Pretty Ugly: Why We Like Some Songs, Faces, Foods, Plays, Pictures, Poems, Etc., and Dislike Others 1527538605, 9781527538603

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PRETTY UGLY

PRETTY UGLY  WHY WE LIKE SOME SONGS, FACES, FOODS, PLAYS, PICTURES, POEMS, ETC., AND DISLIKE OTHERS

 CHARLES MAURER AND

DAPHNE MAURER

Cambridge Scholars Publishing

Pretty Ugly: Why We Like Some Songs, Faces, Foods, Plays, Pictures, Poems, Etc., and Dislike Others By Charles Maurer and Daphne Maurer This book first published 2019. Reprinted with minor corrections 2020. Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2019 by Charles Maurer and Daphne Maurer All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-3860-5 ISBN (13): 978-1-5275-3860-3

TO THE MANY PEOPLE WHO HELPED US WITH THIS BOOK

CONTENTS

1. The Field of Beauty: A Wayward Walkabout

1

Nature and Nurture Science vs. Philosophy The Art of Science

2. Background: Some Arcane Corners of Science

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Energy and Entropy Adaptation Deterministic Chaos Innumerable Dimensions Perceptual Dimensions Precision, Accuracy and Self-Similarity Fourier Transforms

3. The Sound of Music: An Overview of Musical Acoustics

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Harmonic Series Scales Timbre and Speech Strings Winds Singing

4. Seeing an Harmonic Line: Sights Are Like Sounds Parsing Sights Spatial Frequencies Perceptual Constancy Visual Perspective Acoustical Perspective

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5. Loud Colours: Memory, Dreams, Consciousness, Abstraction 91 The Nervous System Memory and Dreams Consciousness Abstraction Unconscious Awareness First Faces I

6. A Nose for Noise: Categorizing Tastes, Smells and Colours

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Taste Smell, Taste and Flavour Elemental Tendencies Categorical Perception Signal vs. Noise Adaptation

7. The Tragedy of Taste: Enjoying Food and Drink

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Reflex, Will and Adaptation Desserts and Drugs Tastes and Taste Cuisines

8. The Face of Beauty: What We See in a Face

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First Faces II Light First Faces III Familiar Proportions Sex and Experience Pretty Faces

9. Timeless Beauty: How We See Art

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Fashion Repetition and Fractals Waves and Wavelets Signal, Noise and Chaos Experience and Context

10. Time and Motion: Architecture, Music and Dance

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Symmetry Time Rhythm and Pitch Dance Modernity

11. Twisting Reality: The Illusion of Naturalism in Art Tonality Colour Verisimilitude Music

225

CONTENTS

12. Literature: Poetry, Prose and Plays

IX

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The Nature of Prose Drama and Humour Metaphor and Abstraction

13. The Human Comedy: A Summary and Extension to Animals 265 Neurons Animals

Notes

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Index

309

1 THE FIELD OF BEAUTY A WAYWARD WALKABOUT

The tribe in New Guinea lived so apart from the modern world that they still used stone axes. None of them had ever seen a photograph, and anthropologist Edmund Carpenter wanted to know how they would react to seeing one for the first time. He showed them Polaroid pictures of themselves and saw complete incomprehension: At first there was no understanding. The photographs were…far removed from any reality they knew. They had to be taught to ‘read’ them. I pointed to a nose in a picture, then touched the real nose, etc. Often one or more boys would intrude into the scene, peering intently from picture to subject, then shout, ‘It’s you!’ Recognition came gradually.1

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Looking at these men, it seems obvious that beauty is in the eye of the beholder—but more than beauty: reality too. Since they are not seeing reality in the photograph before them, the appearance of reality must also be in the eye of the beholder. The eye must learn how to see. Or rather, the brain must learn how to see. The brain must learn how to see that a picture is an image of something, not merely splotches of colour. The development of aesthetic preferences starts at this rudimentary level, and it does so not just for photographs and paintings but also for sculpture, dance, music, poetry, plays, food, drink, and all of our activities and endeavours. The aesthetic engine for all of these is the human brain. Although different parts of the brain end up doing different things, the underlying machinery is similar everywhere. The seemingly different parts of the brain are so alike and so intertwined that all of our aesthetic responses involve similar mechanisms, no matter what senses are involved. In this book we are going to lift the hood and see how the engine of beauty is constructed.

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Conventional studies of aesthetics assume implicitly if not explicitly the cultural preferences of the author’s time and place. For example, the 11th edition of the Encyclopedia Britannica is known as the “scholar’s edition” for its depth and erudition. Its main entry on music is 14,000 words. This article dates from 1910, almost the peak of the British empire. It does not deign even to mention Africa. Nobody could imagine such an omission today. Today, any overview of music purporting to be comprehensive would mention complex African polyrhythms. On the other hand, our current attitude may also be a distortion of the times, a distortion by a contemporary value we have developed in reaction to our colonial past, the desire to appreciate cultures that we have been destroying. According to Princeton Professor Kofi Agawu, a musicologist from Ghana, most observations of African music involve “the pious dignifying of all performances as if they were equally good, of all instruments as if they were tuned in an ‘interesting’ way rather than simply being out of tune, of all informants as if a number of them did not practice systematic deception, and of dirge singing as if the missed entries and resulting heterophony did not result from inattentiveness or drunkenness.”2 This book is an attempt to understand aesthetics irrespective of culture. Of course we are children of our place and time like everybody else, so we are subject to similar biases, but we are hoping to sidestep them by basing the book not on aesthetic appreciations but on science. We are building it from basic work on the sensation, perception, and cognition of adults, and from studies of babies, who were young enough not to have been acculturated. Moreover, we are not creating a self-contained theory with its own system of explanation, we are founding an explanatory framework on physics, physiology, and evolution. Indeed, the next chapter is an introduction to some key concepts of physics and maths. However, we did not write this book specifically for scientists. We also wrote it for artists, musicians, architects, cooks, writers, readers—anyone who enjoys any of the arts. We shall work with concepts, not equations, and show numerous examples. Our argument will draw from many academic disciplines, each of which has a rich and idiosyncratic jargon. This presents a problem.

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Although jargon can be a shortcut to understanding, it is a shortcut only to initiates, and few readers will understand the jargon of all the fields we need to walk through. Moreover, jargon is a shortcut that tends to lead the mind along conventional paths, paths that we shall need to avoid. For these reasons we shall use specialized jargon only in rare instances where ordinary English simply cannot serve, and then we shall explain it. Few readers will have read in all of the fields we shall wander through, so our first approach to every field shall be introductory. However, introductory does not mean elementary. If we seem to start with Music 101—well, we shall not stay at that level for long. Unfortunately, the scope of this book will force us to fly through subjects quickly. During these flights we shall make many assertions that contravene conventional wisdom, and some of these may sound bold and bald. If you find yourself rolling your eyes—if you find yourself wondering how the stupid authors could ignore something obvious that everybody knows—please visit the endnotes. These contain additional discussions and entrées to the academic literature.

NATURE AND NURTURE When we began to research this book, we envisioned ourselves describing the interaction of genetics and the environment. However, although nature and nurture are the most common explanatory mechanisms, we found that explanations based on either of them seem always to lead to a dead end, even when the notions are more sophisticated than “natural beauty.” For example, inside the eye, three sets of conical, light-sensitive cells enable you to see different wavelengths of light as different colours. These cells respond to a limited range of wavelengths, so you cannot see any wavelengths outside that range. This is nature, this is how you are built. For this reason you will never hear a couturier wax lyrical about a lovely infrared or a soothing ultraviolet. However, to state this is merely to state that you cannot appreciate what you cannot see, which is neither helpful nor profound. Nor is nurture more helpful, because nurture by itself cannot explain why a suit of clothes might look lovely during the day but not at night.

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Nature versus nurture is not a model that leads very far because physiology and learning are not separate and distinct, they are inextricable. Learning is not an abstract process, it is a physiological process, ultimately a chemical process, and chemical processes require both nature—the chemicals—and environmental factors like heat. For this reason, we tried to avoid the usual vocabulary of “hard wiring” and “environmental influences,” and to seek more revealing explanations. Ultimately we came to see the sense of beauty as an emergent phenomenon. An emergent phenomenon is something complex that arises from repeating something simple many times. An example is the office towers in a city. To prosper if not merely to survive, people need to exchange goods and services, so individuals have a fundamental need to trade. Proximity facilitates trading, so people decide to move near other people. A village forms. The concentration of people in a village attracts more people so the village becomes a town, then the town becomes a city. Eventually the city runs short of space. At that point people begin to build upwards and office towers emerge. Physical beginnings—nature, if you will—always help to shape emergent phenomena. Amsterdam has soft soil at depths where New Amsterdam has bedrock, so taller buildings emerged in New Amsterdam (New York), but good harbourage saw dockyards emerge in both.3 Human bodies are another emergent phenomenon. Infinitesimally small chemical packets that we call cells combine with other cells, which combine to form the larger packets we call tissues, which combine to form organs, which combine to form a baby. At every stage in this process the packets do nothing more than react to the basic forces of physics and chemistry. Genes do control the development of bodies but as geology controls the development of cities, not through active processes but through structural facilitation and constraint. This is apparent in the brain. The brain looks like a cauliflower and is formed in layers. Broadly speaking—very broadly—nerves to and from the body connect at the lowest levels, the middle levels run things, and the highest levels perceive and think. In none of these levels are the cells smarter than the cells forming a cauliflower. The brain’s chemical

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structures are perfectly dumb, yet these dumb structures interact with one another in ways that permit intelligence to emerge. Intelligence emerges primarily in the cortex, the outermost few millimetres that contain the highest levels of the brain. There as elsewhere in the brain, the environment of each neuron (nerve cell) consists of a chemical bath penetrated by erratic bursts of energy from one or another cell nearby. This energy reaches the neuron, passes along the neuron’s surface in the form of a chemical chain reaction, then reaches the neuron’s far end and crosses the chemical bath to nearby neurons. Its passage through the bath disturbs the bath’s chemistry. It causes slight chemical changes that facilitate another passage of energy through the same route and inhibit the passage of energy through neighbouring routes. Those changes come to form neuronal pathways. From a vast number of these dumb pathways, intelligence emerges. And our sense of beauty emerges from them as well. Unfortunately, this emergence takes a confusing route—or rather, a confusing set of routes. To follow it we shall begin with some basic concepts of mathematics (without equations or numbers), then spiral upward repeatedly through vision and hearing. Eventually we shall reach art, architecture, dance, drama, literature, music, and sculpture. Halfway up the spiral we shall pause to sample tastes, smells, food, and drink.

SCIENCE VS. PHILOSOPHY When we first thought about writing this book, we did not know what we could come up with. A framework that can hold all of aesthetics that is built upon basic physics—how to construct such a thing was not obvious. However, at physiological levels the brain is a machine, so we thought that we ought to be able to come up with something. In any case, we thought, the endeavour would be fun, because our research would take us to so many concerts and museums. That was 30 years ago. A philosopher of aesthetics might have written a book like this faster. A philosopher could have forgone the museums and developed

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the argument from first principles using logic. But we are scientists, not philosophers. Scientists do not start from first principles, scientists try to make sense of what they see. In science, logic guides observations and explains observations, but observations come first and, although it sounds surprising, science does not follow the rules of formal, Aristotelian logic.4 To understand the reasoning of science, consider the basic paradigm of the scientific method: 1. Form an hypothesis. A new drug Memorine enhances memory. 2. Design an experiment to test the hypothesis. Give half a French class Memorine and half the class a placebo, and compare the two groups’ vocabularies before and after the pill. 3. Run the experiment. 4. Examine the data and draw a conclusion. On average, students taking Memorine improved more than the others, so we infer that Memorine does enhance memory.

This sounds sensible and the conclusion may sound logical at first blush, yet that conclusion could not follow logically from any set of real data. We may see an improvement on average but among any group of students, some will learn more words than others for reasons having nothing to do with the drug. Among our group perhaps Alice heard a lot of French at her parent’s cottage in Québec, and the Inuit Bunig never heard any French spoken until she went south to attend university, and Cora is a little dense, and Dorothy prefers dancing to studying, and Elena is already fluent in Spanish and Portuguese. We might be able to allow for some factors like these—perhaps we can exclude from our sample bilingual students— but we can never know about everything that might differentially affect students’ learning. Thus, the most we can conclude is that Memorine may sometimes enhance memory. This may sound like pedantry but it is not. Let us assert that all cats grow tails. If you have ever seen a Manx cat, you will contradict us. “No, it is false that all cats grow tails. Not all cats grow tails. Some cats grow tails but other cats do not.” Now let’s compare cats to Memorine. We hypothesize: •All cats grow tails. •Memorine enhances memory.

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But according to Aristotelian logic, the results of our experiment show the contrary of our hypothesis: •Some cats—not all cats—grow tails. •Memorine may sometimes enhance memory.

Logically, no experiment can prove an hypothesis. All a scientist can do is assume that within an experiment, the influence of uncontrollable factors is the influence of random chance, and then calculate odds like a bookie. Instead of saying, “Memorine enhances memory,” all we can do is report, “We saw an enhancement that would occur by chance less than n% of the time.” That is the only logical conclusion we can draw. Deductions like this are true insofar as they go but they do not go very far. To carry a man to the moon, or to analyze the elements in a gas, or to identify a pathogen, science requires sweeping inductions—generalizations from the particular to the general, like the generalization we accept as a law, that a body in motion tends to stay in motion. Yet according to the strictures of logic, all inductions are fallacies. No matter how many Italian meals you have eaten, you cannot conclude logically that all traditional Italian cooking uses garlic. Indeed, if you do conclude this, you will be wrong. Garlic was deemed the peasant’s spice cupboard—sophisticates looked down on it—and Italian cuisine was developed not by peasants, who could afford little beyond grains and vegetables, but by folks with money in towns.5

THE ART OF SCIENCE Science is not built from logical deduction, it is built from intuitive induction. Strengthening the inductions are associative reasoning— more about that shortly—and the mathematics of probability. In principle these mathematics are simple. Let’s illustrate them with our imaginary Memorine. A test of Memorine finds an amount of improvement that would occur by chance only five percent of the time. This may sound significant but it means the odds are five per cent that these results did occur by chance and that Memorine actually led to no improvement at all. To investigate further we test

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more drugs. We comb the pharmacopoeia and find 99 drugs in the same class as Memorine. We test each of them as we tested Memorine, and we repeat our test on Memorine as well. The result: five of these 100 drugs show results that would occur by chance five percent of the time. This result is exactly what one would expect by chance, so we see no evidence that this class of drugs is useful. However, one of these five drugs is Memorine, so now we have two studies each finding odds of five percent that Memorine can be effective. The odds that both studies found this by chance are lower. Next we test Memorine a third time and find similar results, so the odds become lower still. Now we feel justified to make an inductive leap, to conclude that, although most of the drugs seem useless, Memorine can be effective. In principle that is how science works, but reality is dirty. Scientists do not enjoy repeating experiments, nor can we advance our careers by doing so. Scientists repeating an experiment will usually vary some circumstance, to extend what is known and to extend their lists of publications. Probably no one would retest Memorine with students learning languages but someone might test women in a nursing home on telephone numbers, and a neurophysiologist might give it to rats running mazes. Since each of these studies is different, we could not combine them mathematically. We would be adding apples and oranges. On the other hand, if they showed similar results, they would appear to be converging on a truth. Converging evidence this is called. It is arguing by association rather than logic, so to a logician it carries no force, but it holds all of science together. For example, although no one can prove logically that all species evolved, yet (1) we have seen some species evolve in our lifetimes, (2) we can put together plausible evolutionary trees from physical evidence, (3) we can induce other species to evolve in the lab, and (4) no one has come up with an alternative more plausible than a deus ex machina. This evidence converges so strongly that scientists are forced to see the theory of evolution as more than “just a theory.” Overwhelming converging evidence forces us to conclude that evolution is a mechanism that is fundamental to the development of life in all its forms. In this book we paint a picture from converging evidence. A large picture from an immense body of evidence, evidence from several

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SELECTING EVIDENCE When a teacher demonstrates a classic experiment, the result is seldom exactly what the theory predicts it will be. The world is too messy for theoretical perfection to exist. Moreover, once we leave the basic textbooks, theories cease to be complete and coherent, and observations begin to be so messy that experimental results may look real yet not be. For example, consider Memorine again. By convention, scientists in most fields deem a result to be significant statistically if it has no more than a five percent probability of happening by chance. This means that if our results were entirely random, the most extreme five percent would still look significant. They could not be significant, for they were random, yet out of every 100 tests, five results would look significant.6 This will happen often because scientists hunt in the dark. Although we aim at noises, most noises at night come not from animals but from wind. In experimental psychology something like one-half of studies find no data that are strong enough to publish, despite biases to see significance wherever the psychologist looks. Even when we hear a noise so loud that we know something is present, still we cannot draw a clear bead on our target. No scientific study can control and measure everything well enough always to reveal a phenomenon that actually exists. For a typical study in experimental psychology the odds are only about one in two or three of finding (a) an apparent statistical effect that (b) is not random. In neuroscience the odds are usually lower. Thus, if a study fails to find an outcome that other studies predict, there is an excellent chance that the study is at fault.7 An essential part of science is discriminating meaningful results from meaningless results. Alas, journals rarely publish failures to replicate experiments—word of mouth is often the only way to learn of failures to replicate—and once a scientist enlarges his scope beyond the minutiae of his own research, where any paper is expected to discuss every other paper, he will be open to the charge of selecting his evidence to fit his conclusion. But selecting evidence is not a scientific sin, it is a scientific necessity. Scientists must discriminate among studies based on a sophisticated understanding of statistics and methodology plus sufficient knowledge of a field to know where evidence converges. In science, sin does not lie in discrimination and selection, sin lies in applying prejudice to discrimination and selection.

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sciences plus anthropology and the history of the major arts. Like all evidence of every kind, our body of evidence is not completely consistent, but we do not take inconsistencies lightly and we discuss the more important ones in endnotes. The body of evidence that we deem solid coheres along many dimensions. Finally, we would like to end this introduction with a pedantic note on attributions. For brevity we sometimes use “we” to refer to only one of us, or—in the text but not in the endnotes—to refer to any set of colleagues and/or students with whom Daphne has collaborated. Also, in the text we ascribe studies to the lead author only. Almost every scientific study is actually a collaboration, so if you see only one name, please read an implicit et al. and check the endnotes if you want to know who the others are.

2 BACKGROUND SOME ARCANE CORNERS OF SCIENCE

Nico Machus is a modern son of Aristotle, a Professor of Philosophy, a bearded intellect who treads all walks of learning but particularly enjoys the path to the faculty club’s bar, where he takes lunch and then a short, black espresso.1 A short, black espresso is remarkably bitter yet Machus not only drinks one, he savours it. He deems it an aesthetic pleasure. But examined objectively, this pleasure is bizarre. Nobody is born able to enjoy or even to swallow anything so bitter. If you put a drop of something so bitter as espresso onto a newborn baby’s tongue, he will grimace and spit it out. Bitterness portends poison. Avoiding it helps babies and our species to survive.2

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The good food of infancy is sweet: mother’s milk. Milk from the breast is sweeter than milk from the bottle. Sweet milk and a sweet tooth help a baby learn to nurse. A sweet tooth has proved to be so useful for survival that evolution has fitted every child with one that functions perfectly at birth. Even before birth: the foetal sweet tooth works so well that a Dutch obstetrician used it to try to help pregnant women who were bloated with excessive amniotic fluid. He injected saccharine into the womb to induce the foetus to drink, so that the excessive fluid would pass from the foetus's body through the placenta into the mother’s body, which would then expel it by urinating. The more saccharine he injected, the more the foetus drank. However, this treatment turned out to be temporary, because just as adults become sated with sweets, so did the foetus.3 Although Professor Machus relishes unsweetened espresso, as a boy he had childish tastes and perceptions. Indeed, he began life as an infant with infantile tastes and perceptions. His adult preferences must have somehow been built upon those. Physically, not just poetically, the child is father of the man. To learn about the development of adult aesthetic preferences, we need to begin at their beginning. In our previous book, The World of the Newborn, we developed from the scientific literature a picture of what the world looks and sounds and feels and tastes like to a baby who has just been born. The world of the newborn is where our preferences begin to form, the world where we need to begin this discussion.4 This world we found to be chaotic, chaotic to an extreme. A table stands stolidly but a newborn may perceive it to be moving—until his mother picks him up and carries him around the room. As she does this, the table will slow down. Moreover, not only will the baby see the table, he may hear it and taste it too. Every time he closes and opens his eyes, visions and smells appear and disappear. When he falls asleep, he does not lose consciousness, he becomes conscious of different things. At this time of his life a baby not only does not recognize things, he does not realize that there are things in the world that he might come to recognize. He does not even realize that there are things or a world. He has sensations, a profusion of sensations, but he can

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recognize very few of those sensations. His world is so confused and confusing that any sensation he manages to recognize will attract his attention. If his mother eats anise-flavoured sweets during the fortnight or so before his birth, he will likely recognize the smell of anise and turn his head toward it. This reaction is definitely not innate. The smell of anise causes most newborns to turn up their noses in apparent disgust.5 After birth, a repeated stimulus can generate not just recognition but also a preference. Babies do not usually seek out carrots but if a mother drinks carrot juice four days per week for the first two months she is nursing—only the first two months—then when her baby is six months old, he will usually prefer carrot-flavoured cereal to ordinary cereal. The flavour of carrots passes into the mother’s milk, the baby comes to know the taste of carrots, he comes to expect the taste of carrots when food fills his mouth, and so he comes to feel more satisfaction when he tastes carrots than when he does not. This is the prototype of an aesthetic preference.6 However, it is quite a rudimentary prototype. It is a world away from the aesthetic preference of a sophisticated restaurant critic or even of a gastronomically naive adult. Not only is a baby not an adult, philosopher Machus can mount a powerful argument that a newborn baby is not yet a fully human being, that a newborn is merely the precursor of a human being. He can point out that the foetus just before birth is a larval creature living in a marine environment, a creature that takes oxygen and nourishment through an organ that does not exist in the adult form of the species—the equivalent of a tadpole. He can say that at birth a baby is equivalent to a tadpole that has just begun to breathe air. It is no more a human being, Machus can say, than a tadpole is a frog. He can argue that a newborn baby hardly even looks human, for its proportions are further from a nine-month-old’s than a nine-month-old’s proportions are from an adult’s. He can also point out that a newborn baby exhibits no behaviour that is exclusively human or peculiarly human or even particularly human. In Aristotelian terms, the end (telos) of a newborn is to become human but its substance, essence and material are generically mammalian. In sum, Machus can say, there is no argument that a newborn baby is human save the argument that it will become so some day.

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A philosophical argument like this would not go over well with many people. Professor Machus would never be employed by an evangelical college or St. Anybody’s University. However, although Machus’s colleagues might dispute his philosophy and his conclusions, they cannot gainsay the scientific evidence that a newborn’s perceptions are radically different from an adult’s perceptions or even from the perceptions of an older baby. Relatively few of us see music or taste the colour of the room. We cannot look at a newborn baby, see what he prefers, and assume that those preferences will develop into adult preferences through any simple process like elaboration. Indeed, we know that a newborn’s preferences are not elaborated. An entirely new structure is built upon them, just as a medieval church is built upon a Roman foundation. All that the Roman foundation will have predetermined is the location of the walls. Since aesthetic preferences are formed by the brain and within the brain, we need to begin by understanding some of the brain’s functioning. Moreover, since we intend to root our understanding of aesthetics in the fundaments of basic science—of physics and biology—we must approach the brain at fundamental levels. That is what we are going to do in this chapter. We shall cover material that will seem far removed from aesthetics, and much of it will seem abstract and abstruse—if you have no background in science or mathematics, your head may reel—but please bear with us. This chapter is a necessary foundation, and its concepts will become clearer as we apply them and reapply them throughout the book.

ENERGY AND ENTROPY As civilized human beings we would like to believe that the main function of the brain is to think and feel, but it is not. The brain evolved to control the processing of energy. Every day each of us takes in and expends enough energy to heat sufficient water for a bath. The energy we acquire is mostly latent within chemicals that we ingest as food. The energy we expend takes many forms from flailing arms to radiating heat. Controlling the acquisition of energy— obtaining food and eating it—and controlling the expenditure of energy: this is the brain’s primary job. A brain does come to think and to have aesthetic feelings and emotions, but as we shall see,

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thoughts and feelings are emergent phenomena that develop in different ways to different extents in different organisms.7 The brain is the control room of an energy-processing plant, and wires to and from it—nerves—run everywhere. Sensors react to minuscule changes in pressures, temperatures, and chemicals impinging upon the body. The reactions are electrochemical impulses that run through nerves into the brain. From the brain these impulses go back out to stimulate muscular contractions. The process works like a factory from 1950: sensors send signals to a bank of relays, the relays send signals to solenoids, solenoids control machines. The processing controls of the human factory respond to infinitesimal amounts of energy disturbing electrons. This energy may be the pressure of something touching the skin, or the pressure of air vibrating against the eardrum, or the pressure of photons of light striking the back of the eye. Disturbed electrons set off a microscopic chemical reaction. This chemical reaction sets off more chemical reactions, which set off still more reactions, creating long chains of chemical reactions in various directions. Those chemical reactions pass along nerves into and through the brain, and then out of the brain through more nerves to muscles. The key factor here is that they are all chains of chemical reactions—organized reactions—not a disorganized mass of energy scattering everywhere. The organizing principle of these reactions is built into the chemistry of individual nerve cells, of individual neurons. An electron ramming through neurons acts like a cop pushing through a crowd of people. He pushes his way through by shoving people to the left and right, which makes it easy for his partner to follow him, but pushing people sideways makes the crowd denser toward the sides, so the partner cannot easily deviate leftward or rightward. Neuronal traffic behaves similarly except that the pressures and crowds are atomic. Note that consciousness is not needed for this. If you are in a crowd of people standing about an airport and policemen push through, you and your luggage will be shoved aside no matter whether you see them coming or not. Note, too, that your luggage will never be pushed always and entirely out of everybody’s way. No matter where in the airport your suitcase stands, eventually some clumsy oaf will barge into it with a luggage

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trolley. If it were to stand about the airport for a century or two, enough luggage trolleys would barge into it that eventually it would become battered to bits. To keep your suitcase from disintegrating would require occasional but continual repairs. This illustrates one of the basic laws of physics, the second law of thermodynamics. This law holds that any form of organized energy will lose its organization unless some external force holds it together. Disorganized energy is called entropy, so a short form of this law is, “Entropy tends always to increase.” Or shorter still, “Things fall apart.” A bucket holding water resists the natural tendency of water to spill all over the ground: the bucket resists the water’s entropy. The energy forming the resistance comes from the atomic forces forming material of the pail. A man is not a pail but we can think of a man as a bag—a selfmending bag— that holds four gallons of water plus some shovelsful of chemicals. To be self-mending requires the bag to receive and deploy energy in complex and unpredictable ways. Organizing that energy is the function of the brain.

ADAPTATION Imagine a balloon. The balloon is a membrane, a sheet of particles held together by internal atomic forces. Those forces form an elastic structure strong enough to resist the entropy of air under gentle pressure. A single-celled organism is comparable, except that it is filled with fluid and the pressures within the fluid are physiochemical. When you hit a balloon, it rebounds off your hand mechanically. If it hits a wall, it rebounds off the wall mechanically, following the laws of physics. A single-celled organism functions comparably, except that it does not react mechanically, it reacts physiochemically. A single-celled organism is a tropic creature. In this usage tropic is pronounced with a long o. The word comes from the Greek trop, a

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turning. Tropic with a short o denotes where the sun turns around during its annual meandering northward and southward. In multicellular organisms, the individual cells always behave tropically, even in man. However, if you combine enough automata in the right way, you can end up with a device that behaves as though it has free will. Do plants turn toward the sun tropically or because they want to? We shall not suggest either that plants have free will or that man does not. We do not want to argue with Professor Machus and for our purposes, the philosophical question does not matter. We are dealing in science, not philosophy. We observe that human bodies make a continuum of responses from simple and tropic to complex and adaptive. We also observe that human bodies combine these responses in ways that often form the appearance of free will. For us that is sufficient. To the extent that an organism does not respond to things automatically, it responds adaptively—which brings us to babies again. If the gentle stroke of a hand causes a tropic creature to start, the same stroke will always cause it to start, but this does not happen with a newborn baby. To be sure, a baby is born with some reflexes and with many tropic functions in his innards, but his behavioural reflexes are weak, so much of a newborn’s behaviour cannot be tropic. On the other hand, when a baby first encounters the world, neither can he have adapted to anything in it save a few flavours that may have passed into the womb and some aspects of his mother’s voice. Now remember our description of the newborn’s world: a stream of incoherent sensation. Nothing exists save what is present, and a sight may taste different from a sound just smelled before. There is no world, just a mixture of sensations. To understand that there is a world beyond his sensations, the first thing a baby must do is come to recognize sensations he has encountered before. The mechanism of this recognition is chemical. When the brain is stimulated repeatedly, physiochemical reactions form neurochemical channels. Those channels control energy within the brain, lessening entropy. This channelling permits us simultaneously to adapt to our environment yet be aware of it as well. Once a normal background forms channels, unexpected variations stand out.

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Variations may portend trouble or may indicate food, so an adaptable animal must be able to discriminate helpful variations from harmful. Paradoxically, small variations matter more than large ones. Imagine that you are walking on the veldt and looking off into the distance. Halfway to the horizon you make out this scene. You must realize immediately that you are not seeing a tree stump. If you need to wait until you can see it clearly as a lion, you will never see anything else again. For this reason, mechanisms of adaptation have evolved to enable slight variations from the background to be especially salient. That, we shall see, is the fundamental principle of pleasure. Pleasure is the brain’s response to a change from a pattern in a direction that experience has shown to be positive in some way. This mechanism begins with some of the simplest reflexes that keep the baby alive, it winds its way through sex and sensibility, and it ends with the most sophisticated forms of art.

DETERMINISTIC CHAOS This brings us to another paradox: aesthetic pursuits involve the appearance of choice and free will yet all evolve from the tropic functioning of cells. To understand how this might happen, consider a game of billiards. One ball bumps into another. Both balls rebound from the bumper in different directions, causing them to bump into others, which rebound into others in turn. This is organized motion. Usually the motion stops quickly because the balls and the felt absorb energy, but imagine that each billiard ball contains a source of energy, a source of energy just potent enough to compensate for the energy dissipated by compression and friction. Now the balls will continue to move about and bang into one another indefinitely. If you watch them, their motion will make no sense. It will look chaotic. However, each collision and rebound and new collision will follow predictable physical laws, the laws of action and reaction. The initial break will have started the balls in motion and determined all of the rest. The collisions will occur in an order that develops naturally from the first collision, naturally and ineluctably. It is

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beyond the eye to see this order but it is there. The eye sees only chaos but it is, in fact, a predetermined chaos. A basic dichotomy of physics and philosophy is determinism versus chance. This dichotomy goes back at least to the first century B.C.E., when Lucretius posited atoms that fall in a straight line except for an occasional, erratic swerve. Within this dichotomy, any event is either linked within a chain of cause and effect or it is random. When an event is part of a deterministic chain, then in principle if not in reality, the causes are observable and the event is predictable. In contrast, a random event has no cause and cannot be predicted. Classical physics deals with the first, quantum physics with the second.8 Yet although this dichotomy is logical, events in the real world often seem to combine regularities with randomness, like the weather. In June we can predict with confidence that Winnipeg will freeze in February, but we can only guess what the low will be on the first day of the month. Computers have allowed mathematicians to write simple instructions—trivially simple instructions—and repeat them an astronomical number of times. Some of these can generate patterns like the weather, patterns that develop seemingly at random then become stable in one form, then break up into seeming randomness and stabilize in another form, etc. Mathematicians call these metamorphoses deterministic chaos. Mathematicians define deterministic chaos as non-random but unpredictable behaviour within a deterministic system. It denotes a system that is actually deterministic yet appears to be based on the laws of chance, because the laws of nature driving it are beyond our ability to observe, either because the natural events are too complex to comprehend or because they are so sensitive that we cannot observe them without affecting them unpredictably. A Brazilian butterfly flaps its wings, which initiates a sequence of air currents and countercurrents that might cause a tornado in Texas—or perhaps a hurricane in Havana, depending on the flapping of other butterflies nearby. The second law of thermodynamics states, “Things fall apart.” Stability can only be temporary. What we perceive to be stability is

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just a deterministically chaotic slowing of change. For example, if you have chicken pox as a child, you will get well but the virus will remain in your body. It will stay dormant for decades but eventually—for some equivalent of a butterfly’s flapping wing, like your losing several nights’ sleep by flying to China—some physiological process may weaken enough to let the virus multiply until it can no longer be controlled. If this happens, it will break out through the skin as a painful rash—shingles—and the infection will be stable enough to hurt for months. Although shingles takes days to develop fully, for practical purposes either you have shingles or you do not. Coming down with shingles is not a “linear” change that can be described by a mathematical function, it is all or nothing—a “non-linear” change, like pregnancy. Deterministically chaotic is how a mathematician describes a complex system that shifts from one stable state to another suddenly. Deterministic chaos has proven to be a useful model of many physical systems. Although “deterministic chaos” is a mathematical term and construct, we can easily imagine a comparable mechanism functioning in the real world—a simple change repeated so many zillion times that it forms emergent phenomena. This would be a physical equivalent to deterministic chaos. Brushing the mathematical construct onto the physical world can show us how deterministic events can look like chance.9 Since deterministic chaos is based on the frequent repetition of simple things—unfathomably frequent repetition—a cynic might summarize it with the dictum, “Repetition works in mysterious ways.” Although this is hardly satisfying, mathematicians have proved the dictum to be true. Some repetitive mechanism similar to deterministic chaos is probably what enables the tropic cells forming your body to drive to the grocery store and, we shall see throughout this book, physical evolutions and structures evincing the mathematics of deterministic chaos underly music and art.

INNUMERABLE DIMENSIONS When most people think about dimensions they usually think of only three or four dimensions: length, width, depth, and perhaps time.

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Physical scientists think of at least seven: time, length, mass, electric current, thermodynamic temperature, luminous intensity, and amount of substance (moles). Those are the fundamental dimensions of the Système International d’Unités, the international system of measurement. However, those seven are just a start. They combine in various ways to form every other dimension measured in a physics or chemistry lab: angularity, capacitance, inductance, permeability, viscosity—you name it. Moreover, physicists and chemists see colours, hear sounds, notice tastes and smells, and feel the hardness or the straightness of a chair. Greenness, blueness, redness, yellowness, brightness, timbre, pitch, sweetness, tartness, bitterness, saltiness, muskiness, fruitiness, pain, warmth, cold, humour, sadness—each of these forms a dimension as well, and there are an infinity of dimensions more.10 Philosopher Machus might object that most of these are perceptual dimensions, not physical ones, but we would reply that all dimensions are perceptual. A dimension is a measurement—that is the literal meaning of the term—and a measurement is a perception, no matter what it measures. A measurement may be a perception of something physical but it is a perception nonetheless. If we measure the hardness of a rock, we assume—we have to assume—that we are perceiving a physical reality, and as Johnson famously demonstrated to Boswell, we test the reality of an object through our perceptions: After we came out of the church, we stood talking for some time together of Bishop Berkeley‘s ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it, ‘I refute it thus.’11

Boswell perceived the hardness of the rock by watching Johnson’s foot rebound. A metallurgist testing the rock might perceive its hardness by watching how far a hammer rebounds in a device called a Shore scleroscope. A scleroscope contains a hammer that is more precise and reliable than a foot but is comparable otherwise. Modern scleroscopes use electronic sensors instead of eyes to watch the hammer, but if you trace any electronic sensor back far enough in history, you will find its antecedents in human perception.

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PERCEPTUAL DIMENSIONS One way to think of the Système International is as a framework for standardizing perceptions. We perceive light to have some force, and the Système provides a vocabulary and scales to let us quantify this force in a standard way. However, the Système is severely limited. It standardizes perceptions of physical phenomena but it cannot deal with perceptual phenomena. The Système has units for the radiant energy that a light bulb emits but it has no units for the light bulb’s brightness as registered by the brain. The Système has units for temperature but not for the feeling of warmth. It has units for the frequency of pressure waves in air but not for a pitch we hear. Perceptual dimensions are wooly. Brightness, warmth, clarity, beauty, happiness—these can be defined in innumerable ways and each definition is less precise than the next. For this reason, scientists tend to be wary of popular psychological discourse. However, even if woollen yarns are too soft and fuzzy to measure with callipers, you can still feel which are thicker than others and compare them in a shop. Perceptual dimensions can be measured like that. Facial expressions are a subject wooly enough to knit with, so they make a good example. Here is how we ourselves measured the emotions people read on faces. Many researchers have taken photographs and movies showing an assortment of facial expressions, then asked adults from various cultures to describe them. It turns out that people everywhere identify six expressions: anger, disgust, fear, happiness, sadness, and surprise. Some people and peoples identify other expressions too, but those six seem to be universal. Even six-month-olds have begun both to display them and to read them on others’ faces.12 To explore those dimensions we began with a set of standardized photographs of actors and actresses showing expressions that they believe to show, and that large numbers of people see as, extreme happiness, extreme sadness, etc. The top of the next page shows an example of six extreme expressions with neutral in the centre.

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When the actress formed these expressions, she felt them as expressive dimensions, but you are perceiving them through your eyes, so from your perspective these are visual dimensions. Although we think of happy and sad as opposites, combining two of these photographs shows us that they are not opposite extremes of a single dimension. If they were, then combining happy with sad ought to look neutral; but it does not. In the three photos below, the left and right show extremely happy and sad, and the centre shows the combination. The central picture looks nothing like the neutral picture above.

ANGER

DISGUST

FEAR

HAPPINESS

SADNESS

SURPRISE

To combine those photographs we found landmarks on each face and marked them on each picture—the bottom of the nose, the corners of the eyes, etc. We marked 160 landmarks per picture and then stretched and squeezed the happy face until each landmark was halfway toward sad. With the five pictures on the next page we used the same technique to stretch and squeeze a neutral face toward happy. The three central faces are one quarter of the way toward happy, halfway, and three quarters of the way. Those five expressions are equidistant arithmetically and physically—that’s how we created them—but they are unlikely to be equidistant perceptually, because the brain is more sensitive to small

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variations than to large ones. It is one thing when somebody smiles gently but not broadly and quite another when he does not smile at all.

Had we but students enough, and time, we might have measured the perceptual scale of this dimension by asking numerous people, under controlled conditions, how much happier A is than B, how much happier B is than C, etc. We might then have created an equivalent physical scale by measuring facial landmarks to see how much muscular movement creates how much of an increase in apparent happiness. This would have been interesting, but we preferred to expend our energy on a more subtle and fundamental question: to learn whether the six facial expressions that we all perceive are in some sense primary dimensions, or whether they are formed from some simpler set of primary dimensions, a smaller set of dimensions that are easier for the brain to process. To understand how we did this, let’s taste some apples. For the sake of argument let’s say that most people perceive there to be three basic kinds of apple: cooking apples, juicing apples, and eating apples. Obviously some cooking apples make better pies than others, and some juicing apples make tastier juice, so these categories are dimensions. They are subjective dimensions but they are dimensions nonetheless. Most of us perceive these three dimensions while shopping for apples, yet a cook may tell you that really, those three kinds of apple differ in only two ways. Some of them are sweeter than others, and some of them are firmer. The cook thinks those two dimensions underlie the three dimensions that we perceive. But is this true? To find out you can ask customers in a greengrocer to taste all the varieties on offer and to rate them for cooking, juicing, and eating. Plotting their ratings on a three-dimensional grid creates a three-dimensional graph like the one on the next

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page. Next you can try to draw a two-dimensional surfa f ce that will connect most of the points in the graph. If you can do this, then you will discover two dimensions that describe and presumably underlie the three dimensions you plotted—in this example a curved sheet. Of course, defi f ning the surfa f ce will not label the dimensions, but it seems reasonable to accept the cook’s descriptions: green represents sweetness and blue represents fi f rmness.

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🍎 🍎

🍎🍎

10

8

6

JUICE 4

2

0 10

8

6 8

4

6

EAT

4

2

2 0

0

CO

OK

It is diff fficult to visualize more than three dimensions, but we can use mathematics to fi f t imaginary curves to data that are spread across any number of dimensions. In the lab we studied fa f cial emotions much as we “studied” apples in our imaginary experiment, but to fi f t curves to the data we used those maths. They show that the data can be described by fo f ur curves. These seem to be fo f ur underlying, primary dimensions of emotional expression. The maths do not describe the dimensions but, in order of importance, they appear to involve (1) pleasure, (2) power/weakness or dominance/submission, (3) arousal, and (4) intensity.13 Methods like this let us measure perceptual dimensions reliably. Many of these methods we can also apply to children. Studying children at diff fferent ages shows how adult perceptions develop.

PRECISION, ACCURACY AND SELF-SIMILARITY Most people think “accurate” and “precise” are synonyms but they are not. To say that Moscow is 1.234 km fr f om the Eiff ffel Tower is precise but demonstrably inaccurate. If you walk 1.234 km fr f om the

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Eiffel Tower, you will still be in Paris. On the other hand, to say that Moscow is approximately 2500 km from the Eiffel Tower is imprecise—the measurement implies ±100 km—but it is accurate. Inaccuracy can be demonstrated but accuracy cannot be. Indeed, accuracy cannot be measured at all. Imagine yourself a scientist in a research lab measuring a phenomenon for the very first time. There is no way to look up what the measurement ought to be, so you cannot tell how accurate your measurement is. All you can do is repeat the measurement several times and take an average, assuming that your several measurements surround the accurate number randomly. If you then measure the phenomenon in a different way, you expect different sources of random error, but you still have no way to know what the accurate number is, so again you repeat the measurement several times and take an average. Now you deem the average of the two averages to be correct. The same holds if you measure the phenomenon in a third way and a fourth way. You can never know the accurate number, you can only take the average of different ways of measuring the phenomenon. You may publish this average in books and see it quoted as gospel, but it is still no more than the centre of a cloud of measurements. You can see how reliable your measurements are by how much they vary, but you have no way to measure their accuracy—and if for all of your measurements your scale weighed heavy, your measurements will be reliably wrong. To sound accurate people often state measurements precisely, but precision cannot increase accuracy. Indeed, increasing precision can lessen accuracy. For example, this statement is true: All cows eat grass.

Now let’s add some precision: All cows eat 50 kg of grass per day, give or take 20 kg or so.

This leaves the statement broadly true. It is obviously a generalization. We can readily ignore how much grass lightens when it dries into hay, and we can ignore those cows that are sick and starving, or that eat corn in feed lots instead of hay. However, adding more precision makes the statement indisputably wrong: All cows eat 50.123 kg of grass per day.

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To avoid excessive precision, usually we choose our scale of measurement carefully. However, in some circumstances, the determinism in deterministic chaos makes it sensible to do something that sounds absurd: to measure something at several different scales simultaneously, and to treat the different scales as comparable. This is sensible when similar events occurring at different scales induce similar results at different scales. For example, imagine a rivulet of water flowing off a rock. It runs downhill, zig-zags around obstacles, carves out a narrow path in the mud, then ends in a puddle. Now imagine a creek. It runs downhill, zig-zags around obstacles, carves out a path in the mud, then ends in a pond. A river runs downhill, zig-zags around obstacles, carves out a broad path in the mud, then ends in a lake. Each sequence is the result of water falling on the ground, the scale is all that differs. The largest geological formation in North America—it is one-half the size of the United States—is a region of rivers and lakes called the Canadian Shield. The Shield is an aggregation of rivers, rivulets, lakes, and ponds spanning every size from the largest on earth to the smallest possible. The rivers and lakes of the Shield appear to be chaotic and random, a geological scribble, yet in one way it is organized: its structures are similar at every scale. Every detail differs but overall, small-scale and large-scale maps of the Shield always look the same. You can see this in the two satellite photos on the next page, where we converted the water to black and the land to white. One of these is magnified a hundredfold more than the other, but it is impossible to tell which one. The features on those photos look random yet at both scales, similar features appear. Because similar features exist across scales, across scales the Canadian Shield is not random. Across scales the Shield repeats itself to a remarkable extent. To describe the Shield appropriately we would measure it at different scales, to determine how similar it appears across scales. How similar it appears across scales is its degree of self-similarity.14 Self-similarity is everywhere with us, including within our brain. The brain’s neuronal connections branch and re-branch and rebranch again, creating networks of neurons, and networks of

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Satellite photos of the Canadian Shield showing water as black and land as white. One of these picture is magnified 100 times more than the other, but they are similar at each scale.

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networks of neurons, and networks of networks of networks. As we shall see throughout this book, the repeating, self-similar structures of the world help to shape the self-similar networks of the brain. Since self-similarity is central to the functioning of the brain, it is also central to aesthetics. Note, too, that this book also has a self-similar structure. We shall repeatedly examine similar material at different scales.

FOURIER TRANSFORMS In most ways Homo sapiens are the smartest animals on earth, yet our intelligence is still limited. To comprehend the world, we must simplify it. To make sense of the world, we must concentrate on central tendencies, on essences of things, and we must ignore distracting irregularities. The instruction, “Follow the highway about 80 km until you see the stadium” will take us to the ball game, but a detailed list of lanes and locations would lose us in confusion. At the lowest level of the nervous system, sensory neurons and the brain have evolved to simplify the components of physical stimulation. Energy in an infinity of forms and quanta stimulate the nervous system, but through evolution and individual experience, the nervous system has become adapted so that small parts of it are geared to respond predominantly to energy in specific forms over a small range of intensity. Or rather, to changes in energy over a small range of intensity, for neurons respond to changes in energy, not to constant stimulation. Neurons respond to the honk of a horn, not to the din of traffic. An individual neuron is like a gun. Usually it rests but sometimes it fires, and then after a short time it reloads. Neurons frequently fire without cause. Neurochemical energy sloshes through the brain like chop on the sea, setting off neurons at random. This happens so often that even while you are sound asleep, electrodes will record a cacophony of neuronal firing. This noise is largely random, and it is so constant that the brain ignores it. Within a sea of random events like this, meaning comes with repetition. Repetition is not always meaningful—by chance you may toss heads three times in a row—

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but when trying to distinguish information amidst noise, repetition is the most basic clue. For this reason, brains of every animal have evolved to recognize repetition. Each time a neuron fires, it changes the local neurochemistry to fire more readily under the same circumstances. This also happens with networks of neurons, small networks and large ones alike. After firing the chemistry gradually reverts to normal, unless the neuron or network of neurons fires again. Frequent firing leads to more durable chemical changes and less complete reversions. Regular firing is a chemical oscillation, a chemical pendulum. When we think of a pendulum we think of a grandfather clock. The pendulum moves slowly at first, then picks up speed until it passes the centre, then gradually slows until it stops and reverses direction. This forms a slow oscillation. As it evolves across time, this movement takes the form of a wave. A pendulum is one way to think of an oscillation but pendulums are relatively newfangled notions (at least outside of China). Before Galileo, physicists thought of oscillations not as pendulums but as circular motion stretched out through time. On a clock, the hand moves in a circle, but you can also describe the movement as oscillating down and up between 12 and 6. Here we connect the two perspectives: we plot the movement of the hand downward and upward on a scale defined by the hours the hand points to, which denote equal units of time. The curve shows that vertically, the hand moves more and more slowly as it approaches 6 or 12, and more and more quickly after it changes direction and heads back toward 3 or 9. The shape to the right of the clock is a sine wave. It graphs the upand-down movement of either a clock hand or a pendulum as the movement happens across time. A sine wave of one or another amplitude and frequency can describe any continuous, repetitive movement.

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But that is mathematical theory. Real movements are more complicated than theoretical movements. Real movements are never perfectly even and rarely repeat themselves perfectly. Few movements that occur in nature can be modelled closely by a single sine wave, nor even approximated by one. However, any complicated movement can be seen as containing one overall movement that is perfectly regular plus a remainder of erratic divergences; and that remainder can be seen similarly, and so forth ad infinitum. Each of these regular movements and sub-movements can be described by a sine wave. This allows describing any real movement by some combination of sine waves. A formal statement of this principle is that any waveform can be described by a set of sine waves differing in amplitude, frequency, and phase (timing). This is called a Fourier Transform after Jean Baptiste Joseph Fourier, a physicist and mathematician of Napoleonic France. Fourier measured the transfer of heat in iron bars, worked out the geometry, and generalized the geometry into mathematical laws that revolutionized science. Fourier broke down the movement of heat into a series of sine waves involving a basic or fundamental frequency, plus double that frequency, plus treble it, four times it, five times it, etc. If the fundamental frequency is 100 cycles per second (or cycles per inch, or whatever), then the series runs 100, 200, 300, 400, 500, 600, and so on. Inasmuch as this applies to heat, it applies to everything else, for much as Fourier explained, “Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space.” Heat is the energy dissipated by moving and vibrating particles. In consequence, Fourier’s mathematical laws of heat apply not just to the vibrating molecules of air impinging upon our skin to keep us warm but also to the vibrating air and photons that cause us to hear and to see.15 Moreover, we can substitute another word for heat: entropy. It is possible systematically to set out conventional physics substituting, in every equation, “entropy” for “heat.” Hans Fuchs wrote a university-level physics textbook that does just this. The two words are not synonyms but within the context of a machine like the brain, they refer to the same phenomenon and can be treated similarly for many purposes. Thus, just as we stated earlier that the brain’s basic

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function is controlling entropy, so we can say that its basic function is controlling heat.16 Any device controlling heat must encounter heat and measure it. Since the structure of heat is sinusoidal, a heat controller must respond to and measure energy as sinusoidal waves. The brain does exactly that. Innumerable experiments have shown that to a large extent the brain responds to stimuli by treating them as a combination of sine waves. To a large extent the brain works like a Fourier analyser. It is also possible to understand this in another way. The transfer of heat can be described by a set of sine waves passing through time and space at different frequencies. These frequencies form an arithmetic series—1, 2, 3, 4, 5, 6, 7, 8, 9… ∞ — but they can also be described by a set of structures that are self-similar at different scales—in other words, by a pair of fractals like these. Thus, just as any natural event can be described by an assortment of sine waves, so it can also be described by a combination of fractals.17 It would be oversimple to say that the brain senses the world solely as a set of self-similar structures. The brain is more complicated than that. However, simplification and repetition are fundamental to the brain’s functioning, and self-similar structures both simplify and repeat. The brain responds to them while listening to music, looking at paintings, or even just walking down the street. Self-similarity is a large part of the cement the brain uses to form the aggregate of low-level sensations into what we hear and see. In the next two chapters we shall encounter them at the root of all music and art.

3 THE SOUND OF MUSIC AN OVERVIEW OF MUSICAL ACOUSTICS

In the English language there has never been an encyclopedia that compares to the 11th edition of the Encyclopedia Britannica. It was published in 1910/11 and represents the pinnacle of Edwardian scholarship. Many of its articles are monographs written at the graduate level. Two such article/monographs are “Music” and “India.” At that time the musical traditions of India’s educated classes antedated European equivalents by almost three millennia, yet so little did westerners regard Indian music that “Music” does not mention India and “India” does not mention music. Some of this disregard seems to have been reciprocated. In 1943 a French orientalist and musicologist named Alain Daniélou published

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a book describing the world’s musical scales from eastern points of view. In it he asserts, “Westerners have lost all conception of a music able to express clearly the highest ideas and feelings.”1 “One man’s meat is another man’s poison” may hold more for music than anything else. We personally find little difference between most rock music and the sound of a hammer mill. We personally do not understand why people even put up with it, yet alone how they enjoy it. Nevertheless, just as rock music will deter us from sitting down in a restaurant, so classical music will deter youths from loitering on the street.2 It seems obvious that whatever kind of music any particular person prefers will have been determined largely by historical accident, by what he happened to grow up hearing. Nevertheless, since rock music and Mozart have comparable powers to attract and repel, something fundamental about them must be similar. This similarity lies in the way the brain evolved to organize energy that is funnelled into it from the ear. Imagine one of our earliest animal ancestors walking in a forest. It is heading into the wind. A predator stalks it from behind. To survive, our ancestor needs to sense the predator, to become aware of changes that the predator makes to the physical surroundings. Those changes take three forms: (1) the predator emits chemicals into the air, (2) it reflects some of the sun’s radiation, and (3) underfoot it bends roots and branches, creating minuscule waves of pressure in the air. Our ancestor detects chemicals through its nose, radiation through its eyes, and pressure waves through its ears. However, the predator is behind our ancestor in the lee of the wind, so our ancestor can neither see nor smell it. To survive, our ancestor needs to hear it. Yet the predator is not creating the only pressure waves. Insects and the wind are creating them too. Thus, for our ancestor to survive and reproduce, and to be able to do its part in planting the early seeds of our species, it needs to do more than merely sense the predator’s noise, it needs to be able to perceive the predator’s noises as distinct from other noises. The more distinctly our ancestor can hear the predator, the more likely it is to survive. Just as farmers help nature to create varieties of hen that lay more eggs by eating those hens that lay fewer, so predators help nature to improve the ability of their prey to hear them coming. This natural selection has

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caused most higher animals to evolve more or less comparable neural mechanisms dealing with pressure waves in the air. These mechanisms enable any animal to notice some elements of music— elements forming music, not music per se—and they enable Homo sapiens to learn to hear music as we do.3 An animal’s basic problem is how to distinguish one sound amidst a sea of sound or, in scientific terms, how to distinguish a signal from noise. To discriminate footfalls in the forest we have three clues. The first is obvious: pressure waves reaching the ear at the same time and from the same location are likely to have a common source. The second becomes obvious once you think about it: the more times that a set of pressure waves repeat, the less likely they are to be random. The third clue is less obvious and more interesting: harmonic clarity. That will be the subject of this chapter.

HARMONIC SERIES Imagine yourself walking in a forest. Water running down the path has washed out the earth so that thin tree roots stand taut and proud. You tread on one and hear a sound resembling a weak bass guitar. The root moves down, then it rebounds upward, then it rebounds downward and upward again, and again and again, less and less each time until the movement dies away. Each time the root moves downward, it compresses the air beneath it slightly and rarifies slightly the air above. Each time the root moves upward, it does the reverse. The repeated movements down and up form a wave of compression and rarefaction that travels through the air like a wave across a pond. When it reaches the inside of your ear, the pressure wave crashes into a drumhead—your eardrum—which transfers the energy from the air to saltwater inside a cavity behind the drum. The wave continues through the water and finally enters a channel lined with tiny hairs. Each hair is the end of a cell. When a pressure wave knocks against a hair, the hair acts like a crowbar to pry loose parts of atoms from the body of the cell. Those loose bits of atom—ions—have an electrical charge, so when they bump into cells nearby, they wreak havoc. They start a neurochemical chain response that runs from cell to cell through nerves up into and through the brain. The brain reacts by forming a sensation of sound.

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Now let’s look closer at the root. When you tread on it, you stretch it downwards. Since every action leads to an equal reaction in the opposite direction, the root rebounds until it bows upwards. It then continues to oscillate downward and upward, forming a continuous wave until its movements are damped by internal friction. Like any pendulum, the closer the root approaches the top and bottom of its trajectory, the more slowly it moves. As you will recall from the last chapter, this defines its movement as sinusoidal, so the root is forming a sine wave. A pressure wave moves through air at a constant speed, so as you can see here, if its frequency doubles, its length must halve. The ear senses the length of a pressure wave, not its frequency. A longer wave travels farther along the internal channel before crashing into the side and stimulating hair cells. The location of those hair cells is a measurement of wavelength, which we sense not in millimetres but in the pitch of a sound. However, stepping on the root generates many more frequencies than one. To see how, Imagine springs fastened to a ball like this. If you push down on the ball, it will bounce up and down. Next imagine more balls. Two balls can bounce in two different ways and three can bounce in three.

Four balls can bounce in four ways, five in five, etc. Any number of balls can bounce in exactly that number of ways. In principle all of this also applies to a root you tread on, because you can think of the exposed root as an infinite number of balls connected by an infinite number of springs. After your foot touches it,

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the root vibrates as a whole and also in halves, in thirds, in fourths, in fifths, etc. Physicists call this an harmonic series. The first harmonic is the frequency of the root vibrating as a whole. This is also called the fundamental frequency. The second harmonic is the root vibrating in halves; the third harmonic is the root vibrating in thirds; etc. The first harmonic is the strongest, because it involves the entire root. The other harmonics contain lesser amounts of energy as they involve lesser lengths of root. Each of these harmonics reaches hair cells at different places inside the ear, so each of these harmonics stimulates the ear differently. Although each of these harmonics might be heard on its own, the brain combines the lot of them into a single sound. We can visualize this with waves that stimulate the eye instead of the ear, waves that vary in brightness across space. Here are a single sine wave and, underneath, a set of 16 harmonics added together. In both of these the distance from black to black is the fundamental frequency.

String instruments generate pressure waves as the root does. Our vocal cords work similarly. Wind instruments use a different

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mechanism to induce the vibrations—we shall discuss this later in the chapter—but they create a comparable harmonic series. Pressure waves of a single frequency never exist in nature, because everything that induces a pressure wave vibrates in numerous parts as well as in the whole, but we can learn how individual harmonics interact within the brain by generating individual harmonics electronically. Each individual harmonic sounds like a musical tone, but the tone sounds curiously simple and artificial. Adding harmonics adds aural complexity. The first, second, and fourth harmonics all sound different yet they sound similar as well. The third and fifth harmonics sound totally unlike those others but combine with them mellifluously. The third sounds halfway in pitch between the second and the fourth. These first five harmonics of a pressure wave are consonant in every combination, and they are 5 1 2 3 4 fundamental to the music of every culture we know of. They are the notes marked on this keyboard. Higher harmonics sound less consonant with these and often sound downright dissonant, but these five harmonics contain most of the energy of the complete wave. If a pressure wave contains any frequencies that are not part of the harmonic series, they will sound dissonant with these.4 “Consonant” means “sounding with.” Two consonant waves sound with one another. If they start simultaneously, then they are normally heard as a unitary sound, a sound from a single source. Combining consonant pressure waves into single perceptions evolved to help us sort out pressure waves by their origin. In nature, nothing that vibrates forms a perfect harmonic series, because real structures are more complicated than our simple model of balls and springs, but any sound that we perceive as having a musical pitch contains an imperfect harmonic series. This includes most vocalizations by animals. Each will vary from the ideal in different ways but over time, the average of all the harmonic series that a brain encounters is likely to approach the ideal. In this way, experience and evolution shape the brain’s neuronal pathways so that they are centred around this ideal. This has made the brain so

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sensitive to an harmonic series that it will respond to the merest suggestion of one. Indeed, the brain is so sensitive to an harmonic series that it will infer parts of it that do not exist. When you listen to a double bass on a small radio, the lowest note that the radio’s speaker can emit may be the third or fourth harmonic, yet you will still hear the pitch of the missing first harmonic. That is because your sense of hearing responds not to individual waves but to harmonic structures as a whole. We can see this with sine waves in space instead of time. These two images show the same harmonic series but the one above is complete and the one below is missing the first four harmonics. Although the latter series starts with the fifth harmonic, we can still see the distance from black to black, which is the spatial frequency of the missing first harmonic.

We are using a visual example because it is not possible to present sounds in print, but the auditory system recognizes an harmonic series in exactly the same way. A mathematician might not think this remarkable, because he can show mathematically how a fundamental frequency can be derived from the information implicit in the higher harmonics, but the brain does not discover a pattern by solving equations, the brain perceives the pattern immediately and directly. Hair cells in the ear respond to different frequencies at the same moment and send off similar streams of neurochemical

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reactions into the brain. In milliseconds those reactions begin to spread through the brain’s grey matter, the cortex. The cortex has evolved so that if the pattern is one that is likely to have been formed by a single event, then all of those signals combine into a single perception, a single sound. Physically and mathematically, the most constant feature of a partial harmonic series is the fundamental frequency, so the brain has evolved to perceive a fundamental frequency when any partial set of harmonics is present. Even threemonth-old babies do this. Not only that, the brain perceives the degree of uncertainty of its judgement. This it does by perceiving different degrees of consonance. The more neat and complete the set of harmonics, the more certain the brain can be that they come from one source, and the more unified the tone will sound.5 In nature, no object is likely to create more than one harmonic series, but if two people sing so that their lower harmonics overlap, the brain will still hear consonance. Consonance is the basis of harmony in music, and a preference for consonant music over dissonant music is present at birth.6

SCALES To systematize the pitches that singers sing and musicians play, philosophers in the east and west have plucked strings of various length, listened to their pitches, then identified and named consonant intervals. They have done this over millennia and all of them everywhere have deemed these ratios of string length to be consonant: 2:1 (octave) 3:2 (perfect fifth) 4:3 (perfect fourth) 5:3 (major sixth) 5:4 (major third)

These are all ratios of small integers. Ratios of larger integers leave consonance behind. Some people deem 6:5 (minor third) and 8:5 (minor sixth) to be consonant, but others do not. The intervals 7:8, 8:9, 9:10, and 10:11 sound dissonant to everyone.

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These numerical and musical relationships seem so neat that to ancient philosophers they showed the hand of God. However, the reality is not divine, it’s a mathematical hell. Imagine a pair of musicians playing scales on long strings that they shorten with a finger to create higher notes—a prototypical violin. Robert skips upward eight notes at once five times; Roberta skips upward five notes at once eight times. Both end up 40 notes higher but they don’t end up at the same spot on the string. Robert shortens his string by successive halves, so that his string length is now 1/32 of the original:

¹/2

×

¹/2

×

¹/2

×

¹/2

×

¹/2     = ¹/32  

and Roberta shortens her string by successive two-thirds, so that her string length is now 1/25 of the original. These different lengths of string create different pitches that sound dissonant: 2

/3 × 2/3 × 2/3  × 2/3  × 2/3 × 2/3 × 2/3 × 2/3 

=

256

/6561 ~ ¹ ⁄ 25

This is a mathematical mess that cannot be cleaned up, but the mathematical harmonic series is so neat that musical theorists keep working with it to create new musical scales. As we write this, one web site details over 4800 scales. However, none of these scales permits two instruments to play all of the consonant intervals in tune, because that is mathematically impossible. To work around this, theoreticians devised a “tempered” scale that tempers or fudges every interval except the octave, so that no intervals except octaves are perfectly tuned but none of the consonant intervals is too bad. This scale gradually became the norm in Western Europe during the 18th and 19th centuries.7 In addition to the mathematical realities, physical structures distort theoretical ideals. A piano, for instance, needs to stretch apart the treble and bass to compensate for certain distortions of the harmonic structure that are induced by the steel strings, so that in the piano’s tempered scale, even octaves are fudged. All of this means that if a musician plays notes at their theoretical frequencies, she will rarely sound in tune. If she wants to sound in tune, she must ignore the theoretical frequencies and adjust the pitch from moment to moment, to sound as sweet as possible within the context of the last sound she made and/or the sounds that other musicians are making.

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This is why amateur musicians may tune their instruments yet still sound sour. Tuning a string or wind instrument does not actually tune the notes, it just puts them in the ballpark. A musician still needs to adjust the pitch of each note she plays.

TIMBRE AND SPEECH Unlike mathematical models, physical objects have mass and irregularities. For this reason any real object will vibrate more readily at some frequencies than at others. The exact set of harmonics generated will depend upon the shape, mass, and stiffness of the object. For this reason, the vibrations of a real object will never come close to a perfect harmonic series. For example, here is the spectrum of frequencies generated by a professional violinist playing a long note as steadily as he could—an A at 440 Hz. The complete spectrum is below and an enlargement of the lower harmonics is on the right. Each horizontal line indicates a doubling (upward) or halving (downward) of power. You can see that the harmonics do not diminish regularly as they rise in frequency, nor is each harmonic a single frequency. The harmonics diminish irregularly and, although the harmonics are 440 Hz apart, each harmonic spreads over a range of frequencies. (The weak frequencies scattered far from the harmonics are probably background noise in the room.)

Power e

440 Hz

Frequ q encyy

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Again, this shows a violinist playing a long, steady tone, but most notes in music are short. When a string begins to move, it vibrates across a range of frequencies before settling down to one frequency. Moreover, the wooden body of a violin picks up energy from pressure waves and resonates with them, adding inertia to the system. For these reasons, most harmonics of most notes spread across a range of frequencies and change rapidly with time. The proportions of the harmonics—the relative power of each harmonic—form an instrument’s timbre. Different sets of harmonics make one violin sound different from another and make a violin sound different from a flute. The brain processes these changes very fast. How fast we can see most easily with speech. Speech is a succession of pressure waves that look something like this when plotted on paper. Here are 2.5 seconds of French enunciated clearly by an actor. The height of the wave indicates the power of his voice. The actor is saying, “La première année dans une université française.”

Power

la première année dans une université française

As rapidly as this wave varies in pressure, so it varies in frequency. On the next page is a graph showing this. Darker greys show greater energy. You can see that to some extent the energy of each syllable is concentrated into bands of frequencies, especially below 5000 Hz. Nowhere do these bands form a clear and perfect harmonic series, yet the bands do resemble an harmonic series, an harmonic series evolving through the phrase. Just as the visual portions of your brain notice these harmonic-like patterns, so do the auditory portions. The waves forming speech vary from moment to moment both in pressure and in frequency. Those two dimensions form every word

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Frequency (Hz)

5,000

0

la première année dans une université française

and phrase we hear. The only species with a physical structure (the voice box) able to control these finely is Homo sapiens, but communicating through pressure waves is so important to survival to so many species that nervous systems evolved aeons ago to perceive changes in pressure and to communicate through them. Even some insects can do this. Any form of communication based on pressure alone amounts merely to drumming, but it is worth noting how much information drumming can transmit. Before the days of mobile phones, many aboriginal peoples used drums for telecommunication. With two differently sounding drums an Ashanti could warn of a fire, announce the approach of a European, call men to arms, summon a specific chief, or announce a specific chief’s death.8 Words fly by quickly and syllables fly by even faster, but most evanescent are the tiny chunks of a pressure wave that form the atoms of speech, the bit we hear as the d and ough of “dough” or the r, i, and ng of “ring.” Phonemes these are called—pseudo-Greek for “particles of sound.” The 2.5 seconds of French above contains 33 phonemes, 13 of them per second.

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At first blush it seems miraculous that the brain can make out subtle changes in information flying by so fast. It seems especially miraculous that babies can do it—yet babies can do it even better than adults. Babies are born able to discriminate most of the phonemes of their native tongue, plus phonemes used in other languages that adults have learned to ignore in their own. People often cite this neonatal capability as evidence of some special precocity, but a closer look shows this capability to be more mundane.9 Surprisingly, an appropriate perspective for examining this speed of processing is Einstein’s. Einstein pointed out that since everything in the universe is moving all the time, the speed of any one object cannot be measured except in comparison to another. All of us are hurtling through space yet we do not notice this because all of us are moving through space together. Relative speeds are what we see. That is why, when we are driving on a freeway, we can spend a long time studying a truck in the next lane yet signs on the shoulder zip past fast.10 This is the basis of Einstein’s theory of relativity. Einstein applied it to physics and astrophysics but it is a basic principle that applies to everything in the universe, including the neurochemistry of the brain. Pressure waves stimulate neurochemical reactions that travel through the brain. Speech stimulates and interacts with the brain about as quickly as the brain’s neurochemistry allows. Paradoxically, if we slowed down speech tenfold, then phonemes would enter the ear at one-tenth the rate and there would be a tenfold greater difference in speed between the rate of speech and the rate of neuronal processing. This would make the neural processing of the phonemes inefficient and the speech more difficult to comprehend.11 The particular harmonic patterns of a pressure wave that characterize an individual phoneme are called a formant. Comparable patterns also characterize individual instruments and singers. These patterns are the equivalent of formants but the term “formant” is not used outside linguistics. The words Louis Armstrong sings are clear because his voice creates patterns of harmonics that we hear as English phonemes. Louis Armstrong’s voice sounds unique because his singing voice is defined by comparable patterns of harmonics that are unique. Both of these patterns are aural equivalents to a tiger’s stripes.

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Armstrong sang into a microphone over a handful of musicians but opera singers must make themselves heard without a microphone over 50 musicians or more. They do this by boosting their harmonics unnaturally, so that they contain great power at a frequency high enough (near 3000 Hz) that the natural harmonics of the orchestra’s harmonics have diminished to relatively little. This is the equivalent of boosting the treble of a car’s radio to hear an announcer more clearly over the noise from the engine and tires. Every real set of harmonics differs greatly from the mathematical ideal—for example, clarinets emit virtually no energy in the evenly numbered harmonics—but within any set of instruments that are constructed similarly, the differences are similar. Thus, after hearing a number of clarinets, the brain comes to identify any harmonic series missing the even harmonics as representative of a clarinet. With a little experience the brain will hear this no matter whether the clarinet is a normal soprano instrument or an alto or bass, or even a sopranino (the clarinetist’s answer to the piccolo). The more a sound resembles a prototype—the prototypical loon or the prototypical saxophone or the prototypical harmonic series—the less it sounds like other things. This has two opposite effects. The more prototypical a tone is, the more it will blend in with similar tones but the more it will stand out from different tones. That is why you can never tell how many crickets are chirping in the woods but among a cacophony of crickets you can hear a single mosquito buzz by your ear. It is also why a trumpet can either blend indistinguishably with a mass of brasses or soar out overtop an orchestra on its own. Harmonics are so important that most classical musicians work at least as hard at controlling them as they work on learning how to play the notes of a piece of music. They don’t think of it that way, though. They think of it as working on their tone and intonation (the fine control of pitch). All musicians understand that harmonics shape timbre but fewer realize that the pattern of harmonics affects pitch as well. The normal pattern more or less approximates the mathematical ideal. As we mentioned earlier, if we hear this pattern without the lowest harmonics—if we hear a double bass over a small radio—then we

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will still hear the pitch of the fundamental frequency. If we are in the same room as the instrument, so that we hear all of the harmonics, then if the higher harmonics are stronger or weaker than normal, we are likely to hear the pitch as sharper or flatter. On the other hand, if the harmonics differ wildly from the ideal, then we will likely hear a pitch that is not determined just by the fundamental frequency but is some kind of integrated average. We can see the latter with our sample of speech. Here are the first 5000 Hz. The red lines show the centre of each harmonic. As you can see, the red lines do not rise and fall together from phoneme to phoneme—one moves up while another moves down—so they cannot be neat multiples of the fundamental frequency.

5 kHz

0 Hz

la première année dans une uni versité française

From that graph there is no way to guess the pitch of the speaker’s voice, but below we plotted it in blue. The top and bottom pitch are just over one octave apart. The line stops occasionally because the voice stops momentarily before explosions like pr, and because some

5 kHz

0 Hz

la première année dans une uni versité française

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sounds like s contain so shapeless a distribution of frequencies that the ear does not hear a recognizable pitch. Note that the pitch we hear and the fundamental frequency mostly move independently. This speech stimulates the brain with a clear pattern of harmonics, not a random collection, so the brain hears pitches rather than noises, but no single harmonic determines the pitch. The pitch is the brain’s integrated response to the pattern as a whole. Moreover, the lowest harmonics differ so much from the others that the brain hears them as distinct, as an inchoate resonance underlying the sound. The pitch of the speech is in the tenor range but the rumble of the lowest harmonics forms the voice into a resonant baritone.

STRINGS The ideal harmonic series is the set of vibrations caused by plucking an ideal string. However, an ideal string does not stretch when you pluck it, as any real string does. This stretching creates both problems and possibilities.

BOWS The working surface of a bow is a ribbon of horsehairs stretched by a springy stick. You hold the bow so that the edge of the ribbon rides over the strings, not the flat surface. Pressure on the edge flattens the ribbon against the strings. The hairs wear through and break quickly enough that a professional violinist will re-hair a bow several times a year. Rehairing a bow costs as much as a replacing a tire. Bow-hairs come from light-coloured horses with long tails. Few such horses remain in western countries but they do in China, so nowadays bow-hairs come from China. Bows differ primarily in their stiffness and mass, and in the distribution of their stiffness and mass along their length. Infinitesimal differences affect how well you can control the pressure on the strings while holding your arm at different angles and moving it at different rates. No one bow is optimal for playing every kind of music, and bows can be broken, so professionals usually carry at least two. A professional bow costs as much as a good used car and can reach the price range of a new Mercedes.

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VIOLINS AND VIOLS To our ear the violoncello is the most beautiful of all instruments but it also has the strangest name. Its Italian origin has three parts: viol-onecello. Viol is a stringed instrument; one is a suffix meaning big; and cello is a diminutive. Thus, violoncello means “little big viol.” Western stringed instruments were developed over many centuries in many places by people who spoke different dialects of Italian, which became the musical lingua franca of the western world after Latin disappeared in the Middle Ages. This has left the history of these instruments and their names in a profound and ineluctable mess. “Viol” and “violin,” for example, have sometimes referred to the same instrument and at other times to different instruments, and when differentiated the terms have been differentiated in different ways. Thus, for example, the Oxford English Dictionary defines the “little big viol”— the violoncello—as “a bass violin,” although it also covers the range of a tenor and the larger “bass fiddle” sounds an octave lower. Since the mid-19th century, four string instruments have become more or less standardized in western music. In English the soprano instrument is the violin or fiddle. The alto is the viola, which also doubles as a weak tenor. A tenor and baritone is the violoncello, which is commonly shortened to ‘cello. The bass goes by five names: bass viol, double-bass, string bass, bass violin, and bass fiddle.

When you pluck a string with your finger, you stretch it then let it shrink back to its normal length. Since the length of the string determines the frequencies, and the string shrinks as it sounds, each pluck creates a range of frequencies. Something comparable happens when you bow a violin. Resin on the bow provides a layer of microscopic hooks. Those hooks repeatedly catch the string, stretch it a short distance, then let it go. Moreover, as a violinist bows, the pressure on the bow changes slightly, so that different amounts of the flat bow-hairs contact the string. For these reasons different numbers of hooks are always catching the string and stretching it differing amounts. This creates clusters of harmonic frequencies, harmonics formed not at a single frequency but around one.12 Now let’s look at this clustering and imagine how it would affect the sound. Imagine yourself in a lab with signal generators that let you shape a set of harmonics anyway you like. Begin with an ideal

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harmonic series. This will produce a perfectly defined pitch with a clear timbre. If you add energy around each harmonic—if you add a haze of surrounding frequencies—the ear will still hear the same pitch but the pitch and timbre will sound less pure. The more energy you put into the surrounding frequencies, the fuzzier the pitch and timbre will become. This fuzziness helps string players to sound in tune when playing with one another. You can see why here. The three clear frequencies above will sound like three distinct and dissonant pitches, but the three broader sets of frequencies below will combine to form a single unclear pitch. The massed strings in an orchestra take advantage of this fuzziness, and so do the four instruments forming a standard string quartet like the one on the next page: two violins, a deeper viola (slightly larger), and a much deeper violoncello (so large that it stands on the floor). The harmonics of these instruments are similar enough and fuzzy enough to blend yet different enough to provide variety. Besides getting louder and softer, a musician can adjust the harmonics first to bring out a melody and then to blend. This interplay of fuzzy harmonics enables such a range of musical expression that in western music, the repertory performed in concerts by string quartets like the one on the next page is greater than the repertory performed by any other set of instruments.

WINDS Like everybody else, Louis Armstrong blew raspberries as a child— made farting sounds with his lips. You may want to remind yourself of the pleasure by doing that now. Air pressure builds up inside your mouth, then suddenly the pressure bursts your lips apart. With your lips apart, the air pressure in your mouth collapses. Your lips spring closed again and the cycle repeats. It was by blowing raspberries like this that the adult Armstrong played the trumpet.

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The Müller Brothers, the first touring string quartet, in 1832.13

Of course to make music, Armstrong needed to purée his raspberries into a smooth sound and pour them into notes. To see how he did this, imagine yourself sitting on the ground blowing a raspberry into the end of a tube—perhaps into a thick stick that termites have hollowed out. You are now playing the simplest conceivable wind instrument, the aboriginal Australian’s didgeridoo shown on the next page. Pressure builds in your mouth until it forces your lips apart. This starts a bolus of pressurized air flying toward the bottom of the tube. As the bolus exits the tube, it draws some air behind it. This additional air sucks out more air from farther up the tube, which sucks out air from still farther up, forming a wave of rarefaction that travels back to your lips. Once this wave reaches your lips, it sucks them closed. Since your lips are closed, the air in front of them reaches a pressure slightly less than the atmosphere’s, so air flows in from the bottom of the tube. This incoming air gradually brings the pressure back up to normal—but the air does not stop moving instantly once the pressure has normalized, it continues to flow in under its own momentum and becomes concentrated near your lips. This pressure helps to push your lips open so that they release another bolus of air, and the process starts over again. Thus, your lips end up opening and closing at a regular rate. This rate is defined

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by the speed that pressure waves travel in air and by the length of the tube. It is the tube’s “resonant frequency.” Most of the energy stays within the tube but maybe one percent leaks out the end to tickle your ear and induce the instrument’s sound. When you blow the raspberry to start this process, your lips do not open and close following the profile of a perfect sine wave, they jerk up and down. Sudden jerks include a wide range of frequencies. Some of those frequencies have wavelengths that are neat fractions of the tube’s length. These form harmonics. Between your lips and the end of the tube the harmonic frequencies repeat twice, thrice, four times, five times, etc. Higher harmonics diminish in energy like the harmonics of a vibrating string, but about one percent of each higher harmonic’s energy leaks out the end along with the fundamental frequency. The shape of the tube determines the distribution of harmonics. The job of a didgeridoo player is to keep his lips vibrating as constantly as possible, to reduce the spread of harmonics and to make the pitch and timbre of the aggregate of harmonics sound correct. In engineering terms, he does this by controlling air pressure and flow, by damping a vibrator, and by adjusting additional resonators that can increase the vibrator’s amplitude at certain frequencies. In human terms he controls air pressure with the muscles squeezing his lungs, he controls air flow with the muscles of his throat and tongue, he adjusts damping with the muscles of his lips

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and jaws, and he adjusts resonators by controlling the muscles lining his mouth, throat, and thoracic cavity. The didgeridoo is the archetype of all wind instruments. No other wind instrument is so simple as the didgeridoo, and many instruments use a vibrating reed instead of vibrating lips, but these are differences in detail, not in principle. A cynical physicist might say that the most significant difference between vibrating lips and vibrating reeds is the player’s excuse for playing badly. Instruments can be cylindrical or conical and can differ in size, and these differences will create different resonances and hence different sets of harmonics, but nearly all wind instruments involve similar acoustical mechanisms and comparable principles of control. The only (partial) exceptions are flutes, whose vibrations are formed by an aerodynamic effect at a mouthpiece that is in front of the player’s mouth rather than inside it, so the pressure waves cannot resonate in any of the player’s bodily cavities. That is why flutes have a smaller range of loudness and timbre than the other instruments in an orchestra. There is also no fundamental difference between a wind player and a singer. A singer’s mouth and throat resonate much like a didgeridoo, and those resonances feed back to control vibrating tissue: the vocal cords. Or more correctly, the vocal folds. Medieval anatomists thought these to be sinews and so named them cords, but they are actually folds of tissue.

SINGING A singer controls his vocal folds as a wind player controls her lips or reed, but the vocal folds, throat and mouth are more malleable, so a singer can create a greater range of sounds than any wind instrument. Before electronic entertainment replaced home-made amusement— before the phonograph and radio—most people used to sing. They sang for their own pleasure, they often sang with other people, and

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if they became good enough, they would sing for other people. Some people sang well enough to travel around as troubadours singing for pay. Five hundred years ago in Europe, troubadours wandered the countryside from one great house to another, singing for supper and coin. With industrialization in the 18th century, commerce and money began to become more important to people than land, so wealthy people began to move off the land into cities, where markets were larger. In cities, professional singers could attract audiences larger than a house could hold, so they began to sing in public halls. Entrepreneurs built theatres that could hold hundreds of people with dozens of musicians playing instruments and dozens of people singing. (This is all within Europe: in much of Asia, professional singers still came to homes through the middle of the 20th century.) The larger and richer the cities became, the larger the audience became and the more spectacle the audience expected. By the middle of the 19th century, theatres commonly had 1000 to 3000 seats with orchestra pits and stages that could each hold 50 to 100 performers. Since the end of the 20th century, audiences have become so large, and have demanded so much spectacle, that some singers perform in sports arenas with amplification creating sound pressures comparable to aerial bombardment. These economic developments have shaped the harmonic structures that singers must produce to be heard.14 Singing naturally is a gentle activity like strolling down a street. Singing naturally uses little pressure from the lungs, and the muscles of the mouth and throat are relaxed and flaccid, so that they form weak resonators. Low pressures and weak resonators do not create high harmonics. Without high harmonics the sound is soft and unfocused, the sound of a crooner. It can be beautiful but it does not carry far and is easily masked by instruments. This kind of voice requires amplification to be heard from any distance. Before the days of microphones and loudspeakers, no one could sing like this before much of an audience. With amplification, there is no reason to learn any other form of singing if the goal is merely to be heard. Without amplification, to be audible before an audience a singer needs to generate higher harmonics. In small theatres there is no

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HALLS AND INSTRUMENTS Larger halls changed musical instruments as well. In the 19th century, larger halls saw violin-makers strengthen antique violins for fitting with steel strings instead of gut, and piano-makers develop iron frames that could handle higher tensions than wood. The stronger sound of those instruments then came to shape people’s preferences. Every middle-class family owned a piano and every manufacturer of pianos wanted to sell pianos for homes, which formed the primary market. In the 1850s Henry Steinway (né Heinrich Steinweg) and his sons realized that the best way to sell pianos for homes would be to have people see them used in concert halls, so they designed a piano with an especially powerful and brilliant sound that would carry in a large hall, and got their instruments used on stage. Other manufacturers followed suit, often with more mellifluous instruments better suited to a living room, but the Steinways kept boosting their pianos’ power and eventually their pianos became heard so often that their tonality became the pianistic norm.15

need for a singer to make a great deal of noise, sufficient is sounding sweet. In the days of small theatres, a singer with a sweet voice, a bel canto singer, would do exactly this. The goal was maximal purity with minimal muscular effort. Since relatively little effort was involved, the various muscles could adjust their tension rapidly, to produce cascades of notes, vocal frills and flounces that would decorate melodies like fringes and feathers decorating a dress. A florid bel canto style developed. Composers wrote melodies expecting them to be embellished by the singer, and singers improvised embellishments to show off their skill. However, singing like this is too quiet to make much of an effect in a theatre with thousands of seats. A large hall needs noise. To be heard, a singer must maximize air pressure and resonance at the expense of pure harmonics. She must push her voice to be as loud as possible, and she must ignore the roughness that results. When muscles are tensed to the utmost, they become less flexible, so this kind of voice is incapable of florid, bel canto decoration. A voice like this sounds less ethereal than a bel canto voice—gutsier, more emotional—and needs to sing melodies more simply, without embellishment. Emotion is carried not through sprays of notes but through vocal tension, so Italians called it opera verismo—“realistic opera”—and that is the norm in the opera house today.

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OPERAS VS. MUSICALS Operas used to be popular entertainments—song, dance, and either chanted or spoken dialogue—but in the late 19th century, the term “opera” was hijacked by high-brows. Thereafter, unsophisticates who wanted to watch operas went to see “musicals” instead. Since the last quarter of the 20th century, electronics and amplification have dramatically changed popular music but before then there were no real differences between operas and musicals save the gravitas of marketing and critics, and a snobbish disdain by some audiences for the popular songs of the day (as opposed to the popular songs of the day before). Although operas are often tragic and musicals comic, they need not be. We have never laughed more at anything than the Royal Opera’s production of Shostakovich’s The Nose, and the musical West Side Story is a 20th-century version of Shakespeare’s Romeo and Juliet.16

Of course, realistic opera is an oxymoron. Nothing about opera is the least bit realistic. Everything from the music to the staging is based on artificial conventions, artificial conventions that relatively few people understand and accept. Indeed, to most people living on this earth, all operatic singing is grotesque, and even an opera buff would never call it natural. (Mind you, most people do not know what it sounds like. Most people have never heard any opera save snippets over a radio or television, where it is compressed and distorted into the musical equivalent of a shrunken head.) However, we shall see later that singing and dancing—making music—is a behaviour Homo sapiens evolved that has helped people to work together and, hence, to survive. The nature of music varies across time and space but making some kind of music has likely been an important component of human evolution. For the moment, though, let’s return to the forest and predators stalking our ancestors. Hearing an harmonic series as a single sound helped our ancestors to perceive other beasts in time to avoid being eaten. More than that, it helped our ancestors to understand their environment and, eventually, to describe and discuss it. In the next chapter we shall see that comparable mechanisms have a comparable advantage when applied to waves of light.

4 SEEING HARMONIC LINES SIGHTS ARE LIKE SOUNDS

Before man began to hunt meat in markets, he had to find food in the field. To do this, he needed to see it. He needed to be sensitive to patterns of electromagnetic vibration reaching his body, and he had to become able to interpret those patterns so that he could perceive a deer among trees or a fish in a stream or locusts flying through the air. Thus, the task of the visual system is exactly comparable to that of the auditory system, only the nature of the energy is different: waves of electromagnetic radiation rather than pressure. We think of hearing and seeing as totally different yet they are remarkably similar under the hood. The auditory and visual systems both process vibratory energy. The nature of the energy differs, so

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the organs sensing the energy differ, but both sets of organs convert the vibratory energy into electrochemical impulses that travel through nerves into and through the brain. Within the brain there is no difference whatsoever between impulses from the eyes and impulses from the ears. They take different routes into and through the brain but the neuronal traffic is indistinguishable, and with a network of neurons as with a network of roads, traffic in one area may impinge on traffic in another.

PARSING SIGHTS When you open your eyes in the morning, you see the lamp by your bed, your night table, your bureau, and all the other objects in the room. You can distinguish these even if your eyesight is so bad that you cannot read the headlines of a newspaper without your glasses. You are so used to being able to do this that you do not find it the least surprising, but imagine you have never seen anything at all. Imagine opening your eyes for the first time after birth. Since you have never seen anything, you would not know how to make sense of anything. The world would be terra incognita. It might seem to be formed of parts but could look as enigmatic as this:

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What part of this scene goes with what? Is this a dark grey mass resting atop a layer of speckled white? Or is the speckled white protruding higher than the grey? Are the black specks high or low? Is this a number of different objects or one object containing many parts? Looking at this picture is the visual equivalent of listening to an unknown language. We lack sufficient experience to decipher it, yet we do see clearly that it contains a number of parts. Now imagine yourself on safari in Africa, spending your first night in a tent. The outdoors are alive with whishes, whistles, whoops and roars, but with no experience you cannot begin to tell what animals are nearby. This confusedness is comparable to seeing the picture of terra incognita and comes from comparable processing in the brain. Energy passes into low levels of the brain, coalesces into coherent patterns, then pass into higher levels of the brain, where they form themselves into the things we hear and see, and usually (although perhaps not here) become associated with other things we have heard and seen before. We showed in the last chapter that the first step to hearing patterns is identifying sets of vibrations that emanate from a single source. The same holds for seeing patterns. From the perspective of the brain, the primary difference lies in the dimension of the energy. We hear changes in energy occurring through time but we see changes in energy occurring through space. With sounds we recognize

JABBERWOCKY In a curious way our picture of terra incognita illustrates Lewis Carrol’s “Jabberwocky”: Twas brillig, and the slithy toves Did gyre and gimble in the wabe: All mimsy were the borogoves, And the mome raths outgrabe. As with the ear, so with the eye: the brain learns to identify structures even when those structures are filled with nonsense representing nothing on earth. Meaningless structure can appear to be so meaningful that academic journals have published a number of “scholarly” papers generated by a computer.1

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parts and pieces when (1) changes in energy begin together, (2) changes in energy repeat, and (3) a bolus of energy contains a coherent harmonic structure. The same criteria hold for recognizing the parts and pieces of what we see. In the picture of terra incognita (1) a diagonal line defines a change in energy across the two parts of the picture, (2) each of those parts contains repeated changes in energy, and (3) the picture contains a coherent set of frequencies, frequencies not in time but in space.

SPATIAL FREQUENCIES At the end of chapter two we said that any variation in energy can be described by a set of sine waves differing in frequency, amplitude and phase. In the last chapter STRIPE we applied this Fourier Transform to pressure waves of air. We can also apply it to light. For example, the top of this illustration shows a change COMPONENT of energy forming a blackFREQUENCIES and-white stripe. Beneath it we have broken down the stripe into nine sine waves, each double the wavelength of the one above. Light varies not over time but over space, so spatial frequencies are measured not in cycles per second but in cycles per inch or millimetre or, most commonly, cycles per visual degree, per degree of angle subtended by the object at the eye. Here the tree represents 21 visual degrees. Since light varies over space, changes in light may be vertical, horizontal, or oblique. This means that the spatial frequencies of a scene vary with orientation. You can get a feeling for all of this from the montage on the next page. Frame #9 shows the original picture; the other frames show individual spatial frequencies contained within

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the image. Frame #1 shows the lowest and each successive frame shows a spatial frequency twice as high, the mathematical equivalent of rising an octave in pitch.

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As you can see, most of the information comes from the middle frequencies and the fine detail comes from the highest frequencies. Extremely low frequencies show little. Not coincidentally, this is the case with sound as well. We identify the timbre of an instrument not from the first or second harmonic but from higher harmonics (which is why boosting the treble of a radio clarifies the sound).2 All of us are so familiar with faces that we can see a face in frame #4 but let’s consider a picture we do not recognize, the picture of terra incognita on page 60. We cannot tell what it represents but it clearly divides into parts—and the parts change when we look at isolated frequencies. Below we isolated individual frequencies two “octaves” apart—roughly equivalent to frames one, three, five and seven of the urchin above—but since we have little experience of the original, none of these parts presents enough information to convey any meaning. They look like vague waveforms and nothing more. Since nothing in nature is a pure sine wave, there has been no evolutionary pressure for the brain to develop clear associations with pure sine waves. This holds for sounds as well: a pure sine wave has a clear pitch but otherwise sounds vague and undefined. With sights as with sounds, virtually all the information about the contours of an object is carried through a combination of frequencies.

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The abruptness and breadth of the edge of a line—sharpness or blur—is the equivalent in vision to the timbre of a tone. A sharp edge is the visual equivalent of a clear tone. We have no word in English for the timbre of a line but a Chinese artist might say that it is one sense of bimo—literally “brush ink,” the strength and gradations of line and tone in an ink-brush painting like this.3 A novice playing a musical instrument will come across as having an unfocussed tone of uncertain timbre. That is because instead of creating a neat set of discrete harmonics, a novice creates a sloppy set of harmonics that blur together and sound unclear. When spatial frequencies are poorly aligned, perhaps from sloppy brushwork, then we see blurring. Strictly speaking, the spatial frequencies inducing vision are not harmonic frequencies, because reflected light does not form waves vibrating in the geometric series of halves, thirds, quarters, etc. On the other hand, musical instruments do not vibrate so cleanly as the mathematical model, and ordinary auditory stimuli may not contain a proper harmonic series at all. To be technically correct when speaking of sounds we ought to distinguish between harmonic and non-harmonic constituent frequencies, but for our purposes there is no point to doing so. “Harmonics” is clearer and is accurate enough for our purposes. Similarly, it is technically incorrect yet heuristically appropriate to think of spatial frequencies as spatial harmonics, which we shall do throughout this book.

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PERCEPTUAL CONSTANCY In this photo, most of the bird is so blurred as to retain no features, yet to someone who knows birds it is obviously a cormorant. Just as we can identify a speaker or his speech when harmonics are missing, so we can identify things that we see from only a small part, provided that some idiosyncratic pattern is visible.

The ability to recognize wholes from partial patterns was an evolutionary necessity. Our ancestral Homo sapiens would never have survived Africa if a glimpse of floating “debris” like this seen from afar had not brought to mind the animal on the next page. With the eye as with the ear, a pattern of harmonics defines an object, and with the eye as with the ear, once the brain has learned that pattern, it need not be complete to be identifiable. Just as idiosyncratic patterns of auditory harmonics—formants—allow us to recognize speech, so do idiosyncratic patterns of spatial frequencies

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allow us to recognize objects we see. We might call these patterns visual formants. If a pattern is sufficiently idiosyncratic, remarkably little information will suggest the whole, even in a case like these dissimilar crocodiles. With a set of auditory harmonics, the frequency is less important than the pattern. For our ancestors to survive, a lion needed to sound like a lion no matter what its size. A larger lion has longer vocal folds and a larger chest and mouth, which give its voice lower frequencies, but to survive and reproduce our ancestors needed to recognize the idiosyncratic pattern of harmonics that portend a lion, not the specific frequencies that portend the size of the beast and how quickly someone might be chewed. As with hearing a lion, so with seeing it. What matters is the shape of the beast, not its size—its idiosyncratic pattern of spatial frequencies, not the actual frequencies. You need to distinguish a lion from an ordinary house cat no matter what size it appears in your eye—or at least your ancestors needed to, so they evolved the means to do this. That is why you can see that the kitten-sized image on the next page is a lioness, not a kitten. This is the visual equivalent of hearing a deep organ pipe over a table radio. In both cases, low levels of the brain infer low harmonics from a pattern of higher harmonics that it has learned (in the case of auditory harmonics, beginning within the womb). Hearing deep

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In the picture this cat is the size of a kitten yet we see a lioness.

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organ tones does not show that man was formed to hear church services over the radio, it shows that the brain evolved to respond to patterns of harmonics rather than individual frequencies, and to infer information about size from patterns it has come to recognize. This skill is essential in a state of nature. Lions are potentially dangerous when they are still so distant that they cast a tiny image on the eye.4 Although size and shape are discrete dimensions, objects always exist in a context of other objects—at least they always do outside a psychology lab—and those other objects also impart information about size, especially as we move about. They impart information about size that comes through the eyes and also information that comes from muscles, the muscles of our legs as we walk around and—particularly important for judging distance—the muscles that move our eyes and control their focussing. With this information the brain can figure out that objects do not change their shape and size at different distances. Very low levels of the brain do this. It is so important to survival that the ability evolved long before any form of hominid. Even newborns perceive shapes and sizes not to change with distance.5 With both the eye and the ear, the more distant an object is, the fewer high harmonics we can detect. High harmonics are rapid but small oscillations, and smaller oscillations contain less energy, so they dissipate over shorter distances and merge more easily with background noise. The very highest harmonics that we can see or hear are so faint that we can barely detect them. For this reason, evolutionary pressures have formed both the visual and the auditory systems neither to need them nor to notice when they are not present. This is why people are willing to pay to listen to a violinist in a concert hall yet sit too far from the stage to hear the highest harmonics. It is also why people will happily look at photographs in newspapers although at normal reading distance a newspaper photo is so coarse that it can display only 10% of the spatial frequencies that we are able to see. Moreover, just as we can perceive whole objects from details, so we can perceive missing details from whole objects. For example, consider the self-portrait by Rembrandt on the next page. This

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painting is approximately life-sized, the size of the detail opposite. Rembrandt’s skin is manifestly skin. It is an old man’s skin and it looks impressionistic, but in the context of his face it is clearly skin. Not out of context, though. The inserts show details of two foreheads, one (on the left) from the painting and the other from a life-sized photograph of a man of similar age under similar lighting. The photograph is accurate yet the context makes Rembrandt’s coarse brushstrokes look natural.6 In sum, with sights as with sounds, missing harmonics matter little. We perceive overall patterns. With sights as well as sounds, the brain has evolved to detect information from imperfect signals through waterfalls of noise, and to alloy that information with experience to perceive not whatever is before your eyes but what is probably before them—or rather, what your experience makes your brain expect to be before them. In short, much of what you see is formed not by optics but by expectations based upon your experience.

VISUAL PERSPECTIVE This applies to perspective as well. Art schools teach perspective as a straightforward concept—straight lines converge in the distance—but perspective is not straightforward, because it derives from the artist’s culture and expectations. Imagine

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Rembrandt’s painted brow compared to a photographed brow.

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an international panel of experts convened in the year 1500 to define correct perspective. Italian polymath: It’s mathematical. Accurate perspective is geometrical. Straight lines converge to a point in the distance. Byzantine monk: Nonsense. An accurate perspective relates size to importance. God is greater than an angel, who is greater than a man. An accurate perspective must show this. Chinese scholar: It would be difficult to see in any painting a god that is invisible. Surely the most accurate perspective exhibits a scene to the fullest. An accurate perspective is an omniscient one that shows everything in a scene at once. Japanese gentleman: No, my Chinese master taught me something else. When admiring a scene, sometimes we look at elements that are nearby and large, while other times we look at elements that are distant and small. A natural perspective reflects that.

Clearly, accuracy of perspective is a matter of perspective. Each of these can look natural or unnatural. The next seven pages illustrate this. Despite their variety, all of these notions of perspective have something in common: they reflect some rudimentary functioning of the brain. This is how the argument might continue if those men had read some psychology: Italian polymath: From seven months of age a baby will reach for objects on the ‘nearer’ side of a scene drawn with geometric perspective. This shows that geometric perspective develops naturally.”7 Byzantine monk: Larger objects show more visual energy, so larger objects are more salient to the brain and more important. Chinese scholar: The most accurate information comes from the most complete set of harmonic frequencies. Japanese gentleman: The eye cannot focus on more than one distance at a time, so at any one time you see either the foreground or the background but not both.

Aerial perspective might start some discussion too. With distance the atmosphere causes skies to lighten, colours to become bluish, and details to become hazy and disappear. As a Chinese artist put it, “Far-away mountains have no wrinkles, far-away waters have no

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Geometrical perspective shows lines converging in the distance. Converging horizontal lines often look natural, as they do with the Chinese funerary army above, but converging vertical lines are another story. They make the Taiwanese temple below appear to be falling over backwards. “Accurate” vertical perspective usually looks so bizarre that artists commonly straighten converging vertical lines.8

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This picture looks natural yet we are looking upward, so accurate geometrical perspective would see the pillars lean inward like those of the temple on the last page. To make the church stand upright, the artist ignored geometry vertically and painted the columns plumb.9

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A “big man” means an important person in many societies and in most people’s eyes. That was the basis of Byzantine perspective above, and in the photo below of modern Byzantium (Turkey), the biggest man still looks the most important.10

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The more of a scene that you can see, the more realistic it must be: this is one form of perspective used before the modernization of China. Often this meant removing the roof to permit seeing inside a house. A comparable device here appears to be the circular opening. Circular doorways were decorative, so we would not expect one leading into a merchant’s workroom. This form of perspective is comparable to the omniscient perspective of a novel. Note that, although some lines in this picture converge toward the distance, they do not follow the rules of geometric perspective.11

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A contemporary form of omniscient perspective leaves the walls intact but shows multiple views using mirrors. This photograph looks highly realistic yet it contains no clues to depth from geometric perspective.12

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This Japanese painting shows depth naturally just by shrinking the background. Not only does it show no geometrical perspective, elements of the background are sized absurdly. The paddies on the left would normally be larger than the boat.13

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Like the painting opposite, this photograph also shows depth naturally just by shrinking the background, although here it’s elements of the foreground that are sized absurdly.

ripples, far-away figures have no eyes.” Nevertheless, although we all see aerial perspective, a Byzantine monk might still claim it to be unrealistic. “It’s just a trick of the eyes. The real is the ideal and the ideal does not differ with distance.”14 With the spread and dominance of western culture, almost everyone on earth now accepts the Renaissance understanding of perspective. However, as we saw on page 73, geometrical perspective may not

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reflect what the brain perceives. That is because geometrical perspective is the perspective of a camera, not of the eye. The artists who worked out the geometry probably used a room-sized camera like this one, a camera obscura. (Camera and obscura are Latin for “room” and “dark.”) In a camera obscura the lens might not be glass, it might be a small hole in the wall, but a small hole bends light like a simple glass lens, so it is the equivalent optically.15

Although people commonly compare a camera to the eye, the optics of the two differ fundamentally. The image inside a camera is flat but the image inside the eye is spherical. This picture compares the two. A flashlight shines into an “eyeball” that has its sides cut away. The light shines through curved cut-outs in the ball to create squares of light on a sheet

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of “film,” the table beneath. Thus, straight lines on this “film” are equivalent to curved lines in the “eye.” Geometrical perspective with straight lines is the perspective of the camera, not the perspective of the eye. The optical perspective of the eye itself is curved—what we see in photographs taken with a fish-eye lens, like this one.16

The optical image inside the eye has fish-eye curvature but the brain pays little attention to most of that image. The optical image is formed on a neuronal image sensor, the retina. The retina is a layer of light-sensitive cells spreading over nearly one-half of the eyeball but heavily concentrated in the central 3°, a region called the macula. These cells are so sparse in the periphery that they detect only broad lines. In the periphery they merely alert the visual system that something is present out there and ought to be looked at. Every

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detail of anything that we see comes from looking with the macula. When we look at a painting, we actually hop across it with the macula, sampling a little here and a little there, and then we assemble our impression of the picture from the bits and pieces we saw at different times. We perceive the walls of a house to be straight not because the image shows them to be—inside the eyeball the image has them curved—but because as our eye plays over the scene, the sharp areas are sufficiently small and central that straight lines within the sharp areas seem straight. The brain has seen enough of those straight sections to form a neuronal pattern, a pattern that overlaps with other neuronal patterns representing our previous experience with walls and our understanding of straightness. From all of these patterns the brain infers that any individual wall is likely to be straight, so we perceive every wall to be straight unless some irregularity like this one forces us to see otherwise.

In the Renaissance, painters threw over the Byzantine conventions of the previous millennium in favour of what they and we have deemed to be naturalistic images. Their ideal became a painting so perfect that you would see no trace of the artist’s brush. A few

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artists were able to approach this ideal. Their paintings were and still are technical marvels, apparent evidence in the artist of either God or the devil, depending upon your religious persuasion. By Rembrandt’s time this had become a conventional artistic goal, but Rembrandt came to understand that exquisite detail is not needed to create an illusion of reality. He began his career painting fine details but the older he got, the more suggestive the details became. He did not paint these casually—his coarser detailing took more elaborate technique—but his goal became more impressionistic and less literal.17 Rembrandt could do this because the eye actually sees little fine detail. We interpolate and infer almost all of what we see—virtually everything in a scene beyond the 3° spots that are picked up by the macula. In fact, we commonly do not see high spatial frequencies even with the macula, because even slight movement of the image on the retina blurs them. This can make photographic detail look less naturalistic than blur, as you can see in the waterfalls on the next two pages. Movement also affects perspective in another way: as we move about, our perspective changes. Cinematographers sometimes try to show this by putting the camera at the position of a character’s head and moving it as though the character were walking, aiming it where the character might be looking. However, just as we integrate bits and pieces to see a scene, so we integrate them as we are moving to see changes in space across time. We can see continuous motion only in short spurts, during the fractions of a second that the eyes are still. For this reason a series of short but clear clips can show a shifting world more effectively than a continuous take. One of the most hairraising murders ever portrayed on film is a 40-second sequence in Alfred Hitchcock’s Psycho that is formed from 34 separate clips photographed within a shower.18

ACOUSTICAL PERSPECTIVE When looking at things, details disappear with distance and objects close by loom large. Comparable effects happen with hearing too. With distance, high frequencies—details—disappear. This fading of

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We seldom follow moving water with our eyes, so a blurred waterfall…

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…looks more natural than a sharp waterfall.

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high frequencies forms an impression of distance comparable to visual perspective. We are going to call it acoustical perspective. With pressure waves the cause is simple physics. A wave starts at one point and spreads out spherically. The farther it spreads, the weaker it becomes. Eventually it becomes so weak as to be undetectable. Higher harmonics contain less energy than lower harmonics, so the higher harmonics disappear first. Inside a great cathedral, the highest harmonics of a soprano’s voice may never even reach your ears while a bass note of the organ may resonate for seconds. As canvas and paints cannot reproduce accurately the full set of visual harmonics present in nature, so microphones and loudspeakers cannot reproduce accurately a full set of auditory harmonics, no matter how precise the microphone nor how massive the speakers. To understand why, imagine that sitting in your living room are the most accurate pair of loudspeakers ever made. You also have a music room with a grand piano and sufficient space to stage concerts. You want to record one of your concerts. You own a pair of excellent microphones, which you set above the best seat in the room. That is three metres in front of the piano. After the concert you listen to the recording from three metres in front of the loudspeakers. The situation now is this: the microphones recorded the harmonics three metres from the piano, and the loudspeakers are reproducing these three metres away from you, so the harmonics you are hearing are those of the piano from six metres away. The proportion of harmonics is not what you heard in the concert, so the acoustical perspective is inaccurate. To make the acoustical perspective accurate from where you are sitting, the pressure waves coming from the loudspeakers need to contain the same set of harmonics as those from the piano, so you might try setting the microphones right by the piano. But the piano is a bulky object that emits different sets of harmonics at different places. A microphone adjacent to the instrument can pick up only one set of harmonics, yet the pressure wave that reaches your ear three metres away is a combination of many sets. For this reason, a microphone parked next to the piano cannot provide an accurate perspective either.

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It happens that we used to be so fortunate as to have rooms like these in our home, one with full-range electrostatic loudspeakers and the other with a grand piano. When we recorded concerts and listened to the recordings, the piano sounded remarkably naturalistic. Our piano had an unusual tone and the system captured it well. The recordings also captured the instrument’s full dynamic range, from the loudest pedalled fortissimo to the softest fading-away. In short, the recordings were close to ideal—yet nobody would ever have thought that the piano was actually in the room, because the perspective was not right. With sound as with sight, naturalistic reproduction is an illusion made of fudge—fudge cooked with similar ingredients. For example, the portrait on the next page looks natural but if the candle were really the source of light, it would be much brighter than the face, and the background would disappear into blackness. To light this picture, the artist did the equivalent of recording a violin concerto. To make both the violin and the orchestra clearly audible, a recording engineer uses multiple microphones to modify the balance artificially.19 This is a coarse fudge that is as old as microphones and amplifiers, but subtler fudge came to be cooked with stereophonic sound: distorting phase. Imagine a photograph of a razor blade that looks as sharp as the blade. Take this picture on slide film, duplicate the slide a dozen times, then stack the slides atop one another on a light table. Turn up the lamp beneath them so that you can see through the entire stack. As much as you try to stack the copies perfectly, you will not get them quite right. The blades will not be perfectly aligned, so the edges are slightly fuzzy. In the language of Fourier transforms, the imperfect alignment represents images that are slightly out of phase. When you stacked the images, you generated phase distortion. A photograph blurred by phase distortion is too soft to sell razor blades yet it can sell soap and lotions, for we often enjoy some phase distortion in pictures. We prefer portraits to be soft, for example, and we often prefer backgrounds to be soft. Soft faces look prettier than hard faces, and soft backgrounds separate a subject and propel it to the front. In recordings of music, phase distortion adds comparable softness and separation. Most people think it sounds more pleasant and natural, so most recording techniques generate some.20

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This scene looks as though it is lighted by the candle but…

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…if it were lighted by that candle, it would look something like this.

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With sound as with painting, what makes perspective seem natural varies with the experience, expectations and sensibilities of the perceiver. When a recording engineer jacks up the soprano’s microphone, most people will like the effect. Nowadays few people hear music unamplified, so stage productions employ a sound designer who uses microphones and loudspeakers to distort the amplitude and phase of instruments and voices until most of the audience think the music sounds good. However, to someone used to hearing singers live and unamplified, all of these manipulations sound bizarre. The term “sound designer” seems like an oxymoron, because designs are usually on paper, but it is a sensible analogue to “acoustical perspective.” The machinery of auditory and visual perception is remarkably alike. Of course the neural sensors are different—no one would mistake an eye for an ear—and they lead to different sensations, but the brain uses their signals in much the same way. Neural images from the ear and the eye are like drawings inked on opposite sides of thin paper. Although each drawing is distinct, they are drawn with the same ink on the same base and the ink comes through in places from one drawing to the other, so that parts of the images intermix. These mixtures we shall explore in the next chapter.

5 LOUD COLOURS MEMORY, DREAMS, CONSCIOUSNESS, ABSTRACTION

So far in this book we have discussed vision and hearing as though they are analogues of each other, but they are more than this. They are not merely analogues—they are not independent systems that are similar—they are interacting portions of a single perceptual system. They are like parallel roads in a city. Similar vehicles travel on both, and cars often transfer from one to the other. For this reason, sounds and sights often share some meaning. Loud colours, muted colours, high notes, low notes, bright timbres, dull timbres: these are more than metaphor, these are intermixed sensations. To understand how the arts play in the brain, we need to understand more of how the brain works. That is the purpose of this chapter. It

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may seem like a wild detour, and the first few pages will be rather dry, but we cannot travel to the next peninsula without driving around this bay.

THE NERVOUS SYSTEM In chapter two we showed that single-celled organisms behave tropically, like bouncing balloons. So do individual cells behave within the body of a multicellular organism like man—all individual cells, including neurons. Nerve cells come in an infinity of shapes but their primary tropic response is always the same. One end of the cell is extremely delicate. When something bumps this end, either physically or chemically, the impact shakes up subatomic particles. If the impact is sufficient, some of them push through the cell’s membrane. The particles hold an electrical charge—they are ions—so their passage represents a minute discharge of electricity through the membrane. This discharge stimulates neighbouring ions, so that those ions push through the membrane as well. A chain reaction begins that leads to and across the main body of the cell, then off again along a fibrous projection. The reaction runs along that projection then jumps to a neighbouring cell and “fires” it. A short while later the cell’s chemical machinery pulls the ions back in, leaving the cell ready to fire again. All neurons work that way, from your head to your toe. Some neurons develop shapes that make them especially sensitive to energy in a specific form, but the sensitive end of most neurons is similar, a delicate tree of fine fibres called dendrites, after the Greek word for tree. In this photomicrograph you can see a dendritic tree extending from the body of a cell. In this image the second projection—the exit—is cut off at the bottom. It is called an axon, after the Greek for axle. Although this truncated axon may resemble an

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axle here and in simplified drawings, in reality it looks more like a devil’s tail with branching ends.1 Most of our neurons are surrounded by other neurons, either within strings of tissue called nerves or en masse within the brain. Neurons’ dendrites and axons are thoroughly intermixed. They do not quite touch one another but by firing they form chemical connections that are more or less durable. This is another tropic process. Neurons sit in a chemical soup. When a neuron fires, the energy leaving its axon may pass through the soup to stimulate a nearby dendrite. At first the energy will cross to any dendrite that happens to be close enough, but as it passes through the soup, it alters the ingredients. Passing ions modify the local chemistry much as the energy of sparks in air converts oxygen into smelly ozone. Those chemical changes do two things: they facilitate the passage of more ions along the same route, and they inhibit the passage of ions nearby. The result is an ad hoc neurochemical connection that becomes stronger each time it is used. This connection is called a synapse, from the Greek for “connection.” Nerves to and from the brain end inside the eyes, ears, nose, mouth, skin, muscle, guts, and glands. We have some specialized nerve endings inside the eyes, ears, nose and mouth, but most nerve endings are generic and they are everywhere in the body except inside the brain. Most nerves respond to stimulation from our environment and body, then send it inward and upward to the spinal cord and brain. Others are oriented in the other direction. They receive stimulation from the brain and spinal cord, and then carry it to muscles, glands, and other tissues that may contract or release some chemical when stimulated. All nerves lead to and from the brain, so the brain appears to control the nervous system, but the brain can no more control the entire nervous system than a general can control every part of an army. Small units will respond to firing automatically and independently. When you touch a hot stove, the nerves in your hand induce tropic responses that move your hand long before any neuronal firing reaches the brain. This is a neuronal company of infantry returning fire, using the same sort of dendritic connections as are in the brain. Moreover, unlike a general, the brain does not effect control by issuing commands. The brain is a reactive structure that guides the

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body’s functioning not actively on its own volition but passively, deforming under the pressure of traffic. The brain acts like a blanket of snow covering streets. As a driver forces his car down a street, his tires form tracks. Since it is easier to drive in tracks than to push through fresh snow, drivers following him tend to follow in his tracks. Traffic deforms the snow and those deformations influence traffic in turn. The snow itself is passive. Within the brain, chemical responses to neuronal traffic form channels of synapses, and succeeding neuronal traffic tends to follow those synaptic channels. The brain ends up controlling neuronal traffic passively in that way. This is not how psychologists usually think of the process. Our models usually contain feedback loops and forms of active control. However, those are engineering models looking at neuronal functioning from the outside. The brain’s internal feedback and control mechanisms are not the sort that an engineer would envision. Firing neurons release chemicals, which dissipate in the surrounding space and, according to their concentration, increase or decrease the odds that energy will cross that space to fire nearby neurons. This is the kind of control that a tide exerts on fish in a brackish estuary, sending fresh-water fish swimming in one direction and salt-water fish in the other. To a fisherman the tide seems to control the fish, but the tide is not intending to do this and the fish are merely reacting to a chemical gradient, swimming toward or away from salt. Fundamentally, the system is reactive. Neurons do indeed fire on their own as well, and they do so continually, but spontaneous firing is disorganized energy: entropy. Spontaneous firing channels energy through existing pathways so that the consequences are organized and often look intentional, but entropic energy is random, not purposeful. If a tune runs through your mind’s ear while you are frying eggs, this is because some random firing kicked off a channel formed previously by listening to that song.2 This presents a paradox. A reactive brain is a tropic mechanism yet we are hardly tropic creatures, and the brain is central to everything intelligent and adaptive that we do. It seems impossible that a reactive brain dealing with entropic activity could form an Aristotle. To resolve this paradox we need to see the brain’s intelligence as the sort of emergent phenomenon we described in chapter one. We shall begin by considering a theoretical device that we use every day: a

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von Neumann machine. This is a theoretical machine that does three things: 1) reads numbers from some storage device, 2) adds or subtracts those numbers mechanically or electronically, then 3) returns the result to the storage device. It is the prototypical computer. The computer on your desk is a von Neumann machine in the flesh (or rather, in the silicon). In principle it does nothing more than execute von Neumann’s basic sequence, but it executes the sequence hundreds of millions of times per second. This simple mechanism permits a computer to do astonishingly complicated things, even to adapt its computations to circumstances and to learn. A computer may or may not have intelligence but the answer is sufficiently uncertain that academic careers are based on arguing the question. Much clearer is the cause of the uncertainty: the computations’ inconceivably large scale. The apparent intelligence of a computer emerges from this scale.3 The brain’s principle of operation is even simpler than a von Neumann machine’s. The brain’s functional principle is merely this: 1) local chemistry may permit energy from one neuron to transfer to an adjacent neuron, and 2) any such transfer of energy modifies the local chemistry to alter the efficiency of transfer in the future. To do a job of work, the brain requires scaling this principle to an unimaginable level of complexity: 10 billion neurons admitting 100 trillion possible connections.4 To get a sense of 100 trillion take a period from this book, abut it to another period, then repeat this 100 trillion times. Before you have finished, you will have circuited the earth 1000 times.5 But these do not define all of the possibilities, not by a long shot. A sequence of neurochemical reactions forms a wave across time. The possible connections of a neurochemical wave vary with its phase and frequency, so the possible connections are tenfold greater, on the order of 1000 trillion. Moreover, since a neurochemical reaction in one spot will facilitate and inhibit reactions nearby, a wave of reactions is likely to help shape a succeeding wave of reactions. This does more than make the system unimaginably complicated, it also makes the system unpredictably complex—deterministically chaotic in the general sense we developed in chapter two. Moreover, entropic neuronal firing continually alters the deterministic course.

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Systems like this are difficult to comprehend in the abstract but if you own a home in the north, you understand one of them clearly. In the fall if you forget to drain unheated water pipes, the water will gradually chill and then will suddenly become ice. Emergent phenomena will include burst pipes, a flooded basement, and working overtime to cover the costs. Scientists can follow little of the brain’s complexity but with computers they have created virtual neural networks, computer programmes that model many complex and chaotic behaviours much as they are seen in the lab. These models involve computations rather than chemicals, so they say nothing about the neurochemical processing of the brain, but they do show that naturalistic, complex, adaptive behaviours can grow from the automatic responses of a simple, reactive machine. A computerized neural network has nowhere near enough power to write a philosophical treatise on the nature of beauty but it can categorize a set of faces by attractiveness much as humans do.6 The number of theoretical connections in the brain is so large as to seem infinite, yet at any given moment, the actual number of possible connections is limited, defined by the local chemistry. Any particular passage from axon to dendrite depends upon whether the chemicals around that axon are absorbing energy or passing it on. This depends in turn upon what energy passed nearby shortly before, and what the chemistry was like when the last energy passed by. Connections begin with the first innervation within the embryo, they are shaped by the chemical and physical structure of the body, they are continually reshaped as the body develops, and as we shall see in chapter seven, they are influenced by the intrauterine environment: what a mother eats while she is pregnant can affect what her baby will enjoy. Since human anatomy is the same everywhere, many infant behaviours are universal and appear to be wired into the brain, but most of what appears to be wired in is also influenced by the environment. Take the ability to learn language, for instance. After six months of gestation the ears mature enough to generate neurochemical responses to pressure waves. This means that during the last three months of gestation, pressure waves within the

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mother’s body begin to form neuronal pathways inside the fetus’s brain where nerves from the ears enter it. Most of these pressure waves come from the pumps and plumbing within the mother’s abdomen, but these are overlain forcefully by the pressure waves of the mother’s speech. The latter are so frequent and pronounced that rhythmical constancies become the dominant force in shaping the pathways in those parts of the fetal brain. These neuronal structures become so attuned to the mother’s idiosyncratic rhythms that after a baby is born, he will suck on a pacifier to choose her voice played through a loudspeaker instead of a stranger’s. This attunement to her voice makes it easier for him to recognize specific sounds that she makes repeatedly. Once he recognizes those sounds, he comes to associate them with other sensations—with particular feelings and events—and eventually to treat them symbolically, as words. He also comes to recognize that these words usually appear in a certain order. Thus he begins to learn the syntax of his mother’s language.7 Virtually all of these associations form within the cortex of the brain, the grey matter that forms the mammalian brain’s outer layer. These cortical associations are the subject of this book. For ease of discussion, we shall commonly use phrases like “cortical processing” or “cortical control,” but it is essential to keep in mind that this processing and control is fundamentally reactive, no less reactive than any other part of the brain. The cortex is merely the part of the brain that has the greatest density of neurons and thus permits the greatest variety of neuronal routes.

MEMORY AND DREAMS Wilder Penfield was a neurosurgeon so audacious that he once operated on the brain of his own sister. As Penfield operated on a brain, he systematically explored it, stimulating it here and there and everywhere, to map what different parts of the brain do. (Brain surgery is done under local anaesthetic so that the patient’s responses can guide the surgeon. This is possible because without nerve endings, the brain can sense nothing directly. Anaesthetic is required only to cut through the skin and skull.) Penfield found that stimulating any portion of the brain is likely to bring up a memory, so he concluded that the brain is a neural cabinet with chemical

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pigeon holes for memories. Some of those memories had long been forgotten, so he hypothesized that everything we ever perceive is stored somewhere in the brain.8 Penfield’s observations dovetailed nicely with notions of memory that are century-old furnishings of western intellectual life, notions of repression, suppression and recovery of memories, and “flashbulb” memories impressed indelibly by a traumatic experience. These notions of memory have become rooted in our beliefs and culture as deeply as geocentricity was rooted in medieval Europe. Unfortunately, a vast amount of rigorous, scientific evidence has shown these notions to be comparably wrong.9 You can see that this notion of memory is wrong if you just think about a memory from your childhood. Remember a family dinner. Visualize this in your mind’s eye. Do you see yourself sitting at the table with everybody else around? If so, then it is obvious that you are not remembering what you saw. When you sat at that table you saw the people sitting around you but you did not see yourself. You have never seen yourself anywhere, save in a mirror. If ever you have an image of yourself anywhere doing anything, then you are not remembering that image, you are creating it. A model of memory better fitting the scientific data comes from our model of the brain as neurochemical tire tracks through snow. These neuronal tracks are formed by experience, but they are not memories in and of themselves any more than strengthened fibres in biceps are memories of barbells. In various ways at various levels, experience helps to form every tissue in the body, but we would not say that the shape of any particular tissue per se is a memory. A memory is not neuronal tracks, it is a bolus of chemical energy rolling along neuronal tracks. This energy may come from sensory stimulation, or it may be internal neuronal energy forming thoughts, or it may be neuronal energy that is merely rattling around in a random way forming dreams, but a bolus of energy is required. You will never forget how to ride a bicycle but neither will you remember until you climb into the saddle. You cannot remember how to balance while you are sitting in a chair. Since no single sensory stimulus is likely to be identical in every way to any other, and since no one state of the brain and body can ever

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be identical to one that came before, each bolus of sensory energy slips and slides in the tire tracks a little differently. This means that each recreated memory is likely to be different from the last. Moreover, each passage of energy alters the tracks. The neuronal tracks deepen, so energy is more likely to find its way along them, but they also widen, shift, and distort. The brain has no way to know whether any particular chemical track is the same now as it used to be, or how much it changed, so we have no way to know how accurate our memories are. We may feel absolutely certain that we remember something accurately yet there is every likelihood we do not. We can see this from research following the attack on New York’s World Trade Center. Almost every American remembers what he was doing when he first heard about the attack. Most people believe that so fearful and dramatic an event sears consciousness, burning its image into the brain overtop the ordinary events of the day. To test this belief, on the day after the attack, Jennifer Talarico and David Rubin interviewed students at Duke University about what they were doing when it happened. They also asked each student about something else that had happened within the previous three days. They did this using carefully structured interviews. Either six weeks or 32 weeks later they interviewed each student again about both events. They used the same structure and gave all of the transcripts to third parties to check for inconsistencies and contradictions. The students remembered the 11th of September much more vividly than the other event, and much more confidently, but their memories of both were equally flawed.10 In short, a memory is not a fixture of the brain, it is a replayed perception, a perception that is divorced from sensory input (although a sensation may have triggered it) and is played back on a neurochemical machine that may start from any position and that frequently skips and distorts. The only difference between “real” waking memories and the bizarre memories of a dream lies with entropy. We dream while the brain has lost some of its power to organize energy because its chemical stores need replenishment. During sleep some neurochemical energy still enters the brain from sensory systems but it sloshes about largely at random, stimulating neuronal channels hither and yon. This tends to destroy tenuous neuronal connections, so that we forget much of what we did during the day (although it can also reinforce some recent connections,

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perhaps to solidify the French vocabulary you reviewed just before switching off the light). When this stimulation passes through parts of the brain that form consciousness, we experience a dream.11

CONSCIOUSNESS This brings us to the phenomenon of consciousness. Consciousness, we assert, is the state of the neurons in the cortex as they react to stimulation. It is nothing more than that. There is no reason to hypothesize that consciousness occurs in some higher plane as a consequence of cortical activity. Consciousness is activity in the cortex, just like every other aspect of our mental behaviour. This understanding of consciousness fits both the facts and the phenomenology. A pattern of neural firing changes from moment to moment and what we are conscious of changes with it. While we sleep, cortical activity and consciousness diminish, but some sensory energy is still being processed by lower parts of the brain, so we can sense and respond to some things without being consciously aware of them. While we are awake, sometimes internally induced firing causes neuronal energy within the cortex to flow along pathways that were laid down previously, so we can become conscious of things that we are not sensing—in other words, we can remember things. If the right internally induced firing is juxtaposed to a sensory stimulus, then we can be conscious that we are conscious of something. Cortical pathways can trigger cortical pathways triggering cortical pathways, so that we can be conscious that we are consciously aware of something that we are remembering, and we can discuss all of this consciously with an imaginary interlocutor. Random firing while asleep can trigger comparable sets of pathways, so that we can be conscious of all this as part of a dream.12 On the other hand, we cannot consciously move a muscle. We can use the mind’s voice to say, “Right leg, kick,” and we can be conscious of saying this in the mind’s ear, but this conscious instruction will not cause a muscle to move. Movement is always unconscious. This is because triggering a movement sends neuronal activity away from the cortex. Neuronal activity leaving the cortex is not activity within the cortex, so we are not conscious of it. We can be conscious of a

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movement only after it happens and has triggered sensory neurons feeding back into the brain. This notion of consciousness often breeds the objection that consciousness is too mysterious to be explained so simply. Indeed, it is so mysterious and wonderful that it appears to many to be divine. As we heard a devout neurosurgeon put it, “I have operated on countless brains yet never seen a piece of consciousness.” That is strong rhetoric but weak argument. The patient’s conscious awareness is the patient’s own experience of his neuronal firing, not the surgeon’s experience of the patient’s neuronal firing. When the surgeon tickles part of the brain electrically, the patient sees or hears or feels something and is quite conscious of this experience. Moreover, if a phenomenon is mysterious, the last place to look for clarification would be in theology, since the one thing all divines agree on is that God’s workings are too mysterious to comprehend. A more subtle objection holds that if consciousness were merely cortical activity, then animals would be as conscious as we, but animals lack the language and abstract thought that form consciousness. Yet advanced animal and human behaviours can look so similar that Plato had Socrates joke about the philosophical nature of dogs:13 Socrates: A dog, whenever he sees a stranger, is angry; when an acquaintance, he welcomes him, although the one has never done him any harm, nor the other any good. Did this never strike you as curious? Glaucon: The matter never struck me before; but I quite recognize the truth of your remark. Socrates: And surely this instinct of the dog is very charming;—your dog is a true philosopher. Glaucon: Why? Socrates: Why, because he distinguishes the face of a friend and of an enemy only by the criterion of knowing and not knowing. And must not an animal be a lover of learning who determines what he likes and dislikes by the test of knowledge and ignorance? Glaucon: Most assuredly. Socrates: And is not the love of learning the love of wisdom, which is philosophy? [A Greek pun: philosophia means “love of wisdom.”]

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To abstract something is to draw it away from its surroundings, to separate it in some way from its context. When a mother reads her toddler Babar the Elephant, the child abstracts from the stream of her voice the chunk of sound ˈɛlfənt, he abstracts from the book’s pictures a mental image of a fat animal, and he associates the two abstractions. Later she gives him a stuffed elephant: this he also associates with those abstractions, so that ˈɛlfənt comes to stand for that specific toy as well. A few years later she points out an obese man and says, “Look at that elephant.” Now the sound becomes extended metaphorically to a fat man. Eventually, as an adult, he might abstract the meaning further to talk about the elephant in the room. Animals can also abstract sounds, and it is interesting to note how elephants deal with a man in the room. Around Kenya’s Amboseli National Park, Maasai men often kill female elephants but Kamba men do not. Karen McComb played recordings of Maasai and Kamba men saying naturally in their languages, “Look, look over there, a group of elephants is coming.” She played those recordings to female herds. When the elephants heard someone saying this in Maasai, usually they bunched up defensively, but they did so markedly less when they heard the statement in Kamba. These elephants had abstracted something about the sound of the Maasai language, and associated it with danger—a danger to be avoided. In contrast, the recorded roar of a lion induced herds of elephants to take the offensive and go after the sound en masse. However, we have no reason to think that those elephants were dealing with human speech symbolically. They were probably abstracting the Maasai’s vocal patterns and forming a fixed association, a simple indicator that dangerous bipedal animals are near.14 We do not know if elephants’ own vocalizations represent abstract, symbolic speech, but we do know that some animals other than man can speak symbolically, particularly bonobos. Pygmy chimpanzees they used to be called. Like ordinary chimps, bonobos share 99% of their genes with man. Bonobos are so similar to man that one of them raised like a child learned to understand English as well as a toddler, and learned to “talk” as well as a toddler, using a language of graphical symbols like the icons on a computer. (Apes must speak with their hands because their vocal apparatus is insufficiently flexible.)

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Susan Savage-Rumbaugh conversing with Kanzi (right) and Kanzi’s sister Panbinisha.16

Kanzi is the bonobo who did this. It took him five years to learn what a human infant learns in two, but he manifestly came to understand some English. For example, when a researcher told him, “Knife the orange,” he did so. When the researcher said, “Put your knife down,” he put down the knife and kept the orange. Both of these commands he had never heard before.15 This is clearly not like a dog heeding a command. A dog may obey the command “Find your ball,” but it will not also obey the command, “Put your find down.” However, “Knife the orange” and “Put your knife down” are equivalent to those, and Kanzi did both of them. That shows he understood the English word knife both as a noun and as a verb. He treated the sound nʌf not as referring to a specific object but as a symbol with a meaning that changed according to its context. Moreover, although these are simple sentences, Kanzi also understood complex sentences like, “Take the potato that's in the water outdoors.” Susan Savage-Rumbaugh raised Kanzi from birth on 55 acres of forest owned by Georgia State University. Savage-Rumbaugh tried to make Kanzi’s physical environment and daily activities as bonobo-

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like as possible, gambolling about the forest and searching for food, but she also tried to communicate with Kanzi as though he were a human child, speaking and gesturing naturally, with one important non-human addition: while she spoke, she showed him icons representing English words. She did not try to teach Kanzi either English or the icons, she merely spoke to him and pointed to any icon on a board or computer screen that happened to correspond to a word she spoke. Since pointing is slow, she was able to point at most to only one or two icons in a sentence. Kanzi learned as an infant learns, without any formal instruction. (Strictly speaking these were not icons but symbols—not simplified representations but arbitrary designs. We are calling them icons to make it clear when we refer to the graphic rather than its function— to avoid sentences like, “Kanzi treated the symbol of an orange as a symbol of an orange.”) When Savage-Rumbaugh tested Kanzi’s English comprehension, she gave him instructions from behind a screen, to avoid cueing him with body language. Someone else recorded Kanzi’s responses (while listening to music through headphones, so that he could not be biased by hearing the instructions). Savage-Rumbaugh tested Kanzi with 660 instructions, each of them novel, and in a similar way she tested a two-year-old girl. The results admit no doubt: Kanzi and the girl comprehended English comparably. Kanzi could also make utterances of his own by pointing to icons and gesturing. Savage-Rumbaugh kept careful records of almost every time Kanzi pointed to an icon, and she made a number of reliability checks to ascertain that the observations were accurate. When Kanzi was five and one-half years old, the linguist Patricia Greenfield analysed all of his utterances over a period of five months—13,691 of them. An utterance always began with an icon and often ended with a gesture. Ten percent of Kanzi’s utterances involved two or more elements: those were the sample of his “speech” that Greenwood worked with. Comparable analyses of children’s speech have been based on much smaller samples. Greenfield concluded that by strict linguistic criteria, Kanzi was able to talk. He used each icon as we use a spoken word, as an independent, meaningful, and permanent symbol. To us the sounds ēt

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füd form the sentence “eat food,” and that’s what these two icons meant to Kanzi. The left means “bite” and right means “food.” We always say “Eat food” and “Carry [a] ball” rather than “Food eat” and “Ball carry.” Even a two-year-old will normally use this word order. So did Kanzi. We naturally categorize words and use those categories in grammatical structures. So do two-year-olds and so did Kanzi. We use our categories and grammar to generate novel sentences. So do two-year-olds and so did Kanzi. Moreover, in addition to icons, Kanzi used visual symbols that he defined himself, and he used them in a consistent way. His symbols were gestures, gestures that functioned as pronouns and adverbs, as this, that, me, you, him, her, it, here, and there. In Kanzi’s grammar, gestures had a proper location: last, like the prefixes of separable-prefix verbs in German. Kanzi always pointed to icons first, and only then did he gesture. He did this even when he was right next to something he needed for gesturing and was across the room from his icons: he crossed the room for an icon and then came back to gesture. In sum, Kanzi’s utterances at five and one-half years compared to a typical two-year-old child’s. Of course a typical two-year-old speaks aloud and a bonobo cannot, but that is only because a bonobo’s throat is not formed in a way that lets him articulate consonants. (Kanzi seemed to try to speak English, but since he could not form consonants, his sounds were unintelligible.) Many human children also cannot learn to speak aloud because of a physical constraint: they cannot hear. These children naturally develop a language of gesture. If a deaf child’s parents know no sign language, the child will develop his own; if the parents know a conventional sign language, they will respond to the baby’s unformed gestures with conventional gestures and the baby will grow up learning their sign language as though he were learning English.17 We usually think of language as based on sound but linguists have been unable to discover any requisite of language that is not found in sign languages used by the deaf. This is because sound is not the medium of speech that it appears to be. Sound is not a medium that conveys information from one person to another, sound is a perception that is entirely within the brain of each individual. You move some muscles that create pressure waves through your body

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and the air, then those waves impinge upon your ears and a friend’s ears. Neuronal signals from her and your ears pass into your brains and both of you hear a sound, but you are hearing independently. Indeed, your friend does not hear what you hear, because only pressure waves through the air reach her ears, but you hear those plus a different set of pressure waves that reach your ears through your bones. You hear the difference whenever you hear a recording of your voice. Instead of thinking of vocal sound as a medium of communication, think of it as a perception of hidden movements of somebody’s glottis and of subtle movements of his tongue and lips. These movements can indicate things, and so can larger movements of the tongue and lips, and so can movements of the face, hands, arms, and trunk. The former modulate pressure waves and the latter modulate light waves, but the brain senses neither pressure nor light, it senses only modulations, so either medium can handle communications. Aural communication is practical and convenient but gesture and movement can be communicative enough not just to indicate danger or delight but even to tell a story. Indeed, silent gesture forms the foundation of the motion picture industry. Hollywood was built on silent films. For the first 30 years, the only use for sound that most people could imagine was to provide music. The first sound films were shorts intended to replace the live singers hired to warm up an audience for the feature. Sound was first added to feature films to save the cost of the orchestra that accompanied films in many theatres, and to provide grander music than a piano where no orchestra was available. The first talking feature, The Jazz Singer (1927), played music throughout but presented less than two minutes of dialogue. This dialogue seemed so unimportant that the review in Variety did not mention it. Even in 1929, when talkies with dialogue had become the norm, an aesthete could still publish an article on music in film stating, “Silence is the medium of the movie, as it is the medium of the clown.”18 If this seems surprising and unlikely, you might want to look at a few frames from a silent film. The next four pages are from the first 80 seconds of a 1915 thriller by the director Louis Feuillade, Les Vampires. (The title has nothing to with bats, it’s the name of a fictional gang.) You need no French to follow the plot.19

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Although bonobos communicate naturally using sounds and gestures, and bonobos are capable of symbolic language, they seem not to have developed symbolic language outside SavageRumbaugh’s lab. But this has no bearing on their consciousness. Consciousness does not require language. We can be swept away by a symphony, deeply conscious of its harmonies and melodies, acutely aware of every trumpet call, yet have no verbal thoughts at all. We can be silently conscious of sights as well, awe-struck by mountains towering overhead. Consciousness is no more tied to language than it is tied to any other specific perception. The brain can function in a way that both forms sentences in the mind’s ear and enables us to be conscious of them, but the brain can also function in a way that forms odours in the mind’s nose and enables us to be conscious of what we are smelling. It does not follow that either language or smell is necessary for consciousness. Surely Kanzi was conscious by any human standard, although conscious of different things. He will have been conscious of what matters to a young bonobo, not to what matters to a human child or, especially, to a human adult. Plato’s philosophical dog may be a useful comparison here. It seems manifest that a dog is conscious of smells, far more conscious of them than we. A hound reads his environment with his nose as we read it with our eyes. A dog may even be treating smells symbolically when it tries to urinate higher than another dog. The medieval philosopher William of Ockham used parsimony as a razor to cut off needless explanatory constructs. He saw no need to replace observable explanations with theoretical ones. If William were alive today, and if he had read the scientific literature on animals, we doubt that he would see cause to postulate anything more divine about consciousness than about seeing or hearing. Consciousness looks like cortical processing of perceptions, so we see no reason not to call it that. It is clearly complex processing that feeds back into itself, but we see no reason to think it anything more arcane.20 To visualize the mechanism of consciousness, imagine that you are on holiday and check into a hotel. Across the street is a church with a bell that rings every quarter-hour. The first time the bell rings, it seems so loud that it might be in the room, and you wonder how you

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will be able to sleep, but a few hours later it does not seem so bad, and by the end of the day you cease to notice it. Each time the bell rings, your ears flood the brain with neurochemical signals. At first this flood generates a tidal wave that swamps the cortex and washes about for minutes through distant corners, but after each wave the brain sets up neurochemical sand bags—inhibitory circuits—to contain and damp the wave. Gradually this shortens the wave’s duration, so that you become less and less conscious of the bell. Eventually the wave becomes so short that you cease to be aware of the bell at all and sleeping is no problem. While you are sleeping, parts of your brain shut down to recuperate from the day’s exertions, various parts at various times. Perhaps at 6 a.m. part of the brain’s networks that inhibit the bell happen to shut down, so some energy from the bell washes into the cortex. There it happens by accident to slosh into a network that is usually stimulated while you are riding a bicycle, and it also sloshes into a newly etched network that was formed by the chapter of Don Quixote that you happened to be reading just before you fell asleep. Since the inhibitory networks are shut down, this time the energy is processed for long enough that you become conscious of it again. You become conscious of charging at a windmill on your bicycle, with the blades of the windmill crashing into your helmet and clanging against it like the clapper of a bell. This happens to be a dream formed by an external event, but a dream may have nothing to do with the outside world. While some neurons are shut down in sleep, others are not. These may be stimulated neurochemically from random activity generated by the brain itself. Since the brain’s normal structures are shut down, this energy does not follow normal pathways. Instead it sloshes about randomly. If it sloshes about for a long time and stimulates clearly defined pathways, then you are conscious of those pathways, even if they are pathways that normally are not stimulated together, like tilting at windmills and riding a bike. That is why and how you dream. Dreams are likely to involve pathways that were active and deepened during the day but beyond that, they indicate no more about a person’s past, present, or future than the positions of stars or the disposition of tea leaves in a cup. Dreams are merely random neurochemical activities that extend for a long enough time to create perceptions.21

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PAIN We would be surprised if other animals were not conscious of pain as man is—not from the same causes but from the same neuronal mechanisms. If you touch a hot stove, you will withdraw your hand instantly, then later you will be conscious of pain. An extreme amount of heat wallops nerve endings in your finger, which send a neurochemical tidal wave into your nervous system. This elicits a reflexive, tropic response to reverse your muscles’ movement, then the wave crashes through the brain into the cortex. There it splashes around for seconds or minutes, intermixing with signals from other sensory organs and with patterns that have been formed by experience. This splashing about becomes a perception that something is seriously wrong: this is pain. Pain is not a sensory system—the body has no pain receptors of any kind—it is the perception of some physical impingement that is outside the normal range. The impingement can be in any form and anywhere in or on the body where nerve endings are found (which means, ironically, everywhere except inside the brain). Pain is the perception of unusually intense stimulation from any source. However, like all perceptions, pain is a neuronal pattern, so it takes time to form; and if the physical impingements are extreme, the neuronal traffic can take a long time to become organized enough for pain to be perceived. That is why, when an industrial accident suddenly severs a limb, the workman will not usually feel pain until some time has passed.22

UNCONSCIOUS AWARENESS A human brain looks like a cauliflower. Its outer layer, the cortex, is a mass of folds and fissures, and a stem connects the brain to roots in the nervous system. The “grey matter” of the cortex differs from the “white matter” inside, but within each of these layers, tissue in any one region looks just like tissue in any other, either to the naked eye or under the microscope. The density of neurons varies somewhat but that is all. Nevertheless, this homogeneous mass contains structures, structures that form neuronal firing into patterns. These structures are functional rather than physical, like the organizational structures of an army. Since patterns of neuronal firing form consciousness, the shapes of the brain’s functional structures shape consciousness.

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These structures are not reflected by the shape of the brain. Just as every normal baby is born with five toes on each foot, so he is born with a specific set of lumps and lobes in his brain. These lumps and lobes act as landmarks to let neurologists draw maps and name parts, but the specific number of lumps and lobes affects a brain’s functioning no more than our having five toes instead of four or six affects our ability to walk. On the other hand, the shape of the body does affect the brain. To understand how, imagine a large railway station, the kind of metropolitan terminus that fills a city block with streets along every side. People enter the station through many doors. Most of them head toward the centre of the station, where they buy tickets, sit down for a coffee, stop in a shop, and then eventually walk to the tracks. But of course, not everybody does this. Some people walk straight from the door to the tracks and others wander about obliquely. The brain works something like that. Nerves from sensory organs are the doors from the street and nerves to muscles are the tracks. The clearest path from the sensory nerves leads to the functional centre of the brain, the cortex, but since the physical structure is an inchoate mat of fibres, sensory energy from one organ will intermix with sensory energy from another, and the closer together the pathways from organs end up within the brain, the more their output becomes entwined. We are blithely unaware of these intermixtures but you can experience one of them by standing on one foot. You can probably balance easily while keeping your head still, but if you close your eyes you will soon tip over. This shows that energy from the visual system is intermixing with energy from the organ of balance in the inner ear. Introspective perceptions are not strong evidence of anything but controlled experiments are, and a host of well controlled experiments have found that senses influence one another without our knowledge. For example, Debra Zellner found that colours can strengthen odours. She asked undergraduates to sniff test tubes containing food flavourings—strawberry, mint, lemon—and to rate the intensity of the odours they smelled. The flavourings varied in concentration.

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Some of the flavourings were coloured appropriately (red for strawberry), some were coloured inappropriately (red for lemon), and some were clear. Sometimes the undergrads could see the test tubes and sometimes they were blindfolded. Zellner found that when the students were able to see a colour in the test tubes, even an inappropriate colour, then they reported the odour to be stronger than when there was no colour or they were blindfolded.23 This drawing shows another sensory intermixture that is even more surprising. If you cannot see one of your hands (because a board blocks your view), and if somebody strokes both the hand that you cannot see and a rubber model that you can see, then the senses of touch and sight become mixed up and you come to feel the rubber hand as your own.24

Many labs have studied variants of this illusion and found it to be surprisingly powerful. For example, here is a description from one scientific paper that was corroborated by physiological measurements:

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The illusion was very vivid for many subjects as evidenced by remarks such as, “wow”, “that was bizarre” or “oh my God!” Some subjects reported that the illusion was so convincing that they found themselves wondering why their hand was so white or how they had bruised their hand (there was a small ink smudge on the fake hand). Furthermore,…many subjects behaved as if they anticipated pain when the rubber finger was bent back: they laughed nervously, widely opened their eyes, flinched, and even pulled their real hand away.… Two…subjects even reported feeling pain when the fake finger was bent back. [Italics in original.]25

A third example shows that a glimpse of a smile or frown will affect your thirst, even a glimpse too short to be aware of. This we see in an experiment by Piotr Winkielman. Winkielman brought undergraduates into his lab, asked them how thirsty they were, then sat them in front of a computer looking at a cross. Suddenly the computer flashed a face on the screen for 1/60 second—too quick to notice—and then the computer showed another face and left it on for close to half a second. The computer showed the cross and faces eight times. For any one observer, the face that flashed up for a moment was either happy or sad or neutral. The second face was always neutral. Afterwards Winkielman offered the volunteers a pitcher of Kool-Aid. Of the undergraduates who had said they were thirsty, those who had first glimpsed the happy face poured and drank more Kool-Aid than those had glimpsed the neutral face, and those who had glimpsed the sad face poured the least. None of those students had been conscious of seeing the first face—that face flitted by so quickly that nobody noticed it—but its expression affected their sense of thirst.26 Note that this is not the subliminal perception purportedly abused by advertisers flashing slogans at us as we watch movies or television. Those subliminal ads are an urban myth that originated in a hoax perpetrated in 1957 by a New York publicist named James Vicary, to sell his services. Vicary claimed to have raised snack-bar sales in a movie theatre by repeatedly flashing onto the screen “Eat popcorn” and “Drink Coca-Cola” for 1/3000 second at a time. Vicary’s claims were proclaimed to the world not through a scientific journal but through Senior Scholastic, a magazine for schoolchildren in grades seven to nine. Some real subliminal effects have indeed been shown in the lab but they are too arcane and subtle for any use in marketing or propaganda.27

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Note, too, that this kind of unconscious perception has nothing to do with the “Unconscious” of Freud and of popular psychology. We are not positing a hidden, internal, personal demiurge and erecting a self-contained theory atop uncontrolled observations. We are describing observable neurochemistry: a confusion of neuronal pathways that rigorous experiments have found time and time again in a variety of species. In the neuronal cotton wool that forms a brain, energy from one wad of neurons can impinge upon another wad of neurons nearby. In this way one set of neuronal pathways can affect both related pathways and also unrelated pathways. We are unaware of all this because it happens at low physiological levels, yet it forms what we perceive.

FIRST FACES I The study flashing faces at undergraduates was designed to investigate the intermixture of senses, but it also shows how salient faces are to our experience, and how important to us are facial expressions. But this is hardly surprising. Faces fascinate us all. It is hardly an accident that so much of art is portraiture. However, contrary to common belief, no part of the brain has evolved specifically to recognize human expressions. The brain begins as a general-purpose processor with no specific abilities, just some structural propensities, and our attraction to faces develops much like our attraction to anything else.28 Imagine yourself to be a brain, the brain of a fetus soon to be born. Most of your body’s sensory apparatus has fed you neurochemical signals, so you have developed a few basic patterns shaping your sensations of taste, pressure and sound, but there has been no reason for you to perceive these sensations as coming from outside your body. You have sensations and that is all. Now, suddenly, your body leaves its liquid environment for a gaseous one, and sheds an organ (the placenta). The body you are in has now been born, but of course you do not understand this, for you are just as immature as you were one hour before. Perhaps the greatest difference is that now you are being walloped by neuronal energy from sensory organs you had not known before, the organs we know as eyes. You find

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yourself perceiving this energy as vague colours and shapes that have no order. To you they are not outside your body nor even inside it, for you have not come to realize that you are within a body. You are simply receiving sensory stimulation and perceiving it semi-consciously. Larger and contrastier objects represent more optical energy, so up to a point—you are easily overwhelmed— they cause more neuronal firing. As you develop, these larger and contrastier objects form the first neurochemical pathways within the parts of your grey matter that connect most directly to the eyes. Those pathways form feelings of recognition each time they are stimulated. Your low levels respond tropically to this energy, shooting some of it to the muscles moving the eyes. Those muscles, in turn, contract tropically to turn the eyes toward the stimulation. This leaves the eyes staring at big, contrasty elements, so that big, contrasty elements stand out even more. At the same time, another part of the body feeding you signals begins to touch things: a hand. (Initially the hands work one at a time.) This generates tactile stimulation. During the second month after birth, pathways within your visual cortex guide more neuronal traffic, so that you respond in more complex ways to energy stimulating your eyes. You begin to recognize more complicated patterns. One pattern you have long recognized is an oval with more energy toward the top and a familiar smell but now you notice energy inside the oval, and your eyes are attracted there. Once they are, rhythmical stimulation often comes from the ears, rhythmical stimulation containing modest amounts of power— the sound of someone addressing you in baby talk. When your eyes look inside the oval and you happen to feel muscles around your eyes contract, then the sounds are likely to become louder, higher, and more rhythmical, so that the patterns become clearer, and the oval develops more lines, which add optical energy—the sights and sounds of parents responding to what they perceive to be a smile. These effects strengthen pathways, creating some order amidst your sensory chaos and often causing your facial muscles to contract again into what adults interpret as a smile. At that point you have come to associate the sight of this oval with the feeling of a face, but you still have not learned that the face you are seeing is not your own. Soon, though, you realize that the sight and the feeling are not

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LEARNING TO SEE AS AN ADULT All babies learn how to see like this and, under unusual circumstances, so may an adult. A blind woman named Sheila Hocken had her sight restored surgically at age 29. Later she wrote about her re-encounter with a visual world that she had not known since she lost her sight in childhood. “[A difficulty] was to crop up quite frequently in those first few days out of hospital. This was the problem of relating the reality of the image transmitted through the eyes to the brain, to a previous reality which was conditioned by touch or verbal description. Some objects that I saw for the first time I could identify immediately, although I still do not know why. But with others I had not the least notion of what they might be, until I felt them.… When Don brought me a cup of tea,… I looked at the cup and had no idea what it was until I touched it.”29

closely correlated, so you distinguish the face you see from the face you feel—but incompletely. The connection of a seen face and a felt one still exists. This connection is the basis of the infectious social smile. At about this time, energy from the eyes mixes with tactile energy and follows some of the same pathways, so that you come to see that you have hands. Through the next two or three months you begin to develop neuronal pathways that correlate sight with touch and that identify both of those sensations with external events. This is not merely a connection between two senses, it is an interconnection. Energy from two sensory systems intermingles in such a way that the sensations are intermingled. The intermingling of sensations is called synaesthesia. Although we normally think of sensations as separate, in fact they intermingle synaesthetically to a significant extent. Synaesthesia we think the root not only of a social smile but of virtually all social interaction. That is why portraits interest us so much: to a certain extent we literally see ourselves and feel ourselves in the picture. The term synaesthesia usually denotes sensory admixtures so pronounced that people are conscious of them. For example, a synaesthete might see colours while listening to music or he might taste the shapes he sees. Some psychologists think that if somebody is not conscious of a sensory mixture, then he is not synaesthetic.

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However, we can be more or less conscious at different times, and conscious of different things at different times. Consciousness is a continuum, not a discrete category, and so are intermixtures of the senses. It may sometimes be useful to identify a pronounced synaesthesia. For example, it may be useful for a teacher to know if a child sees the numeral 4 as red and 6 as green, because the child will have difficulty learning multiplication tables if an arithmetic book prints them the other way around. However, for understanding human perception the conventional definition of synaesthesia is too limited. Synaesthetic admixtures in human behaviour are almost everywhere we look and are a fundamental aspect of aesthetic preferences. We shall encounter them throughout this book.

6 A NOSE FOR NOISE CATEGORIZING TASTES, SMELLS AND COLOURS

While we were writing this book we changed our telephone service. We switched from conventional telephones to voice-over-internet, from analogue signals sent through copper wires to digital packets sent through fibre optics. One of our first telephone calls on the new service happened to be from a violinist. “What’s wrong with your telephone?” he asked. “As soon as you stop talking, the line becomes silent. It doesn’t sound right.” Nature abhors a vacuum and in a universe of noise and information, silence is equivalent to a vacuum. The nervous system has evolved within a universe of constant stimulation spanning a certain range, so it has evolved to function within that range. Inside the brain,

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every pattern of neuronal activity feeds directly into other patterns. This activity expends energy, so it requires a certain amount of chemical fuel plus the oxygen required to burn that fuel. Arterial structures make fuel and oxygen available constantly and the brain has no way to deal with a surplus, so the brain must maintain a normal level of activity even if that requires stimulating itself. Thus we dream and day-dream or, when sensory stimulation is lowered unnaturally in a psychology lab, we hallucinate. When sensory stimulation overall is within a normal range but is unusually low in some one area, we merely feel as though something is wrong. Thus to our musician, no auditory stimulation from the telephone sounded stranger than a low level of auditory stimulation carrying no information. The unexpected silence was more awkward than random noise.1 As the brain’s structures evolved to expect a certain level of noise, its structures also evolved to detect signals through that noise. Some of these structures are synaesthetic reinforcements across sensory systems. You may not quite catch what somebody said but you are more likely to if you can see his lips, because the sight of his lips strengthens the sound. At first blush this appears to be adding together redundant information—you hear a sound and see its source, so you add the two together—but combining senses actually multiplies information. For example, here are three crosses. The central cross is formed from twice as many dots as the lefthand cross, so it contains twice the density of spatial information. The red cross also contains twice the density of information but spread across two dimensions, space and colour. The next page shows the same three crosses masked with noise in both space and colour. The noise is enough to mask the two grey crosses but the second dimension, colour, allows the red cross to remain detectable. If the brain

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merely added perceptual dimensions, then colouring the dots would be equivalent to doubling the number of dots. This multiplicative mechanism is what enables police to catch drunk drivers. Every year at Christmastime, the police in Ontario erect roadblocks to look for drivers with sufficient alcohol in their blood to be charged with drunken driving. A driver stops and rolls down the window, the policeman looks inside the car, sniffs the air and asks the driver if she has been drinking. If he smells beer and the driver’s speech is slurred, then the policeman has the driver blow into a breathalyzer. The police may stop one million cars and charge or warn 1000 drivers.2 To detect drunks, the police use a particular form of mathematical reasoning. They do this intuitively without using actual numbers, but we can follow their reasoning by inventing numbers. When a policeman approaches a car, the odds that this driver is drunk are one in 1000. When the driver opens the window, he smells beer. This raises the odds that the driver is drunk from one in 1000 to one in 100. The driver says that she has not been drinking yet she speaks unclearly. It is possible that the she is tired or has a speech impediment or is struggling in a second language, but drink is again a tenfold better bet. This raises the odds that the driver is drunk from one in 100 to one in 10. The policeman expects to test 10 drivers for every one charged, so he brings out a balloon. Once a policeman stops a car, he calculates and recalculates probabilities as the evidence accumulates. In mathematical jargon the policeman makes a Bayesian calculation of probabilities. A mathematician does this precisely using a computer but all of us do it intuitively all of the time. To a large extent the neurochemical networks of the brain integrate with one another to function as a Bayesian calculator. That is why combining perceptual dimensions

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multiplies information, why the cross above stands out when it is red.3

TASTE A young child will put anything in her mouth, including poisons, yet even before manufacturers and pharmacists started to use childproof packaging, remarkably few children ever swallowed enough poison to die. This is because our chemical senses have evolved as Bayesian processors that distinguish the relatively few things that are likely to be edible from the many that are not.4 Long ago our evolutionary ancestors evolved structures in the mouth and gut that respond to the most important categories of chemical that we might ingest, and instigate tropic responses that aid survival. We are aware of these structures in the mouth and call them taste buds. They influence what we swallow. The comparable structures in the gut we are unconscious of but they influence the release of digestive enzymes and may start us vomiting. Here are the categories. The + and – indicate innate attraction or repulsion.5 + Glutamates. Nuts, seeds, and meats contain glutamates—those foods with the highest concentration of calories. We sense glutamates as savoury and enjoy the sensation from birth. Cooked and fermented meats have especially strong concentrations, so they taste especially savoury, and this savouriness seems to have been instrumental in the prehistory of man. Tenderizing meat through cooking is probably what enabled early hominids to chew enough food to grow the brain to its current size. The taste buds for savouriness were discovered fairly recently by Japanese researchers, so this taste is often called by its Japanese name, umami.6 + Sugars. Sweetness signals calories and babies are born enjoying it. Sugars supply the calories in fruit and some sugars are formed when chewing starches. + Salts. Our physiology requires salt and we lose salt through sweat, so man evolved a feedback system to regulate salt intake. A set of taste buds responds to salts, then low levels of the brain form a sensation of saltiness that is more or less pleasant, according to the body’s need and experience. Babies evince this four to eight month after birth.7

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– Acids. Many poisons are acidic, so taste buds have evolved to warn of acidity. These trigger the sensation of sourness and, in babies, a reflex to avoid it. However, most fruits contain acids and many fermented products are safe only when acidic enough. As we learn about these, we eventually come to enjoy some tart flavours like grapefruit or sour cream, depending upon the food or beverage and our experience.8 – Toxicants. It is possible to drink or chew a large assortment of poisons that are not acid, so our ancestors evolved taste buds to detect many of them. These taste buds trigger the sensation of bitterness and, beginning at birth, a reflex to spit out a bitter substance. However, just as we can learn to enjoy sour cream, so we can learn to enjoy bitter chocolate and coffee. – Strong chemicals. Poisons may be potent enough to stimulate not just specialized taste buds but ordinary nerve endings. We feel these as burning and we may feel them first in the eyes. Children avoid such substances from birth but again, experience can overcome these aversions to a certain extent. Many people learn to enjoy raw onion on a hamburger or hot pepper in a stew.

These categories are so coarse and so approximate that they might not apply to an entire dinner. You might start with a succulent fish that is poisoned undetectably with botulism, then move to a tart salad alongside a spicy chili, both washed down with home-made mageu, which is deadly if insufficiently acidic. Bitter chocolate and espresso would make a nice finish. But although these categories imperfectly define what is edible, they are valuable nonetheless. Each of them represents an imperfect yet significant Bayesian indicator of nutrition or risk.

SMELL, TASTE AND FLAVOUR Plants and animals are leaky bags filled with chemicals. The chemicals and seepage differ from one plant or animal to the next and from one minute to the next as a creature becomes fearful or hungry or horny, or when a plant becomes attacked by a predator. This seepage can be useful to other animals. To find food, to find mates, and to notice hidden predators, eons ago most animals evolved to identify trace amounts of these chemicals that escaped into the air.9

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We sense chemicals in the air somewhat as we sense them in the mouth, although the sensors in the nose are more sensitive. These chemicals exist in three forms: (1) individual atoms, (2) bunches of atoms called molecules, and (3) tiny pieces of atoms called ions. You can visualize these as individual grapes, bunches of grapes, and loose grape seeds. All of these are vibrating and moving in every direction, like motes of dust floating in the air. But these are not solid particles as we think of them. At atomic levels there is no clear distinction between a particle and energy. An electron, for example, is simultaneously a subatomic particle and the fundamental unit of electrical energy. We can imagine atoms more accurately if we think of them not as little solid bits but as little bundles of force—bundles of several sorts of force, including forces that resist other forces in ways that let us feel and measure mass. If this seems incomprehensible, consider Parliament or Congress. The elements of these bodies are Members. Each Member is simultaneously a material body and a political force. As a material body, a Member cannot be divided into pieces. As a force, a Member is attracted to similar forces—he will often converse with other members of his party—but he is repelled by dissimilar forces, by Members belonging to other parties. An atom is the smallest assortment of these forces that holds together stably, but usually an atom’s set of forces is not maximally stable, so usually several atoms with complementary sets of forces clump together. These are molecules. A few molecules may also clump together into ligands, and many atoms or molecules may clump together into liquid or solid substances that we can see and handle. At an atomic scale, air is a sea of ions, atoms, molecules, and ligands. A chemist would categorize 78% of the molecules as nitrogen, 20% as oxygen, 1% as argon, and 1% as various miscellany. Amidst all of this, one molecule in a million or billion may represent something that we need to be aware of because it indicates something edible or poisonous. Those rare molecules we want to detect and discriminate among. Our most rudimentary chemical detectors are the ordinary nerve endings at or near the surface of the eyes, nose, and mouth. Anything

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that bangs into one of those nerve endings with sufficient energy will set it off, including chemicals in the air. But more discriminating are systems that respond to specific combinations of a molecule’s shape and vibrational structure. A molecule is held together by elastic forces, the subatomic equivalent of coiled springs. The atoms within a molecule bounce about. They swing one way and stretch the springs, then the springs contract and swing them the other way, so that they oscillate like the pendulum of a clock, a clock that is kept wound forever by the energy of heat and, in the case of chemical receptors, by the energy of other molecules slamming into it. The sensory tissue inside the nose is like a rocky stream with mucous replacing water. The rocks are proteins, large and complex molecules that cap the ends of sensory nerves. Ligands in air touch the mucous and are carried by it over the proteins. From time to time a ligand bumps against a protein with a complementary shape (i.e., a complementary set of forces) or a complementary rate of vibration. In either case the ligand sticks momentarily to the protein, and the momentary increment of force stimulates the nerve beneath. When this happens often enough, the brain detects an odour. Our taste buds work similarly, although the structures in our mouth are less sensitive and the ligands are carried by saliva rather than mucous.10 Chemicals in air enter the nose through both the front and rear entrances: the nostrils and the throat. Chemicals in water—food— we sense in the mouth. The neuronal signals from both the nose and the mouth pass through the same set of nerves into adjacent parts of the brain, where they merge into our perception of flavour. Of course they do not merge completely—we can smell things without tasting them when they are outside the mouth, and we can taste salt without smelling it—but for the most part taste and smell combine into a single perception. Signals from the mouth and nose end up in the cortex of the brain alongside signals from the eyes and ears, so to some extent all of these signals are processed similarly. If you notice a bird in your peripheral vision and want to see where it is, you turn your head and eyes until both eyes bear on the bird and your sight of the bird is the strongest. If you hear a bird and want to locate the sound, you turn

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your head to the left and right until both ears pick up the sound equally and the sound is strongest. If you are a dog following a scent, then you will sniff to the left and to the right, and go where the scent is centred and strongest—and if you are an undergraduate given the task of following a scent across a field, you follow the scent like a dog.11 Chemicals seldom appear suddenly like a crash of thunder, they coalesce into gradients of concentration. A chemical’s wafting and your moving and breathing cause concentrations to ebb and flow within your nose, so the energy impinging upon your sensory neurons ebbs and flows. Energy that ebbs and flows is a wave. Thus, much like sounds, smells are stimulated by waves, waves of chemical changes. Chemicals in the mouth create comparable waves of stimulation over the taste buds. Smells and tastes change and develop over seconds. Flavours develop similarly. After swallowing a mouthful of wine, the flavour lingers for a time and gradually changes its characteristics as its constituent chemicals dissipate. One signal difference between a foul wine and a fine one is the development of these lingering flavours. A foul wine leaves a sour and/or bitter aftertaste; a fine wine evolves from one pleasant flavour to another as the phrases and lines of a song evolve. Oenophiles enjoy sniffing wines, and some of them spend a lot of time discriminating among aromas and publishing the results in reviews. Unfortunately, every oenophile’s characterization and categorization seems to differ, and to us at least, few of their descriptions seem intelligible. We used to think this a personal failing until we came upon a study of wine experts’ terminology. Twenty-nine experts from New Zealand were asked for two words that best characterized the aroma of a particular chardonnay and a particular pinot noir. The next page shows the descriptors they chose and how often they used each descriptor. If you have ever failed to understand a wine critic’s description—well, now you can see why you have had trouble.12 Oenophiles describe wines differently because human perceptions of odour do not fall into natural categories, not even when academics try to guide them. For example, a researcher at the University of California, Davis, worked out a standardized system of wine aromas “to facilitate communication among members of the wine industry.”

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PINOT NOIR

CHARDONNAY Description Oak/oaky Fruity Butter/buttery Minerally Lime Stonefruit Milk Wood Toasty Aged flowers Mealy Honey/floral Grandmother’s talc Sweet Ripe peach Honey Honey dew Creamy Nuts/cereal Vanilla Lemons Banana Sizzled butter Syrupy Herbal Youthful/fresh Malo/oak Apricots Citrus Butter/cream Fresh/crisp Fresh Peachy/buttery Peach Defined fruit Smoothness Ripe fruit Oak/vanilla Nectarine Alcohol/hot

Uses 10 4 4 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Description

Uses

Plum(s), plummy Berry/berries Cherry/cherries Black cherry Spicy Black pepper Blackberries Jammy Raspberries Sun-dried tomatoes/savoury Good sausages Fresh Cherry/plum Savoury/mealy Violet/floral Berry/fruity Fresh/clean Volatile/acetone Cassis Dark berry Strawberry Nutmeg/spice Smoky Leafy Geranium leaves Sweetness Tannins Currant Buttery Nutty Oaky Earthy Spicy oak Pinot-like/Ribena Liquorice Brettanomyces [yeast] Oak char Green capsicum Red currants

7 4 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Twenty-nine wine experts used these descriptors when asked for two words best characterizing this pair of wines. The Chardonnay had been aged in oak.

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Here is the standardized system. As you see, the subcategories of “fruity” include most of the fruits commonly seen in American kitchens and none of the many other fruits of the world. This may be a useful system but it is obviously artificial.13

Standardized System of Wine Aromas Microbiological Yeasty Flor-yeast Leesy Lactic Sauerkraut Butyric acid Sweaty Lactic Other Horsey Mousey Floral Floral Linalool Orange blossom Rose Spicy Spicy Cloves Black pepper Licorice, anise Fruity Citrus Grapefruit Lemon Berry Blackberry Raspberry Strawberry Black currant/cassis Tree fruit Cherry Apricot Peach Apple Tropical fruit Pineapple Melon Banana Dried fruit Strawberry jam Raisin Prune Fig Other Artificial fruit Methyl anthranilate

Herbaceous/vegetative Fresh Stemmy Grass, cut green Bell pepper Eucalyptus Mint Canned/cooked Green beans Asparagus Green olive Black olive Artichoke Dried Hay/straw Tea Tobacco Nutty Nutty Walnut Hazelnut Almond Caramelized Carmel Honey Butterscotch Butter Soy sauce Chocolate Molasses Wood Phenolic Phenolic Vanilla Resinous Cedar Oak Burned Smoky Burnt toast/charred Coffee Earthy Earthy Dusty Mushroom Mouldy Musty (mildew) Mouldy cork

Chemical Petroleum Tar Plastic Kerosene Diesel Sulfur Rubbery Hydrogen sulfide Mercaptan Garlic Skunk Cabbage Burnt match Sulfur dioxide Wet wool, wet dog Papery Filter pad Wet cardboard Pungent Ethyl acetate Acetic acid Ethanol Sulfur dioxide Other Fishy Soapy Sorbate Fusel alcohol Pungent Hot Alcohol Cool Menthol Oxidized Oxidized Acetaldehyde

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The senses of flavour are so inchoate that even professional judges of wine are unreliable—inconsistent when rating multiple glasses of the same wine intermixed with others, and different from one judge to the next. For example, the left column below shows how four judges rated 50 wines at the California State Fair Commercial Wine Competition, before they discussed their ratings to arrive at a consensus. Each row is a wine, each column is a judge, each colour is a rating of quality. As you can see, they agreed on the two worst wines, and some of them agreed on other bad ones, but the rest are all over the map.

Quality: 80 84 86 88 90 92 94 96

For comparison, the central panel shows how the results would have looked if the judges had agreed on which wines were the worst, which ones were best, and the order in between. The right-hand panel shows a set of random results. As the authors of the study conclude, “There is more randomness than consensus in wine ratings.”14

ELEMENTAL TENDENCIES People tend to think that everything is composed of some number of basic elements. What we deem to be basic depends upon context and experience—we consider the elements of mayonnaise to be oil and eggs, not atoms of carbon, hydrogen, oxygen, etc.—yet the notion of elemental parts seems fundamental to our understanding of the

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world. Every educated person used to know that the body is formed of blood, phlegm, yellow bile and black bile; that the universe is formed of air, earth, fire and water; and that all Gaul was divided into three parts. Nowadays we know other things instead but the principle is the same: we perceive that everything is or ought to be divisible into elements. This has engendered a continuing search for primary perceptions. However, it is one thing to break down a physical structure and another to break down a perception. Perceptions are the activity of neuronal pathways, and neuronal pathways are in constant flux. Energy impinges upon the body and then, depending upon the structure of the energy, it stimulates one or another set of sensory neurons. That particular set of sensory neurons releases a bolus of neurochemical energy into some adjacent neurons, beginning a chain reaction. The chain reaction follows the easiest route. The exact route depends upon where nerves feed into and through the brain plus extremely localized chemistry, chemistry that was formed by previous stimulation and is continuously being changed by other stimuli passing through the neighbourhood. For this reason, it makes little sense to look for fixed elements of perception, it makes more sense to search for elemental tendencies in how we process neurochemical energy. Let’s revisit the sense of taste taking this approach. Cellular structures on the tongue pass chemical energy into the nerves that serve the mouth. All of those structures will react to a variety of molecules but some of them are more responsive to specific molecular structures than to others—to the structures of sugars or acids or salts or alkalis, etc. Now, if you ask people in a lab to stimulate those structures by tasting a broad assortment of chemicals, you will find that the chemicals elicit tastes that people sort into six categories: salt, sweet, sour, savoury, bitter, and piquant. This demonstrates a natural, elemental tendency in how we process neurochemical energy. Another elemental tendency we see with colours. Psychologists have handed bundles of paint chips to people from many cultures, and asked them to sort the chips into colours. Invariably the chips end up in four piles: red, green, yellow and blue. Four-month-old babies see the same four categories. These four hues appear to be primary

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in some way, and closer examination shows them to have a particular interrelationship. The primary hues at the corners of this diagram naturally merge into one another in these ways and only in these ways. We can perceive a reddish yellow or a reddish blue but we cannot perceive a reddish green.15 We see colours like this because the eye has evolved a peculiar mechanism for sorting out wavelengths. The light receptors we use in daylight are conical neurons called cones. Each cone contains one of three pigments. To some extent each of these pigments absorbs all the visible wavelengths of light, but they absorb the wavelengths differentially. One set is most sensitive to longer wavelengths, a second set is most sensitive to medium wavelengths, and a third set is most sensitive to shorter wavelengths. The signals from those cones feed immediately into neurochemical circuitry that adds and compares them. The box below shows how.

WAVELENGTH TO COLOUR

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Left: brightness results from the sum of all the wavelengths. Centre: green/neutral/red result from medium wavelengths compared to long wavelengths. Right: blue/neutral/yellow result from short wavelengths compared to the sum of the others.16 Note that this system evolved so that the short wavelengths have less import than the others. This is efficient. The sun emits less radiation at shorter wavelengths, so there is little if any reason to respond to short wavelengths in the absence of longer ones.

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CATEGORICAL PERCEPTION Of the structural tendencies of human perception, perhaps the most profound is our propensity to divide the world into categories. All kinds of categories. Sweet wines/dry wines, classical music/popular music, art/erotica, liberal/conservative, fat/thin, rural/urban, smart/stupid—the list is infinite. Some of our categorizations are simple like those but others are remarkably complex, like the hierarchy of categories on the next page that describes your family dog to a biologist.17 But those are not the only categories we use for describing dogs. Kennel clubs distinguish different genres of dog—toy, hound, terrier, sporting, working, etc.—plus more than 500 distinct breeds, and of course everybody categorizes dogs in other ways as well, as large/medium/small, black/brown/white, quiet/yippy, playful/placid, long-haired/short-haired, healthy/sick, trained/untrained, friendly/aggressive, etc.18 Although we perceive these categories to be natural, when we look hard at individual specimens, it becomes clear that categorization lies more in the perception of the beholder than in nature. For example, Riesling comes in a continuous range from dry to sweet. Many pop songs are based on classical pieces. The serious artist Boucher painted sensual masterworks for Madame la Pompadour’s bedroom, to help King Louis get in the mood. Nor are scientific taxonomies always so clear on the ground as they are on paper. Given the chance, an appropriately sized Canis lupus familiaris will be able and willing to become familiar with 16 other species of Canis lupus, 14 of which are known as wolves. Indeed, it is difficult for ordinary folks to see why biologists deem a Siberian husky to be closer to a chihuahua than to a wolf.19 Of course our categories do reflect reality to some extent, but reality as it has been filtered and defined by our experience. Within the brain, when neurochemical energy passes along some route, that route changes chemically in a way that makes neurochemical energy coming nearby more likely to follow that route again and less likely to detour onto neighbouring routes. As additional bursts of neurochemical energy follow that route, the chemical changes become reinforced. This is the neuronal mechanism of category

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A BIOLOGIST’S FAMILY DOG Cellular organisms Eukaryota Fungi/Metazoa group Metazoa Eumetazoa Bilateria Coelomata Deuterostomia Chordata Craniata Vertebrata Gnathostomata Teleostomi Euteleostomi Sarcopterygii Tetrapoda Amniota Mammalia Theria Eutheria Laurasiatheria Carnivora Caniformia Canis Canis lupus Canis lupus familiaris

formation. It means that any given neurochemical reaction is more likely to be routed through network A or network C than through network B in the middle. This holds for small networks forming lowlevel sensations, it holds for large networks forming low-level perceptions, and it holds for networks of networks of networks that form our cognition and language.

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This is, of course, the same mechanism as adaptation. Creating perceptual categories is how we adapt to stimulation that we have encountered before. For example, imagine yourself lost between the Amazon and the Cerrado (savannah) of Brazil, with no way to cook anything. You are starving but the only foodstuff you happen upon is cassava, a shrub you know to be bitter and poisonous when eaten raw. On the other hand, you also know that some cassava bushes have leaves that are only slightly bitter and can be eaten without evident harm. You are so desperate that you sample some. From a shrub here and a shrub there, you smell a leaf and sometimes take a bite. The bitterness comes from a poison, and the concentrations of poison in cassava leaves form a continuum, but instead of a continuum of cassava you will divide the leaves into two distinct categories, safe and poisonous, and you will be exquisitely sensitive to the degree of bitterness that forms the divide between them.20 This is a useful distinction to make but it is a curious distinction to be able to make. Instead of trying to imagine what cassava leaves taste like, consider coffee. In France a standard cup of espresso is about 25 ml and is brewed with 7 g of beans. In the centre of the United States, cafés use the same weight of beans to brew 10 times as much coffee. Between those extremes, the difference in bitterness is extreme. To a farmer in Nebraska, a French coffee tastes like poison, but a Frenchman will call the Nebraskan’s coffee jus de chaussettes—the juice of socks. Each thinks the local concentration makes the best cup of coffee and the other extreme is not potable. Moreover, other people have different opinions. Their ideal cup of coffee has the same weight of beans making 60 ml of coffee, or 120 ml, or only 12 ml for an Italian ristretto. In their minds, each of these concentrations forms a category—a qualitative category, the category “good coffee.”21 There is nothing whatsoever that makes any of these concentrations qualitatively different from any other—they differ quantitatively— yet any coffee drinker will be willing to describe any cup of coffee in qualitative terms, as good, or not so good, or bad. Any coffee drinker will take a point on this continuum of quantity and ascribe this point as the centre of a qualitative category. By any standard of logic, this is nonsensical, but although it is illogical, it is normal and natural: this point represents a neuronal network that has been etched more deeply than others by experience.

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In fact, each of our sensory systems responds only to quantitative differences. Qualitative differences exist only within the brain. The qualitative differences of colour are induced within the brain by quantitative differences in the lengths of electromagnetic waves. Qualitative differences in sounds—timbres—are induced by quantitative differences in pressure waves. Qualitative differences in flavour are induced by quantitative differences in chemical pressure. Converting quantities into qualities is one of the fundamental functions of the brain. To create categories, neuronal networks combine in complex ways, facilitating transmission here and inhibiting it there. We are reasonably sure that these mechanisms are deterministic, because we can create simple, deterministic models of neural networks in a computer and watch them develop categories in a human way. Of course these models are simpler than reality but we would expect the infinite complexity of real neuronal networks to be able to form in deterministic ways every category that we perceive.

SIGNAL VS. NOISE We began this chapter by showing how combining several senses can clarify subtle signals by reducing noise. “Signal” and “noise” have specific meanings in specific fields of endeavour but a single broad statement subsumes them all: within a given context, anything of interest is signal and everything else is noise. This distinction sounds banal but is not. To survive we must attend to things that might matter to us, and the only way we can do that is by ignoring things that probably do not. Human functioning— indeed, the functioning of any adaptive animal—requires constantly dividing sensory stimulation into things that might matter and things that probably do not. Within any given context, whatever might matter is signal and all the rest is noise. The absolute strength of a signal rarely matters, what matters is that a signal becomes evident as soon as it pokes its head above the noise. Consider snakes, for example. Any snake large enough to harm you is large enough to be seen easily inside a cage at the zoo, but no

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snake is easy to see in the wild, because snakes blend in with the background. In the wild a snake presents just as strong a signal to the eye as it does in the zoo but in the wild, much of that signal is masked by noise. To survive in the jungle, our ancestors rarely needed to strain their senses to detect faint signals but they frequently needed to separate signals from noise. The same is true now in a city when crossing the street. We do not need to strain our eyes to make out a car that may run into us—that car will be big enough to see easily—but we do need to distinguish that car from all the other cars nearby. Or, from the driver’s perspective, we need to distinguish somebody starting to run across the street from the parked cars and lampposts nearby. Discriminating signal from noise is so important that a neural mechanism evolved specifically for the purpose. This is the mechanism of attention. We began this chapter with it because it is also the underlying cause of categorization. Let’s journey back in time to visit one of our ancestors in Africa. It is nighttime. Our ancestor is asleep but hyenas and lions are not. The veldt is alive with noises but our ancestor needs to sleep through them—unless the noises are from hyenas or lions. Those noises must wake him up. This means that he needs to ignore most of the usual racket yet awaken at the slightest unusual noise. After morning comes, our ancestor walks down toward the river for a drink, and so do hyenas and lions. To avoid them he needs to look far ahead for mud-coloured patterns that stand out very slightly from the bank. With both his ears and his eyes our ancestor needs to perceive signals that are embedded in a mass of noise. Both aurally and visually the ratio of signal to noise is low. Any structural propensity of the brain that could enhance this ratio would increase the likelihood of survival. Low-level structures and functions evolved to do this. To see how, let’s move our imagination to the city and look at cars. Imagine that you need to record how many cars of each colour drive down a busy highway. You realize that you are bound to make mistakes, so you ask some friends to help you out. You can employ them in two ways. The obvious way is to ask each person to do the same job, to check your work. However, if any one person is likely to average, say, one mistake in every 10 observations, then six people are likely to make six mistakes in 60 observations. The extra helpers will buy no

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improvement in the ratio of signal to noise. Better is to have each person look only for cars of a single colour then combine all of their results. Looking for a single colour is easier, so mistakes will be fewer. Both approaches will record all of the cars and colours, so both approaches will be equally sensitive to the signal, but specialization will lower the noise. This is how the brain detects lions. Sensors within the eye react to spots of light—or rather, to changes in spots of light—and send neurochemical signals into the brain. Low levels of the brain aggregate those signals, sort them, and send them only a little higher, where neurons have evolved to react to lines in different combinations and at different orientations. If a number of these neurons suddenly fire, a change becomes obvious and a tropic reaction follows, a kick on the neurochemical accelerator. You start to attention. Now the firing reaches higher levels of your brain: you see a lion land on an antelope and tear open its throat. From this experience the neuronal pattern representing the shape of a lion becomes chemically etched in your brain. The next time you walk there, the sight of the place will spill energy into that neuronal pattern, thereby generating a memory, and you will react by boosting the neurological idle speed of the visual portions of your brain—i.e., by becoming more alert.

ADAPTATION Attention, memory, and perceptual categorization are fundamental skills for an adaptive organism, so all three of these are evident at birth. If you show a young baby a sheet of grey paper, you will attract his attention, but if you show him one grey after another, he will lose interest. He will lose interest even if each of the greys is a different shade. He has remembered a succession of greys and formed them into a perceptual category. If you then show him red paper he will perk up. The next page illustrates this. A newborn baby behaves this way even though his visual cortex is barely functioning. These functions are built into the lowest levels of the brain.22 Once higher levels of the brain become involved and combine information from the lower levels, these functionalities merge into a

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1

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When we showed a baby six different shades of grey, she gradually became bored (pictures 1-6), but when we then showed him a red, he perked up (picture 7). In this way the baby showed us that he had formed the greys into a perceptual category.

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complex perceptual stew. An adult does not merely stare at something, she interprets what she sees. To perceive a set of lines as the category tiger, an adult must remember what tigers look like and must pay attention to how the lines are similar and different from her memory. To remember what tigers look like, she must pay attention to how the lines resemble the category tiger. And to pay attention to similarities and differences she must remember the category tiger. This sounds circular because it is. In adults the three functionalities form a logical circle: •Perceptual categorization requires attention and memory. •Memory requires perceptual categorization and attention. •Attention requires memory and perceptual categorization.

Since each of these statements requires the other two, they form a logical unity. They are three faces of a three-sided coin, which looks to us like a single basic function of the neurology of the brain. We do not think they describe three distinct mechanisms of neuronal adaptation, we think they describe three views of a single mechanism. Innumerable academic careers have been built on studying categorization, memory, and attention, examining specific characteristics under specific circumstances. This includes our own. However, when we concentrate on these details, we miss the larger picture. At a basic level it matters little to an organism which wavelengths of light most readily stimulate the eye, or which wavelengths the eye combines into categories, or which categories the brain most easily remembers. What matters is that the organism notice combinations of wavelength that differ slightly from others. Very slightly. What matters is noticing that a vague hint of a stripe is not part of a tree. What matters is noticing this before a huge mass of colour charges you. This is how the mechanism of adaptation helped higher animal species to survive and evolve. Since the mechanism of adaption is a function of the brain, under the hood it has a self-similar structure of neural networks, which enables it to function across a wide range of scales. At a coarse level it keeps us from walking into walls as a tropic automaton. At the other extreme it lets us notice a kink in a

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straight line that is finer than any line the eye can see. This mechanism, we are about to see, also forms a root of beauty.

7 THE TRAGEDY OF TASTE ENJOYING FOOD AND DRINK

Shakespeare’s Othello “is of a free and open nature, that thinks men honest that but seem to be so, and will as tenderly be led by the nose as asses are.” The man who speaks that line leads Othello to slaughter his innocent wife in a fit of baseless jealousy. Othello is a great man but his trusting nature is a weakness that creates a tragedy.1 Take a great man with a weakness and watch with pity and fear what comes to pass as this “tragic flaw” leads him to doom: this, Aristotle described, is the essence of tragedy. Our society has so levelled now that the man who falls need no longer be great—Arthur Miller could form a travelling salesman into a tragic figure—and we may feel emotions other than pity and fear, yet the essence of tragedy

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is still the interaction of free will with fate. Ineluctable doom is sad but not tragic. To create tragedy a play must maintain the hope that discretion will defeat destiny.2 Fate, destiny, kismet, doom: philosophers and theologians have argued for millennia whether the life of man is preordained or the product of free will. However, if we leave metaphysics for what is or at least appears to be reality, then it seems apparent that neither preordination nor free will is entirely the case. We are surely not the master of everything we do—we cannot stop breathing—yet we can control our breathing to a certain extent, so we do appear to have some free will. The same holds at a higher level of functioning. On the one hand, nothing is forcing you to read this book (unless you postulate the will of God or ineluctable determinism from the beginning of time); on the other hand, few people are able to remove an abdominal spare tire, and many smokers find stopping to be impossible. Some things we seem to do of our own volition but other things we seem fated either to do or never to do, if not by kismet then by ingrained reflex or force of habit. Moreover, sometimes reflexes continue for long enough that they seem to develop minds of their own. Imagine two boys roughhousing in a school-yard. At first they punch each other playfully but if Tom accidentally punches Dick hard enough to hurt, Dick reflexively punches back harder, then Tom punches back harder still, and they brawl. This is a circular reaction, a reaction that continues by stimulating itself. In a circular reaction, a series of reflexive behaviours become short-circuited so that they continue to elicit one another independently of whatever started them off. An adult example is going out for a long walk or run. Starting out requires an act of will but once you warm up and reach your stride, each step leads reflexively to the next. You can stop whenever you like but walking or running has come to feel like the natural state. One step stimulates the next such that now stopping feels awkward.

REFLEX, WILL AND ADAPTATION Individual cells have no free will. They are microscopic machines. Indeed, at the level of cellular functioning, chemical mechanisms

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merge into physical mechanisms and are described by physical chemistry. Tissues, which are agglomerations of cells, also behave tropically, as do organs, which are agglomerations of tissues. So, to some extent, does the body, which is an agglomeration of organs. Predictably and mechanically, removing heat from a warm-blooded body will raise its metabolic rate, and applying an electric shock will cause it to start. However, the brain is able to raise the body’s reactions to a different level of complexity, a level that permits responding adaptively rather than tropically. Yet even adaptations involve tropic behaviours. When first learning to ride a bicycle, the only free will involved is climbing into the saddle and pushing down on the pedal. Once you are moving, you are forced to learn how to balance but you have no idea how this happens. Riding a bike is not something you can instruct your body to do, your body just figures out how, often contrary to your expectations. For example, when you first try to turn left, you may consciously turn the handlebars to the left, but if you do, you will find the bike turning right. To initiate a left-hand turn from any speed faster than a snail’s pace, you need first to turn the handlebars slightly to the right. This pushes the left side of the bicycle downward. To catch yourself from falling, reflexively you turn the handlebars back to the left and overcompensate a little. Now you are leaning leftward and the front wheel is pointing leftward: now you are turning left.3 But this is hardly obvious. Indeed, few bicyclists realize that this is what they do. The body figures out how to ride a bicycle all by itself, by monitoring the results of tropic responses, complicated tropic responses that we call reflexes. When you feel yourself falling toward one side, you reflexively lean toward the other, and when you notice a swing of the handlebars taking you in the wrong direction, you reflexively swing them the other way. Initially these reflexes are sluggish, so that you need to make large corrections, but soon you learn to respond to smaller and smaller deviations until eventually you can ride without wobbling more than a hand’s-breadth. Your brain has enabled this by forming and refining perceptual categories, categories of the vestibular system, categories of falling leftward, falling rightward, moving leftward, and moving rightward. Initially the boundaries between these pairs of category are broad and vague, and you are conscious of the

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categories—you are fully aware of your imbalance and your direction—but the more you experience first one category and then the next, the more sharply etched the categories become, the more acutely you discriminate between them, and the less consciously you notice them. Of course, this is what a psychologist sees. A physicist watching you ride a bicycle would not see a nervous system assorting movements into categories, he would see a homeostatic system of movable masses, a system that maintains its equilibrium by compensating for perturbations automatically, like a pendulum. But consider a pendulum. We can see a pendulum in these two different ways: either swinging from one extreme to the other or swinging around a central position. Both perspectives accurately depict a pendulum yet they are mutually exclusive. We can understand and describe any phenomenon in different ways. Conceptual models are simplifications, like models of ships. Even a small ship is so large that no human being can picture it entire, so shipwrights used to show their customers models. Conceptual models are comparable. They are simplifications and reductions that help us to understand complex phenomena. But no model can possibly describe every aspect of a ship. If it could, it would not be a model, it would be a proper ship. To delineate every aspect of either a ship or a natural phenomenon requires multiple models. The most efficient set of models would have each model show what no other model shows, so that each model is entirely different from all the others. The logical implication is that to represent a natural phenomenon completely, the most parsimonious explanation requires two models that are mutually exclusive. That is why physicists can model light as both particles and waves, and it is why balancing on a bike can be seen as either swinging from one side to the other or as swaying around a position that’s upright. Most natural phenomena are so complex that we cannot describe them from even two perspectives. When confronted with nature,

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scientists are like the six blind men in the Indian fable exploring an elephant. Each man feels part of an elephant then forms a model of an elephant in his mind and argues ever after about what an elephant is like: a mud wall, a spear, a rope, a serpent, a fan, or a palm tree. In this book we are attempting to envision a whole rather than parts, so in the last chapter we tried to define the elephant of the brain’s functioning with three descriptors: attention, memory, and categorization. Now we would like to add two more: learning and stability. As a descriptor of the brain’s function, memory is self-evident—it is inextricable from learning and largely synonymous—but stability requires some explanation. We pointed out above that neurological adaptations involve tropic processes. These processes maintain biological stability, which biologists call homeostasis. To see how it works, imagine that enzymes A and B combine in sunlight to form enzyme C—but since too much of any chemical can kill, even too much water, the body evolved a controlling mechanism: enzyme C makes you tired, so you nap in the dark until it's used up. This is a chemical pendulum that swings around a chemical equilibrium, maintaining a homeostatic balance.4 Every living process is a chemical pendulum that swings about a homeostatic centre. Whenever a process ceases to maintain homeostasis, entropy takes over and the organism dies. A fatal illness is a failure of homeostasis. When a tree grows up listing to leeward, it is maintaining its balance homeostatically by developing durable structures. The structures are not neurochemical but they are chemical structures forming living tissue, structures that develop in response to stimulation. This is equivalent to animal learning. The learning and homeostatic behaviours of a tree are orders of magnitude slower and simpler than our learning to ride a bicycle, so it is easier for us to grasp. Sapience comes with so much more complexity that we require conceptual models even to begin to understand it. Five of these models are memory, learning, attention, categorization, and stability. However, these are five different views of an elephant, five different views of a single natural phenomenon, the phenomenon by

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which sapient animals adapt their perceptions and activities to their environment.

DESSERTS AND DRUGS A complex organism functions adaptively on many levels at once. For example, consider Harold Basset. Harold was a basset hound, an independent and pensive beast, a canine counterpart of a university professor. For dinner Harold preferred to take bread and cheese, but usually we managed to keep these out of his reach so that he was obliged to dine on kibble. Whenever we filled his dish with kibble, Harold emptied it. Whatever quantity we put in his bowl, he ate it all. Inexorably he put on weight. We put less and less food in his bowl but still he put on weight. Finally we tried an experiment. We bought a bowl large enough to feed a rhinoceros and filled it to the brim. Harold walked over and stared at it, then he looked up and to the left, then to the right, then behind him, and finally back toward the bowl. After several seconds he reached in and took a mouthful. Just one mouthful. Occasionally through the rest of the day he walked back for another mouthful. By the end of the day he had eaten less than we had ever dared to give him. As long as we kept the bowl full, he ate modestly, but if we ever let him eat more than half the food in the bowl, he wolfed it all. Every day an animal expends a certain number of calories to maintain itself, so on average the animal must ingest food containing exactly that many calories to stay alive. However, animals do not replace calories one for one, they tie their eating to their experience and expectations. For example, when Harold feared he might run out of food, he ate like hunter-gatherers who fear hunger and so binge whenever they can. Temperature also affects how much we eat. Cold requires the body to generate more heat, yet away from the world of supermarkets, food in the winter can be scarce. To generate more heat from less food, in winter the body modifies its chemical processes to use food more efficiently. Some of these processes require fat—so much fat that in northern Canada, trappers who run out of fats to eat can stuff themselves with all the rabbit they can chew yet still starve to

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death. Conversely, in hot weather the body does not need to generate any more heat than is necessary to run its basic chemical processes, and food is more abundant. The human body’s special summertime task is to replenish salt that is lost in the sweat secreted for evaporative cooling.5 Just as the body adapts to winter and summer, it adapts to other cycles as well. Human beings have no physiological requirement for three meals a day. The number of meals people eat per day may be as few as one for a Buddhist monk or as many as six for a contemporary American (breakfast, morning snack, lunch, afternoon snack, dinner, midnight snack). Even within a specific country and era, the hours of eating vary with working hours, social circumstances, and the time and resources available for cooking. A broad variety of dietary regimes can be healthful. It can even be healthful to eat less than dieticians deem necessary. The people with the longest life expectancy on earth appear to be elderly Okinawans, whose diet before 1960 used to contain 11% fewer calories than the normal recommendation for maintaining their weight. (Their diet has enlarged with Japan’s wealth and westernization, as have their sizes and shapes, while the life expectancy of younger Okinawans has shrunk.) It is even possible for a man to survive on a vegetarian diet of only 1200 calories per day. Japanese monks do this routinely at Eihei-ji, a Zen temple in Fukui. When novices first start the diet, they lose weight, but after three months they begin to regain it. Within broad limits, the body adapts to whatever number of calories and meals it is used to having, and comes to want that number.6 The body also adapts to require the foodstuffs that it usually eats and, if it is used to eating them at specific times or under specific circumstances, to require them under those specific conditions. That is why some of us cannot open our eyes in the morning without a coffee. The body learns to expect a jolt of caffeine after getting out of bed, so it slows the heart in anticipation and requires the caffeine of a coffee to raise the heartbeat to normal. Cocaine is like caffeine in this way, although it is more powerful. Opiates like heroin are also comparable, although they depress the nervous system instead of stimulating it. Cocaine’s and heroin’s chemical effects are stronger than coffee’s, which leads to stronger countervailing chemical changes and, hence, to stronger cravings,

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but the cravings still depend on expectation. That is why U.S. soldiers addicted to heroin in Viet Nam lost their addiction once they returned home: their situation and expectations changed. It is also how heroin addicts die of an overdose: they take their normal amount but not in their normal circumstances—perhaps in an alley instead of a bedroom—so the body does not prepare for the heroin by boosting the heartbeat.7 People normally distinguish among foods, drinks and drugs. Foods are ingestible solids, drinks are ingestible fluids, and drugs are substances taken into the body by any means either for medical purposes or for recreation. However, from the perspective of the body, these categories are artificial. Foods, drinks and drugs are all chemicals that affect the on-going chemical reactions of body and brain in comparable if different ways. If your brain expects a strong coffee with breakfast, it prepares for the stimulating jolt by slowing your metabolism as you get out of bed, so that you feel sluggish until you take your fix. If you are also used to bacon and eggs, your brain anticipates them by having your gut release the enzymes needed to digest bacon and eggs. (The gut contains as many neurons as the spinal cord.) The same goes if you take toast and jam with your bacon and eggs. With the digestive juices for bacon and eggs sloshing about in your stomach, you will not be satisfied by fruit and yogurt no matter how large the serving—and if you then eat a satisfying amount of bacon and eggs, you will still crave the toast and jam.8 That is why you can eat until you feel like bursting yet still have room for dessert. The enzymes for digesting turkey are used up but the enzymes for digesting pumpkin pie have been released.

TASTES AND TASTE Desserts taste good because they contain sugar and because each of us is born with a sweet tooth. You can see this in the photo on the next page showing a newborn baby’s reaction to sugared water. Liking sugar rewards a newborn baby for taking milk from the breast, and so helps him learn to nurse. Of course our reactions to sugar develop and elaborate with experience, but even those of us who find most desserts too sweet enjoy the natural sugars in fruit.

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Aside from a congenital taste for sugars, and a comparable liking for glutamates, the primary mechanism for enjoying particular foods is that the brain creates a craving or a modest desire or simple expectation, and then creates a feeling of pleasure when that craving or desire or expectation is satisfied. This response is a mechanism that the body uses from birth to maintain its chemical balances. The newborn’s brain learns rapidly that his belly will have a load of milk to be dealt with every few hours, so his brain has his belly secrete digestive juices at the expected time, in anticipation. Once those are released, he feels the chemical imbalance as hunger.9 That was also the behaviour of Pavlov’s dogs’ salivating to a bell. It is Pavlovian conditioning in its simplest form. In a more sophisticated form children are served food not presaged immediately by a ringing bell but presaged by a campaign of television commercials showing people enjoying breakfast, accompanied by a jingle: Snap! Crackle! Pop! (Or Piff! Paff! Puff! in Denmark; or Riks! Raks! Roks! in Finland; or Knisper! Knasper! Knusper! in Germany.) The product is just sweetened rice that is browned in an oven but the commercials make eating it seem special and fun. Eventually the trademark becomes so closely associated with enjoyable breakfasting that a comparable product from a different box becomes less satisfying. With experience the circumstances inducing these responses and their means of satisfaction become elaborated, but the basic mechanism remains the same. Imagine an archetypical American schoolboy of the 20th century. Before taking him to school, his mother handed him a bowl of cereal to bolt down, but on weekends she had time to cook bacon, eggs and toast, and he had time to enjoy them. His relaxed weekend breakfasts were more pleasant, so bacon and eggs soon came to taste better than cereal, despite the sugar in the cereal. As an adult he still enjoys his bacon and eggs, and the closer they are to the way his mother used to make them—to what he is used to—the more he enjoys them. In contrast, a Frenchman who is used to coffee and bread will find the idea of breakfasting on bacon and eggs to be repugnant.10

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This kind of story, with twists and elaborations, forms most of our preferences for flavours, but how good a food tastes will be affected by other bodily needs as well. When your metabolic balance requires salt or fat, foods taste better with more salt or fat. This mechanism is so subtle yet so powerful that it can even make babies drink cod liver oil of their own volition, if—but only if—they have a vitamin deficiency.11 All of this is simpler than hearing and vision. Compared to hearing and vision, the chemical senses are older phylogenetically and more straightforward. Modulated changes of air pressure need a lot of processing to become a voice asking for popcorn. A series of twodimensional patterns of electromagnetic radiation require a lot of processing to become a three-dimensional image of a bag of popcorn being filled. In contrast, as soon as chemicals stimulate nerve endings in the nose and that stimulation reaches the cortex, the aroma of popcorn floods in. On the other hand, flooding takes time and floodwaters touch everything they are near. Chemicals take longer to process than light or pressure waves, and signals from the chemicals mix with all other senses. That is why colours strengthen smells, as we saw in chapter five, and why children may perceive that one brand of cereal tastes better than others because they knisper, knasper, and knusper, or whatever.12 And of course, a specific brand may indeed be slightly different. Other manufacturers may use different sugars and brown the rice a little more or a little less. If so, the chemical differences will be slight but with flavour as with every other perception, slight variations are peculiarly salient. From infancy we associate sweet drinks with pleasantness. Mother’s milk is sweeter than cow’s milk, especially after the cow’s milk has been stripped of its fat and pasteurized. However, an infinity of influences come into play and the complexity begins before birth. The chemicals creating the flavours of food and drink are often absorbed by the blood along with the nutrients, and can pass from the blood into amniotic fluid and milk. We mentioned in chapter two that if a mother drinks a dozen glasses of carrot juice during her first two months of nursing, then when her baby is six months old, he will

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probably prefer carrot-flavoured cereal to plain cereal. The same thing will happen if she drinks the carrot juice during the last trimester of pregnancy. Thus we can see that the fetus and later the nursing baby experiences in a diluted form some of the flavours of his mother’s food and drink.12 Whatever flavours a baby experiences he is likely to come to like, even if those flavours seem nasty to most adults, like those of baby formulas that are based on artificial concoctions of proteins (hydrolysates) rather than milk. Those formulas have sour and bitter flavours that mothers describe as “obnoxious” and “horrible,” yet babies reared on them come to prefer them to sweeter, milk-based formulas. Indeed, a baby’s experience of tastes shapes his perception of tastes for years to come. For example, five-year-old children prefer their apple juice more bitter if they were reared on soy-based formula than if they were reared on milk-based formulas, and children who were reared on hydrolysate-based formula prefer their apple juice more tart.13 Note, however, that the type of formula the children grew up with is not related to how sweet they like their juice. Likings for tartness and bitterness need to be acquired but a liking for sweetness comes naturally. A sweet tooth will grow or shrink in proportion to the amount of sweet foods that a child encounters, but in no one does it entirely disappear. Even adults who dislike desserts will enjoy a piece of fruit.

CUISINES These mechanisms influence more than individual tastes: they also help to form the world’s cuisines. Homo sapiens evolved as scavengers and hunters. Nowadays when we go out to pick mushrooms, we can carry along a booklet to show us which are poisonous, but our palaeolithic ancestors could not. When a caveman picked something he did not recognize, nothing could help him decide whether to eat it or put it down other than its smell and taste. Sweet foods are rarely poisonous or indigestible, and poisonous or indigestible foods tend to be sour or bitter, so liking

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sweetness and disliking sourness and bitterness helped cavemen to survive. These preferences help to keep children alive even today, as you can see from this newborn baby turning away from a taste of quinine.14 Meat is another matter, though. Meats contain hardly any sugars, so meats are not sweet. Neither are insects. Most of us in the developed world no longer think of insects as food, but insects used to be and still are meat for many people. For example, in the 18th-century Fouchon d’Obsonville observed:15 Most of the Africans, and many people of Asia, particularly the Arabs, take pleasure in eating locusts.… One sees considerable heaps of them in their market places, fried or roasted, in which state they may be preserved some time, by sprinkling a little salt over them; and this is what the captains of coasting vessels in this country do. Those with whom I have travelled served them for a desert, or when they drank coffee. As this insect seems to ruminate, I should suppose, that is the reason why the Jews and Arabs have classed them among the clean or pure animals, though they would shudder at the idea of eating the turtle, the oyster, or the frog. It is certain, that this food offers nothing offensive to the sight or the imagination: the taste is something like that of the shrimp, and perhaps is more delicate, especially the ovarious female.

We personally did not enjoy the mopane worms we were served in southern Africa, but they had been fried in rancid oil. Aristotle probably had a better cook. He enjoyed cicadas, especially as grubs— “The creature is sweetest to the taste at this stage”—but also as adults. “At first the males are the sweeter eating; but, after copulation, the females, as they are full then of white eggs.”16 Meats—especially insects—are more dense with calories than plants, so a caveman living anywhere outside Eden would benefit from eating any animal or insect that he could catch. Any caveman’s child who was picky about eating meats and bugs would have been less likely to grow up, so there was survival value to the species in

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not finding meat and bugs distasteful. Indeed, there was survival value in finding them tasty, because the more of them a chld ate, the stronger and healthier he was likely to grow, and the more likely to find a mate and reproduce. In consequence of this, our species evolved to like the taste of meat at birth, through a liking of glutamates.17 On most parts of the globe, populations of man grew too dense to survive on scavenging and hunting, so people were forced to farm. To eat plants is an order of magnitude more efficient than to feed plants to animals and then eat the animals, so in most parts of the world for most of the history of the world, people have eaten mostly plants. Until recently, relatively few people raised animals to eat. Most people raised animals for work, wool, and milk. Even today, most of the world’s population gets most of their protein from plants.18 The staple grains and tubers that maintain man have one common characteristic: all of them are bland. Homo sapiens and our ancestors have eaten meat for untold millions of years, so we have had a long time to evolve a liking for it, but people have farmed for only a few tens of thousands of years. Evolution has had time to fit every person with taste buds for sweet and savoury but evolution has not had time enough to form taste buds specialized for barley mush. Nevertheless, enough people have lived on bland staples for enough generations that some strains of humanity have evolved structurally in a way that makes bland foods taste better. These people have more taste buds on the tongue. More taste buds make everything taste stronger. Supertasters they are called.19 Most people are not supertasters, so most people do not particularly enjoy the staple foodstuffs that most of us must eat. We want more flavour—savoury flavour. For this reason, in most places on earth people have learned to obtain savoury flavours through fermentation. Yogurt, cheese, bread, beer, sauerkraut, pickles, soy sauce—these are some of the fermented products we encounter in the west, but cuisines elsewhere and everywhere incorporate fermentation. Wheat, rye, rice, sorghum, millet, maize, teff, barley, cassava, mung beans— just about every grain and root that people consume as staples people also ferment, as well as a host of vegetables. (Also meat: bacon and ham are fermented pork.) There may be some farming

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tribe somewhere that eats no fermented foods but we have not found mention of it. Fermentation is also useful, because fermented foods keep longer than fresh ones. Fermentation can even denature some poisons, increase the density of nutrients, and reduce cooking times.20 Today the developed world can sate itself on meat, yet even so, much of our cuisine derives from the era of subsistence farming. This is most obviously so in Japan. The Japanese started out as huntergatherers. Later, when game could no longer support the population, they began to farm. Japanese who lived near the coast also fished but before the 20th century Japan was predominantly a country of subsistence farmers, farmers living off the produce of just an acre or two of land. Japanese farmers grew and ate mostly barley and millet, typically with soy products for protein, and added small amounts of anything flavourful that they could find or could manage to purchase. For most of the year, the only flavourful foodstuffs most farmers had available were fermented grains, fermented soybeans, fermented vegetables, and occasionally a piece of fish, often fermented. Soybeans ferment into soy sauce or miso; rice ferments into vinegar; fish and vegetables ferment into pickles after soaking in vinegar or brine. A tasty morsel of this and a tasty morsel of that, with barley, millet, or (for the more affluent) rice to fill you up: such was the origin of Japanese cuisine. More affluence bought more morsels, another bit of fresh this or fermented that. Originally the Japanese cooked everything together in one pot but in the late Edo period—toward the beginning of the 19th century—samurai and then merchant households began to serve the fermented vegetables—pickles—as side dishes surrounding rice. A century later this became the norm. Eventually, among the few who could afford to concern themselves with dining rather than eating, a sophisticated aesthetic developed that involved the elegant presentation over time and space of morsels that contrasted in colour, flavour, texture and temperature. The selection and presentation of each morsel might be elaborate and time-consuming but the actual cooking was not. Today the Japanese have come to eat more meat and to eat a lot of fresh fish and vegetables, and exquisite care over presentation has become a culinary norm, but the cuisine is still rooted in the savoury fermentations of a subsistence farm.21

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Until the 20th century China was much wealthier than Japan—for most of recorded history it was the richest country on earth—but in China as elsewhere, the wealthy were always a minority and the poor people in China ate much as they did in Japan. On the other hand, the wealthy could eat very well, as you can tell from the box below.22 Far to the west of these regions were little-habited lands of mountain and desert leading to the sea, a sea deemed by the locals to be at the centre of the earth, the Mediterranean Sea (medius = middle, terra = earth). Since before the dawn of recorded history the people living around the Mediterranean have traded extensively with one another and formed trading networks with people living farther away. When transport was by foot and oar, goods coming from afar were costly, but trade generates wealth, so the Mediterranean region developed a significant population of middle and upper classes who could afford to pay for exotic merchandise. These people could also afford to teach their children how to read and write, instead of requiring the children to work. Where the land could no longer support hunting and gathering, most people ate much as in Japan, cooking up pots of whatever grain they grew with whatever flavourful morsels they could find and, commonly, ferment, but wealthier families could purchase spices and other savouries imported from distant lands. Then as now, imported goods were exotic and using them demonstrated sophistication and wealth. The more spices people used, the more sophisticated and wealthy they showed themselves

A MEAGRE BREAKFAST As a six-year-old, the last emperor of China had his meals rationed. He was limited to approximately 25 dishes. One breakfast offered spring rolls; four-hour steamed chicken with mushrooms; Triple Delight Duck (duck, ham, chicken with sauce); diced chicken with vegetables; steamed ham; Yunnan pot ham; simmered tripe and lungs; diced beef with cabbage; spiced lamb; sweet potatoes with cherries; lamb with green vegetables and mushrooms; steamed pork and vegetables; sea slugs in duck stock; Peking duck; spiced duck; diced pork and broccoli; cubed lamb with spicy vegetables; lamb with scallions; tripe marinated in wine and spices; bean curds with soya sauce and spices; bean curd with bean sprouts and ginger; sautéed vegetables; spiced cabbage; spiced fowl; and white rice.23

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to be. Then as now, sophisticates discussed their likes and dislikes, formulated canons of how things ought to be done, and set down those canons in writing for the instruction of others. Good cooking came to be defined as cooking that used a lot of spices. Details differed from region to region according to the foodstuffs that were available, but until modern times, most meals around the Mediterranean still saw local staples as the centre of the meal, with more flavourful exotica on the side.24 Throughout most of history, meat was so expensive in Europe that most people could not afford it. (A signal exception was 1350 to 1550, because the plague killed so many people that the price of labour skyrocketed and extra land became available for the survivors to farm.) Even in England, which we think a land of carnivores, before the 20th century most people could rarely afford to eat meat. Europeans (like other peoples) might raise goats or sheep or chickens or cattle but for milk, wool, eggs, and labour, not to eat. Meat would come from old or surplus animals, or from the occasional rabbit or other piece of game. Additional affluence might allow people to raise some pigs for meat—pigs because they will eat almost anything that might otherwise be wasted and can be self-sufficient on forested lands—but most pork was served not as roasted slabs but as fermented delicatessen—bacon, sausages and hams. Grandes chateaux raised beef, and the nobility hunted deer and pheasant, but in most parts of Europe until relatively modern times, and in some parts of Europe until very recent times, a peasant’s diet was mostly staple grains and fermented odds and ends, much as in Japan. The specific staples and fermented foods varied with climate and soil but regional cuisines developed using the same mechanism as Japanese cuisine: children are born liking sweet and savoury, and they come to enjoy the tastes that they encounter when they are young, beginning with the flavours in amniotic fluid and breast milk.25 This pattern has been followed all over the world, whenever and wherever the increase of human population has seen subsistence farming replace foraging. Since farmers have become more efficient, more people can indulge a taste for meat, but in most countries this has seen menus elaborated, not fundamentally transformed. For example, in 1981 we spent seven months in Germany working at a research institute. Every day the institute’s cafeteria served a tasty three-course lunch. This was the offering:

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Soup Bread — Most days meat, some days fish Most days potatoes, some days noodles Most days cole slaw, some days sauerkraut Bread — Pastry

Aside from the meat, which came in copious quantities, this was remarkably similar to meals eaten by poor farmers. Soup is whatever you can throw in a pot to flavour water. Potatoes are a bland staple. Noodles are a fancy form of bland staple. Bread is a bland staple that has been fermented. Cake is sweetened bread (although nowadays bakers imitate its fermentation with a weak acid and sodium bicarbonate). Sauerkraut is a fermented vegetable. Cole slaw is a vegetable coated with vegetable oil and a product of fermentation (vinegar). In the west, an apparent change of cuisine came in 17th-century France. In the first half of the century, Paris saw the emergence of a plutocracy so rich that they could afford to buy not just meat but whole estates—estates in the vicinity of Paris, no less—and to equip those estates with the greenhouses and labour needed to nurse fruits and vegetables into ripeness all the year round. Thus, in rich Parisian houses (although not at the court, which was more conservative) fresh foods came to define a new standard of sophistication. Moreover, spices were becoming bourgeois, because the Dutch East India Company were bringing in so many shipsful that their prices had plummeted. Rich sophisticates did not want to mask the expensive fresh flavours with bourgeois spices, they wanted to bring them out and enhance them. This was the origin of French haute cuisine. We can see the difference in these two recipes for the stuffing to be cooked inside a suckling pig. The first is from approximately 1393, the second from 1691:26 “Take twenty eggs and cook them hard, and some sweet chestnuts cooked in water and peeled: then take the egg yolks, sweet chestnuts, fine old cheese, and the cooked meat of a leg of pork, and mince it, then mash with some saffron and a great abundance of powdered ginger.…”27

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“The Flesh of the Pig, a piece of very tender Veal, a little raw Gammon, and Bacon; also, a little Parsly, chopt Chibbol [a vegetable resembling both a leek and an onion], and all sorts of fine Herbs, except Rosemary and Sage. In the mean while, two Bay-leaves, some Thyme, sweet Basil, Savoury, three Cloves of Garlick, and two or three Shalots; this Liquor when half boil’d away will serve to moisten your Farce [stuffing]. Let some Pistachoes and Almonds be also scalded, according to discretion, and let six Eggs be harden’d to get their Yolks: Afterwards let some of your Bacon and Gammon be cut into thick Slices, taking only the lean part of the Gammon: When they are all well season’d, let a Slice of Gammon, another of Bacon; as also, a Lay of Almonds, another of Pistachoes, and a third of hard Yolks be set in order. Besides, you must put into the Farce, some Truffles and Mushrooms cut small, with a little Milkcream, and soak them in your strong Liquor; adding afterwards the Yolk of one Egg.…”28

To an historian of food these recipes seem to differ fundamentally. The old cheese and powdered ginger of the earlier recipe would form a far sharper flavour than the herbs and nuts of the later. The later recipe does call for onions, garlic and shallots but cooking those destroys their noxious chemicals and converts their starches to sugars. There is, however, a fundamental similarity: both recipes are built on the savoury flavours of fermentation. The earlier recipe includes fermented milk (cheese), and the later includes two forms of fermented pork (bacon and gammon) plus a fungus that is not fermented but smells as though it is (truffles, which smell like a mixture of old socks and sex). A baby is born biased toward sweets and savouries, and experience develops his palate in line with these biases. Many common foods are fermented, so the baby develops his liking for savouries with his mother’s milk. The products of fermentation are commonly acidic and sometimes bitter, so besides liking sweetness and savoury, at some point the child or the man will come to enjoy tartness and bitterness in juxtaposition to sweet or savoury. Tea is bitter but we enjoy it because it is also savoury, although we may add sweetness and tartness with sugar and lemon. Tastes can and do change—an oenophile is made, not born—but the development of the palate largely follows our fate inexorably, like a tragedy. We want to taste the chemicals that we are used to tasting, with only so much variation. We do not take easily to culinary surprises. They are both literally and figuratively too difficult to digest.29

8 THE FACE OF BEAUTY WHAT WE SEE IN A FACE

Pretty faces built Hollywood and most of those faces have been sexy. Sex has always been tied to beauty, and Freud was certain that beauty derived “from the realms of sexual sensation.” However, you can see from the beautiful woman on the next page that beauty and sexiness are not the same.1 After pubescence everyone is attracted by a sexy face—we shall discuss this toward the end of the chapter—but factors other than sex influence beauty. That’s why, when men and women assess women’s portraits for attractiveness, they make similar judgments— and why both women and men make similar judgments of men. Neither the age of the judge nor the age of the portrayed makes

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Sexiness and beauty are altogether different.

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much of a difference. Within any culture to a large extent, a pretty face is a pretty face is a pretty face. Indeed, we shall see later that this tends to hold across cultures too. And people respond more positively to pretty faces. For example: •Comely people are more likely to be hired after mock interviews and real interviews. •Comely lawyers earn higher salaries than homely lawyers who graduated from the same school in the same class with similar grades. •Comely candidates are more likely to be elected to professional associations. •Comely people pay lower bail and fines for misdemeanours.

Once again, this is irrespective of gender. Studies showing these differences compare comely men to homely men and comely women to homely women.2 Indeed, this preference starts long before sex begins to glint in any eye. Pre-school children prefer to make friends with comelier classmates. Eight- to 12-year-olds judge more attractive adults to be more trustworthy. In grades three to five, teachers give more attractive children higher grades despite similar scores in achievement tests. Even babies share the preference. Six-month-olds look longer at pictures of men, women, or babies whom adults deem more attractive. This holds even when comparing pictures of tigers.3

FIRST FACES II When a newborn baby first opens his eyes, he does not expect to see faces. Indeed, he does not know that there are such things as faces. He does not even perceive that there are creatures in the world other than himself, or that a world exists. All he perceives is a morass of patterns—uninterpretable patterns, patterns even less meaningful than the sounds of a language you do not know. Listen to someone speak a language you do not know, a language that is completely unrelated to your own. You hear a stream of meaningless sound, a continuous stream that varies in pitch and that

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pauses occasionally for varying lengths of time. This is the aural equivalent of a newborn baby’s first sight of his world—except that you understand more of what you hear than a newborn understands of what he sees, because you understand that you are listening to a person’s voice. The newborn has no concept of other people—neither a concept of people nor a concept of other.4 Despite this limitation, the literature of psychology is filled with claims of a “hard wired” preference to look at faces. Many labs have found such a preference and we ourselves found one in babies less than one hour old. When we showed 12 of them these two images, nine looked toward the one on the left that is arranged like a face, two showed no preference, and only one looked toward the one on the right.5 However, to explain this we do not need to hypothesize any congenital fascination with faces, we need only remember that a baby is born with a nose. You probably never see your nose because you have learned to ignore it, but try this experiment. If you wear glasses, remove them. Now close one eye and then the other. Do this repeatedly, as fast as you can, while noticing how your nose shapes your field of view. Your nose blocks information from each side of the bottom, leaving your field of view heart-shaped. As you can see here, objects that are larger on top are more congruent with the field of view. Congruence is a form of self-similarity, which is processed efficiently by the brain. Several labs have found that newborns prefer top-heavy images, like the one on the left here, no matter what the features look like.6 This may seem a heartless, mechanical explanation but it is appropriate. Toward the end of gestation a fetus senses the womb through his ears and taste buds, so they begin to stimulate his brain and build neuronal networks in the brain’s cortex, but not until he is born has he anything to see, so at birth his visual cortex barely functions. This leaves the newborn’s vision rudimentary. For example, when looking at a face, the visual cortex normally directs our gaze to the eyes and mouth as in the left here, but the visual cortex will not do this Two months old

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BABIES AND MONKEYS The human face rapidly becomes special to a baby, and particular areas of the brain come to specialize in recognizing faces, but this is not because the human face is intrinsically special, it’s because babies see more human faces than anything else. We can tell this by comparing babies with monkeys. At first babies can discriminate among simian faces as well as they can discriminate among human faces, but after six to nine months they have learned enough about how people look to see subtler differences among human faces. As this happens they lose their ability to discriminate among simian faces. In contrast, monkeys learn the opposite—unless the monkeys have been raised not by monkeys but by people, and are prevented from ever seeing any other monkey or a mirror. Those monkeys discriminate faces as though they were children.7

for a month or two. We found that during the first month after birth a baby does not look beyond the hairline or chin, as shown on the right.8

LIGHT During the first months after birth the baby’s visual cortex develops and the brain begins to respond appropriately to a basic physical characteristic of the world: darkness against brightness is likely to be more important than brightness against darkness. Imagine yourself standing on the veldt. You hear the cry of a bird and look up to see its silhouette against the sky. From the energy impinging upon your ears and your eyes, your brain perceives regularities—signals against backgrounds. The cry is formed

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by energy above the ambient level but the silhouette is darker than the background, so the silhouette is formed by energy below the ambient level. This happens even when the bird is white, as you can see on the previous page. To understand this, imagine you are outdoors on a sunny day. The sun is behind you and illuminates everything you see. The odds are even that any one object will be lighter or darker than what’s behind it. However, the chances are that the sun will not be behind you. Probably it will be on your left or on your right or overhead or in front. If it is anywhere other than behind you, then it will illuminate directly little of what you look at, leaving most things illuminated indirectly—i.e., in shadow. For example, in the picture on the last page the sun is on the left and illuminates directly just the left side of the bird and branch. From every other direction the sun illuminates the objects indirectly, by reflecting off the surroundings—in this case the sky. This leaves most of the white bird darker than the sky. Natural backgrounds are not brighter all the time and indoor lighting is more variable, yet backgrounds will still be brighter more often than not. For this reason the brain becomes more used to darks against lights. Adults see darks against lights more quickly than the opposite, and when three-month-old babies are shown a pattern like this one, they look toward the dark bars first.9

FIRST FACES III In the last two sections of this chapter we saw the baby’s “innate” face detector: his brain more easily processes shapes that are congruent with his field of view, and his brain soon becomes more efficient at processing darker features against a lighter background. Faces have two eyes above one nose and one mouth, and the eyes and mouth are usually darker than skin no matter what the skin’s colour, so faces are easy to look at. In addition, a baby will see a lot of faces up close. For these reasons a baby comes to look at a face in preference to another object before knowing what a face is.

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The first time a baby looks at a face, he sees a sea of visual noise. As he sees more faces, the repeated faces gradually form within his brain the neurological pattern face, but the background keeps changing, so no pattern background is formed. Each time he sees another face, parts of the pattern face are reinforced while the always-changing noise in the background is not reinforced. The strong pattern face that eventually emerges represents an average of all the patterns that formed it. When this pattern is stimulated he becomes aware of a face, especially when the face is close to the average. The next two pages illustrate this using images of words instead of images of people. Any new face that the baby encounters will stand out more clearly if it resembles the stereotype that has formed. By the time he is six months old a baby knows that other people exist and he knows something about faces, yet still, the closer a face is to the average face, the more salient it will appear to be and thus the more strongly it will catch his eye. The same thing holds with adults. If we ignore movie stars and fashion models, faces that we find most attractive are usually those that look most average. We can see this if we take a number of portraits and morph them together to form an average. The average will usually look more attractive than any of the individuals.10 Here is an example. The central face is the average of the four surrounding faces. To create it, on each of the surrounding faces we defined 189 comparable points—centres of eyes, centre of chin, etc.— then we calculated the average position of each point and created a face defined by those points. Unfortunately we were not able to do this with hairstyles, so hair ended up as a blurred mélange.11

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FACE FACE FACE FA FACE FACE !"#$ !"#$ FACE FACE ! " # $ !"#$ FACE 1. These represent different faces that a newborn encounters.

apien dui sapien porta magna purus. Pulvinar pellentesque a duis adipiscingg nte aenean quis vulputate fermentum, eu enim vehicula curabitur quisque,, uis a enim porttitor eget, enim molestie eget. Sed integer elit lorem sed riss do autem ut molestie orci id, non arcu vivamus, commodo aliquam aliquam laa tae augue. Est sed quos, facilisis soluta molestie, inceptos urna ut, neque euu ugue viverra sed, a mi amet nibh. Erat sed aliquam facilisis urna massa et,, se arcu non vestibulum maecenas, et dignissim diam suscipit. Quis massa s ongue, nibh dui eget dignissim bibendum pede, congue tempus. Lobortis vel j et curabitur mauris, vel tincidunt, donec placerat suspendisse purus mi rhoo utpat at. Sagittis ut nec elit at elit, ratione egestas mi mauris, ipsum non mollis, proin etiam in nostra. Felis non id vestibulum vel neque, at risus id v m tellus velit, risus velit et erat donec, enim maecenas curabitur tortor niss m t sem volutpat. Phasellus ad ornare adipiscing, magna lectus. Sem ut quam s nibh consectetuer ipsum primis, mollis vestibulum tellus rutrum vivamus sum mauris venenatis porttitor sit velit. Diam nulla eu nec. In ut fringilla a lutpat urna, magna fringilla placerat sollicitudin vitae. Id nonummy liberoo magna, at interdum maecenas orci tellus, lorem quam mauris molestie ege auris eget nulla provident wisi. Non tincidunt, eu lorem commodo auctor r t ttit t di i f i ill bl dit

FACE FACE FACE FA FACE FACE "#$ !"#$ FACE !"#$ AC F FACE !"#$ F !"#$ FACE 2. At first the brain’s responses to the faces are lost amidst a sea of noise.

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3. Experience with faces forms neuronal pathways superimposed upon one another to form a strong pathway representing a stereotypical face.

apien dui sapien porta magna purus. Pulvinar pellentesque a duis adipiscing nte aenean quis vulputate fermentum, eu enim vehicula curabitur quisque uis a enim porttitor eget, enim molestie eget. Sed integer elit lorem sed ris do autem ut molestie orci id, non arcu vivamus, commodo aliquam aliquam l tae augue. Est sed quos, facilisis soluta molestie, inceptos urna ut, neque eu uugue viverra sed, a mi amet nibh. Erat sed aliquam facilisis urna massa et, se arcu non vestibulum maecenas, et dignissim diam suscipit. Quis massa s ongue, nibh dui eget dignissim bibendum pede, congue tempus. Lobortis vel j et curabitur mauris, vel tincidunt, donec placerat suspendisse purus mi rho utpat at. Sagittis ut nec elit at elit, ratione egestas mi mauris, ipsum non mollis, proin etiam in nostra. Felis non id vestibulum vel neque, at risus id v m tellus velit, risus velit et erat donec, enim maecenas curabitur tortor nis t sem volutpat. Phasellus ad ornare adipiscing, magna lectus. Sem ut quam s nibh consectetuer ipsum primis, mollis vestibulum tellus rutrum vivamus sum mauris venenatis porttitor sit velit. Diam nulla eu nec. In ut fringilla a olutpat urna, magna fringilla placerat sollicitudin vitae. Id nonummy liber magna, at interdum maecenas orci tellus, lorem quam mauris molestie ege auris eget nulla provident wisi. Non tincidunt, eu lorem commodo auctor r i f i ill bl dit di t ttit t 4. This stereotype stands out through the noise, so that any face triggering the stereotype’s pathway is seen.

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FAMILIAR PROPORTIONS As Athena was born from the brow of Zeus, so the word aesthetics was born from the brow of a German philosopher, Alexander Baumgarten. Although Baumgarten used it to refer to the philosophy of taste, the word is an anglicized form of an ancient Greek word that has nothing to do with beauty. The Greek aesthétikos denotes sensory perceptions. Only in this sense is a baby’s response to pretty faces an aesthetic response. A baby’s preference for faces that we deem to be pretty is a function of his low-level neuronal functioning. With time that low-level functioning will come to shape higher-level functioning, will come to shape complex sets of learned associations. With time those associations will become rich enough to form an aesthetic preference in the modern sense. However, time and the development of complexity are key. There is no special moment in development at which a low-level preference becomes an aesthetic preference, there is a continuum of development with definable ends but no clear boundary. Fundamental to any aesthetic preference is familiarity. Thus, to us the sheet of paper on the next page looks like a shipping label yet to a Chinese aesthete it is equivalent to a copy of a drawing by Rembrandt.12 Familiarity is only one of several factors that will combine to form aesthetic preferences, but it forms the core. Clothing à la mode looks nicer than clothing that is out of style, yet the only difference is familiarity. This is obvious but less obvious is how deeply the phenomenon is rooted. We can see its depth by looking at what people find attractive in faces at different ages. Two factors turn out to have subtle effects. One is the disproportionately large cranium that a baby is born with, to house a disproportionately large brain. A baby’s cranium stands so high that the facial features look disproportionately low compared to an adult’s. The lower part of the skull gradually catches up but not until adolescence does the face attain its adult proportions.13 The second factor is foreshortening caused by differences in height. Babies usually must look upward to see anybody’s face. Young children usually look upward to see adults but look straight ahead

THE FACE OF BEAUTY

to see their schoolmates. Adults generally see people more or less straight on but tall adults do look downwards more often than upwards, and short adults look upwards more often. A child or adult who looks upward sees a larger chin with the features higher in the face, while anyone who looks downward sees the opposite. Here Gottfried Schadow shows the difference of proportions with the same head viewed from from above and below.14 People are normally oblivious to these differences but our lab found that they combine to form aesthetic preferences, aesthetic preferences that develop with age. To study this we used a computer to raise and lower features in faces to resemble the differences in proportion

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when a face is seen from different heights. An example is here. The height of the features in the central face is average for adults. On each side we lowered and raised the features to levels seen in only five percent of the adult population. By showing people pictures like these under controlled conditions, we found that at every age people prefer the perspective they are used to seeing in everyday life:15 •Five-month-olds look and smile longer at faces with higher features. Since babies usually look at adults from below, they are used to seeing a larger chin and higher features. •Three-year-olds prefer faces with lower features, but only if they go to day care, where they spend a lot of time with other threeyear-olds, whose features are still childishly low. •Twelve-year-olds are close to adult height. They find features in an average position to be most attractive. Low-featured, more childish faces come second. Twelve-year-olds also dislike the high features of someone viewed from below. •Compared to shorter adults, taller adults find faces with lower features to be more attractive, features reflecting their higher point of view.

The first picture in this book shows some New Guineans adorned with bones in their noses. It takes more experience of bony adornments than most of us have had to find those faces beautiful, but we found that it requires remarkably little experience to change how we respond to variations with a range that is closer to our norm. We showed university students 40 photos like those three above. Each student saw only one of the heights. We explained that this was an experiment about memory, and we asked the students to keep track of how many times they saw each face. A few minutes later we asked them to participate in a second experiment. In this one we showed them a different face with movable features, and we asked them to put the features where the face looked most attractive. Students who had just seen high features preferred the features higher, students who had just seen low features preferred the features lower, and the others preferred them in between. Thus does seeing what we are used to seeing form fashion.16

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SEX AND EXPERIENCE We find average faces attractive because the brain’s neuronal networks have become attuned to them, making them easier to process. For views from the front we also find symmetry attractive, in faces and in everything else. The reason is similar: symmetry duplicates the information on frequency and amplitude, making the information easier to process.17 In a lab it is possible to tease out symmetry from averageness, and to tease out other factors too. It turns out that averageness attracts the eye more than symmetry, and other factors attract as well, factors that clump together into two: experience and sex. Every sense of experience and every sense of sex from pleasure to procreation.18 We have seen how one form of experience influences faces, the normal point of view formed by height, but other experiential factors are powerful too, like the face of a mother. Imagine that you are in a psychology lab. A technician shows you photos of a man and four women, none of whom you know. All five people in these photos are in their twenties. You are asked to guess which woman is the man’s wife. Of course you have no idea, yet the odds are a little better than chance that you will guess correctly. That is because men tend to be drawn toward women who look a little like themselves. Now the technician replaces the photo of the man with a photo of the man’s mother in her twenties, and he asks, “Which of the four young women is this new woman’s daughter-in-law?” This question turns out to be easier to answer. That is because, although men are drawn to women who look a little like themselves, they are even more strongly drawn toward women who resemble their mothers. The same holds for women, although they are drawn to men who look like the men they grew up with, who are not necessarily the biological father.19 Doubtless straightforward familiarity has a role in this but so do the pleasant associations that form affection. In the study we just described, each man in the photographs took a written test that enabled the psychologists to assess how close or distant he was to his mother as he grew up. It turned out that the closer he was, both physically and emotionally, the greater the likelihood that his wife’s face resembled his mother’s.

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After puberty, sex attracts too—or rather, sexual stereotypes. These also develop from the average man and average woman but as the antitheses of those averages. The most masculine men are those who differ most from the average woman, and the most feminine women are those who differ most from the average man—the ends of the bar in this diagram. When considering mates we have no way to measure fitness for purpose—fertility, endurance, resistance to disease—but the appearance of things is usually so tied to their function that we cannot divorce the two. We naturally and unconsciously assume that someone who looks MASCULINITY FEMININITY more feminine will function better as a woman, and that someone who looks more masculine will function AVERAGE AVERAGE better as a man. The most feminine women have fuller lips and larger MEN WOMEN eyes than average women. These women look more attractive both to men and to other women. The same holds for more masculine men, men with craggy brows and a substantial jaw.20 That said, to a certain extent experience still trumps sex. Adolescents attending an all-girls’ school learn to prefer more feminine girls’ faces and more feminine boys’ faces, compared to their friends at a co-ed school, especially those girls who have no brothers. Similarly, boys attending an all-boys’ school learn to prefer more masculine-looking boys’ faces, especially those boys who have no sisters. On the other hand, the sex hormones of adolescent boys cannot be ignored. No matter what their school, boys tend to prefer more feminine girls.21 It is obvious that sex and experience are intimately related but some preferences can sensibly be ascribed more to one factor than another. For example, as sexual hormones change with time, so do the faces that people find more attractive. When women are between pubescence and menopause, they tend to prefer more masculine men than they do earlier or later in their lives. Also, women’s preference for masculinity is greatest during the time of the month

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that they are the most fertile. Something comparable happens with men. At times when men have higher levels of testosterone, they tend to prefer more feminine women.22 Sex pheromones also come into play. Pheromones are chemicals that animals secrete, chemicals that affect the behaviour of other members of the species. Pheromones induce ants to forage for food in groups, they induce rabbit pups to nurse, and they induce women who work together to menstruate together. We are not consciously aware of our own species’ pheromones—we may be more cognizant of the pheromones of a male cat—but we do secrete sex pheromones and we unwittingly respond to the sex pheromones secreted by other people. Pheromones help to attract the opposite sex and they are intimately tied to how we see and smell the opposite sex. Young women who prefer more masculine smells also prefer more masculine faces, and young men who prefer more feminine smells prefer more feminine faces.23

PRETTY FACES It is clear from what we have seen that the prettiness of a face is not solely in the eye of a beholder. To a large extent a pretty face looks pretty to every beholder. This can involve sex appeal but even sixmonth-old babies prefer the same faces as adults. The single most basic factor is the relationship of a face to the average face that the beholder has encountered. Since all faces have commonalities, average faces have commonalities, and so do all beholders. But there is more. In chapter six we saw that an adaptive organism will find comfort in what it knows, and will find particularly salient any stimulus that differs very slightly from what it knows. This is how our brain reacts within all of our sensory domains. When the brain encounters a stimulus that differs slightly from the norm, the neurochemical traffic ceases to be routine, so it ceases to stay confined within routine neuronal networks. It jumps elsewhere and is processed more. In this way we attend to something unwonted with extra care. The additional neuronal networks were formed by earlier neuronal traffic, so activating them brings previous experiences to bear on the current stimulus. These experiences may

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be positive, negative, or both. Their integrated sum biases our reaction to the new stimulus positively or negatively. One attribute that biases you positively is a similarity toward yourself. You can see this in a study executed during a particularly divisive election for the presidency of the United States, when John Kerry ran against George W. Bush. Three months before the election, a reasonably representative sample of interested voters had their pictures taken, then one week before the election they filled in a questionnaire that showed pictures of Bush and Kerry. A few respondents thought that the photos had been retouched or “photoshopped” but no one had any idea of the reality: one of the two pictures had been morphed with a picture of the viewer himself or herself. Of those who unknowingly viewed something of themselves in Bush, a plurality said that they would vote for Bush, and of those who unknowingly viewed themselves in Kerry, a plurality said they would vote for Kerry. Strongly partisan respondents were not affected by this but weakly partisan respondents and independents were. The more of themselves had been morphed into the picture, the more suitable the candidate looked.24 Bias is a form of memory. We remember enjoying white wines from New Zealand, so we are biased toward ordering one with dinner. We remember enjoying performances by Kenneth Branagh, so we are biased toward seeing his new film. We remember being bored by exhibits of abstract art, so we are biased toward forgoing the Museum of Contemporary Art. Bias does not apply solely to sights or sounds or smells or tastes, it applies to all perceptual circumstances, including some that may seem unlikely. For example, to keep your balance while you walk in mountains, your brain constantly senses sights, pressures, and the position of your limbs. If a set of sensations is unusual, the brain enlarges its neuronal networks. This taps more experience. The integrated average of that experience biases your perceptions toward pleasure or fear. You may feel pleasantly secure within a context of risk or you may feel as though you are in mortal danger of falling off a cliff. The initial measure of beauty derives from averageness, then biases add to or subtract from that measure. Several labs have shown this

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with adults and we have shown it with five-year-olds. The basic approach is this. Photograph 60 faces, then create two averages, one of all 60 and another of the 15 prettiest. The second average is measurably different—the eyes are 10% larger, the lips are 5% fuller, etc. Measure 256 points of difference and arbitrarily define this set of differences as one unit of bias. Now take the average face and modify it by adding or subtracting units of bias. Finally, ask volunteers to rate the new faces for attractiveness, and plot the result. You will see a bell-shaped curve like this with the peak—the most attractive face—showing roughly two units of bias added to the average face.25 These studies all use arbitrary stimuli and arbitrary units, so the actual numbers they report do not generalize to other circumstances, but the effect they show is clear. The brain forms biases from experience and applies them to its perceptions. Insofar as we share many experiences, we develop similar biases in similar circumstances.

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That’s why all of us like sexy faces more than average faces: all of us like sex. But we also like kindliness and wisdom. The Chinese woman at the beginning of this chapter radiates kindliness and wisdom. She looks like an ideal grandmother. This strong affect adds to her average proportions to make her beautiful.

9 TIMELESS BEAUTY HOW WE SEE ART

In 1968, a U.S. anti-war activist named Abbie Hoffman tried to enter a government building in Washington. He showed up wearing a shirt that resembled the American flag. This so infuriated the police that they literally ripped the shirt off his back then arrested him. At that time few people ever wore a flag on clothing, so this shirt was unusual. Moreover, Hoffman was an anarchist. The police were unused to his attire and disliked him. They saw him as profaning a virtually holy symbol and charged him with desecrating the flag.1 One generation later U.S. police, firefighters, and even truck drivers routinely decorated their clothing with the flag. Blue-collar America

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was still nationalistic and still supported the war du jour—their fundamental attitudes had not changed—but after one generation, fashion had inverted.

FASHION Averages adjusted by bias form fashion. We want to wear what everyone else is wearing but better is something a little different that both fits with the times and tickles people’s fancy. Fashion houses spend vast sums to market what they hope to be the colour of the season, and they hope to supply all of the variations that their market deems appropriate.2 With bodies as with colours, we prefer the shapes that we are used to seeing, adjusted by bias formed by experience. In the twentieth century, the western body beautiful arose from the picture press and movies, which fed the world images of svelte young women, but this was quite a change. Nowadays in developed countries, cheap foods like fries are fattening and few poor people spend their days at hard labour—machines have replaced the shovel and axe—so poorer people tend to be fatter than wealthier people, but in most times and places only rich folks have had the means to overeat, and rich folks do not labour, so in most times and places it was mostly the rich who got fat. This exchange of corpulence developed during the last century. The same century saw the development of fancy factorymade clothing and expensive brand names. Before the 20th century, fine clothing was always sewn to order and the people who defined fashions were the women who partied a lot and were rich enough to have more than the usual amounts of clothing made up—rich women, who tended to be plump. When these women dressed up, they functioned as fashion models, so plump women used to form the fashionable ideal.3 We can see this in the paintings of the 17th-century Flemish artist Peter Paul Rubens. Rubens was not only a great artist, he was also a social lion and diplomat. All over Europe his works were in demand, so much demand that he ran his studio like a factory and shipped canvases everywhere. His paintings were large and elaborate, ideal for displaying wealth and sophistication. He was particularly

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good at producing monumental paintings showing stories from Grecian mythology and the Bible. Those subjects were in vogue and he could make any of them tastefully lascivious. For example, here is a detail of a life-sized Venus (with Adonis and Cupid), the goddess of beauty and love. By today’s standards of beauty this Venus is plump, but in the 17th century she exemplified the feminine ideal.4 However, with something so basic as body, fashion does not explain every preference. The availability of food also comes into play. When university men are hungry, they prefer women to be fatter, and so do men and women labouring in a subsistence economy. The experience of the stomach biases the appetite of the eye.5

REPETITION AND FRACTALS As we look around the world, we believe that the things we see reflect an optical reality, but to a remarkable extent they do not. For example, take another look on the next page at the submerged crocodile. Although you see the head of a crocodile, no crocodile is actually to be seen. There are just a few splotches that might be driftwood. This bears little resemblance to the complete head underneath, which is formed from tooth and jaw. In the first photo

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you are not seeing a crocodile, you are inferring a crocodile, and doing so from little information.

We infer almost everything that we see. The eye samples a few spots of a scene and the brain infers the rest. Eyes can see sharply only a tiny region, an area about the width of your thumb when your arm is outstretched. When you look at a scene, you move your eyes across it rapidly and stop to sample tiny bits of it for half a second here and a second there. While your eyes are moving rapidly,

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your brain ignores them. Thus, most of what the brain perceives is not an optical image, it is an inference formed from a succession of small sharp bits amidst a sea of blur, and from probabilistic weightings of previous experience. Below is an example. A Soviet psychologist Alfred Yarbus observed people’s eye movements while they looked at the painting shown in the insert. The large image shows the information that one person’s eyes took in during the first 35 seconds.6 Repetition builds patterns in the brain, so it helps us to make these inferences, and across short distances, symmetry is a special case of repetition. Not only is the human body symmetrical bilaterally, so is the brain. The right side of each eye feeds the left side of the brain and the left side of each eye feeds the right side of the brain, then

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after a short delay, each side of the brain feeds the other. Thus, when we look at something that is symmetrical from left to right, each side of the brain has an original image to work with plus a mirror image that arrives moments later. The word symmetry means “same measure” in Greek, so by definition symmetrical objects contain similar measurements. We usually measure things that we see in linear dimensions— WOW feet and metres—but instead we can measure the angles that they subtend at the eye. When objects are symmetrical in angles but not in length, like this, they are symmetrical in scale.

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Symmetry across scales can also be measured not in angles but in repetitions of an algorithm. Put one toaster in a box, put 10 boxes into a shipping carton, put 10 shipping cartons onto a pallet, put 10 pallets into a container, and load 10 containers aboard a ship. This is another form of self-similarity. Nothing changes but the scale of the packaging: 1, 10, 100, etc. Self-similarity has attracted close attention from mathematicians, who have identified within it an abstruse dimension. To understand this dimension, let’s look again at the self-similar structure—the fractal—on page 30, the rivers and lakes of the Canadian Shield. As you will recall, those two photographs look similar but are a hundredfold different in scale. Let us now look closely at one imaginary lake. For the sake of simplicity let it be symmetrical with pointed bays. Consider this star to be a map of this lake. Now let’s double the scale of the map. Since the lake has a self-similar structure, in the second map more bays become visible. Finally—the next page—let’s lighten the newly visible bays, so that we can see what they add to the lake. Each new bay increases the perimeter from six units to eight. This means that the total perimeter is increased by fully one-third, yet the additional area is trivial.

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If we magnified this more, we would see more and more bays, and each additional magnification would add an additional, disproportionate length to the shoreline. This disproportionality is the lake’s fractal dimension. The lake’s fractal dimension is the rate by which the shoreline increases disproportionately more than the area. Mathematicians have devised ways to calculate the fractal dimension of a structure. Of course, mathematical fractals are abstractions. They have no material existence that is subject to the laws of physics, so they can maintain perfect self-similarity at any scale. However, within limits, fractal geometry can be applied to physical structures in the real world just as conventional geometry can. It turns out that a typical shoreline has a fractal dimension between 1 and 1.5. Fractals may sound like a mathematical curiosity but they are not. Self-similar structures are ubiquitous in nature. A seedling develops two branches, then each of those two develops two branches, then each of those four develops two branches, etc. In field and forest, almost everything you see has a self-similar structure. So does much of the human body, including our system of blood vessels and capillaries, which forms our largest organ. Our nervous system is also a self-similar structure, including the brain. The cortex of the brain has a fractal dimension between 2 and 3.7 The self-similar neuronal networks forming the brain are particularly sensitive to stimuli with a self-similar structure. We saw this with pressure waves. A plucked string vibrates as a self-similar structure—as a whole and also in halves, thirds, fourths, fifths, etc.—and we hear such a series with greater clarity than disorganized waves containing the same amount of energy overall. A self-similar series sounds like a musical tone but disorganized waves sound like noise. When sets of pressure waves start and stop regularly, the brain can also notice self-similarity in their duration. A common example of this involves waves switching on and off at scales of 800 msec, 400 msec, 200 msec, 100  msec, and 50  msec. These we would hear in music as quarter notes, eighth notes, sixteenth notes, etc. Going longer, 1.6 sec would form a half note and 3.2 sec a whole note, which is the basic unit of western music.8

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From birth if not before, the brain becomes attuned by experience to patterns of pressure waves that are self-similar in frequency and duration. The particulars of those patterns determine the sort of music that the brain responds to most readily, the sort of music that any individual will prefer. Some of those neuronal circuits become so deeply etched that energy will activate them even without any pressure waves entering the ear, energy from elsewhere in the brain: these you hear in your mind’s ear. Since one part of the brain can usually influence another, you can usually control those imagined sounds as well, and vary them. If you have heard many such patterns and you can process them flexibly, then you can also generate new patterns—i.e., you can compose music. Once you have formed a sufficiently deep set of neuronal patterns, you no longer need ears to hear your music. If you have also learned to write down the sounds you hear using a symbolic notation, then you might be another Beethoven.

WAVES AND WAVELETS We saw in chapter four that every scene can be described by sine waves of differing frequency, amplitude, orientation and phase—by Fourier transforms. This is a useful mathematical tool for comparing visual information, and the visual system does function to some extent like a Fourier analyser, but the idea of spatial frequencies across a scene is a mathematical abstraction that does not fit the real world closely. Visual information is formed less by sine waves spread over a broad area than by bits of sine waves that are not continuous but appear, fade in and out, and disappear. These are called wavelets. Everything that we see originates as an image cast by the lens of the eye onto the retina, and no lens can image a point of light as a point. Every lens spreads every point into a fuzzy disk. The blurring of a lens is never sinusoidal but it is likely to be closer to sinusoidal than to anything else. In the back of the eye, sensors translate the blurry points and lines that are imaged by the lens into neurochemical indicators of brightness, which feed into the brain. Within the brain at the lowest levels of the cortex, different neurons are sensitive to different rates of change in brightness—i.e., to different breadths of

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blur, or different spatial frequencies. These are the first neurochemical tracks in the visual system. They combine into deeper tracks, to enable the brain to sense and discriminate lines of different width, which is the first thing the brain must do if we are to see. Thus, to a first approximation, when the eye looks at something, it senses optical changes that resemble wavelets, and the brain interprets them as such, sorting them into categories.9 Wavelets link Fourier analysis with fractals. On the one hand, wavelets are little sine waves, so we can combine them mathematically into larger sine waves; on the other hand, they form the building blocks of the visual brain’s self-similar structures. For this reason, just as any scene can be described by a set of sine waves, so any scene can also be described by a set of simple fractals. Indeed, a mathematician named Jürgen Schmidhuber created this face by instructing a computer to reiterate a few simple fractals many times.10 We have seen that the brain evolved to process easily whatever it has encountered before, and to prefer that up to a point. This is fundamental neurochemical bias that derives from the brain’s physical structure, so it ought to vary from one person to another no more than the proportions of limbs or facial features. Within a scene, self-similarity provides intrinsic repetition—repetition at different scales—so the fractal dimension of a scene is a measurement of its self-similarity. Since our preference for repetition is structural, we would expect people to prefer scenes with a similar fractal dimension—and so they do. Beautiful cumulous clouds have a fractal dimension around 1.3, a drip painting by Jackson Pollock is around 1.5, and people prefer landscapes in the range of 1.3 to 1.5.11 Self-similarity is one of the characteristics of attractive designs in the decorative arts. For example, it is implicit in all the design using the golden section, a self-similar structure that has been remarked upon by aesthetic theorists since the ancient Greeks. Take a line

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and divide it so that the smaller part is to the larger as the larger is to the whole: this can also be done with the area of a rectangle. When repeated at different scales it creates a pleasing proportion, as you can see here. An understanding of fractals has begun to seep beyond mathematicians to the general public, inducing some graphic artists to create fractal art. The artist defines instructions that the computer repeats many times. The skill lies in knowing how to define instructions that lead to an effective picture. It is possible to generate attractive things this way but we think their attraction is limited. One of the more impressive images we have seen is the face on the last page, but we think it impressive as a dancing elephant is impressive: not because it dances gracefully but because, against the odds, someone has taught it to move in a way that resembles dancing. A competent illustrator can paint a far more credible face in much less time than Schmidhuber needed to figure out how to have his computer generate a face. As a portrait of a living person, the computer’s picture doesn’t hold a candle to this one by the Toronto artist Alan King. That is because fractals are merely a form of repetition. The brain finds repetition easy to process, so we find it attractive up to a

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point, but beauty appears when repetition ends. Beauty appears when our expectations are exceeded, when something familiar deviates in a direction that experience has biased us to like.12

SIGNAL, NOISE AND CHAOS So far in this chapter we have been discussing objects that the brain perceives as though those objects exist independently of other objects. That is how we think of them, but we need to remember chapter six: we do not perceive anything by itself, we perceive everything juxtaposed to other things that are incidental to the primary perception—that is to say, we perceive every signal juxtaposed to noise. On the other hand, what is noise at one moment may be signal the next. For example, in this Himalayan scene we alternate rapidly between seeing rock against a background of featureless glacier and glaciers against a background of featureless rock. In more general terms we might oversimplify for the sake of discussion and say that the visual system is perceiving one of two possible signals—glacier or rock—against a background of noise.

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A multitude of cells form these two perceptions. Output from the light-sensitive cells of the eye becomes agglomerated into a smaller set of neurochemical pathways that have been etched by experience, pathways that later interconnect and elaborate many times over. Each of these pathways filters out only a small amount of the signal from the enveloping noise but—this is why we process sensory information so quickly—within the brain, 10 or 100 neuronal pathways process stimuli simultaneously. Each of these pathways can filter out only one piece of a signal but working in parallel they can filter an entire signal rapidly, so that you become conscious of rocks only about one-tenth of a second after your brain stops noticing glaciers and starts to look at dark blobs.13 The fundamental question is how and why the brain comes to treat some stimuli as signal and others as noise. To answer this we need to return to the concept of deterministic chaos that we introduced in chapter two. Scientists assume that outside the world of quantum physics, any movement or change appearing to be random or chaotic was likely started by a deterministic event and is unfolding through a set of incalculable but deterministic rules. Frequently we can see this apparent chaos leading from one stable circumstance to another. The sky is clear for days, then clouds roil over randomly and the sky turns grey for days. Skin starts to itch and redden, then becomes covered with a rash that will not go away. A hippopotamus meanders across the veldt, others follow, and a hippo highway forms like this. In each of these situations, something disturbs a pattern or equilibrium, then the system adjusts to the disturbance and a new pattern or equilibrium forms. This is how the brain works too. One

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set of neuronal patterns forms one set of perceptions, then a change in stimulus causes the patterns to shift and another set of perceptions forms. The change in stimulus may seem like chance, and sometimes it involves entropic firing, but usually the current neuronal pattern feeds back into the brain in a way that helps to form the next neuronal pattern. At any given time, the pattern of neuronal firing in the brain forms our perceptions and our attention, so these shifts in pattern form shifts in attention. It is impossible to see this happening within the brain but it is possible to understand it through a comparable mechanism: building roads. In North America, when deer moved around the countryside, they avoided obstacles and formed tracks like narrow versions of the hippo highway on the last page. Indians walking from one village to another followed those tracks, broadening them into footpaths. European settlers riding from one settlement to another followed the Indians’ footpaths and widened them into wagon roads. Toward the end of the 19th century, bicyclists lobbied governments to pave those wagon roads with asphalt. In the early 20th century, motorists lobbied governments to widen and straighten the paved roads, and form them into a network of national motoring routes. The automotive and trucking industries then lobbied governments to convert those routes into rivers of concrete. This happened tropically—animals and people always took the easiest route available— but the result permits efficient transport. If the earth were sensate, those roads would represent some kind of memory or perception. Now let us create many such networks of “roads” on a table. We can do this using, of all things, slime mould. This is an amoeboid organism that spreads out to engulf microscopic particles of food—a minuscule version of the man-eating monstrosity in the classic comic horror film, The Blob. Slime mould generates facilitating and inhibiting chemicals much as nerve cells do, and spreads tropically toward food and away from obstacles and culinary deserts. If you cut a piece of blotting paper into the shape of Canada or the USA or any other country, then put some oat flakes where the cities would be and deposit a little slime mould somewhere, within days the slime mould will create a network of “roads” that might have been designed by a traffic engineer. Each time you do this an efficient network will form because slime mould takes easy paths just like animals and people.14

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If these networks were neuronal pathways, one network would represent some kind of memory or perception, and each new network would represent a different memory or perception. Each of these networks is similar to the next in some way—you begin with oat flakes in similar places, so that nodes always develop in similar places—but each network differs. If you watch a network of slime mould developing, you see the equivalent of a neuronal network developing. If you do this without changing the blotting paper but by merely cleaning it imperfectly, then you see that the shape of one old and faded network will influence the shape of the next. This shows how what we perceived in the past affects both what we perceive now and what we shall perceive. This shows how the brain’s experience helps to shape all information—how experience defines the difference between signal and noise and defines everything that we perceive.

EXPERIENCE AND CONTEXT You have never seen images quite like those below, yet still you probably see them as faces. They lack noses, nothing in them is to scale, and the tones are bizarre, yet still they resemble faces. That is because you have grown up with cartoon characters and these cartoon faces share some characteristics with other cartoon faces, like large oval eyes and asymmetrical squiggles for eyebrows and

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mouth. On the other hand, these faces have no nose, the tonalities are bizarre even by the standards of cartoons, and circular human heads look monstrous. Thus, not only are these faces far from the average cartoon face, experience with both real faces and with cartoon faces will bias anyone against them. They would never win a beauty contest, not even in Mad Magazine. This is how experience forms aesthetic judgments, but our experience is also affected by structures of our body. In these cartoons, for example, the eyes in both faces are drawn with the same shade of ink, yet neurons inside our eyeball tint the eyes darker in the righthand cartoon. Visual information does not come from absolute levels of brightness—if you carry this book outside, the text will read the same—so the eye evolved a neuronal structure that ignores brightness and responds only to contrast. Because of this neuronal structure, within our field of view, the lightest portion looks white and everything else appears darker. When you stare at the features inside the cartoon on the left, the dark background forms the equivalent of a dark field of view, so the features look white.15 Museum curators ignore this illusion at their cost—or rather, at the cost of the museum’s visitors and works of art. Consider one function of paintings. Two millennia ago or today, in Paris or Palmyra, in palace or presbytery, people purchasing a picture to hang on a wall have intended it to decorate the wall. They surely want a nice picture but they want a decoration too. Nowadays some painters expect to sell their works to museums but with those exceptions, canvases, panels and frescoes are and always have been intended for decoration, to one extent or another. Paintings are not only a conspicuous form of decoration, they are also a form of conspicuous consumption. This is true now and it used to be even more true, because painting requires pigments and pigments used to be expensive. Before Europe industrialized, pigments were so costly that an artist’s contract for a painting often specified which of them were to be used. More saturated colours displayed more money and plain white was seldom fashionable. Moreover, most white walls would have been dully whitewashed, not brightly painted. In an encyclopedic book on the subject, Architectural Colour in British Interiors 1615-1840, only one of 212 illustrations shows white walls.16

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White walls in museums are part of an academic vogue to ignore history while looking at “texts”—written texts and also other kinds of “text” including works of art. Since we can see and talk only in the present, history is useless. This is a theoretical approach called deconstruction. We confess to not understanding it at all. Before the Second World War, painters coloured nearly all paintings expecting them to hang on walls that would not be bright white and would likely be rather dark. By hanging these paintings on a “neutral” white wall, colours look duller and tinted whites like the cartoon eyes on the last page look not white but dirty. To our eyes, by ignoring this history of interior decoration, museum curators deconstruct nothing but the colours and effect of the paintings they display.17 As children we never thought of vogue and fashion in antiquity. We assumed that the antique paintings in art museums limned antique worlds that never changed except for the century when men wore wigs. However, as we have become antique ourselves, we have seen how fashions continually evolve, and we have come to realize that fashions always have evolved—fashions not just of dress but of all forms of human behaviour. The academic study of this is called social history, and it can be enlightening. Social history offers vicarious experience that can radically alter our reaction to a work of art. We would like to end this chapter by demonstrating this point. On the next page is an engraving of a theatrical audience that we happen to have on our walls. William Hogarth printed it in 1733. Below the audience we see three musicians from the orchestra. Based on our experience of theatres today, it looks droll and seems delightful. But now let’s imagine London at that time. London was reputed internationally to be the bawdiest city in Europe. Streetwalkers were ubiquitous and they were forward enough to grab a man’s arm as he walked down the street. Streetwalkers did not merely walk the streets, they often worked in the streets. (Beds cost money, most men were poor, alleys were free and dark.) In addition, tens of thousands of higher-class men visited many thousands of higher-class prostitutes, and aristocrats kept courtesans. Inside theatres women sold oranges—equivalent to ice-cream today—and normally turned tricks on the side. The chief orange-seller would serve as the madam.

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Syphilis afflicted tens of percent of the population. Probably a higher proportion of theatre-goers had syphilis than stay-at-homes, because theatres attracted roués who were out for a night on the town. Signs of syphylis included a deformed nose, rashes on the face, and rotting teeth.18 This droll caricature shows three orange-sellers enticing customers and a number of men displaying the disease.

10 TIME AND MOTION ARCHITECTURE, MUSIC AND DANCE

To construct a simple building needs little knowledge or planning. We know an African fellow who is building himself a house. He laid out a floor plan with concrete blocks and occasionally piles a few blocks on top, leaving holes for windows here and there. He has been doing this for years, whenever he can scrape up enough cash to buy a block or two. However, most houses require more planning, and the grandiose buildings of popes and potentates can hardly be built on the fly. Before modern times, the people who designed large buildings were not architects, they were the equivalent of the building contractors who design most houses today. A building contractor will consider

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the aesthetic preferences of his customers, and he may work with sketches or drawings that a customer supplies, but the contractor must make sure that the building will not fall down. Few builders understand the physics of buildings—few builders can calculate stresses and strains with any computer more sophisticated than the seat of the pants—so few builders will follow any part of a customer’s design that leads beyond conventional practices. Nowadays a structural engineer can calculate stresses, strains, and strengths, and an engineer’s approval is required for every large building, but this is new. It used to be that nobody understood why some buildings fell down and others did not. To ensure that a cathedral would not collapse, medieval monks were left with prayer: “And, deare Lord, support our roof this night, that it may in no wyse fall upon us and styfle us, Amen.”1 A medieval builder might have prayed too, but he did not trust solely to God, he also trusted to his experience. He knew what worked, and he would have been loath to do anything much different. For this reason it has taken millennia for the appearance of buildings to evolve.

SYMMETRY In Europe, first people built frameworks of timber and filled the spaces with whatever was handy, then folks living near the Mediterranean learned to farm and fish efficiently enough that they had time to cut and build with a soft local stone that they called marmaros and we call marble. Stone walls require less maintenance than wood and do not rot, so they are more durable, but openings in stone walls are problematic. That is because every opening requires a lintel across the top to support the wall and roof—you can see Greek examples atop the next page—and surprising as it may seem, a beam cut from stone is weaker than a beam cut from timber. History does not record how many walls collapsed before builders learned how long marble lintels can be, but it took a millennium before builders experimented enough to discover that an arch can support a vastly greater weight.

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Because of this conservatism, and to achieve economies of scale, and to create tidy-looking symmetries, builders tried not to vary structural patterns from one part of a building to the next but to repeat as much as they could. Repetition, symmetry and the arch characterized Roman architecture. Builders built structures like the picture below for more than a millennium before they experimented with arches that were not round. Who would risk having the tower fall down just for decorative detail? In the 12th century, Europe’s economies boomed. The princes of the Church had money to burn, money to spend on new buildings everywhere. Size impresses, so they liked to build big. Builders experimented with higher arches and finally discovered that it is safe to bring an arch to a point. Pointy arches became a new fashion, a fashion that we have come to call Gothic.

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Pointy arches enabled soaring roofs but most builders did not want to raise the roof enough to risk collapse, so they soared gently and continued basic practices like repeating as many structural patterns as they could. Symmetry continued to seem sensible. At the same time, a few princes of the Church were willing to take risks to make an impression, and a few builders will risk anything for money, so a few churches soared to the sky. These are the Gothic wonders we see today, although often they have newer towers because the original ones fell down.2

The Collapse of Old St. Chad’s Church, 1788.3

Gothic churches appeared everywhere but the clergy and nobility who governed Europe were conservative men. To many of them architecture seemed to be becoming dangerously licentious. They were ripe for a stylistic backlash. In the 16th century a Venetian named Andrea Palladio led a back-to-basics movement that made him an architectural celebrity. Palladio studied the design of ancient buildings then elaborated a version of Greco-Roman architecture that formed and remained the root of all styles of European architecture until well into the 19th century. The next page shows cathedrals before and after Palladio. As an architectural reactionary, Palladio promulgated the ideal of symmetry at least as strongly as his predecessors.4

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St. Paul’s Cathedral in London. Above is a Gothic building that burned down in 1666 (showing the spire that had collapsed a century before). Below is the Palladian replacement designed by Christopher Wren.5

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Builders like symmetry. It is easier to duplicate sub-structures than to create new ones, and in architectural drawings, symmetry delights the eye and impresses clients. For these reasons, Palladio and his spiritual successors built countless great buildings in a symmetrical and more or less Greco-Roman style well into the 20th century. Nevertheless, even by the beginning of the 20th century, it looks to us as though most of those buildings either were razed or were modified to be asymmetrical. If you search the web for images of old chateaux, you will see some that retain their symmetry but not many. Someone always has a reason for razing a great building or for modifying the work of a master. The rooms are too dark, the hall is too small, the facade is unfashionable. However, the fact remains that, throughout centuries of celebrating symmetry as an architectural ideal, innumerable owners of symmetrical buildings have found reason to rebuild them asymmetrically. For this we can see only two possible reasons. Either people are perverse or the idea of symmetry wears better than the reality. The latter seems more likely, especially if we consider architecture in relation to time. We see buildings by walking around and through them—by seeing them across time. A facade may have symmetrical wings with symmetrical windows but when we walk to a door at the end of a wing, we do not see symmetry, we see a number of similar windows, each one looming up and then receding. If we look closely at each window, we may see differences in decoration—variations in the statuary or carving—but the primary effect overall is not symmetry, it is repetition. The symmetry may be pleasing when we stand along the building’s axis of symmetry but this is something that only tourists do, and even tourists won’t stand in the perfect spot for long. Repetition pleases up to a point but if you live or work in a symmetrical building, you will tend to adapt to the repetition and to notice instead the important asymmetries, like the doormat defining the entrance to your rooms. You will also notice that the windows forming part of the classical facade do not make your rooms easy to furnish. The architect’s theoretical ideal loses importance and quotidian practicalities become more salient. Eventually you get fed up and decide to remodel the building. It seems a shame but after

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all, you say to yourself, this building is intended to serve living people, not the memory of a dead architect. In short, symmetrical buildings seem ideal in theory but the practicalities of time make them wear badly.

TIME We look at an architectural drawing one spot at a time and see the whole thing because the brain integrates all of those spots over time. We also see a building one spot at a time, but we see and integrate those spots over a much longer span of time as we walk or drive about. The great difference in these time-spans means architectural drawings bear little relationship to our experience of the actual building even when the drawing does not, like this picture of Luxembourg Palace, show a view that could be enjoyed only by a bird.6

Time is key with other perceptions as well. Remember that the brain senses nothing directly save the chemicals bathing it. The

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brain has no direct contact with the world, the brain merely reacts to neurochemical signals generated by sensory neurons. These sensory neurons are stimulated by changes in energy—by changes in pressure, changes in light, changes in chemistry, etc. The sensory organs and the brain can respond only to changes, and every change is a change across time, so time is fundamental to our perceptions. No perception can be formed independently from time. We are physically incapable of perceiving anything that does not change over time at least a little.7 We have talked repeatedly about one basic series in time, the harmonic series of pressure waves. The archetypical generator of these is a string vibrating along all of its length, one-half of its length, one-third of its length, etc. The string’s vibrations induce changes in air pressure that vary in time. These vibrations induce corresponding sets of neuronal patterns within the brain. The neuronal patterns are chemical and build up in space, yet they evolve through time as well as space. These changes in time we perceive as sounds. Both singing and speaking are formed by the same set of bodily strings: the vocal folds. Both of them involve similar changes over similar times, which makes them fundamentally the same. Indeed, they are virtual twins. Lyrics can be as cogent as any speech, chants are a combination of song and speech, and speech can be as nonsensical as skat singing: “Ooo-bop-sha-bam-klook-a-mop.” The primary differences are that singing spends more time on vowels and spreads the voice over a broader range of pitch.8 The seeds of song and speech are planted in the seventh month of gestation, when the fetus develops sufficient neural circuitry to hear. By birth, neuronal firing has ploughed enough auditory pathways into the brain that a baby hears pitch and timbre, hears some aspects of rhythm and harmony, recognizes the rhythmic and melodic patterns of his mother’s speech, and recognizes some rhythmic and harmonic patterns used in music. After half a year a baby comes to distinguish happy music from sad music, will match happy music to happy faces, and will match happy and angry voices to the appropriate facial expression. Toward the end of the first year the modest range of wavelets forming phonemes become adopted for symbolic communication—i.e., speech.9

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RHYTHM AND PITCH Toward the beginning of the 11th century, European musicians began to work out notations to map onto paper the fractal structures that we hear purely as music. These notations show time horizontally and pitch vertically. As you can see in this bit of Bach, in their modern form even someone untrained in music can perceive some

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structure. A trained musician can see and hear structures within structures within structures.10 It is possible to put a score like this into a computer, then have the computer synthesize the music. A computer can easily create the theoretically perfect harmonic series for every note of every instrument. However, this kind of computer synthesis sounds unrealistic, because it is formed from the constant harmonic contents of long notes. We perceive changes in energy, not consistency. The start of a bellow is what distinguishes an elephant from a hippopotamus or from a tuba. The sudden change of energy starting a note—the note’s attack—contains most of the information that we use to distinguish one instrument from another. 11 Consonants are the attacks of speech and vowels are continuous tones. Try saying “Go to bed’ without the consonants. Say it aloud with just the vowels. No matter how long you let the vowels sound, they carry no meaning. On the other hand, if you say the consonants, you can short-change or modify the vowels yet still recognize the words. Discrete syllables pass into the ear at rates comparable to discrete musical notes. In both cases the brain attends to a quick change then adapts quickly to any continuous energy following the change. A b is quick, so the brain notices it, then the brain adapts to the longer e that follows. Although musical attacks are short, they are very complex wavelets. They are so complex and so important that the usual way to produce a note of music on a computer is not to try to synthesize it mathematically from sine waves but to record a real instrument and use small samples of the recording. To sound natural, synthesized music can require many samples. As we are writing this, a product sold for that purpose by the Vienna Philharmonic consists of 2,718,744 samples of sound.12 As soon as an instrument settles down into a steady resonance, it forms an harmonic series sufficiently simple and stable that it makes sense to think of it as a combination of waves—but then it becomes sufficiently simple and stable that the auditory system begins to ignore it. To keep a note alive in the ear—to avoid adaptation— musicians commonly make sounds vibrate or tremble with vibrato

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or tremolo. Today vibrato refers to oscillating pitch and tremolo to oscillating loudness, but “vibrate” and “tremble” are basically synonyms, so over the centuries their meanings have inverted. In practice, altering either pitch or loudness alters the other, and alters timbre as well.13 Music is formed by combining individual tones into longer fractal structures: meter and rhythm. Meter denotes regular beats; rhythm refers to sounds that are based on an underlying meter but are variously longer and shorter than the beat. Metrical music is boring to hear because time and again a beat wallops your ear much like second-rate verse from a poet perverse. Rhythm is more variable and hence more interesting. For example, consider this sentence by Robert Louis Stevenson from Travels with a Donkey: From time to time a warm wind rustled down the valley and set all the chestnuts dangling their bundles of foliage and fruit; the ear was filled with whispering music, and the shadows danced in tune.

Stevenson’s prose shows no obvious meter yet has rhythm enough to show onomatopoeic effects. To bring these out, beat time slowly with your toe and fill a beat with each of these lines, stretching and compressing the words as necessary. From time to time a w a r m w i n d rustled down the valley and set a l l the c h e s t n u t s dangling their bundles of foliage and fruit;————— the ear was filled with whispering music, and the s h a d o w s danced in tune.—————

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It is possible to speak all of those lines to the beat of your toe but you might naturally lengthen “w h i s pering” and then catch up to the meter by speeding up the next line. Also, you might feel like slowing down toward the end. In music, robbing time from the meter like this is called by the Italian word for robbed, rubato.14 Rubato and other forms of rhythmic flexibility form much of the difference between an ordinary performance and an extraordinary one. An ordinary performance presents all notes normally; an extraordinary performance varies some notes slightly in unexpected but pleasing ways. A fine musician varies the duration, tone, loudness, and pitch of individual notes. Most people think of notes as fixed pitches, pitches defined by the musical scale. However, as we showed in chapter three, scales are invented by musical theorists but the brain does not hear musical theories. The brain has evolved to hear frequencies in the ratios of 1:2 and 2:3 as perfectly consonant—octaves and perfect fifths—and to hear other ratios on a continuum from slightly less consonant to very dissonant. Since we like consonance, the more dissonant a sound becomes, the more we wish it would become consonant. Moving toward dissonance creates a perceptual tension and moving back toward consonance releases that tension. Melodies are rhythmic changes in tension of this sort. People in different cultures are accustomed to different degrees of movement but this is not a fundamental difference, it is merely a difference in aural cuisine.15 Notes on any scale represent customary stepping stones between octaves and perfect fifths. Within any one theoretical system of music notes are precise and constant, but nobody walking in a garden treads solely on stepping stones, and during a performance musicians continually walk on the grass. To both a musician and the audience, every note is defined by its context. We sense contrasts in energy, not absolute amounts of energy, so we hear a note by contrasting it to other notes that we are hearing at the same time or to the notes we heard immediately before. The average change from one note to the next will approximate a musical system’s theoretical ideals but individual notes will be all over the map. When a jazz soprano holds a note that is too low to sound perfectly consonant, then wobbles a little up and down, and finally raises her

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pitch to where we want it to be, she may sound gorgeous but she is breaking the rules of western musical theory. She is not moving by the whole- and half-tones of western scales, she is employing microtonal techniques like those of traditional musicians throughout Asia and the Middle East. Western musical theory does not define or formally admit microtones yet she is using them—and as far as we can tell, theory notwithstanding, western music always has. Nowadays western audiences accept as an artistic convention that a quavering of the voice represents great emotion in music, so our musicians routinely make long notes wobble, especially consonant notes. Although we call this vibrato, we might instead call it microtonal trills.

DANCE At the same time that a baby learns to hear structures in time, he also learns to move in synchrony with them. When a baby is born, he has already learned enough basic rhythms of his mother’s language that if he moves while someone is talking, he will synchronize his movements with phonemes. He will move at the start of a b or an m or an s instead of during it. Sights are just a bright confusion but sounds have some regularities that he recognizes, regularities that feel more comfortable than the rest of his chaotic experience.16 A baby is born with clogged ear canals but after the canals clear, the sounds he hears clarify, and he soon comes to recognize specific shapes that often accompany the clearest and most regular sounds. These are his parents speaking to him in a high-pitched, sing-song voice, and accentuating the rhythms of their speech with exaggerated movements of the eyes, mouth and head. Insofar as those sights have become familiar, they are welcome. Sometimes the sounds that he knows are even clearer than usual—more rhythmical because his mother is singing to him rather than speaking—and sometimes while this happens, he sees and feels his arms move and he sees other movements simultaneously, perhaps because his mother is playing pat-a-cake. The rhythms reinforce one another and feel nicely clear. His brain begins to develop a set of neurons that respond both to other people’s movements and to his own, as though they

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were the same. “Mirror neurons” these are called. They are the physical instantiation of a form of synaesthesia, synaesthesia intermixing the senses of sight and proprioception (the position of the limbs). Combining senses dramatically clarifies the world, as we saw in chapter six.17 Shortly afterwards a baby comes to realize that he is looking at another person and that he is seeing and feeling both his arms and another’s arms. However, the clear rhythms and the synchrony that he senses still feel good, so he continues to enjoy pat-a-cake and he comes to enjoy synchrony in a social setting, synchrony with other people. Decades later his sense of social synchrony will see him play pat-a-cake with his own babies and enjoy moving together with other adults by dancing and playing team sports. Social synchrony is pleasant enough to compensate for considerable discomfort. This is the reason people pay money to go to someplace where they can jump up and down with other people, when they could exercise as effectively and more cheaply at home on their own. In a group you see other legs moving while you feel your own legs moving. The former reinforces the latter synaesthetically so that you perceive your legs’ movement more strongly against the background noise of muscles aching from fatigue. The pleasures of social synchrony can overcome even onerous circumstances, to bond individuals into groups. That is why soldiers are forced to drill on a parade ground and march in step, sometimes singing. This is not because generals expect them to march onto a battlefield then stand at attention and present arms, it is because synchronous exercises bond men and women into a cohesive social unit. Scott Wiltermuth showed how effective these techniques are by walking groups of undergraduates around Stanford University either in step or out of step, and by having groups of undergraduates sing and beat time to recordings that either were synchronized with one another or were off-beat. Afterwards the students played a kind of game structured as a “prisoner’s dilemma,” a game that pays individuals to behave selfishly but pays the entire group more if everybody cooperates instead. (The original prototype: two crooks talk separately to police. If each blames the other, both serve two years; if Alan blames Bob and Bob remains silent, then Alan is freed and Bob serves three years. If both remain silent, both serve one

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year.) The students who had walked in step or had sung and beat time together behaved more cooperatively in the game.18 Social bonding is the raison d’être for tribal dancing all over the world, and for ballroom dancing in Europe. Social synchrony bonds dancers even when the “dancers” are babies. Fourteen-month-olds “danced” by being bounced up and down in a woman’s arms. While a baby “danced,” he could see a second woman bouncing at the same rate, either in time with him or out of sync. Afterward the second woman played with him and asked him to give her a hand by picking up a block or some other toy that she had “accidentally” dropped. When this woman had earlier bounced in time with the baby, the baby was more likely to help.19 Western societies have come to draw a clear distinction between music and dance. Music has come to mean motionless sound and dance to mean movement to music. However, this distinction is largely artificial and is neither universal among the world’s cultures nor applied consistently even within our own. Within the brain, rhythmical sounds and movements are inextricable. It is impossible for a human being to produce rhythmical sounds without moving muscles rhythmically, and it is difficult to listen to rhythmical sounds without twitching at least some muscles in synchrony with the rhythm. From a baby’s first experience playing pat-a-cake, rhythmical motions accompany rhythmical sounds, and the brain perceives this juxtaposition so often that rhythmical stimulation comes to entrain processing within the brain’s auditory pathways, visual pathways, and proprioceptive pathways (the pathways that sense the position and movement of muscles). It is not an accident that jazz singers and classical violinists bob and weave, and moving while playing helps musicians to play together. One technique all chamber musicians must learn is how to move in ways that cue entrances and tempi to other players. An orchestral musician may learn to minimize his movements, because he has been told that they look distracting to an audience, but only wind players can play their instruments without broad movements and even they cannot avoid tensing muscles rhythmically, they can only shape their muscular activity to make it less obvious. Moreover, less obvious to an audience also means less obvious to other players. When musicians cannot easily

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see one another move, playing together becomes more difficult, so musicians tend to play more metronomically and mechanically. Before the phonograph, most people could hear music only when they or their friends made it themselves, so many if not most people learned to play an instrument or sing—and not just among the politer classes. In 1834-36, when the young Richard Henry Dana spent his two years before the mast, the salts in the forecastle were hardly a company of aesthetes yet they sang more than choristers in church: At night, some of us got a boat and went on board, and found a large, roomy forecastle,… and a crew of a dozen or fifteen men and boys, sitting around on their chests, smoking and talking, and ready to give a welcome to any of our ship’s company.… Among her crew were two English man-of-war’s-men, so that, of course, we soon had music. They sang in the true sailor’s style, and the rest of the crew, which was a remarkably musical one, joined in the choruses. They had many of the latest sailor songs, which had not yet got about among our merchantmen, and which they were very choice of. They began soon after we came on board, and kept it up until after two bells, when the second mate came forward and… [sent us] away! Battle-songs, drinking-songs, boat-songs, lovesongs, and everything else, they seemed to have a complete assortment of, and I was glad to find that “All in the Downs,” “Poor Tom Bowline,” “The Bay of Biscay,” “List, ye Landsmen!” and all those classical songs of the sea, still held their places. In addition to these, they had picked up at the theatres and other places a few songs of a little more genteel cast, which they were very proud of; and I shall never forget hearing an old salt, who had broken his voice by hard drinking on shore, and bellowing from the mast-head in a hundred northwesters, with all manner of ungovernable trills and quavers in the high notes, breaking into a rough falsetto—and in the low ones, growling along like the dying away of the boatswain's “all hands ahoy!" down the hatch-way, singing, “Oh, no, we never mention him.”20

Sailors danced as well, because both music and dancing were as central to society as movies and television are today. Indeed, during the U.S. Civil War, the Northern Navy supplied every warship with musical instruments, and men at sea might amuse themselves by dancing quadrilles. Mind you, a quadrille danced by naval ratings was likely to be not the gentle dance popular in polite society but, in the words of a contemporary book on dancing, “the quadrille of

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former times…adopted as a medium for the display of agility, and the indulgence of violent exercise.”21 To set up a dance was easy. All you needed to do was move some furniture and take out a fiddle, as you can see in this American painting from 1883.22

Dancing might be more vigorous or less, depending upon the social class and age of the dancers, and the weight and drape of their clothing. Formal balls served a number of functions, including maintenance of the social pecking order through richness of costume and through the processes of an elegant, stately dance that might be executed in order of rank by one couple at a time: the minuet. In Europe, aristocratic adolescents took dancing lessons for years to learn how to carry themselves elegantly and naturally while executing complex evolutions. Occasionally, some courtiers who were especially good dancers might display their skills in a little ball—a ballette—at one end of a large room in a palace. This was the origin of ballet. Since anyone could sing and dance but instruments were costly, more people sang and danced than played. Instrumental musicians and composers were employed primarily to support singing and dancing, but sometimes they played by themselves to provide a diverting

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background for conversation. These divertimenti gradually became elaborated and formed into symphonic and other musical structures that demanded greater attention, but all of the forms musicians knew were songs and dances, so songs and dances formed the core and substance of every piece they composed or played, no matter how grand and complicated the piece became. The songs and dances might be too dramatic or complex actually to sing or to dance, yet they were still fundamentally songs and dances. A composer might incorporate sound effects into a dance, like the cuckoos in Beethoven’s Pastorale Symphony, or build a dramatic cacophony, or—usually for a church—a polyphonic evocation of heaven, but the vast bulk of western music, like all other music, is song and dance at the core.

MODERNITY Styles in dance and music have continually evolved over time just like styles in art and clothing, but industrialization brought unprecedented change at unprecedented speeds. Before industrialization, most sights and sounds were formed by natural movements through time, by rhythmical but imperfectly metrical movements. Since industrialization, sights and sounds have become regularized, so regularized that most popular music is based on the metronomy of electronic drums. This presents some interesting problems for contemporary musicians and audiences. Virtually the only surviving dances (so to speak) that antedate the waltz are marches and church processionals. People may have seen snippets of a minuet in costume dramas on film but rare is the person who has any conception of the badinerie, the bourrée, the courante, the gigue, the gavotte, the forlane, the pavane, the passepied, the polonaise, the réjouissance, the rondeau, or the sarabande. However, those dances are ubiquitous in music— J.S. Bach uses them all in his orchestral suites, for example—and other dances are common as well. Sometimes they are mentioned by name but popular dances did not need to be and often they were not. Just as we would recognize a waltz embedded in a movie’s sound track, so would anyone between 1650 and 1850 have recognized a minuet embedded in an opera. Composers assumed this, and used

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this kind of recognition to develop the characters and reinforce the drama of their operas. For example, in Mozart’s Don Giovanni, when a lascivious aristocrat sings to the rhythm of a country dance and a servant girl sings to the rhythm of a minuet, an 18th-century audience would have perceived obvious incongruities and a moral inversion.23 Not only do modern audiences hear no social significance in dance tunes, we are likely to hear dance tunes played quite unlike the way they were intended to be played, because musicians understand as little of old dances as audiences do. Take minuets, for example. A minuet was written with three beats to the bar and the only dance written in three that today’s musicians know is the waltz, so musicians commonly play a minuet as a waltz. However, the two dances bear no resemblance. A minuet was a formal, stately evolution of men and women moving in parallel; a waltz has men and women embracing each other and circling rapidly and repeatedly across the floor. Although minuets are notated on paper with three beats per measure, the minuet was actually played in six. This shows how the beats of a minuet and waltz compare.24 Minuet:

1

Waltz:

123123123123123123

2 3 4

5 6

1

2 3 4

5 6

Printed music allows different interpretations just as printed English does. For example, Shakespeare supplied this text: To be, or not to be? That is the question—

Shakespeare does not indicate whether or how those words are to be accented, and we do not know how he would have spoken the line, but to a native anglophone today it should obviously be spoken like this, with only modest changes of pitch: To be, or not to be? That is the question—

In contrast, a francophone might stress all the words equally but change the pitch of his voice more and lengthen some phonemes: To be or not to beee? That is the questionnnnne—

For the generation who saw the overlap of minuet and waltz, the two dances and their music were as different as chalk and cheese.

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Although a minuet played as a waltz is anachronistic, it can still fulfill a modern audience’s expectations and thus can be enjoyed, but other dances are often another story. For example, consider the pavane: A cavalier may dance the pavan wearing his cloak and sword, and others…dressed in…long gowns, walking with decorum and measured gravity. And the damsels with demure mien, their eyes lowered save to cast an occasional glance of virginal modesty at the onlookers. On solemn feast days the pavan is employed by kings, princes and great noblemen to display themselves in their fine mantles and ceremonial robes. They are accompanied by queens, princesses and great ladies, the long trains of their dresses loosened and sweeping behind them, sometimes borne by damsels. And it is the said pavans, played by hautboys and sackbuts, that announce the grand ball and are arranged to last until the dancers have circled the hall two or three times, unless they prefer to dance it by advancing and retreating. Pavans are also used in masquerades to herald the entrance of the gods and goddesses in their triumphal chariots or emperors and kings in full majesty.25

Today neither audiences nor musicians have any experience of slow dances like this, which leads to some of the dullest moments in music: long, dolorous notes and chords that open many classical pieces. But imagine yourself at an 18th-century concert. You might be in a small theatre within a palace, but you are more likely to be in a room like the one on the next page. In any case the important people are not the hired help who play the music, they are the aristocrats and beau monde who form the audience—people like yourself. Of course you have come to be entertained but you particularly want to chat with your friends about Lady Alphazed’s latest affair, and you would not think of stopping your gossip just because a few men start working. To attract your attention, the musicians noodle a little before they start to play. If only a few musicians were playing, they might tune and improvise a bit much as you might hear in a jazz club today, but an orchestra doing this would create cacophony, so the composer has written down some organized noodling—a prelude of long notes and chords to be played before the symphony proper begins. The court musicians earn their living as dance musicians—most of them only moonlight at the court—and slow dances start all evenings of dance, so they naturally play this prelude with a gentle dancing lilt. While they do this, the concertmaster catches people’s ears by improvising some decorous embellishment.26

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Today, the ultimate musical anachronism may be the medieval music of the Japanese court, gagaku. Gagaku (“refined, elegant music”) must be the slowest music on earth. Listening to it is the aural equivalent of watching paint dry. If you have the patience to sit through a piece, and have drunk enough coffee to stay awake, then you will discern patterns vaguely resembling music but they are so prolonged that by contrast a funeral dirge sounds like a jig. However, when we played some gagaku through our computer and doubled its speed, then doubled it a second time, and a third and a fourth and a fifth, it came to sound like ordinary song and dance. Oriental song and dance to be sure, but song and dance. We suspect that, to increase the dignity of their performances, over the years the court’s musicians played their pieces more and more slowly, and the slowing compounded like interest over 1400 years to increase the time of a performance thirtyfold.27 We cannot sense directly changes that have been evolving through centuries but we can look at end points and consider their implications. For example, the photographs on the next page show a German cathedral from the 18th century on the top and, on the bottom, what to contemporary designers and architects amounts to a cathedral of the practical arts. The left side of each picture hints of

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Dresden Cathedral

The Bauhaus in Dessau, designed by Walter Gropius

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neighbouring buildings: complex facades in the one, sere slabs in the other. If you could walk into the picture and around the buildings, the first would show your eyes structural repetition with extreme variation, and the second would change little from one place to another. Anyone used to the first will soon be bored by the second; anyone used to the second will likely find the first excessive.28 When Mozart lived, nothing like the Bauhaus existed. The cities he knew would have looked like this postcard of Munich. The photograph is from the 1890s but the buildings date from long before Mozart was born.29

In 1789, when he was 33 years old, Mozart travelled to Dresden and played the palace. The cathedral atop the last page was the palace church, so he would have seen it. It had opened only five years before his birth and was a rich exemplar of the contemporary style, a mixture of classical symmetry with ebullient variety. Notice that each of the sculptures is different. The interior is comparable, a symmetrical space with an asymmetrical pulpit that stands out wildly. You can see the pulpit on the next page.30

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The pulpit of the 18th-century Dresden Cathedral.

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This is the architecture that was à la mode while Mozart was alive: repetitive structures forming a background, continually varying decorative details to keep the background alive, asymmetrical structures to catch the eye, and ebullient decoration. When Mozart walked around buildings like these, those were the kinds of structure that he saw unfolding through time. Mozart also enjoyed dancing, especially the minuet—his wife said that he preferred dance to music—and the evolutions of the minuet unfolded through time in a comparable way. Those are the kinds of structure that his brain was used to. Those kinds of structure would have spilled from the visual portions of his brain into the auditory portions, and helped to form his taste in music.31 Nowadays most people who live and write about music studied and work in buildings resembling the Bauhaus (page 218). In performances of Mozart and his contemporaries they tend to hear exuberance and rhythmical irregularities as inappropriate. Indeed, they quote writers of his time, who proclaimed a new aesthetic of simplicity. For example this is from a French book on interior decoration published in 1812.32 The nature…of every piece of furniture is…the function, the practicality for its use. Among the several characteristics of a chair, for example, some are dictated by the form of our body, by considerations of necessity or practicality.… Those are the nature of the thing. What remains for art? To refine the forms dictated by convenience, to combine them with the simplest contours, and to carry out these essentials without ever disguising its character.

But simplicity two centuries ago was not the same as simplicity today. The next page shows the authors’ example of a functionally simple chair. When we look at the photo of the Bauhaus and think of all the utilitarian structures like it that have been built since the war, we think that we understand one reason why many of today’s sophisticates hear nothing wrong with Mozart’s slow, introductory dances played as a series of lifeless chords, and why people have come to accept and enjoy the mechanical regularity and percussiveness of much popular music today.33 Just as musicians often intermix historical styles, so do architects— and artists, sculptors, chefs, and writers. Critics used to call this

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A simple chair in 1812.

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ANACHRONISM AND SHAKESPEARE Perhaps nowhere are anachronisms so problematic as in Shakespeare. Much of his language is quite lost to a modern audience. For example, consider these famous lines from As You Like It, which are recited by a melancholy man:34 [The fool] drew a dial from his poke, And, looking on it with lack-lustre eye, Says very wisely, ‘It is ten o’clock;   Thus may we see,’ quoth he, ‘how the world wags: ’Tis but an hour ago since it was nine, And after one hour more ‘twill be eleven; And so, from hour to hour we ripe and ripe, And then from hour to hour we rot and rot,   And thereby hangs a tale.’ When I did hear The motley fool thus moral on the time, My lungs began to crow like chanticleer, That fools should be so deep-contemplative, And I did laugh sans intermission   An hour by his dial. Why would a melancholy man laugh at this? Because it’s a ribald joke. In Elizabethan English, hour and whore were both pronounced ore, and syphilis, which was rampant, people often described as bodily rot.35

anachronism, although the notion of anachronism seems itself becoming anachronistic, because we live in a time when little history is taught or learned, and when artists are judged not on how well they create works within accepted norms—i.e., within an accepted style—but on how imaginatively they violate norms. There is nothing intrinsically wrong with anachronisms, with playing a minuet as a waltz. Most people can enjoy it that way and western art incorporates a long tradition of nonsensical anachronistic pleasures. For example, for most of a millennium Europeans have commissioned “realistic” sculpture in white marble to ape ancient Greek and Roman statuary. However realism demands colour and when they were new, Greek and Roman sculptures were coloured like the Gothic sculpture on the next page. Ancient statuary is white only because, over two millennia, its paint peeled off and faded.36

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Classical sculpture was normally painted like this life-sized medieval wood carving.

11 TWISTING REALITY THE ILLUSION OF NATURALISM IN ART

In 1897 the British sacked Benin (now in Nigeria) and brought home bronze sculptures of Africans’ heads, some to keep as souvenirs of war and others to sell as scrap metal. But they found these sculptures puzzling. Unlike other African sculptures, these were neither stylized nor primitive. These heads were naturalistic, and some of them were crafted as finely as European heads sculpted in the Renaissance. An example is on the next page. The original is life-size. How did these sculptures come to be made? asked Europeans. Sculpture may be the most sophisticated form of visual art, so primitive Africans could not possibly have been the source. The

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sculptures must have originated in antiquity. Perhaps they were Carthaginian or Egyptian. Or remember that some Portuguese visited Benin in 1485: perhaps they brought some sculptors with them, sculptors who made some of the heads—the best, of course— and taught Africans how to make more.1 As an example of demeaning prejudice this is breathtaking— and it is also ironic, because sculpture is not the most sophisticated visual art. Technologically, sculpting is more rudimentary than painting. Appropriate and durable materials for sculpting you can just pick up off the ground: some wet clay, a rock, a chunk of wood. In contrast, painting requires a flat surface. Some natural surfaces are flat enough to paint—parched earth, cliffs, cave walls, cloven boulders— but none of these is practical. Earth moves, cliffs are high, caves are dark, and boulders are hard to pick up and carry home. A surface that is practical for pictures must be manufactured, and before the industrial revolution, manufacturing a flat surface took a lot of work. In ancient Egypt you might fell a tree with an axe, saw the trunk into planks, then scrape the surfaces smooth. Or you might dig up some gypsum, pulverize it, mix it with water, and plaster a wall with the mixture. Although plastering was easier than forming a smooth plank, building the wall was not. Of course, to mould a finely finished bronze like this head requires sophisticated techniques, yet those techniques appeared five millennia ago and developed independently in distant cultures. We do not know for sure but painting on stretched cloth appears to have come much later.2 Sculpting is also simpler than painting perceptually, because sculpting deals more directly with depth. We see depth in a number of ways, of which these are the most important:3 •Close one eye, hold out your hand, line up a finger with the edge of something, and stare at the edge. Now if you move your head

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sideways, you will see the finger move sideways in the other direction—motion parallax this is called—and if you move closer to your finger, you will see the finger enlarge and blur. Motion parallax, optical expansion, and defocussing all describe depth. •Since each eye sees the world from a different place, each eye sees the scene differently. The brain interprets this disparity as depth. This forms what we usually think of as stereoscopic vision. •To look at something, your eyes need to rotate toward it; to focus on something, the curvature of each lens needs to change. Muscles do both. As the muscles contract, sensors within them send neural signals back to the brain. Those signals describe depth.

While a sculptor works, his brain uses each of these mechanisms both when he looks at his model and when he looks at the clay he is forming into a three-dimensional simulacrum of the model. While a painter works, she sees the model in the same ways—but when she looks at her canvas, the same perceptual mechanisms tell her that the object in front of her is flat. Thus, a sculptor forms a threedimensional copy of what he sees but a painter limns a two-dimensional abstraction. Creating an illusory third dimension is more complex cognitively than copying a real one.

TONALITY To make sense of the world, lines are less important than we think. As we look about, we have the impression that lines define objects, but this is an illusion. We actually get most of our information from changes in tonality that are not sharp but are spread over a sufficient breadth to look blurry. If you look again at the boy on page 63, you will see that most of the optical energy is in the fourth, fifth and sixth photos, yet none of these contains a sharp line. Only in the seventh and eighth photos do we perceive any sharpness, and those photos are more difficult to make out.4 The information in a scene comes from the brightness of different objects in it. The brightnesses we see are induced by light reflecting off objects, so let's consider the reflections in a scene. Imagine we are walking through the forest on the next page and measuring the light at different spots:

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On paper this scene’s range of brightness is compressed from 1:100,000 to 1:100.

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•Light from the sun reflects off shiny leaves like a mirror. These specular reflections are as bright as the sun, so they are too bright to look at. There is no need to measure them. However, slightly duller leaves scatter the sun’s light in all directions, leaving the portion entering our eyes dim enough to view. The brightest of these leaves is the brightest tone we can look at. We point an imaginary light meter at this and calibrate the meter so that it reads 1.0. •Most of the sun’s light reflects off microscopic particles of water in the sky, leaving the sky blue. In round numbers—throughout this example we shall use very round numbers—the sky reflects 10% of the sunlight. Some direct sunlight also passes through the surface layer of foliage to be reflected by green pigment. The pigment also reflects 10% of the light . Thus, when we point our light meter at either the sky or the sunlit foliage, we read 0.1. •Of the skylight, 10% passes through the forest’s canopy of leaves. In the open shade where the sun does not reach directly, this light provides the illumination. If we measure a sheet of white paper here, we read 10% of 0.1, or 0.01. That is a measure of the open shade reflected off paper, but leaves reflect only 10% as much light as paper. When we point our meter at the brighter portions of the shaded shrubbery, we read 0.001. •This shrubbery reflects light not just into our eyes but also down toward the ground, onto spaces that are shaded not just from the sun but from the skylight. The vegetation littering these spaces reflects 10% of that light back towards us, so we measure the brightness of the ground as 0.0001. •The ground reflects light not just into our eyes but also upwards to illuminate the lower half of the log. The log reflects 10% of that light, so we measure the log as 0.00001.

In sum, the surfaces in this scene span a range of tones from 1 to 0.00001, or 1:100,000—not counting the sun and its specular reflections. That is the tonal range of the scene in nature yet the printed picture on the next page has a tonal range of only about 100:1, because that is the range of ink on paper. Oil paints and computer screens can be richer but their tonal range is still but a fraction more than two orders of magnitude. It is physically impossible to reproduce the actual range of tones found in most natural scenes. Painting a truncated range of tones that looks naturalistic is likely to be the most difficult artistic challenge that an artist will face once he has

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determined a painting’s basic composition and sketched its elements, and it is just as much a challenge with photography and cinematography. The eye needs to deal with light across 10 orders of magnitude—a ratio of 1:10,000,000,000—yet a single sensory receptor can respond to no more than one or two orders of magnitude before its response tops out. To handle this range, the eye evolved sensory receptors with different levels of sensitivity, and both the eye and the brain evolved complex physiology that opens and closes neuronal window shades throughout the structures and pathways of the visual system. All of these together function like an electronic circuit called an automatic gain control.5 “Gain” is the amount by which an amplifier multiplies a signal. If an amplifier boosts a signal tenfold, its gain is 10. If a signal bounces about from 1 volt to 10 volts, and must be amplified to feed a device that requires a signal of exactly 50 volts, then the gain of the amplifier must be adjusted continually between 50 and 5. Automatic gain control does this automatically, by hiving off a small amount of the signal and feeding it back into a circuit that controls the amplification. Automatic gain control is used in telephones, so that no matter whether someone’s voice is loud or soft, he will be comparably audible. The visual system has an equivalent system to keep the cortex stimulated but not overloaded, no matter how bright or dim the day. Automatic gain control destroys information about the physical intensity of light. Just as you cannot hear over the telephone the amplitude of the pressure waves leaving your interlocutor’s mouth, so you cannot see the amount of light an object is reflecting. However, the brain processes something far more informative: relative brightness. If a leaf reflects 10% of the sunlight striking it, the same leaf will also reflect 10% of the moonlight, so the leaf will look like a leaf both day and night. That is why in the checkerboard on the next page square A looks darker than square B, although as the vertical bands show, both are actually the same shade of grey. Relative brightness is much more important than absolute brightness. Relative brightness, not absolute brightness, carries the information needed to survive. You would have a hard time recognizing a tiger if its stripes looked different at different times of day.6

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In sum, the brain does not perceive contrasts in any way that is linked directly and predictably to light entering the eye. The responses of the brain to different quanta of light are often qualitative as well as quantitative. The brain commonly responds to different quanta by shaping them into relative categories like bright versus dark, into categories that intermix quantity with quality. The nature of the categorization is affected by other neural pathways that happen to be active at the moment, and by nearby neural pathways that had just been active and so are now inhibited. An impression of brightness may indeed correlate somewhat to the quanta of light— we always perceive a sunny day to be bright and a moonless night to be dark—but this correlation holds with certainty only toward the extremes. A cloudy day we may perceive as either bright or dark, depending upon what came just before, and as we see in the illusion above, the same intensity of light can look like different tones. Since the brain intermixes quantity and quality, it will happily ignore much if not most quantitative information. For example, the next page shows two versions of the same scene. The first of these looks naturalistic. We see the sun illuminating a meadow and a forest formed of individual trees. However, optically that picture is bizarre. The clouds ought to be brighter than everything except the sun, yet the meadow looks as bright as the sky. The second shows the correct tonal relations insofar as they can be shown with ink on paper. The first image we doctored to make it look natural; the second image is straight from the camera. To capture that scene, the photographic process needed to compress the range of tones from approximately 100,000:1 to 100:1—roughly one-thousandfold. Photographic processes are calibrated to display

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This picture looks naturalistic but none of the meadow could have been brighter than any of the clouds.

This picture shows the scene as recorded by the camera. All of the sky is brighter than any of the meadow. The meadow looks black because the tonal range of this image exceeds the tonal range of ink on paper.

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the middle tones of a scene more or less accurately across one order of magnitude, and to compress all the other tones. This left the ordering of tones correct—lighter objects ended up lighter—but contrasts got lost so that objects disappeared. To make the picture appear realistic required restoring those lost contrasts at the expense of correct ordering and optical reality. Painters need to compress tonality as much as photographers do—a little more for watercolours, a little less for oils—so painters distort tonal relations too. They create comparable impossibilities to make a scene look natural. Here is an example of this by Johannes

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Vermeer. The window is the source of light, so it ought to be the brightest part of the painting, but it’s not.7 The optical reality of any contrast is unimportant, what matters is the perceptual category the contrast fits into. In the mountain scene on the page 232, the small light spots against dark greens fall into our category of flowers, and the grey splotches near the sun fall into our category of clouds, and clouds are lighter than flowers, so we do not notice that these particular clouds are darker than those particular flowers. The brain is perceiving the quantity of the tones—their brightness—through qualitative categories. Similarly, since Vermeer’s milkmaid looks like a milkmaid, we do not notice the impossible lighting. The same process can happen in reverse when the tonal range of a dull scene is less than the tonal range of pigment on paper. Since we are used to photographs that exhibit a tonal range of 100:1, a photograph with a range of 10:1 will usually seem unnaturally flat. Here, for example, the portrait on the left is correct optically but extra contrast on the right brings the woman to life.

COLOUR Tonality involves more than brightness and darkness, it also involves colours, which like all other perceptions exist solely in the brain. We perceive different colours in response to three characteristics of light: •its total energy, •the wavelengths forming this energy, and •the distribution of these wavelengths.

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Each of these is a physical quantity that we can measure with instruments, yet to a large extent the colours we perceive do not reflect the physical quantity. For example, this spectrum shows the colours we see when each wavelength reflects a similar amount of energy. Obviously the hues bear no relationship to the wavelengths on the scale. Red is not more than blue, let alone twice as much. The hues differ qualitatively. We can say that red looks brighter than blue and that yellow looks the brightest, but these different brightnesses bear no relationship to the length of the light wave, they reflect the sensitivity of the receptors inside the eye.

400

500 nm

600 nmWavelength (nm)

When we combine wavelengths by mixing paints or coloured lights, we perceive the hues to lose purity—to lose saturation, in the language of art. Combining all wavelengths of paint turns colours grey or black; combining all wavelengths of light turns colours white.9 Although colours are qualitative perceptions, they are formed in the brain from the three dimensions we have mentioned in these paragraphs: hue, saturation, and brightness. This model shows how the dimensions relate to one another. Hue is the circumference, saturation the radius, and brightness the vertical axis. These are perceptual dimensions, not physical dimensions, so we cannot measure them in fixed units like pounds or inches, but

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they are dimensions nonetheless. This model is a useful tool for thinking of colour and a useful tool for comparing colours. “This red is more saturated but brighter and closer to yellow.”10

BRIGHT VS. LIGHT VS. ENGLISH The language of light is so confusing that even professionals in the field often find themselves mixed up, so we would like to clarify some basic concepts and terms—or at least try to. The sun or a lamp emits electromagnetic radiation across a broad range of wavelengths. Energy across a narrow portion of those wavelengths stimulates specialized neurons at the back of the eye, which stimulate the brain and induce us to see something bright that we call light. A physicist can measure the energy of electromagnetic radiation but light—what we perceive—is the product of the radiation’s strength and of the eye’s sensitivity to various wavelengths. To measure light we need first to measure the radiant energy of visible wavelengths and then to adjust that measurement to match the sensitivity of the eye. To determine the eye’s sensitivity, psychophysicists park university students inside pitch-black rooms and ask them to spend hours at a time comparing spots of light. This testing is exceedingly unnatural and leads to wildly differing outcomes, but engineers want to calibrate light meters, so they deem the average outcome from these labs to represent normal vision.8 Although light meters can be precise, they measure the length of an amoeba. Our perceptions of brightness are so variable and complex that even hearing can be involved. Raising the pitch of background music will make a scene look brighter.9 Or maybe it will make the scene look lighter. There are technical distinctions between “brightness” and “lightness. However, some of the technical usages are inconsistent and so are some definitions by standards bureaux. That is why we can read a statement like this in Wikipedia: “Brightness is…a color coordinate in HSL color space: hue, saturation, and lightness, meaning here brightness.”11 Although we write our scientific papers using the technical language common to our field, in this book we are sticking to English. We shall ignore all of the scientific usages and deem that light, the sun, and snow are all bright.

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VERISIMILITUDE An image on canvas or paper usually requires compressing and/or expanding tonal contrasts, so accurate reproduction of tones is rarely possible. Indeed, in most circumstances the very notion of accurate tonality is an oxymoron. That’s because our perception of brightness interacts with size. When you stare at a spot of light, the image of that spot within your eye illuminates a certain number of receptors on your retina. The output of the individual receptors is accumulated by a smaller number of “ganglion cells” immediately behind. The broader or lighter the spot, the more ganglion cells are triggered. This causes size and brightness to trade off one against the other so that larger objects look brighter. That is why, whenever you paint a room, the walls seem not to match the paint chip.12 Accurate reproduction of hue is also an oxymoron. Dyes and pigments all interact differently with light under different conditions. Even if you could find a magical paint that looked the same in every light, still the hues would change with the other hues nearby. The brain processes differences in stimulation, not constancies, so neighbouring colours interact. For example, inside this circle, the green and blue lines are actually the same colour of ink. Fortunately for the visual arts, verisimilitude does not require accurate colour, because our expectations can make a broad range of colours seem acceptable. For example, look at the photograph on the next page. It is a frame of the first feature film distributed by Technicolor, The Toll of the Sea. It dates from 1922. When it came out, the New York Times described it as, “A picture whose colors are independently good. The scenes of The Toll of the Sea are nearly all satisfying to the eye and many of them are distinctly pleasing.” The New York Herald wrote, “If this process is not perfect then, at least we could find no flaws in it.”13

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By today’s standards this colour is not perfect yet it seems fine for a snapshot. The background shows a beach with sea and sky. On the other hand, if you look closely you will see that the picture is devoid of blue. Not until 10 years later was Technicolor able to create any shade of blue. All of the images that critics deemed stunningly realistic were formed entirely of red and green. We expect both the sea and the sky to be blue, so with nothing nearby to show otherwise, we see them as blue. To see how strongly expectation influences us, look at the meadow on the next page. The photograph has all of the hues of the rainbow: red flowers, yellow flowers, violet flowers, and green foliage. The close-up shows these clearly. But as you can see, when we matched leaves to paint chips—or rather, when we did the equivalent in a computer—we found much of the green foliage to be yellow. It is possible that some of this is an artefact of the model of colour used by the computer, the model published by the Commission International de l'Eclairage (CIE). The CIE model is a standard designed for engineering, not for predicting human perceptions. It permits precise standardization of cameras and instruments but does

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The top panel shows a meadow. In the central panel a computer searches that meadow for pure yellows and turns them into magenta. In the bottom panel the computer turns all yellows into magenta. As you can see, all of the “green” foliage is some shade of yellow and much of it is a pure yellow.

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not model accurately how people see. However, if some of this is an artefact, most of it is not likely to be. The chlorophyll that colours leaves reflects light across the entire range of wavelengths that we see as green and yellow, but we are more sensitive to the latter, so the latter has more clout. The distribution of wavelengths differs among plants and environments, but those we usually see as yellow tend to dominate. We see foliage as green because the wavelengths of foliage differ from the wavelengths of flowers, and the dominant wavelengths of nearly all foliage would put it on the green side of yellow. The brain responds to this contrast by sharpening it, by putting foliage into a category of hue different from the flowers—by sliding its normal categorization of yellow into green.14 In short, just as the brain does not measure or register the absolute intensity of light, so it does not measure or register wavelengths either. It responds to contrasts in intensity and contrasts of wavelength, nothing more. (Or rather, the brain responds to contrasts in the proportions of wavelengths, as we described in chapter six.) Because the brain perceives only contrasts, it hardly matters what those contrasts are. For example the picture on the left here is obviously Abraham Lincoln, yet the only relationship its tones bear to the original photograph in the centre is that his eyes, hair and beard are darker than his skin. The picture stops looking like Lincoln only if we invert the colours so that his hair is lighter than his face. That is the picture on the right.15

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As a practical matter, any one kind of contrast can usually substitute for any other. If paper or canvas cannot represent a range of brightness needed to make a naturalistic contrast, then an artist can enhance a difference in saturation and/or create differences in hue. Arbitrary contrasts are the stock in trade of naturalistic painters. You can see that in Rembrandt’s face on page 71. Theatrical lighting is often distorted comparably. Highlights and shadows form important cues to depth, but covering a stage with light requires so many lamps that highlights and shadows appear everywhere and provide inconsistent information. To compensate, lighting designers create arbitrary contrasts in hue. All the lights aimed rightward might be tinted red and all the lights aimed leftward might be tinted blue.16 On paper and canvas, adding artificial contrasts can also enhance verisimilitude. You can see this here. The woman on the left is not alive, she is a Renaissance sculpture, but artificially deep contrasts on her face and to the background bring her to life. On the right is the museum’s reference photo. Both have the same tonal range.17

When we see real faces, we find attractiveness in the familiar and we find beauty in slight positive variation. When we see paintings of

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faces, we find the same. Ditto sculpted faces, or paintings or sculptures of anything else. Since paintings are intrinsically unrealistic, familiarity with painted faces is based on techniques that are common enough to have become cultural conventions. The most obvious cultural convention is perspective, which we discussed in chapter four. Appropriate tonality is also conventional. The cheeks of the sculpture on the last page are rosy but to a 19thcentury Japanese, beautiful faces are not rosy, they are pale. To make them beautiful, in this group portrait a Japanese artist painted the family’s faces as pale as possible. This was clearly intent, not ineptitude. As you can see from the enlarged details, the artist was skilled enough to shade cheeks naturally, and he did so with the darker servant.18

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BROWN You may have wondered why we have not mentioned brown. That is because browns are actually darkened reds. You can see this here, where we superimpose a grey shoe over the red one. So many natural objects are darkened reds that we form those colours into a distinct perceptual category that we call brown.

MUSIC Throughout this book we have drawn parallels between the way we see and the way we hear—not rhetorical analogies but physical equivalents rooted in the physiology of the brain and the physics of

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waves and wavelets. It ought to be no surprise that the contrasts we hear in music resemble those we see in paintings. Like the eyes, the ears receive energy over a range of intensities that is astronomical, and the parts of the brain that are fed by the ears have the same neurophysiology as the parts that are fed by the eyes. This limits the range of auditory processing in the same way it limits the range of visual processing, so like the visual system, the auditory system has also evolved automatic gain control. Just as automatic gain control prevents us from seeing absolute levels of light, so it prevents us from hearing the absolute intensity of pressure waves. Just as we can see only contrasts, so we can hear only contrasts. For the brain as the telephone, the range of audible contrast runs through two orders of magnitude, from barely audible to so loud that you hold the receiver away from your ear. These are the black and white of the auditory system. Noise loud enough to hurt is overloading the system, is staring at the sun. When a tenor alters the harmonic structure of his voice to become audible over the other soloists, we describe him as altering the colour of his voice to stand out over the others. This is the equivalent of boosting a visual contrast by modifying a hue.19 Chopin was sickly and weak, so when he performed on the piano, he used contrasts rather than power to mesmerize his audiences. We have descriptions of this from two pianists who shared his stage, Ignaz Moscheles and Franz Liszt. Moscheles wrote, “His piano is such a whisper that he needs no powerful forte to bring out desired contrasts; so one does not need the orchestral effects that the German school demands of a pianist.” According to Liszt, “He always undulated the melody, like a skiff carried on the roll of a powerful wave; or he moved indistinctly, like a floating apparition that materialized unexpectedly in the tangible and palpable world.” Instead of regular rhythms Liszt described “tempos stolen, interrupted, flexible, abrupt and languid at times, flickering like a flame beneath agitated breath, like weeds on an undulating field under the gentle pressure of a warm wind, like the tops of trees bent here and there by the vagaries of a strong wind.”20 The brain hears contrasts much as it sees them: neuronal pathways form categories based largely on experience, and chemical responses both facilitate passage along those pathways and inhibit passage

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SEEING AND HEARING THROUGH THE SKIN If patterned energy reaching the eyes and ears is processed similarly, then we would expect patterned energy on the skin to be processed similarly as well, and so it seems to be. The blind feel letters in braille and process them as words just as the sighted read print. Someone who is deaf can also enjoy music. For example, here is a description of Helen Keller, a remarkable woman who was profoundly deaf and totally blind, by the husband of her teacher: “Music probably can mean little to her but beat and pulsation. She cannot sing and she cannot play the piano, although, as some early experiments show, she could learn mechanically to beat out a tune on the keys. Her enjoyment of music, however, is very genuine, for she has a tactile recognition of sound when the waves of air beat against her. Part of her experience of the rhythm of music comes, no doubt, from the vibration of solid objects which she is touching: the floor, or, what is more evident, the case of the piano, on which her hand rests. But she seems to feel the pulsation of the air itself. When the organ was played for her in St. Bartholomew's, the whole building shook with the great pedal notes, but that does not altogether account for what she felt and enjoyed. The vibration of the air as the organ notes swelled made her sway in answer. Sometimes she puts her hand on a singer's throat to feel the muscular thrill and contraction, and from this she gets genuine pleasure.”21

along neighbouring pathways. The eye does this across space and the ear does this in time, at scales down to milliseconds. In the auditory system this enables us to discriminate one phoneme from another or the attack of one instrument from the attack of another. Of course, overall magnitude can and does affect us. Bigger objects look brighter and a powerful bass we may feel as strongly as we hear. The brain adapts physiologically to a certain level of stimulation, so if we become used to hearing voices or instruments preternaturally loud, that is how we will enjoy them. But no matter whether we prefer an acoustic guitar in a living room or a rock concert as loud as a hammer mill, arbitrary contrasts form our experience and expectations.

12 LITERATURE POETRY, PROSE AND PLAYS

Musicologists often distinguish “pure” or “absolute” music both from songs and from “programme music,” which tells a story. Pure music is deemed to be more abstract. However, this is the perspective of a musicologist, not the perspective of the brain. Pure music is perceived directly and exclusively from the ears, but involving a song or story complicates music with the abstractions of language. Songs are poems—rhythmical speech. These rhythms resemble music and in many cultures poems are chanted—ancient Greek poetry, for example. In contrast, prose lacks rhythm. This explains a puzzling paradox. We think of poetry as the most sophisticated form of literature yet The Canterbury Tales, The Iliad, and The

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Odyssey came centuries before memorable English and Greek literary prose. A poem’s rhythm is seldom tub-thumping but all poems have a verbal beat. That is what makes them poems. Often this is accentuated by rhyme but not necessarily. Poetry in Western Europe did not rhyme until Rome became influenced by a Persian cult during the 2nd century C.E. However, some rhythm is requisite, and rhythm functions in poetry as it does in music. It serves as a sonic theme with variations that suits the fractal structures of the brain. This rhythmicity makes the sounds of poetry easier to remember than the sounds of prose, and so more suitable to an oral tradition.1 To see how poetry is more direct than prose, let’s look back six centuries to a time when the printing press did not exist, when paper was a luxury, when Latin was the language of western literature, and when English was just a set of local dialects spoken in a small island. At that time Geoffrey Chaucer wrote a series of English poems called The Canterbury Tales. He wrote not in modern English but in an earlier form that scholars call Middle English. Here is the start of one of these poems, printed with modernized spellings underneath. Read it aloud. As you read it, pronounce all the letters that are silent in modern English—the k and gh in knight, the ed in called, etc. Ther was, as telleth Titus Livius, A knyght that called was Virginius, Fulfild of honour and of worthynesse, And strong of freendes, and of greet richesse. This knyght a doghter hadde by his wyf, No children hadde he mo in al his lyf. Fair was this mayde in excellent beautee Aboven every wight that man may see.2 [There was, as telleth Titus Livius, A knight that called was Virginius, Fulfilled of honour and of worthiness, And strong of friends, and of great riches. This knight a daughter had by his wife, No children had he more in all his life. Fair was this maid in excellent beauty Above every wight that man may see.]

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This verse is nothing special yet its rhythms hold the ear and help the sense of an unfamiliar language pour through. In contrast, Chaucer’s prose is more difficult to follow. Here is part of an introduction to the astrolabe he wrote for a boy, a paragraph explaining why he is writing in English rather than Latin. The version underneath has some modernized phrases as well as modern spellings. This tretis, diuided in 5 partis, wole I shewe the under ful lighte rewles & naked wordes in englissh; for latyn ne kanstow yit but smal, my lite sone. But natheles, suffise to the thise trewe conclusiouns in English, as wel as suffyisith to thise noble clerkes grekes thise same conclusions in greek, & to arabiens in arabik, & to Iewes in Ebrew, & to the latyn folk in latyn whiche latyn folk han hem furst owt of othre diuerse languages, & writen in hir owne tonge, that is to sein, in latyn.3 [This treatise, divided into five parts, will I show thee under full light rules and naked words in English; for Latin you don’t know but small, my little son. But nonetheless, suffice to thee these true conclusions in English, as wall as suffice to these noble Greek clerks these same conclusions in Greek, and to Arabians in Arabic, and to Jews in Hebrew, and to the Latin folk in Latin; which Latin folk have them first out of other diverse languages, and written in their own tongue, that is to say, in Latin.]

THE NATURE OF PROSE This piece of Chaucer’s prose has no rhythm to enforce a structure and was shaped by no tradition of literary form or style. Nevertheless, we can still comprehend it because circumscription and indirection form our cognitive norm. In chapter nine we showed that when we look at a scene, we see tiny portions of it and piece the sensations together: this holds for everything we look at, including text on a page. We neither see nor read one letter at a time nor one word at a time, we see small areas one after the other. You can see this on the next page in a plot that we made with an electronic eye-tracker. The white splotches show what parts of the page the eyes actually looked at while reading. As with scenes, the brain infers the intermediate portions based on indistinct forms seen through peripheral vision and interpreted by experience. That is why the more we know about a subject, the more quickly and accurately we can read about it. It is

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A plot from an electronic eye-tracker showing what the eyes looked at while reading.

also why writers incorporate redundancies. A good writer tries to match the level of redundancy to the knowledge of his reader, repeating enough to clarify inferences yet varying the repetition sufficiently to elaborate ideas in ways that will hold the reader’s attention.4 Speech we piece together similarly. We do not remember and process every word we hear, we assemble meanings from shreds and patches. Since the ear cannot return to a phrase and hear it again, intelligible speech requires numerous redundancies, many more than we need in writing. For example, compare these two sentences. The first looks prolix and repetitive on paper but sounds natural when spoken. The second is clear and would be appropriate as part of a written invitation but sounds unnaturally clipped when spoken aloud. After we finish eating our dinner, we’ll get out the playing cards and play some bridge. After dining we shall play bridge.

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The adult’s cortex generates speech much as it hears speech, not through logical analyses and syntheses but by combining broad associations with deeply formed patterns, associations and patterns from hither, yon and below. These combinations contain uncertainties, redundancies, inconsistencies, and errors—all manner of indirection and inefficiency. As a result we tend to speak in fits and starts, generally going forwards but often going round about in different directions, much as our eyes scan text. Some people learn to speak in polished sentences but most of us do not, so most normal speech looks foolish when transcribed verbatim. For example, the U.S. President Richard Nixon once told his cabinet something to this effect: At the leaders’ meeting I plan to talk only about Vietnam but I shall probably need to answer questions about Cambodia and Laos. Negotiations with Cambodia and Laos are more general but vitally important. Henry, tell us about them.

But these were his actual words:5 In terms of what it means for Cambodia and Laos, and so forth— I—I think it’s a—let let me—let me say this at this point, since this is a subject that will come up with the leaders’ meeting, in other words we’ll probably have to answer, I think it would be well for Henry to take just a moment on Cambodia and Laos, because the Vietnam thing is all I'm really going to talk about but, I don't think there’s various settings(?) that this [document] covers—Vietnam, and has an understanding with regard to Cambodia and Laos. Now, negotiating the understanding with Cambodia and Laos are not all that specific, but they’re vitally important. Go ahead Henry, take a minute on that.

Here is an example of Nixon’s speech when he had nothing specific to say, when he was just making small talk to a man honoured as the truck driver of the year:6 You know, the thing that always impresses me about all those in your profession is that, and I have often said this is their enormous courtesy. You know, you have this, you develop, I mean, I used to drive a lot although I don’t now, because they have a driver. I haven’t driven a car for four years ok? Well they, the Secret Service drives, of course. Anyway—the—the—way that the people on the road with the truck drivers, they always [unclear] cars on [unclear], that courteous driving makes an enormous impression.

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Both of those conversations were late in the afternoon, when Nixon might have been boozed up—he drank heavily while he was President —but he gave this warning to his Secretary of State William Rogers at 8:49 in the morning:7 I had a thought. Uh in reading the morning paper I notice that uhhh Pompidou uuuh and Brezhnev were making a lot of noise about the European Security Conference. And uh I think uh it’d be well — and uh — we can talk about it when you come over tomorrow but I think it’d be well if uh — if uh — if uh you keep the keep the thing very very cool, I mean on the thing. If you of course have said we don’t want the damn thing—well, we may have to have it at some point but let’s — these damn Europeans, the way they played, I’d uh — I think it’s I think it’s very very much in our interest to do that and also we have laid the foundation with the Russians because — uh you know and I [unintelligible] we played it very cool with Brezhnev and I mean, with uh — what the hell — Gromyko.

Like all neuronal structures, the brain adapts to repetition or constancy but responds to sudden changes. At the lowest scale of language, vowels are relatively constant and consonants form sudden changes, so consonants carry most meaning. At longer scales of time, the constants become linguistic particles like “uh” and words like “this” that carry sense but are so common that they tend to disappear. At these scales meaning comes from unusual repetition, unusual words, unusual loudness, unusual slowness, and anticipatory pauses. In the case of Nixon’s instructions above, Rogers would have registered something like this. Thought. Reading paper Pompidou Brezhnev making noise European Security Conference………[hesitant] We talk tomorrow………If [hesitant] very very cool. If you we don’t want damn thing……… may have to………damn Europeans, way they played………I think our interest that………laid foundation with the Russians………I we played cool with Brezhnev Gromyko.

From that Rogers would have abstracted this information: New problem with Pompidou, Brezhnev, and European Security Conference. Worrisome. Need to be careful. Will talk tomorrow.

We are quoting Richard Nixon because his conversations in the White House were taped yet clearly he was not talking to the tape recorder. He was a good debater and under the press of circumstance,

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he could speak effectively off the cuff. However, in ordinary situations and ordinary conversation like this, his brain processed language in ordinary ways. That means frequently forming words into unclear phrases, redundant clauses, and sentences that convey impressions more than logic or fact. He spoke that way and people understood him because redundancies suit the structure of the brain.

DRAMA AND HUMOUR Nowadays we distinguish between written and spoken forms of a language, but this is a fairly recent differentiation. Before the printing press, when books were copied out by hand, they were not primarily objects of silent contemplation as they are today, they were often if not usually read aloud, commonly in the company of other people. In late classical times silent reading was sufficiently unusual as to be cause for comment. For example, this is St. Augustine’s reminiscence of St. Ambrose (c. 340-397): When he read his eyes ran over the page and his heart searched out the meaning, but his voice and his tongue were at rest. Often when I was present…I have seen him reading thus silently, never in fact otherwise. We would sit there in long silence (for who would venture to intrude upon him so intent upon his study?) and go our way. We hazarded conjectures as to his reasons for reading thus; and some thought that he wished to avoid the necessity of explaining obscurities of his text to a chance listener, or that he avoid thus the discussion of the difficult problems that would arise and prevent him from doing the amount of reading that he had planned in a given time. But the preservation of his voice, which easily became hoarse, may well have been the true reason of his silent reading.8

In the late 15th century, the printing press cut the price of books dramatically, yet as late as the beginning of the 19th century, English day schools still did not bother to teach silent reading. For most people silent reading was unnecessary. Most people had time to read only at night after work, and candles and lamp oil were expensive. The cost of light measured in working hours was roughly 1000 times higher in 1800 than in modern times. Few households could afford enough light in the sitting room to let everyone in the family read silently. One person would read aloud. In libraries and offices, where reading aloud would disturb other people, some people

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would read silently but you would probably have heard a chorus of mumbling.9 In fact, even silent reading is intrinsically aural. An experienced silent reader will not read every word of a text internally in his mind’s ear unless the passage is difficult or he is savouring its style, yet even when we read silently, the muscles of the mouth are innervated, and words that are harder to pronounce are harder to read, although they might have the same number of letters.10 Nonetheless, written language is more compact than spoken language. Human conversation contains more information than letters can carry—tones of voice, expressions of the face, pauses—and human conversation is dilute, even ignoring all of the meaningless, gapfilling particles like um and like. This makes dialogue too voluminous and vaporous to recreate verbatim. Writers must compress the spoken language as painters must compress visual information. Much like paintings, poetry and prose form meaning through repetition and contrast. Some redundancy is necessary for understanding but too much repetition bores. With words as with paint, beauty comes with variations from the norm in directions that we have become biased to deem pleasant, and ugliness comes with comparable variations in directions that we have become biased to deem unpleasant. When pleasant and unpleasant pathways are both stimulated, ambivalence can result. The tension between them creates drama. We know that the bad guy ought to get his comeuppance but will he? At the end of a symphony, we expect that the crescendo of dissonances and sonic instabilities will resolve into a glorious, consonant chord, but when will it arrive? A painting like the one on the next page uses the techniques and colours of beautiful art to depict horrors like the detail: ought we to enjoy it or cringe? This is the equivalent of musical dissonance. In psychological jargon it’s “cognitive dissonance.”11 The longer expectations teeter between nice and nasty, the more tension an audience feels. Like all other perceptions, dramatic tension is created by contrasts. Shouting may indicate emotion but the most dramatic moments on stage often come from unexpected

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silence. Actors must play silence as deliberately as musicians must play a rest, and for similar reasons. Consider: Are you pregnant? Yes. Are you pregnant? [long silence] Yes.

Humour is another variation of this mechanism, when energy is suddenly diverted from one network to another, forming surprise and incongruity. A baby laughs at an adult imitating a dog; a child laughs at a pratfall; an adolescent laughs at a teacher employing a

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scatological term. Once we have seen enough pratfalls and heard enough scatology, we become adapted to them and laugh at more abstract surprises, at novel turns of phrase or at a picture that combines perceptual categories in a novel way, like this caricature of Charles Darwin.12 Wit does not require words but it does require shared knowledge or experience, else it falls flat. Nothing carries less meaning than an “in” joke to an outsider. On the other hand, with sufficient shared experience, any anomalous perception can be funny, even perceptions of “pure” instrumental music like symphonies and string quartets. During his lifetime critics compared the composer Joseph Haydn to the English satirist Laurence Sterne. Unfortunately, after 200 years our experience has diverged so far from theirs that few people now hear Haydn’s ironies (or read Sterne).13 Laughter often accompanies humour experienced in company. Laughter begins in young babies as a reflexive response to simple pleasure. Although laughing to sheer pleasure diminishes with age, it does not disappear altogether. Even adults will sometimes laugh not because something is funny but just because they are having a good time. All in all, laughter appears to us a phylogenetic vestige, a vehicle for aural communication that our speechless ancestors would have used much as chimpanzees use similar sounds today. The sounds of laughter require no specialized vocal apparatus and in lieu of speech they would have been formed by experience to suit several social functions, as chimps’ sounds become formed for different functions. Now, however, speech has supplanted its utility and largely obviated its use for all but two purposes: as a social response to humour (most often) or as an indication of uncertainty.14

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METAPHOR AND ABSTRACTION With language as with our other perceptions, as neuronal signals from sensory organs travel deep within the brain, they intermix. That is why we speak of dark and bright sounds, high and low pitches, loud and muted colours, soft and hard words. We make these associations as babies—not with words, of course, but with perceptions. For example, if you show a three- or four-month old a spot of light moving up and down a screen while a musical tone rises and falls in pitch, he will look longer at the screen if the spot and sound rise and fall together.15 An engineer would call these metaphors sensory crosstalk. The extreme of sensory crosstalk is full-blown synaesthesia. In 10% to 15% of people, one sensory perception will induce a second. Most commonly a synaesthete will see letters of the alphabet in colour. The next page shows the different forms of this crosstalk reported in a sample of 1143 synaesthetes. However, most metaphors are not synaesthetic. Life is a rollercoaster, home is a prison, his heart is a rock—ordinary metaphors like these do not intermix sensory systems because, except for words that are onomatopoeic, words convey meanings not at sensory levels but as symbols, which are abstract (see chapter five).16 Literary critics agree that any symbol can stand for anything, yet they elaborate taxonomies of metaphor and debate how many taxonomic categories are natural. In contrast, scientists denigrate explanation by metaphor as argument by analogy, yet they spend their careers discussing physical and/or mathematical metaphors they call models. It seems clear that even in academia, thought and reason are not the same. In fact, all of the brain’s processing is analogical, not logical. Perceptions fill in sensory holes using analogous information from the past, and cognition works similarly at more abstract levels. Analogues form because the brain’s processing is always associational. One neuronal pathway fires another based on proximity and prior association. As for logical thinking—well, if you have studied logic, then some of your brain’s associations some of the time may form logical

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FORMS OF SYNAESTHESIA

O C

EM

LO U O R TI FL O AV N O LE U TT R M ER O V M EME US IC NT N AL O N SO O -MU U N D O SIC D PE U R A L RS SO O U SP N N AT A D L IA I T TE L L Y O M C P TO ERA ATI O T U C UR N H E

EXTRA PERCEPTION

COLOUR EMOTION FLAVOUR LETTER MOVEMENT MUSICAL NOTE MUSICAL SOUND NON-MUSICAL SOUND

NORMAL PERCEPTION

NUMBER ODOUR ORGASM PAIN

PERSONALITY PHONEME BODY POSITION SPATIAL LOCATION TEMPERATURE TIME TOUCH WORD PROPORTION OF 1143 SYNAESTHETES SHOWING EACH FORM

0