significance as far as doing cosmology is concerned consists in something else. The General Theory of Relativity has an undeniable mathematical beauty, and its cosmological applications provide a field in which one can demonstrate one’s mastership in dealing with mathematical structures. For many scientists this is a sufficient motive for working in cosmology. This was especially true in the first decades of the development of relativistic cosmology when the paucity of empirical data with cosmological significance was hardly a concurrence for purely theoretical work. Lemaître was a mathematician by training and there is rich evidence that he took great pleasure in doing mathematics – indeed, at the end of his life he completely switched to numerical calculations. However, quite early, probably through his contacts with Canadian and American astronomers, he understood that if cosmology had to be a science then it had to change into a physics of the universe. This could be done in two steps. First, one had to choose the option that best approximates the structure of our universe from among a manifold of available solutions to the Einstein equations or at least to identify a class of such solutions; secondly, to fill in this solution (or this class of solutions) with the physical processes that led to the evolution of our universe from the very beginning to the present epoch. This constituted for Lemaître a program which he, at least in 1927, tried to implement. In his time there were only a few empirical hints that would help him in this enterprise, but he utilised them with great ingenuity. Red shift measurements, data concerning the age of the universe, inputs from thermodynamics and quantum physics, attempts to identify cosmic rays as remnants of a disintegration of the Primeval Atom – all of these effects found their place in Lemaître’s cosmological scenario. Today we know vastly more about the structure of the universe and its contents and it is no wonder that the Lemaître model can be viewed as only a precursor of the contemporary image of the world.

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It is now commonly agreed that the main criterion for a theory or model to be regarded as a part of science is its relation to experimentation. If a theory or model makes some predictions that can be confronted with experimental results, they have the right to be classed as scientific; if no such predictions follow, they do not belong to science. The precise meaning of this criterion is subject to extensive debate among philosophers of science, but by the great majority of working scientists it is believed to be the corner-stone of the scientific method. Many of them would add to it the criterion of mathematical elegance and simplicity. It is, of course, difficult, if not impossible, to formalize this aesthetic criterion, but for some theoreticians it is no less important than agreement with empirical results. Einstein was used to speak about an “inner perfection” of a theory and, as long as his own conceptions did not attain this state of perfection, he looked for others. I would augment these two criteria with a third one, often overlooked by philosophers but no less important that the other two – the criterion of the organic unity with the rest of physics. It says that no theory is fully scientific unless it enters into interaction with other physical theories in such a way that without it other physical theories would lose something of their theoretical utility. Nobody doubts that classical mechanics or relativity theory are scientific theories and, indeed, without any of them contemporary physics would be unthinkable. They are organic parts of the body of physics and something similar happens where cosmology is concerned. When Hoyle led battles with Lemaître against the “violent beginning of the universe”, cosmology was in fact an exotic conception on a margin of physics. Today cosmology provides a backdrop against which other physical theories may develop. Without this backdrop they would merely hang in the air. Our theoretical ideas concerning the synthesis of chemical elements, the evolution of stars and galaxies, the interpretation of microwave background radiation are first among the most obvious examples of the strong links between physics and cosmology. Without any help from cosmology these problems, and many others as well, could not even be correctly formulated. Needless to say, this depend-

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ence is reciprocal and there is hardly a department of physics in the world that is not be employed in the service of cosmology. The thread leading from cosmology as a marginal speculation to cosmology as an organic component of modern physics certainly leads through Lemaître’s work. There is yet one more lesson that we should learn from Lemaître. After overcoming some concordistic tendencies in his early years, Lemaître was keen to keep his philosophical and theological convictions separate from his scientific work. This of course does not mean that he had no such convictions; he had them and was firmly attached to them, but he strived to prevent them from biasing his cosmological theories. He tried to formulate them in such a way that they would be acceptable for “materialists” and “believers” 3 alike. Unfortunately, today this attitude towards the realm of speculations is to a large extent forgotten. Many ideas, such as brane worlds and the so-called landscape of the string theory, manifold versions of cyclic universes, the Everett quantum multiverse, various anthropic principles, the universe as a computer simulation, and quite a number of other highly speculative ideas are often presented to a disoriented reader of popular books as almost the last word in cosmology. Some of these ideas are interesting and ought to be discussed, but their methodological status should always be clearly displayed. It is, of course, a matter of guesswork to speculate as to how Lemaître would react to such ideas. However, we have a hint: when the steady-state propaganda was on the increase, he simply stopped doing cosmology and turned to his old passion – numerical calculations. I do not recommend this attitude. While Lemaître was on his deathbed, microwave background radiation was discovered and cosmology assumed a totally new turn.

  Lemaître’s own formulation from his “The Primaeval Atom Hypothesis and the Problem of the Clusters of Galaxies”, in: La structure et l’evolution de l’univers, R. Stoops, Bruxelles, 1958, p. 7. 3

Bibliography of Msgr. Georges Lemaître1

1921a. “Les trois premières paroles de Dieu” in Mgr Georges Lemaître savant et croyant. Actes du colloque tenu in Louvain-la-Neuve le 4 novembre 1994, followed by “La physique d’Einstein”, unpublished text of Georges Lemaître (J.-F. Stoffel, ed.) Louvain-la-Neuve, Centre interfacultaire d’étude en histoire des sciences, 1996, Réminisciences 3: 145-175. 1922a. “La physique d’Einstein”, in Mgr Georges Lemaître, op. cit.: 223360. 1922b. “Note signalant les points du mémoires ‘La physique d’Einstein’ qui sont originaux en quelques manières’’ in Georges Lemaître, op. cit.: 20-21. 1923a. “Sur une propriété des hamiltoniens d’un multiplicateur” (note introduced by Th. De Donder during the meeting of 4 August 1923) Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. IX, 1923, no 7-9: 380-388. 1923b,* “Sur une propriété des hamiltoniens d’un multiplicateur” in Geor­ ges Lemaître et l’Académie royale de Belgique: Oeuvres choisies et notice biographique (preface by Ph. Roberts-Jones), Brussels, Académie royale de Belgique, 1995: 25-33, Mémoires de la Classe des sciences, 3e série, t. X.   The symbol “*” means a republication. The reader may also refer to the bibliography provided in: Mgr Georges Lemaître savant et croyant. Actes du colloque tenu à Louvain-la-Neuve le 4 novembre 1994, followed by La physique d’Einstein, unpublished text of Georges Lemaître (J.-F. Stoffel, ed.) Louvain-la-Neuve, Centre interfacultaire d’étude en histoire des sciences, 1996, Réminisciences 3: 145-175. 1

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1924a. “The motion of a rigid solid according to the relativity principle” (sent with a brief introduction by A.S. Eddington), Philosophical Magazine, Vol. XLVIII, July 1924: 164-176. 1925a. “Note on de Sitter’s universe” (summary of the lecture given during the 133rd conference of the American Physical Society held in Washington on 24-25 April 1925), The Physical Review, 2nd series, Vol. XXV, June 1925, no 6: 903. 1925b.* “Note on de Sitter’s universe”, Harvard College Observatory, March 1925, no 17: 37-41. 1925c. “Note on de Sitter’s universe”, Journal of Mathematics and Physics, Vol. IV, May 1925, no 3: 188-192. 1925d. “Note on the theory of pulsating stars”, Harvard College Observatory, Circular no 282, 10 May 1925, 6 pages. 1926a. “La théorie de la relativité et l’expérience” (lecture given on Monday 12 April 1926 in Brussels during the session of the fiftieth anniversary of the Scientific Society), Revue des questions scientifiques, 45e année, t. LXXXIX (4e série, t. IX) avril 1926: 346-374. 1926b.* “La théorie de la relativité et l’expérience”, in Pour découvrir ou redécouvrir Georges Lemaître: Quelques textes de Georges Lemaître parus dans cette revue (introduction of D. Lambert), Revue des ques­ tions scientifiques, t. CLXVI, 1995, no 2: 115-138. 1926c. “Compte rendu de G. Juvet: ‘Mécanique analytique et théorie des quanta’ (1926)” Revue des questions scientifiques, 45e année, t. XC (4e série, t. X), 20 juillet 1926: 210-211. 1927a. “Compte rendu de F. Gonseth: ‘Les fondements des mathématiques’ (1926)” Revue des questions scientifiques, 45e année, t. XCI (4e série, t. XI), 20 janvier 1927: 195-197. 1927b. “À propos d’une note du P. Schaffers sur la relativité” (séance du 27 janvier 1927, 2e section), Annales de la Société scientifique de Bruxel-

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Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 125129, Mémoire de la classe des sciences, 3e série, t. X. 1949g. “The cosmological constant”, in Albert Einstein: Philosopher-Scientist (P.A. Schilpp ed.), Evanston IL, The Library of Living Philosophers, 1949: 439-456, The Library of Living Philosophers, 7, 1949: 439-456. 1950a. “Application des méthodes de la mécanique céleste au problème de Størmer” (session of 27 April 1950, 3rd section), Annales de la Société scientifique de Bruxelles, série 1: sciences mathématiques, astronomiques et physiques, t. LXI, 2 juin 1949, no 2: 83-97, Ière partie: comptes rendus des séances, t. LXIV, 22 juin 1950, no 1-2: 76-82. 1950b. “Compte-rendu de P. Couderc: ‘L’expansion de l’univers’ (1950)”, Annales d’astrophysique, t. XIII, 1950, no 3: 344-345. 1950c. “L’univers”, Louvain, E. Nauwelaerts, 1950, 72 pages, causeries de l’Université radiophonique internationale, Paris, 1950. 1950d. “Laplace et la mécanique céleste” (lecture given on 6 November 1949 under the sponsorship of de Société astronomique de France), L’astronomie, t. LXIV, 1950: 23-31. 1951a. “Modèles mécaniques d’amas de nébuleuses” (session of 7 April 1951), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XXXVII, 1951: 291-306. 1951b. “Modèles mécaniques d’amas de nébuleuses”, in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 131-146, Mémoire de la classe des sciences, 3e série, t. X. 1952a. “Clusters of nebulae in an expanding universe”, Monthly Notes of the Astronomical Society of South Africa, Vol. XI, 1952: 110-117. 1952b. “Coordonnées symétriques dans le problème des trois corps (I)” (session of 7 June 1952), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XXXVIII, 1952: 582-592.

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1952c.* “Coordonnées symétriques dans le problème des trois corps”, in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 147-158, Mémoire de la classe des sciences, 3e série, t. X. 1952d. “The Clusters of Nebulae in the Expanding Universe” (paper read in July 1952 in section A of the South African Association for the Advancement of Science in Cape Town), South African Journal of Science, Vol. XLIX, October-November 1952, no 3-4: 80-86. 1952e. “Coordonées symétriques dans le problème des trois corps (II)” (session of 13 December 1952), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XXXVIII, 1952: 1218-1234. 1952f.* “Coordonées symétriques dans le problème des trois corps”, in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 159-175, Mémoire de la classe des sciences, 3e série, t. X. 1954a. “Calculons sans fatigue”, Louvain, E. Nauwelaerts, 1954, 41 pages. 1954b. “Comment calculer?”, Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XL, 1954: 683-691. 1954c.* “Comment calculer?”, in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 177-184, Mémoire de la classe des sciences, 3e série, t. X. 1954d. “Régularisation dans le problème des trois corps” (session of 3 August 1954), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XL, 1954: 759-767. 1954e.* “Régularisation dans le problème des trois corps”, in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 185-194, Mémoire de la classe des sciences, 3e série, t. X.

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1955a. “Réunion intime en l’honneur du chanoine G. Lemaître à l’occasion de la remise de son buste à la classe: réponse du chanoine Lemaître” (session of 5 February 1955), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XLI, 1955: 77. 1955b. “Pourquoi de nouveaux chiffres?”, Revue des questions scientifiques, 68e année, t. LXXXIX, 5e série, t. XVI, 20 juillet 1955: 379-398. 1955c.* “Pourquoi de nouveaux chiffres?”, in Pour découvrir ou redécouvrir Georges Lemaître: quelques textes de Georges Lemaître parus dans cette revue (introduction of D. Lambert), Revue des questions scientifiques, t. CLXVI, 1995, no 2: 139-158. 1955d. “Compte rendu de H. Bondi: ‘cosmology’ (1952)”, Revue des questions scientifiques, 68th année, t. CXXXVI, 5e série, t. XVI, 1955: 584. 1955e. “Compte rendu de C. Payne-Gaposchkin: ‘Introduction to astronomy’ (1954)”, Revue des questions scientifiques, 68e année, t. CXXXVI, 5e série, t. XVI, 1955: 584. 1955f. “Compte rendu de E.A. Milne: ‘Modern Cosmology and the Christian Idea of God’ (1951)”, Revue des questions scientifiques, 68e année, t. CXXXVI, 5e série, t. XVI, 1955: 585. 1955g. “Compte rendu de E. Whittaker: ‘Eddington’s Philosophy of Science’”, Revue des questions scientifiques, 68e année, t. CXXXVI, 5e série, t. XVI, 1955: 585. 1955h. “L’Oeuvre scientifique d’Albert Einstein” (lecture given on 14 June 1955 during the evening organized as an initiative of the Belgian Office of the World Jewish Congress in honor of A. Einstein), Revue des questions scientifiques, 68e année, t. CXXXVI, 5e série, t. XVI, 20 octobre 1955: 475-487. 1955j. “Regularization of the three-body problem”, Vistas in Astronomy, Vol. I, 1955: 207-215. 1956a. “Intégration par analyse harmonique” (session of 19 April 1956, Ie section), Annales de la Société scientifique de Bruxelles, série 1:

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sciences mathématiques, astronomiques et physiques, t. LXX, 17 août 1956, no 2: 117-123. 1956b. “Le calcul élémentaire” (session of 8 December 1956), Bulletin de la classe des sciences de l’Académie royale de Belgique, 5e série, t. XLII, 1956: 1140-1145. 1956c.* “Le calcul élémentaire” in Georges Lemaître et l’Académie royale de Belgique: Oeuvres choisie et notice biographique (preface by Ph. Robert-Jones), Bruxelles, Académie royale de Belgique, 1995: 195200, Mémoire de la classe des sciences, 3e série, t. X. 1958a. “Instability in the expanding universe and its astronomical implications” in Semaine d’étude sur le problème des populations stellaires: Rome, 20-28 mai 1957, In Civitate Vaticana, Pontificiae Academiae scientiarum, 1958: 475-486, Pontificiae Academiae scientiarum scripta varia, 16. 1958b.* “Instability in the expanding universe and its astronomical implications”, in Stellar populations: Proceedings of the Conference Spon­ sored by the Pontifical Academy of Sciences and the Vatican Obser­ vatory, 20-28 May 1957 (D.D.K. O’Connell, ed.), Città del Vaticano, Specola Vaticana, 1958: 475-486, Ricerche astronomiche, 5. 1958c.* “Instability in the expanding universe and its astronomical implications”, in L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à l’occasion du cinquième anniversaire de sa mort, In Civitate Vaticana, Pontificia Academia scientiarum, 1972: 207-219, Pontificiae Academiae scientiarum scripta varia, 36. 1958d. “Rencontre avec A. Einstein” (Program on the Belgian National Radio 27 April 1957 on the occasion of the second anniversary of the death of Albert Einstein), Revue des questions scientifiques, 68e année, t. CXXIX, 5e série, t. XIX, 20 janvier 1955: 129-132. 1958e.* “Rencontre avec A. Einstein” Pour découvrir ou redécouvrir Georges Lemaître: Quelques textes de Georges Lemaître parus dans cette revue (introduction of D. Lambert), Revue des questions scientifiques, t. CLXVI, 1995, no 2: 159-164.

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1958f. “The primeval atom hypothesis and the problem of the clusters of galaxies”, in La structure et l’évolution de l’univers. Rapports et discussions. IIe Conseil de physique held at the Université of Bruxelles du 9 au 13 June 1958, Brussels, R. Stoops, 1958: 1-25 (discussion: 26-31). 1958g.* “L’hypothèse de l’atome primitif et le problème des amas de galaxies: rapport présenté par Georges Lemaître au 11e conseil de physique de l’Institut international de physique de Solvay, juin 1958”, in 1946e: 1-35 (supplement). 1958h. “Contribution au problème des amas de galaxie” (with A. Bartholomé; session of 30 October 1958, Ist section), Annales de la Société scientifique de Bruxelles, série 1: sciences mathématiques, astronomiques et physiques, t. LXXII, 20 décembre 1958, no 3: 97-102. 1960a. “L’étrangeté de l’univers” (lecture given 8 April 1960), in La scuola in Azione, Varese, Multa Paucis, 1960: 3-22, Notiziaro per gli allievi, 15. 1960b.* “L’étrangeté de l’univers”, La revue générale belge, t. XCVI, juin 1960: 1-14. 1961c.* “L’étrangeté de l’univers”, in Un nouveau système de chiffres et autres essais (preface of M. Boldrini), Varese, Multa Paucis, 1961: 2741, Scuola di studi superiori sugli idrocarburi dell’Ente nazionale idrocarburi, Quaderni, 10. 1961a. “Remarques sur certaines méthodes d’intégration des systèmes d’équations différentielles”, in Colloque sur l’analyse numérique held in Mons on 22-24 March 1961, Paris / Louvain, Librairie Gauthier-Villars / Librairie universitaire, 1961: 9-23, Centre belge de recherche mathématiques. 1961b. “Un nouveau système de chiffre”, in Un nouveau système de chiffres et autres essais (preface by M. Boldrini), Varese, Multa Paucis, 1961: 11-26, Scuola di studi superiori sugli idrocarburi dell’Ente nazionale idrocarburi, Quaderni, 10. 1961c.* “Un nouveau système de chiffre”, in L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à l’oc-

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casion du cinquième anniversaire de sa mort, In Civitate Vaticana, Pontificia Academia scientiarum, 1972: 257-273, Pontificiae Academiae scientiarum scripta varia, 36. 1961d. “Les rayons cosmiques”, in Un nouveau système de chiffres et autres essais (Foreword by M. Boldrini), Varese, Multa Paucis, 1961: 43-57, Scuola di studi superiori sugli idrocarburi dell’Ente nazionale idrocarburi, Quaderni, 10. 1961e. “Exchange of galaxies between clusters and field”, The Astronomical Journal, Vol. LXVI, December 1961, no 10: 603-606. 1962a. “Nim ou Pythagore?” (lecture given on 26 June 1962 at the Chamber of Commerce for Belgium and Luxembourg in Canada), Chamber of Commerce for Belgium and Luxembourg in Canada, 1962, no 1112: 5-8. 1962b. “Charles-Jean de la Vallée Poussin” (eulogy pronounced on 4 October 1962 during the plenary session of the Pontifical Academy of Sciences), Pontificiae Academiae scientiarum commentarii, t. I, 1962, no 8: 1-4. 1962c.* “Charles-Jean de la Vallée Poussin”, in L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à l’occasion du cinquième anniversaire de sa mort, In Civitate Vaticana, Pontificia Academia scientiarum, 1972: 281-284, Pontificiae Academiae scientiarum scripta varia, 36. 1963a. “Howard Percy Robertson” (1903-1961), in The American Philosophical Society: Year book 1962 (January 1, 1962 – December 31, 1962), Philadelphia, The American Philosophical Society, 1963: 164-168. 1963b. “The Three-Body Problem”, Berkeley, University of California, 1963, 40 pages, Space Sciences Laboratory, Technical Report Series, 4, Vol. 49. 1965a. “Code machine symbolique pour la calculatrice NCR-Elliott 802”, Louvain, Laboratoire de recherche numérique, mai 1965, 25 pages.

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1965b. “Emploi des routines classiques dans le code machine symbolique pour calculatrice NCR-Elliott 802”, Louvain, Laboratoire de recherche numérique, 1965, 29 pages. 1967a. “A.V. Douglas”, Journal of the Royal Astronomical Society of Canada, Vol. LXI, 1967: 77-80. 1967b. “L’expansion de l’univers: réponse à des questions posées par Radio Canada le 15 avril 1966”, Revue des questions scientifiques, t. CXXXVIII, 5e série, t. XXVIII, avril 1967, no 2: 153-162, (version edited and adapted by O. Godart). 1967c. “L’expansion de l’univers” in Pour découvrir ou redécouvrir Georges Lemaître: Quelques textes de Georges Lemaître parus dans cette revue (introduction by D. Lambert), Revue des questions scientifiques, t. CLXVI, 1995, no 2: 165-174. 1967d. “Le principe de continuité d’après Jean-Victor Poncelet”, Revue des questions scientifiques, t. CXXXVIII, 5e série, t. XXVIII, juillet 1967, no 3: 381-395. 1967e. “Le principe de continuité d’après Jean-Victor Poncelet”, in Pour découvrir ou redécouvrir Georges Lemaître: Quelques textes de Georges Lemaître parus dans cette revue (introduction by D. Lambert), Revue des questions scientifiques, t. CLXVI, 1995, no 2: 175-224. 1972a. “L’étrangeté de l’univers” (lecture delivered 8 January 1960 at Circolo di Roma), in L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à l’occasion du cinquième anniversaire de sa mort, In Civitate Vaticana, Pontificia Academia scientiarum, 1972: 239-254, Pontificiae Academiae scientiarum scripta varia, 36. 1972b. “Les rayons cosmiques et l’univers” (lecture delivered 14 February 1961 at the Gregorian University) in L’Académie pontificale des sciences en mémoire de son second président, Georges Lemaître, à  l’occasion du cinquième anniversaire de sa mort, In Civitate Vaticana, Pontificia Academia scientiarum, 1972: 223-237, Pontificiae Academiae scientiarum scripta varia, 36.

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1978a. “Un travail inconnu de George Lemaître: ‘L’univers, problème accessible à la science humaine’” (text from a lecture given by Lemaître at the Institut Catholique de Paris, written around 1950, introduction by O. Godart and M. Heller), Revue d’histoire des sciences, t. XXXI, octobre 1978, no 4: 345-359. 1985a. “The Expanding Universe: Lemaître Unknown Manuscript” (introduction by O. Godart and M. Heller), Tucson, Pachart Publishing House, 1985, 50 pages, History of Astronomy Series, 2. 2012. “La théorie de l’atome primitif a 80 ans” (edition with introduction of all papers published by G. Lemaître in the Revue des Questions Scientifiques, edited by G. Demortier and D. Lambert), Revue des Questions Scientifiques, t. 183, 2012, no 4. 2013. “Une paire de Molière(s)” (conferences of G. Lemaître about Molière; edition and introduction by D. Lambert and J.-F. Viot), Bruxelles, SAMSA, Académie Royale de Langue et de Littérature Françaises, 2013, Collection Histoire Littéraire.

Index of Persons

Aikman D.: 42, 44, 210-211 Albert Ier: 99, 133, 269 Albert A.: 181, 233 Allaer J. (Canon): 67, 69-70, 72-74, 98100, 168, 276, 344, 351 Alliaume M.: 51-52, 62-64, 66, 75, 78, 82, 183, 285, 290-291, 313, 319, 425 Antoine J.-P.: 16, 239, 410 Arty P.: 18, 413 Aubert R. (Canon): 17

Bouckaert L.: 254-255, 258, 260, 318, 392 Bourbaki N.: 49, 221, 232, 235-236, 239, 355 Brillouin L.: 123, 319 Bris I.: 31 Broucke R.: 16, 237-239, 269 Brohée A.: 168-169 Buckens F.: 410 Budinich P.: 222 Bruylants P.: 24, 183, 417 Bush V.: 250, 316

Ballieu R.F.: 286, 299, 318, 408, 412 Barbier D.: 139 Bartholomé A.: 16, 26, 75, 305, 311, 318, 320-321, 405, 408 Baudouin Ier: 269 Belzer J.: 304 Berger A.: 15, 25-26, 28, 47, 264, 329, 360 Belpaire Th.: 76 Berenda W.: 379 Billiauw J. (Msgr.): 17, 69, 74 Birkeland K.: 246-247, 252 Birkhoff G.: 233 Bloy L.: 58 Boigelot R. (S.J.): 382 Boland A.: 167-173 Bondi H.: 106, 187, 336, 340 Bonnor W.B.: 307-308 Borel E.: 290 Bosmans H. (S.J.): 43-44, 63, 272, 288, 297, 389 Bossy L.: 15, 27, 75, 79, 249, 255, 258, 261, 309, 316, 356

Carter B.: 194 Clay J.: 245, 252 Cameron H.: 143-144, 241 Cammaert F. (Msgr.): 29, 75 Capron P.: 177 Cartan E.: 6, 96, 229, 234-239, 270-271, 282, 296, 322, 328-330, 423-424 Caupain A.: 17, 61, 75, 169, 209, 221, 276, 278, 280 Cerulus F.: 16, 410 Charue A.-M. (Msgr.): 71, 334 Chevalley C.: 231, 235-236, 330 Claudel P.: 94, 376 Clifford W.K.: 208, 227-229, 231-232, 236-237, 276, 423 Couderc P.: 117, 139-140 Cox J.: 18, 121, 268 Courtoy Ch. (S.J.): 16, 45, 177-178, 279, 294, 374 Curtis H.D.: 115, 118 De Baleine Ph.: 348 de Callatay X.: 18, 295

460 De Donder Th.: 63, 75, 78, 80, 82-83, 93, 108, 117, 122, 133, 189, 223224, 226, 268, 270-271, 274 Dehaene S.: 402-403 de Hemptinne M.: 94, 166, 175-177, 280, 321, 408-410 Dejaiffe R.J.: 16, 28, 30, 44, 57, 220, 322-323, 329, 354 Delaunay Ch. E.: 259-260, 291-292, 326, 407 De la Vallée Poussin Ch.: 17, 47-49, 52, 64-66, 76-77, 96, 98-100, 111, 122, 171, 285-289, 313-314, 367, 425 Delfosse J.M.: 175, 177, 408 Dell’Acqua A. (Msgr.): 349, 357, 361362, 364 Delmer M.: 16-17, 220, 343-344, 348 Deltheil R.: 290 de Maere Th.: 17-18, 269 Demaret J.: 15, 127, 194 Demeure A.: 393 Demeure Ch.: 18, 393 de Meurs Ch.: 17 Demoulin J.-P.: 18, 383, 386 Descamps A. (Msgr.): 241, 248-249, 258, 416 d’Ocagne M.: 63, 288 Dockx S. (O.P.): 18, 51, 139-140, 274, 319, 371, 414 Deprit A.: 16, 26, 30, 47-48, 51, 53, 55, 75, 92, 94, 117, 175, 239, 252, 255, 286, 289, 312, 316, 321-322, 326-330, 348-349, 351, 355-356, 360, 405, 407, 412 de Riedmatten H. (O.P.): 364-365, 415 Descartes R.: 289, 346, 379 de Sitter W.: 10, 81, 88, 95, 101-107, 109, 116, 119, 123-126, 130-133, 135137, 151, 160, 184, 188-189, 193, 199, 274, 283, 336, 422-423, 432 de Trooz Ch.: 354, 390-391 De Vogelaere R.: 258, 312, 414 Dirac P.A.M.: 6, 24, 157, 214, 221-224, 226, 228, 232-234, 328, 356, 423, Dopp H. (S.J.): 76, 245, 368

The Atom of the Universe

Drago L. (Msgr.): 172 Durt H.: 17, 280-282 Eddington A.: 5-6, 11-12, 30, 43, 60, 76, 79, 81-82, 84, 87-88, 90-94, 96, 98, 100-109, 111-114, 119, 122, 124, 128-129, 132, 135-137, 140-142, 145-147, 149, 151, 163, 181, 184, 188, 194, 197, 200, 207213, 222-236, 239, 276, 290, 303, 341, 368, 370, 377, 381, 419, 422423, 432 Eccles J.: 356-357 Ehrenfest P.: 222 Einstein A.: 5, 6, 9-10, 13, 24, 27, 43, 60, 75, 78-83, 88-90, 94, 100-102, 104, 107-109, 112-113, 118, 123125, 128- 129, 131-137, 140, 142143, 160, 180, 184, 186, 188-190, 192, 194-196, 198-200, 211, 213214, 226-227, 234, 269, 274, 282283, 301, 306, 368, 375, 382, 391, 422-423, 429, 432-434 Elisabeth Ière (de Belgique): 269 Finkelstein D.: 194 Fourez G. (S.J.): 16, 99, 134 Fraipont E. (O.S.U): 17, 267, 297-298, 393 Frédérique (Papy-Lenger): 401-402 Friedmann A.: 9-10, 27, 126, 133-134, 136-137, 158, 190, 192, 196, 199, 201-202, 205, 286, 306, 313, 432 Godart O.: 14-15, 24-28, 31, 38-40, 44, 46, 75, 148, 156, 162, 165, 174175, 180, 218, 235, 254-255, 258259, 286, 292, 294, 311, 317, 335, 337, 349, 351, 354, 392, 406, 408410, 413, 415 Gamow G.: 162, 198, 304, 432 Garçon M.: 390-391 Gastmans R.: 410 Gauss K.F.: 44, 47, 272, 282, 297, 301, 309, 312-315, 425

Index of Persons

Gemelli A. (O.F.M.): 217-219, 355, 357, 360-361, 363, 421 Gérard C.: 53 Germain P.: 170, 213 Gesché A.: 354, 392 Gibbons G.W.: 227, 232 Goedseels P.J.E.: 51-52, 62, 64, 75, 183, 291 Goetals M.: 56 Gold T.: 106, 336, 340 Godart O.: 14-15, 24-28, 31, 38-40, 44, 46, 75, 148, 156, 162, 165, 174175, 180, 218, 235, 254-255, 258259, 286, 292, 294, 311, 317, 335, 337, 349, 351, 354, 392, 406, 408410, 413, 415 Gödel K.: 181, 223, 225, 233-234 Goeyvaerts J. (Canon): 17, 29, 68, 71, 74-75, 297, 351 Gonseth F.: 69, 117, 125, 128, 142, 145, 154, 161, 186, 191, 283, 302, 367371, 373, 377, 381 Goosens P. (Msgr.): 41, 416-417 Graas R. (F.S.C.): 17, 50-51, 287, 290, 313-314, 374 Grib A.: 27, 137 Grison M.: 382 Guérard des Lauriers M.-L. (O.P.): 367 Hagiara Y.: 92 Haldane J.B.S.: 275-276, 347 Harmignies M.: 122, 367 Hawking S.: 196-197 Heckman O.: 273, 307 Heller M.: 14, 19, 24-25, 28, 31, 129, 335, 337, 349, 431 Heinrich W.W.: 259, 291-292, 325, 419 Henriet L.: 18, 268, 415 Henroteau F.: 97, 121 Hestenes D.: 231 Heymans P.: 94, 99-100 Heyters H.: 61, 169, 220, 343-344, 347, 351 Hill R.: 258-259, 311-312 Hillas M.: 243

461 Hoover H.: 84, 174 Hopf H.: 221, 229, 328 Houziaux L.: Hoyle F.: 9, 106, 336-337, 339-340, 411, 434 Hubble E.: 10-13, 27, 95, 114-119, 121, 127-128, 130-135, 138-139, 143, 159, 191, 201-202, 204, 211, 304, 419, 422, 432 Janssens B. (O.S.B.): 170 Janssens J.-B. (S.J.): 385-387 Janssens G.: 18 Janssens H.: 264, 269 Javet P.: 273 John XXIII: 355, 357, 362-363, 420 Jungers J.C.: 175-176 Juvet G.: 232 Kapteyn J.C.: 115 Kasner E.: 131, 196 Keil R.: 303 Keller G.: 304 Kellog Ch.: 84 Kerkhofs L.-J.: 334 Kilmister C.W.: 222, 229-230, 232, 370 Koch-Miramond L.: 18, 261 Kragh H.: 25, 95, 127, 143-144, 162, 273, 276, 335-337, 347, 431-432 Krasinski A.: 187-189 Kruskal M.D.: 194 Kummer E.E.: 227, 232-233 Kustaanheimo P.: 221, 229, 327-328 Labérenne P.: 210, 347 Ladeuze P. (Msgr.): 62, 122, 166, 171, 174, 176, 179, 184, 266, 286 Ladous R.: 217-219, 337, 349, 356 Ladrière J.: 16, 29, 42, 61, 263, 286, 376, 383 Lamal P.: 94 Lamotte E. (Msgr.): 280 Lannoy (Lemaître) M.: 17, 33, 36-37, 85 Laporte Ch.: 412-413

462 Leavitt H.S.: 97, 115 Lebbe V. (C.M.): 6, 30-31, 46, 68, 165170, 174 Le Bon D.: 18, 401 Leclerc J. (Msgr.): 174, 412 Leclerc O.: 33, 40 Lederer A.: 294 Ledoux P.: 316 le Hodey Ph.: 21 le Maire M. (S.J.): 416 Lemaître Joseph: 33, 38, 45 Lemaître Gilbert: 16, 28, 37-38, 40, 74, 148, 266, 279, 315, 317, 321-322, 401, 409-410, 416 Lenaerts M.: 17, 29 Lenotre G.: 390 Leo XIII: 59, 168-169 Léopold III: 183, 269 Leprince-Ringuet L.: 241-242 Levi-Civita T.: 324-325, 327-328 Lifshitz E.M.: 306-307 Lipnik P.: 16, 30, 396, 401 Lizin J. (S.D.B.): 16, 294, 296 Locht P. de (Canon): 17, 75-76, 363364 Lounesto P.: 231-232 Lou Tseng Tsiang P.C. (O.S.B.): 170 Lubac H. de (Cardinal): 169 Luminet J.-P.: 15, 27, 129, 137-138 Macq P.: 16, 342 Mc Crea W.H.H.: 87, 91, 140, 142, 156 Mc Vittie G.C.: 24, 135, 140, 142 Mahieux M.: 18, 401 Manneback Ch.: 24, 46-47, 56, 64, 94, 148, 156, 176-177, 183, 244, 267, 286, 292, 319, 322, 367-368, 370, 407-408, 416 Maritain J.: 58, 94 Massaux E. (Msgr.): 17, 75, 150, 354, 413, 416 Masset J.: 16, 297, 319, 404, 407-408, 410 Mathys M.: 94 Mawhin J.: 17, 24, 47

The Atom of the Universe

Mayer M.:162-163 Meinguet J.: 410 Menger K.: 233, 289 Mercier D.: 29, 45-46, 48, 67-72, 8485, 98-100, 150, 234 Micara Cl. (Msgr.): 71, 218 Michotte A.: 46, 218, 367 Millikan R.A.: 118, 119, 143-144, 151152, 155, 163, 211, 241-242 Milne E.A.: 151, 273-275, 335, 371 Moeller Ch. (Msgr.): 354, 366, 392 Moens L.: 15, 28, 137 Molière: 391-392, 402 Montini G.-B. (see Paulus VI) Moors-De Coninck A.-M.: 280 Nève de Mévergnies Th. (O.S.B.): 17, 29, 393 Neut E. (O.S.B.): 172 Nolet de Brauwere Y. (O.P.): 17, 74 O’Connell D. (S.J.): 99-100, 337, 349, 361 Oddi S. (Cardinal): 413-414, 416 Ore O.: 181, 233 Pacelli E. (see Pius XII) Papeians Ch. (O.S.B.): 17, 29 Paquet P.: 16 Pascal B.: 22, 276, 289, 334, 375-376 Pasquier E.: 47-49, 51, 59, 62, 183 Papy G.: 269, 401-402 Paulus VI: 349, 357-361, 363, 414, 420 Peebles P.J.E.: 9, 19, 25, 136, 204, 306308, 424 Péguy Ch.: 58, 387 Penrose R.: 194, 196-197, 225 Penzias A.: 22, 155, 415 Peters J.: 16, 280, 410, 414-415 Picard A.: 133 Picard L.: 166 Pius XI: 166, 217, 219, 345, 357, 421 Pius XII: 219, 220, 337-350, 360, 380, 387-388, 420

463

Index of Persons

Piveteau P.: 383 Poincaré H.: 47, 49, 56, 58, 247, 256, 258-260, 270, 275, 282, 292, 301, 311, 322-323, 326, 330, 346, 378379, 381, 406, 424 Poncelet J.-V.: 287, 291, 313-314 Ratti A. (see Pius XI) Reeves H.: 410-411 Renoirte F. (Canon): 42-43, 61, 263, 367-368 Reyntens L.: 61, 169, 263, 344 Riesz M.: 231, 232 Robertson H.P.: 96, 106, 124, 131-132, 135-136, 432 Rossi B.: 246, 253 Rousseau R.: 184, 354 Rutherford E.: 87, 219, 345 Russo F.: 151, 347 Ruysbroek (or Van Ruusbroek): 28, 276-277, 389 Ryan J.H.: 182 Salviucci P.: 25 Sánchez Sorondo M. (Msgr.): 219, 337 Sauter F.: 232 Sauvage P. (S.J.): 15, 174, 383 Schatzman E.: 210 Scheuer P. (S.J.): 334 Schücking E.: 307 Schwarzschild K.: 78-79, 81, 90, 104, 107-110, 124, 131, 187-188, 192194, 197 Sertillanges A.-G. (O.P.): 381 Shapley H.: 93, 97-98, 100, 101, 115, 179, 184, 186, 191 Smeyers J.: 16, 277 Sepulchre D.: 280 Sepulchre J.-B.: 15, 280 Silberstein L.: 95-96, 101, 103, 116, 123, 131, 419, 422 Soetens Cl.: 17, 30, 68, 166, 168-169, 363 Speiser D.: 16, 410 Stanford E.V.: 182

Stone M.: 233 Størmer C.: 7, 241, 244-261, 271, 277, 291-292, 294, 296, 303, 308-310, 312-313, 316, 318, 322-323, 326, 329, 357, 359, 405, 419, 424-425 Stein G.: 339, 340, 344-345 Steward R.M.: 97 Stiefel E.: 221, 229, 327-328 Stoffel J.-F.: 15, 24, 26 Suenens L.-J. (Cardinal): 71, 268, 278 Sundman K.: 324-325, 327 Swann W.F.C.: 253 Szekeres G.: 194 Tardini D. (Cardinal): 349-350 Tchang-Hwai E.: 68, 167 Tchang-Yong-Li: 6, 174-175, 177-178, 255-256, 258 Teilhard de Chardin P. (S.J.): 8, 18, 169, 183, 260, 381-388, 425-426 Thill G.: 16, 140, 297 Thils G.: 17, 69, 72, 75 Thomas Aquinas: 338, 345, 381, 421 Thoreau V.: 167 Thoreau J.: 167 Tolman R.C.: 6, 106, 109, 130, 136, 180, 184, 186-190, 193, 196, 423, 425 Topel B.J.: 289 Turek J.: 19, 31, 348, 349 Taylor H.: 176, 177, 181, 183, 255, 281, 282, 341 Teller E.: 162, 163 Thibaudeau A.: 94 Thibaudeau M.: 94 Tits J.: 19, 238, 239, 269 Trautman A.: 222, 225 Unsoeld A.: 344 Valembois J.: 16, 318, 398, 405-408 Vallarta M. S.: 94, 111, 113, 180, 244246, 250-253, 255-258, 261, 315316, 356, 414 Valensin A.: 169 Vanacker D.: 57

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Van Cangh J.-M. (O.P.): 18, 140, 274 Vander Borg R.: 304 Vanderlinden H.: 78, 117, 121 van Innis G. (Canon): 17, 29, 75 Van Roey J.-E. (Cardinal): 71-72, 169, 172, 184, 278, 332-334 Van Severen J.: 57-58 Van Steenberghen F. (Canon): 17, 29, 73, 75, 122, 342-343, 345, 412 Van Waeyenbergh H. (Msgr.): 266268, 320 Veblen O.: 180, 227, 229, 232, 234 Verbeure A.: 410 Verriest G.: 49-50, 221, 412, 414 Viot J.-F.: 389 Von Neumann J.: 181, 227, 232-233

Wiesner J.K.: 360 Wéry L. (Canon): 171 Weverbergh R.: 16, 292, 406, 410, 416 Weyers J.: 16, 239, 410 Weyl H.: 10, 76, 79, 83, 102, 112, 132, 199, 210, 227, 232, 234, 274, 330, 370-372 Whittaker E.-T.: 123, 234, 259, 311, 324, 341-344 Willems E.: 122 Wijngaarden A.: 322 Willockx F.: 29, 71-72, 122-123, 167168, 367, 411 Wilson R.: 22, 155, 241-242, 415 Wirtz C.W.: 103 Wuillaume L. (S.J.): 17, 334

Walker A.G.: 194, 432 Wiener N.: 111, 113, 316 Weil A.: 235, 255, 260, 287, 330, 392 Weinberg S.: 199, 203

Yeddanappalli L. (S.J.): 281-282 Zanstra H.: 245 Zeldovich Y.: 234

Photos

I

Georges Lemaître at the end of the First World War with his uniform of an artillery adjutant (NCO). He is wearing on his left arm the decorations called «chevrons de front» testifying that he spent all the war near the front line (AL).

II

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Georges Lemaître (the fourth from the right) and some soldiers of his regiment in a village of Flanders during the First World War (AL).

Georges Lemaître, 17 July 1924. Lemaître Archives (AL).

Photos

III

Blue Hills (Boston), 5 October 1924. From left to right: Pierre Wibaut, Georges Lemaître, Edouard Willocx. Beneath: Gaston Dept. The photo was taken during the very first stay of Lemaître in U.S.A. (private collection of Prof. Robert Willocx).

Canon Allaer, director of the Maison Saint-Rombaut, the first Canon in charge of the “Amis de Jésus”; April 1927 (private collection of F. Van Steeberghen).

IV

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Abbé Lemaître with the father of Prof. Jean-Marie Jadin in Gistel, near Antwerpen, at the beginning of the 1930s (private collection of Prof. J.-M. Jadin).

L’abbé Lemaître, 1934, the year he received the famous Francqui Prize (AL).

Photos

V

Some of the ‘Amis de Jésus’ at the Regina Pacis retreat house in Schilde (near Antwerpen), Saturday, 11 August 1934. From left to right: Abbés Lemaître, Lambot, Hens, Van Haeperen, Froidure and Vaes (private collection of J. Goeyvaerts).

From left to right: R.A. Millikan, G. Lemaître and A. Einstein at the Athenaeum of the California Institute of Technology in January 1933 (Los Angeles Bureau, Wideworld Photos, AL).

VI

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From left to right: G. Lemaître, M.S. Vallarta, Marguerite Lemaître-Lanoy, Maria Louisa Vallarta-Margain, Joseph Lemaître, on a trip in the ruins of the Villers-la-Ville Abbey during the 1935-36 academic year (AL).

Tchang Yong-Li, the Chinese student of Lemaître (AL, gift from the Zhang family).

Photos

VII

The Pope Pius XII spoke with Canon Lemaître, 3 December 1939, during the plenary session of the Pontifical Academy of Sciences inside the Casina Pio IV (Vatican). At the right of the Pope, Fr. Agostino Gemelli, O.F.M., first President of the Pontifical Academy of Sciences (AL).

Lucien Bossy seated on the left of Georges Lemaître during a trip (AL).

VIII

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Taken with the camera of Canon Lemaître on Tuesday, 26 May 1942 on the top floor of the Collège des Prémontrés. First row: Claire Van Dongen, (?), Francine Thiry-Quinet. Second row: the future Msgr. Gillon, Willy Van Hamme, Jacqueline Van Hamme-Van Ysacker, Andrée Chalet-Jacquemain, Maurice Chalet, a technician, G. Lemaître (private collection of the Chalet-Jacquemain family; AL).

Louvain (Leuven) in the 1950s, Canon Lemaître giving a class on Poncelet polygons (AL).

Photos

IX

Class of Celestial Mechanics at the Collège des Prémontrés in April 1952 (AL).

Class of Mechanics, 1st year Bachelor (1ère candidature), November 1949 (AL).

X

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Caricature made by Xavier de Callataÿ (19321998), Student-engineer at UCL from 1951 to 1955, later a painter of international renown (Copyright A. de Callataÿ).

Visit to the Royal Observatory of Belgium, April 1951 (AL).

Photos

G. Lemaître and Carl Størmer at the University of Liège in August 1955 (AL).

XI

A Mercedes calculator, 1933–1958 (AL).

The “Computing Room” of the Laboratory of Numerical Research in May 1959. (Foreground) Miss Andrée Bartholomé at the controls of the E 101, and Canon Lemaître adjusting the plate with the programming needles. The perforated tape reader is immediately in front of him. (Background) A technician (AL).

XII

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From left to right: André Deprit; Andrée Deprit-Bartholomé and Odon Godart (AL).

Teatime at the Lemaître “Laboratory” (Collège des Prémontrés) in May 1960. From left to right: P. Paquet, J. Lizin and A. Deprit (private collection of Fr. J. Lizin).

Photos

XIII

The table at the Majestic (Leuven, Bondgenotenlaan; Avenue des Alliés) Clockwise: G. Lemaître, R. Rousseau, Msgr. E. Massaux, Msgr. Litt, Msgr. Ch. Moeller, P. Francard (AL).

Msgr. Lemaître in his room of the Collège des Prémontrés à Louvain, some days after his nomination as President of the Pontifical Academy of Sciences. Near Msgr. Lemaître, we see, from left to right, André Deprit et Odon Godart (AL).

XIV

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Tea-time in the Collège des Prémontrés, at the beginning of the 1960s. From left to right: d’Odon Godart, Andrée Bartholomé and Msgr. Lemaître (AL).

Georges Lemaître with his famous camera, during a session of the Pontifical Academy of Sciences (AL).

Photos

XV

Photograph taken by Léo Houziaux (Postdoc in Caltech) in Berkeley, 1961, during the General Assembly of the International Astronomical Union. From left to right: Y. Hagiara (specialist of celestial mechanics, friend of Lemaître since his stay in Cambridge, UK, 1923), G. Lemaître, S. Arend (Uccle Observatory, Belgium), Y. Kondo (NASA). Between Lemaître and Hagiara: O. Heckmann (Hamburg), President of the International Astronomical Union (private collection of Prof. L. Houziaux).

Cardinal Van Roey on a visit to Lemaître’s Saint Henri parish in Brussels. On his right, Canon Lemaître (AL).

XVI

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Pope John XXIII receiving the members of the Pontifical Academy of Sciences for an audience; On the right: Msgr. Lemaître (Centre de Documentation sur l’histoire de l’Université de Louvain, Louvain-la-Neuve).

Official procession for the beginning of the last academic year of Msgr. Lemaître, Leuven, October 1964 (AL, donation from Louis Bouckaert).

Photos

XVII

Georges Lemaître and his mother on holiday in Switzerland (AL).

Canon Lemaître with his family. Party for the Jubilee of Mother Lucie Choppinet belonging to the Congregation of the Dames de Saint-André, Brussels, September 1955 (AL. Photography of Mrs. Suzanne Lemaître).

XVIII

One of the last photos of Msgr. Lemaître, taken in 1966, by Jean-Marie Jadin (nephew of Canon Louis Jadin), in his parents house in Gistel, near Antwerpen (private collection of Prof. J.-M. Jadin).

Msgr. Lemaître at the end of his life (AL).

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Photos

Poster ATV-5 (© ESA- P.Carril)

XIX