On Digital Architecture in Ten Books. Volume 2 On Digital Architecture in Ten Books: Vol. 2: Books IV–VI. 9783035626032, 9783035625998

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ON DIGITAL ARCHITECTURE

BIRKHÄUSER ETH ZURICH

DECODING and the PRIVATE

BOOKS IV–VI

CODING and the PUBLIC

VOLUME II

ENCODING and the SACRED

LUDGER HOVESTADT

IV

V

VI

ENCODING and the SACRED

CODING and the PUBLIC

DECODING and the PRIVATE

IV

V

VI

ENCODING and the SACRED

ON DIGITAL ARCHITECTURE IN TEN BOOKS

CODING and the PUBLIC DECODING and the PRIVATE

APPLIED VIRTUALITY BOOK SERIES VOL. 20

IV

V

VI

ON DIGITAL ARCHITECTURE

BIRKHÄUSER ETH ZURICH

DECODING and the PRIVATE

BOOKS IV–VI

CODING and the PUBLIC

VOLUME II

ENCODING and the SACRED

LUDGER HOVESTADT

IV

V

VI

ENCODING and the SACRED

THE TEN BOOKS

CODING and the PUBLIC

DECODING and the PRIVATE

IV

V

VI

OBSTACLE

VOLUMEI.I

The ARCHITECT

VOLUME I ↖

About the INCONCEIVABLE OBSTACLE and the RESPONSIBILITY the author takes.

OBJECTIVITY

ENCODING and the SACRED

BOOK I

VOLUMEI.II

CODING and the PUBLIC

The COMPLEX PLANE of PERSPECTIVE PROJECTION BOOK II

The VISUAL

VOLUME I ↖

It establishes the DISTINCTIONS in TWOS: TIME | SPACE MACHINE | MECHANICS ORNAMENT | LINEAMENT … BOOK III

The AUDITIVE About the SPACE axis of OBJECTIVITY. It is about CIRCULARITY: proportions and synchronicity, right and wrong, the distinct and the PARADOX. It is articulated by CHARACTERS. It establishes the CYCLING through FOUR: INNER | PAST | OUTER | FUTURE AIR | FIRE | EARTH | WATER IDEA | MEMORY | PICTURE | VISION …

VOLUME I ↖

DECODING and the PRIVATE

About the TIME axis of OBJECTIVITY. It is about LINEARITY: cause and effect, origin and truth, the continuous and the INFINITE. It works with NUMBERS.

CHARACTERS and STABILITY

VOLUMEII

IV The TRIVIUM, the three verbal subjects of the seven liberal arts. Applying the schemes of OBJECTIVITY to the PROPORTION of the HUMAN BODY: SEE | TALK | SHOW | HEAR SEX | MEMORY | BODY | HEALTH MODULE | COLUMN | WALL | ROOF BOOK IV

ENCODING and the SACRED

75–447 ↗

Leaving home, reading and forgetting. RATIONALISATION.

V

It is about the GRAMMAR, the ORTHOGRAPHIA, the TRAGEDY, the SACRED BUILDINGS, the ENCODING … BOOK V

CODING and the PUBLIC

448–704 ↗

Negotiation in public, the global balance with the other migrants, the inconceivable. It is about the DIALECTIC, the SCAENOGRAPHIA, the COMEDY, the PUBLIC BUILDINGS, the CODING … BOOK VI

DECODING and the PRIVATE Coming back home, applying the contracts to the local reality. REALISATION.

VI

It is about the RHETORIC, the ICHNOGRAPHIA, the SATIRE, the PRIVATE BUILDINGS, the DECODING …

705–1114 ↗

NUMBERS and OPERABILITIY

VOLUMEIII

BOOK VII

AIR and ARTIFICIAL INTELLIGENCE

VOLUME III ↗

It is about the GEOMETRY, the AIR, the COLOURING (Vitruvius), the VISUAL SENSE, the ARTIFICIAL INTELLIGENCE today …

WATER and NATURAL COMMUNICATION

VOLUME III ↗

How to connect the subject to other cultures. It is about the MUSIC / ALGEBRA, the WATER, the LEVELLING (Vitruvius), the AUDITIVE SENSE, the NATURAL COMMUNICATION today … BOOK IX

FIRE and DIGITAL ARTICULATION

VOLUME III ↗

It is about the ASTRONOMY / LOGIC, the FIRE, the GNOMONICS (Vitruvius), the AUDITIVE ACT, the DIGITAL ARTICULATION …

EARTH and CULTURAL HERITAGE How to anchor the subject to the Old Masters. It is about the ARITHMETIC, the EARTH, the MACHINES (Vitruvius), the VISUAL ACT, the CULTURAL HERITAGE ...

VOLUME III ↗

DECODING and the PRIVATE

How to model the subject in today’s terms.

BOOK X

CODING and the PUBLIC

How to see the subject with today’s EYES. A mood board.

BOOK VIII

ENCODING and the SACRED

The QUADRIVIUM, the four mathematical subjects of the seven liberal arts.

IV

V

VI

BOOKSIV–VI

ENCODING and the SACRED

CODING and the PUBLIC

DECODING and the PRIVATE

IV

V

VI

CHARACTERS and STABILITY

VOLUMEII

ENCODING and the SACRED CODING and the PUBLIC

It was a PUBLIC VOICE that reasoned what ARCHITECTURE is about [Book I], and that learned about the OBJECTIVITY of our world [Books II & III]. These Books IV–VI ask: WHAT TO TALK about.

1 ↗ 11 ↗ 17 ↗ 24 ↗ 31 ↗ 56 ↗ 67 ↗

DECODING and the PRIVATE

TRIVIUM LEAVING HOME TALKING IN PUBLIC COMING BACK HOME TUNING CLASSICAL ORDER THE 20TH CENTURY

IV

V

VI

The STABILITY of ARCHITECTURE

2

“He took the three elements of the same, the other, and the essence, and mingled them into one form, compressing by force the reluctant and unsociable nature of the other into the same. When he had mingled them with the essence and out of three made one, he again divided this whole into as many portions as was fitting, each portion being a compound of the same, the other, and the essence …”

3

ENCODING and the SACRED

TRIVIUM

1

Plato, Timaeus 35a, c. 360 BC. 4

5

It’s crowded out here. Everything and everybody of different realities. And tongues.

6

What to talk about with all the eras, all the cultures all the nature?

7

What to talk about towards a common wealth?

8

DECODING and the PRIVATE

In the DAY I, the PUBLIC, left home, and I am meeting the others.

CODING and the PUBLIC

Oskar Schlemmer, Triadisches Ballett, 1922.

9

10

IV 11

I, part of the Western PUBLIC, follow my Western metaphors in three steps: LEAVING HOME, TALKING IN PUBLIC, COMING BACK HOME.

LEAVING HOME

12

V Peter Zumthor, Hjortshøj, Kolumba museum, 2007.

13

VI

Leaving home is like travelling to the edge of the world. Step by step I am leaving my PEOPLE and my things behind, I ENCODE them, give them NAMES, MEMORISE these things, fading away. All these things of where I am coming from. Like a stone dropped into the water. The wave spreading out and vanishing on the horizon.

14

15

ENCODING and the SACRED

This is me, at the edge of the world. A SACRED place. Embracing anything and everything forgotten in MEMORIES of the PAST.

Sebastiano Serlio, Tragedy, I sette libri dell’architettura, 1537–1575.

TALKING IN PUBLIC

16

17

CODING and the PUBLIC

A CATHARSIS, the TRAGEDY. ORTHOGRAPHIA. BOOK IV.

18

DECODING and the PRIVATE

Civic Architects, LocHal in Tilburg, 2019.

At this point of the future, at the edge of the world, myself forgotten in the memories of the past, with clear eyes towards the world, I am meeting the others. We stage our views, find a common language, and start to talk. This is smart, surprising, funny, weird … I never could imagine those twists and turns.

20

There is a lot to think and a lot to laugh about at the edge of the world.

21

And we try to find a CODE of what to do that fits us all.

IV

19

V 22

Sebastiano Serlio, Comedy, I sette libri dell’architettura, 1537–1575.

VI

23

The COMEDY, the DIALECTIC. SCAENOGRAPHIA. BOOK V.

25

26

My things at home become sharper, they get tuned in their colours. My PEOPLE get synchronised with the world.

27

Lives prosper because they are safe at home. Like the other homes out there, in all their differences.

28

29

Sebastiano Serlio, Satire, I sette libri dell’architettura, 1537–1575.

DECODING and the PRIVATE

I am coming home. Step by step I DECODE the public CODES I agreed on with my new friends.

CODING and the PUBLIC

Ryue Nishizawa, House A, 2007.

ENCODING and the SACRED

COMING BACK HOME

24

30

IV

31

SATIRE, RHETORIC. ICHNOGRAPHIA. BOOK VI.

TUNING I think of the LEAVING HOME, the TALKING IN PUBLIC, the COMING BACK HOME as TEMPERAMENTS. Wherever I am: every landscape, every city, every street, every building, every room, every place … there is a taste of them proportioned: the SACRED, the PUBLIC, and the PRIVATE.

33

Like the tuning of instruments in music: The Pythagorean school distinguished the 2 and the 3 as fundamental principles.

34

The powers of 2 were about the LINE, the EYE, the SAME, the ORTHOGRAPHIA in my metaphors.

V

32

VI

Both principles are INCOMMENSURABLE, and they constitute the RATIONAL world.

36

This is how they become multifaceted …

37

major = (2/3)#&/@ Range@5 minor = (3/2)#&/@ Range@6

38

2 4 8 16 32 { , , , , } 3 9 27 81 243

39

3 9 27 16 243 729 { , , , , , } 2 4 8 81 32 64

40

… and projected to a helix.

41

42

CODING and the PUBLIC

35

ENCODING and the SACRED

The powers of 3 about the CIRCLE, the EARS, the OTHER, the ICHNOGRAPHIA.

The Pythagorean proportions of the EYE, 2n, and the EAR, 3n, in minor, blue, and major, red.

43

 MINOR  with COMING HOME, with DECODING, and SATIRE.

44

The ‘actual music’ with the PUBLIC TALK, with CODING, and COMEDY.

45

DECODING and the PRIVATE

I associate  MAJOR  with LEAVING HOME, with ENCODING, and TRAGEDY.

This is how to project the helix to a unit circle, to make it ONE …

47

maj = NestWhile[#*2&,#,#2&]&/@minor

48

4 16 32 128 256 { , , , , } 3 9 27 81 243

49

3 9 27 81 243 729 { , , , , , } 2 8 16 64 128 512

IV

46

50

51

… and, respectively, project it to a line, used to tune an instrument.

52

V

53

Heinrich Klaffs, Eberhard Weber, 1971.

VI

54

The actual music is played with frequencies of both: MAJOR and MINOR.

55

And I turn the circle to c-minor playing Bach 582, or to D-major playing Vivaldi 589 … to get music of different TEMPERAMENTS.

In architecture we know three classical orders: Doric, Ionic, and Corinthian.

57

58

I associate the DORIC order with major tuning, a ‘leaving home’, ENCODING, TRAGEDY.

60

Yes it is tragic, it is leaving everything behind in favour of these new LINES in SPACE.

61

DECODING and the PRIVATE

59

CODING and the PUBLIC

DORIC – 7th century BC mainland Greece – is of CIRCULAR LINES, GEOMETRY taking SPACE. This order is articulated by CHARACTERS.

ENCODING and the SACRED

CLASSICAL ORDER

56

62

IV IONIC – 6th century BC Asia Minor – is of LINEAR CIRCLES, ARITHMETIC giving TIME. This order is driven by NUMBERS.

64

I associate the IONIC order with minor tuning, DECODING, a ‘coming home’, SATIRE.

V

63

65

66

VI

CORINTHIAN – ~3th century BC Rome – I prefer to read this order as a PROPORTIONAL CONSTITUTION of DORIC and IONIC, as a ‘public talk’, CODING, COMEDY.

And I like to continue with my speculation with these symmetries, to enrich this unconventional perspective.

68

69

70

71

Aldo Rossi, Bonnefantenmuseum, Maastricht, 1995.

DECODING and the PRIVATE

1900+ the PUBLIC learnt to symbolise, to LEAVE HOME, to SCREEN the world. The MAJOR tuning, ENCODING, the sacrifice, the tragedy. DORIC.

CODING and the PUBLIC

Weissenhofsiedlung, Stuttgart, 1929.

ENCODING and the SACRED

The 20th Century

67

72

IV

1960+ the PUBLIC learnt to symbolise COMING BACK HOME, to IMAGINE the world. The MINOR tuning, DECODING, the private, the oikos, the satire. IONIC.

73

Sanaa Architects, Dior Omotesando, Tokyo, 2003.

V 74

Since 2000+ the PUBLIC has been learning to symbolise the PUBLIC TALK, WHAT to SAY towards the cosmos. CODING, the public, the comedy. CORINTHIAN.

VI

ENCODING and the SACRED

BOOKIV

ENCODING and the SACRED CODING and the PUBLIC

75 ↗

The MAJOR Circle of the DAY POINT – INNER ANYWHERE LINE – POEM PICTURE – OUTER EVERYWHERE VISION – NOVEL SUMMARY of the MAJOR CIRCLE

123 ↗ 161 ↗ 191 ↗ 213 ↗ 245 ↗

The MINOR Circle of the NIGHT EVALUATION – INVARIANCE IMAGE – HEALTH TEXTURE – SYNCHRONICITY GRAMMAR – ENVIRONMENT

270 ↗ 295 ↗ 340 ↗ 378 ↗

EPILOGUE ON COLOURS ON IMAGES ON DRAWINGS

408 ↗ 426 ↗ 437 ↗

DECODING and the PRIVATE

PREFACE

IV

V

VI

This book is about the TRAGEDY of leaving all things behind, the temperament of going to the edge of the world. The sacrifice of what PEOPLE know if the PUBLIC is ‘leaving home’.

76

ENCODING and the SACRED

PREFACE

75

77

78

A lot of events, a lot of waves and a horizon, witnessing all of them.

79

The Big Bang at the beginning of time and the entropic horizon of thermal death at the end of time.

80

At this horizon I see nothing, because there is everything: white noise.

81

DECODING and the PRIVATE

Like throwing a stone into the water. Waves are spreading. They witness the past event.

CODING and the PUBLIC

A touch of the water surface spreads to the horizon. The horizon memorises the past looking at future touches.

82

IV

I want to name this movement, the sacrifice towards the entropic horizon, with the technical term: ENCODING.

84

It is not easy to affirm that ENCODING is a sacrifice. Current information techniques want to keep things as they are.

85

The pragmatic didactics of AI: How to ENCODE for example an image, process it with a neural network [CODING] and DECODE it, for example to a known concept.

86

Or Shannon’s scheme for technical COMMUNICATION, 1948: How to pack and protect a message [ENCODE], how to send it exposed to white noise [CODE], and how to receive and repair it [DECODE]. Every effort is made not to change anything.

87

ENCRYPTION tells a different story:

V

83

Take for example this image …

88

eastwood =

;

VI … take a partition of the entropic horizon as a key …

key = RandomInteger[1, {450, 600}];

89

… make an addition of the bits of image and key without a carryover [ENCODE] … crypt = Mod[eastwood + key, 2]

91 92

ENCODING and the SACRED

90

… and as a result the image has vanished, there is nothing to see. 93

The only way to get the image back is to add the key again [DECODE] … Mod[crypt + key,2]

94

^

95

CODING and the PUBLIC

White noise swallows up all data. No way to see anything at the horizon of everything.

… and here he is, Eastwood back on earth.

And of course the nothingness of everything can come back differently with a different key: Mod[crypt + key2,2]

96 97

David Bowie, 1976. Everything can turn into anything via the circular horizon.

DECODING and the PRIVATE

I have to be aware that the key has to be thought not as an image or an object, but as the route towards the horizon: 1 turn left, 0 turn right: if you know the way back, you get the image back.

98

IV Furoshiki wrappings and the celebration of the appearance of things. 99

ENCODING is a projection from the rational PLANE to the irrational CIRCLE or a sphere.

V

A CIRCLE is not an OBJECT, because it is irrational. A CIRCLE is not VISIBLE.

101

CODING takes place on a CIRCLE on an invisible domain. It is about TALKING.

102

DECODING is a projection back from the irrational CIRCLE to the rational and visible PLANE of objects.

103

In mathematics multiplication or the EXPONENTIAL projects from the plane to a circle. – stereographic projection – – encoding – encryption – Division or the LOGARITHM projects from the circle to the plane. – perspective projection – – decoding – decryption –

104

CODING takes place on the irrational domain. This is why everything can turn into anything. This is why ENCODING is a sacrifice, CODING a public talk, and DECODING satirical.

105

A complication which is hardly reflected and very unusual.

VI

100

106

107

ENCODING and the SACRED CODING and the PUBLIC

I remember when I learned to ride a bike. Trying and trying, again and again … and suddenly I got it. I was riding! And I was fast, faster than ever before. I embodied everything needed, whatever it was. My body integrated riding. I changed. I became a rider.

108

DECODING and the PRIVATE

The Caryatid porch of the Erechtheion, ca. 410 BC.

Or the contrapposto : it is safe to think within the body of the  REAL  scalarity – engage leg – and complicated to learn to move within the body of the  COMPLEX  scalarity – balance the free leg.

110

This book explores the MECHANICS of the  COMPLEX  scalarity:

111

The reference is a COMPLEX plane with an IMAGINARY and a REAL axis, indexed with the PAST –R and the FUTURE R and the INSIDE –� and the OUTSIDE �.

IV

109

112

V

PAST

–i

R

INSIDE –R

OUTSIDE

i

FUTURE

This complex plane is read in two circles:

114

The  MAJOR  circle of  CHARACTERS  … inside – past – outside – future – inside … with the chapters point – line – picture – vision.

115

The  MINOR  circle of  NUMBERS  … inside – future – outside – past – inside … with the chapters value – image – texture – grammar.

VI

113

E SE

TE LA

RT A

N

SE

D

A LI

N A

U IC

O

ST ER

ENCODING and the SACRED

D

RA TI

N

GRAMMAR

U

LINE

116

–i

TEXTURE

POINT

–R R

VALUE

PICTURE

N

O RM

A

IMAGE

H

LI

SE

VISION

W

RE A

R

O

EA

SH

H

E IS

i

Do not read the terms as definite CONCEPTS. Better keep them vague, look them up in their etymological vividness and bring them into CONSTELLATIONS to give them mutual stability.

118

The text is a MECHANICS to LIBERATE the PUBLIC VOICE from the RIGIDITY of LANGUAGE. The way a POEM or CODE does.

119

DECODING and the PRIVATE

117

CODING and the PUBLIC

The writing is very schematic and should be read as a circular MECHANICS in these SYMMETRIES.

IV

V

VI

ENCODING and the SACRED

BOOKIV

ENCODING and the SACRED

123 ↗ 161 ↗ 191 ↗ 213 ↗ 245 ↗

DECODING and the PRIVATE

The MAJOR Circle of the DAY POINT – INNER ANYWHERE LINE – POEM PICTURE – OUTER EVERYWHERE VISION – NOVEL SUMMARY of the MAJOR CIRCLE

CODING and the PUBLIC

The MAJOR Circle of the DAY

120

IV Elisabetta Sirani, Beatrice Cenci, 1590s.

V

121

On the REAL AXIS the MAJOR circle ENCODES the INSIDE R as an OMNIPRESENT POINT by CHARACTERS and the OUTSIDE –R as a PRESENT PICTURE by NUMBERS.

122

On the IMAGINARY AXIS the MAJOR circle ENCODES the DAY –� by writing POEMS with CHARACTERS as an IDEA of the PAST towards the FUTURE, and the NIGHT � by reading NOVELS of NUMBERS as a FUTURE VISION of the PAST.

123

POINT – INNER ANYWHERE

VI 124

The PUBLIC ENCODES its PRESENT SELF by LISTENING as a POINT: ALGEBRA MAJOR.

LINE

LA

E SE

RT

I

CU A

–i

–R

POINT

–R

W

PICTURE

O

EA R

VISION

SH

H

i

The AUDITIVE BEING, or : How to CHARACTERISE ANY SET of NUMBERS.

126

“A point is that which has no part.”

127

ENCODING and the SACRED

TE

125

Euclid, Elements, Book I, Def. 1., ca. 300 BC.

The POINT HEARS the FUTURE VISION as HEALTH to be SEEN by the MEMORY of the PAST as ENVIRONMENT.

129

IDEA LIGHT ENERGY

130

The POINT is SPHERICAL to SEE a DIRECTION. The POINT is out of TIME, it is not about the PAST, not about the FUTURE. The POINT takes no SPACE, it is the INVARIANT INSIDE of EVERY OUTSIDE.

131

As a POINT the PUBLIC ENCODES the ASPECT of an OMNIPRESENT LISTENER.

132

DECODING and the PRIVATE

128

CODING and the PUBLIC

The POINT LISTENS and is not yet visual. It is sensual and active.

133

IV ENCODING of POINTS

135

A POINT is ENCODED by SYMBOLIC NAMES.

136

A symbolic name ‘a’ can ENCODE anything:

137

any number

138

a = 3;

139

any text

140

a = “INTRODUCTION. When on board H.M.S. ‘Beagle,’ as naturalist, I was much struck with certain facts in the distribution of the inhabitants of South America, and in the geological relations of the present to the past inhabitants of that continent. These facts seemed to me to throw some light on the origin of species—— that mystery of mysteries, as it has been called by one of our greatest philosophers.”

141

any list

142

a = {1,2,3}

143

any dataset

144

a = { {“George”,“Washington”,1789,False}, {“John”“Adams”,1797,True}, {“Thomas”,“Jefferson”,1801,True} };

V

134

VI

145

a = WeatherData[“Chicago”,“Temperature”]

146

8.30001 °C

147

any time

148

a = Interpreter[“DateTime”][“now”]

149

  Sun 24 Oct 2021 14:15:59GMT+2 

150

any URL

151

a = “https://www.kunstkopie.de/kunst/ parmigianino/Turkish-Slave.jpg”

152

any image

153

ENCODING and the SACRED

any temperature

154

;

any sound a =

;

any geometry

155

156

CODING and the PUBLIC

a =

157

158 a =

;

159

a[x_,y_] = a + b

160

…

DECODING and the PRIVATE

any code

161

162

LINE – POEM

IV

The PUBLIC ENCODES its MEMORY of the PAST by SEEING LINES: GEOMETRY MAJOR.

SE

A

E

RT

I

CU

LA

LINE

TE

163

POINT

W

PICTURE

R

SH

EA

O

H

VISION

The VISUAL MEMORY, or: How to FORGET ANY NUMBER by CHARACTERS.

165

The LINE SEES and is not auditive yet. It is sensual and active.

166

The LINE SEES the INNER ANYWHERE as INVARIANCE to ARTICULATE the OUTER EVERYWHERE in SYNCHRONICITY.

167

MEMORY VELOCITY

168

The LINE is SPHERICAL to INSTALL a PROPORTION. The LINE is out of SPACE, has no INSIDE, no OUTSIDE, but a beginning and an end. A LINE connects the PAST with the FUTURE.

V

164

VI

ENCODING of LINES

170

A LINE is ENCODED as CONNECTIONS, as CATEGORIES, as ALPHABETS.

171

LINES are ENCODED as GRAPHS, with named VERTICES and EDGES not to be confused with GEOMETRIC OBJECTS.

172

{{a, b, c}, {a → b, b → c, c → a}};

173 174

c

a

CODING and the PUBLIC

169

ENCODING and the SACRED

As a LINE the PUBLIC ENCODES the ASPECT of a PERCEPTIVE SCREEN.

b 175

176

DECODING and the PRIVATE

GRAPHS ENCODE MAPS.

GRAPHS ENCODE MECHANICS.

177

178

to the duct

14

4 13 15

10

8 16

12

11

IV

D 1

9 5

3

6

2 7

179

LINES are not about OBJECTS they are about MOVEMENTS, or VELOCITIES.

180

V 181

182

LINES ENCODE COMMUNITIES in NETWORKS as GRAPHS.

VI

183

184 rain

sun

cloud

LINES ENCODE LAYOUTS of floorplans as GRAPHS.

185

ex

v₅

v₄

v₂

v₃

v₄

v₃

v₂

v₁

v₆

v₁

v₇

v₇

v₆ v₅

lamedh [l]

beth [b]

mem [m]

gimmel [g]

nun [n]

daleth [d]

samekh [s]

he [h]

‘ayin [‘]

waw [w]

pe [p]

zayin [z]

tsade [s] .

heth [h] .

qoph [q]

teth [t] .

reš [r]

yodh [y]

šin [r]

kaph [k]

taw [t]

188

DECODING and the PRIVATE

’aleph [’]

187

CODING and the PUBLIC

186

The VERTICES of LINES crystallise to a compact SET of CHARACTERS, an ALPHABET, to be able to TALK to the FUTURE. These can be read as vertices of a GRAPH.

ENCODING and the SACRED

LINES ENCODE PROBABILITIES of EVENTS as GRAPHS with weighted edges.

IV

189

The WRITING of LINES follows the MECHANICAL schemes of POETICS. These can be ENCODED like a MECHANICS as GRAPHS.

190

“Painting is silent poetry and poetry is painting that speaks.” Plutarch, The Glory of the Athenians 3.1, 346f–347a.

191

192

PICTURE – OUTER EVERYWHERE

V

The PUBLIC ENCODES its PRESENT BODY by ARTICULATING PICTURES: LOGOS MAJOR.

SE

A

E

RT

I

CU

LA

LINE

TE

193

POINT

W

PICTURE

R

SH

EA

O

H

VISION

The AUDITIVE PRESENCE, or: How to PROPORTION EVERY LIST of CHARACTERS by NUMBERS.

195

The PICTURE is ARTICULATED and is not yet visual. It is actual and passive.

VI

194

197

A PICTURE is DIRECTIONAL to SHOW a WAY. The PICTURE is out of TIME, it is not about the PAST, not about the FUTURE. The PICTURE takes SPACE, it is the OMNIPRESENT OUTSIDE of ANY INSIDE.

198

As a PICTURE the PUBLIC ENCODES the ASPECT of an ARTICULATED BODY.

199

ENCODING OF PICTURES

200

PICTURES are ENCODED as GRAPHICS, with named VERTICES, EDGES, and COORDINATES.

201

{{a, b, c}, {a → b, b → c, c → a}, {{0, 0}, {1, 2 }, {2, 0}}};

202

203

DECODING and the PRIVATE

FIELD GRAVITY POTENTIAL

CODING and the PUBLIC

196

ENCODING and the SACRED

The PICTURE is ARTICULATED by the MEMORY of the PAST as ENVIRONMENT, to SHOW the FUTURE VISION in HEALTH.

204

IV

Dodecahedron.

205

PICTURES ENCODE models of chemical molecules.

206

C11H18OS.

207

V

PICTURES ENCODE architectural models.

208

Andrea Palladio, La Rotonda, 1567–1571.

VI

209

210

ENCODING and the SACRED

PICTURES ENCODE city models.

Map of London.

211

CODING and the PUBLIC

PICTURES are not visible. They are a voice, talking, proportioning SPACE. A technical metaphor, they are wireframe models, with infinitely thin edges. PICTURES are encoded as a sequences of CHARACTERS, as TEXT or CODE spoken out loud, to take SPACE by PROPORTIONS of NUMBERS.

212

DECODING and the PRIVATE

Dante Alighieri, Divine Comedy, 1321. Banco Rari 215, p19.

213

214

VISION – NOVEL

IV

The PUBLIC ENCODES the COURSE of the FUTURE by SHOWING GRIDS: ARITHMETIC MAJOR.

SE

A

E

RT

I

CU

LA

LINE

TE

215

POINT

W

PICTURE

R

SH

EA

O

H

VISION

The VISUAL ANALYSIS, or: How to INCLUDE EVERY CHARACTER by NUMBERS.

217

The VISION is SHOWN and is not auditive yet. It is actual and passive.

218

The VISION is SHOWN by the OUTER EVERYWHERE as SYNCHRONICITY to be HEARD by the INNER ANYWHERE in INVARIANCE.

219

WEIGHT MATERIAL

V

216

VI

As a VISION the PUBLIC ENCODES the ASPECT of a PRODUCTIVE SCHEME.

221

ENCODING of VISIONS

222

VISIONS are ENCODED as RENDERINGS, VISUALISING for example GRAPHICS, known as GIF compression.

223

224

CODING and the PUBLIC

220

ENCODING and the SACRED

The VISION is DIRECTIONAL to HEAR the HARMONY. There is no inside and no outside. The VISION is out of SPACE, has no INSIDE, no OUTSIDE, but an end and a beginning. The VISION connects the FUTURE with the PAST.

225

DECODING and the PRIVATE

VISIONS are encoded as ARRAYS of NUMBERS without NAMES.

226

227

IV 228

1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.85 0.79

1.00 1.00 1.00 1.00 1.00 1.00 0.60 0.04 0.64

1.00 1.00 1.00 1.00 0.92 0.31 0.00 0.00 0.64

1.00 1.00 1.00 0.72 0.09 0.00 0.00 0.00 0.64

1.00 0.97 0.43 0.00 0.00 0.00 0.00 0.00 0.64

0.82 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.64

0.82 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.64

1.00 0.97 0.43 0.00 0.00 0.00 0.00 0.00 0.64

1.00 1.00 1.00 0.72 0.09 0.00 0.00 0.00 0.64

1.00 1.00 1.00 1.00 0.92 0.31 0.00 0.00 0.64

1.00 1.00 1.00 1.00 1.00 1.00 0.60 0.04 0.64

VISIONS of NUMBERS are perpetual schemes, MACHINES to PRODUCE the IMAGINATION of graphics, for example.

229

V

230

231

VISIONS of NUMBERS ENCODE architecture parametric models as MACHINES to PRODUCE the IMAGINATION of FORCES.

232

VI Foster + Partners, Great Court at the British Museum, 2000.

1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.85 0.79

233

234

235

236

237

Frequencies can be added …

CODING and the PUBLIC

VISIONS of NUMBERS ENCODE FREQUENCIES to PRODUCE the IMAGINATION of an IMAGE (JPEG compression).

ENCODING and the SACRED

VISIONS of NUMBERS ENCODE SYSTEMS of LINEAR EQUATIONS and anchor it to GRAVITY (PAST) to render it along its flow of forces from the perspective of LIGHT (FUTURE).

238

DECODING and the PRIVATE

… to IMAGINE visual differences …

239

IV

… in colours …

240

… and different resolutions.

241

242

VISIONS of NUMBERS ENCODE connected movements according to specific boundary conditions: SIMULATION and Finite Element Method (FEM).

V VI

243

244

ENCODING and the SACRED

VISIONS of NUMBERS ENCODE the growth of species of a specific kind along STOCHASTIC PARAMETERS.

…

246

The VISUAL axis: the LINE and the GRID: The LINE is PROJECTIVE, in the DAY towards the SUN, the GRID is REFLECTIVE, at NIGHT under the SKY.

247

DECODING and the PRIVATE

A short meditation on the symmetries of the mechanics presented:

CODING and the PUBLIC

SUMMARY of the MAJOR CIRCLE

245

The LINE as a CONSTITUTION of a MECHANICS, the GRID as an CONSTRUCTION of a MACHINE.

249

The LINE can be seen as MOVEMENT in the AIR, the GRID as REPETITION on EARTH.

250

And I, the PUBLIC, remember: my EYE is able to see colours only, which are frequencies, changes in time, and NOT elements in space.

251

A LINE SEES a MOVEMENT LIBERATED from the GROUND, a GRID MAPS what is DONE, EMANCIPATED from DIFFERENCES.

IV

248

252

V

The VISUAL is LINEAR and directive, the AUDITIVE is CIRCULAR and omnidirective. 253

The AUDITIVE axis: the POINT and the PICTURE: The POINT is LISTENING to all DIRECTIONS, the PICTURE is ARTICULATING in all DIRECTIONS. The POINT hears the OMNIPRESENCE of all the things around, the PICTURE articulates the PRESENCE of the things around.

255

Out of time nothing to SEE … The POINT is OMNIPRESENT, the PICTURE is of PRESENCE.

256

A PICTURE is a sculptural body which can be IMAGINED by GRIDS. A POINT is an inner self, which can be SEEN by LINES.

VI

254

…

ENCODING and the SACRED

BOOKIV

ENCODING and the SACRED

270 ↗ 295 ↗ 340 ↗ 378 ↗

DECODING and the PRIVATE

The MINOR Circle of the NIGHT EVALUATION – INVARIANCE IMAGE – HEALTH TEXTURE – SYNCHRONICITY GRAMMAR – ENVIRONMENT

CODING and the PUBLIC

The MINOR Circle of the NIGHT

The  MAJOR  circle is about the AIR and growing into LIGHT. The complementary  MINOR  circle REALISES things on EARTH.

258

Like a  POINT  on a SCREEN and the actual  COLOUR . Or a wireframe  MODEL  and its  TEXTURE . Or a  GRAMMAR  and a  VOCABULARY . …

259

Vivid things are of both circles: they  SHOW  and  TELL  they  SEE  and  HEAR .

260

The  MAJOR  circle is about a RENAISSANCE and a LIBERATION towards the RATIO and AIR,

261

The  MINOR  circle is about a REVOLUTION and an EMANCIPATION in REALITY and EARTH.

IV

257

V 262

VI

John Opie, Mary Wollstonecraft, 1797.

264

–R The  EVALUATION  rationalises (visual passive, encoded by numbers) to the sound of the  POINT  (auditive passive, encoded by characters).

265

� The  IMAGE  harmonises (auditive passive, encoded by numbers) the routines of the  VISION  (visual active, encoded by numbers).

266

R The  TEXTURE  realises (visual active, encoded by characters) the articulation of the  PICTURE  (auditive active, encoded by numbers).

267

–� The  GRAMMAR  understands (auditive active, encoded by characters) what is seen by the  LINES  (visual passive, encoded by characters).

268

In a PUBLIC TALK the bodies of thinking rotate these circles, they become vivid, ACTIVE SUBJECTS in rotation.

269

DECODING and the PRIVATE

On the IMAGINARY AXIS the  MINOR  circle ENCODES the PAST –� as ENVIRONMENTAL TEMPERAMENTS of CHARACTERS and the FUTURE � as HEALTHY QUANTITIES of NUMBERS.

CODING and the PUBLIC

263

ENCODING and the SACRED

On the REAL AXIS the  MINOR  circle ENCODES the INSIDE –R as an INVARIANT EVALUATION of CHARACTERS and the OUTSIDE R as SYNCHRONISED TEXTURES of NUMBERS.

The PUBLIC ENCODES its PRESENT INVARIANCE by the RATIO of a VALUE: GEOMETRY MINOR.

N

N

SE

A

LI

ST

A

ER

O

D

TI

N

RA

U

GRAMMAR

272

D

–i

R

TEXTURE –R

IS N

SE

RM

IMAGE

O

LI A RE

E

VALUE i

A

IV

271

  EVALUATION –  INVARIANCE

H

270

V VI

273

The VISUAL INVARIANCE, or: How to EVALUATE ANY LIST of CHARACTERS.

274

The EVALUATION is SEEN | RATIONALISED and not auditive yet. It is passive and sensory.

275

The VALUE RATIONALISES the ENVIRONMENT as the MEMORY of the PAST to be HARMONISED by the HEALTH as FUTURE VISION.

276

ATOM

277

The VALUE is SPHERICAL to GIVE BALANCE. The VALUE is out of TIME, it is not about the PAST, not about the FUTURE.

As a VALUE the PUBLIC ENCODES the ASPECT of a PRESENT SENSE.

279

ENCODING of VALUES

280

A VALUE is ENCODED by NUMBERS SIGNIFYING CHARACTERISTICS.

281

NUMBERS work with an ordered list of CIPHERS.

282

{0,1,2,3,4,5,6,7,8,9}

283

These CIPHERS are BRANCHING for higher RESOLUTION.

284

1/10,12/100,112/1000 …

285

CODING and the PUBLIC

278

ENCODING and the SACRED

The VALUE takes no SPACE, it is the VARIANT INSIDE of EVERY OUTSIDE.

286

And they are able to do that on the COMPLEX PLANE of TIME and SPACE.

287

DECODING and the PRIVATE

Branching on a RATIONAL plane.

288

IV Branching on a COMPLEX scale.

289

SENSORS and Analogue-to-Digital Converters (ADCs) ENCODE any QUALITY all over the world.

290

A sensor on any physical property …

291 K₁

= &

Ue

C

K₂

Q₀ Q₁ Qn

counter

V

Ur sawtooth generator

square wave generator

292

… ENCODED from analogue to digital …

293

{0.788235, 0.752941, 0.717647}

VI

… presents its values from everywhere to anywhere. 294

NUMBERS ENCODE the TEMPERAMENT of the WORLD towards the INVARIANCE of EVALUATION.

The PUBLIC ENCODES the HEALTH of THINGS by a HARMONIC IMAGE: ALGEBRA MINOR.

297

N

N

SE

A

LI

ST

A

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O

D

TI

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GRAMMAR

U D

–i

R

TEXTURE –R

IS N

SE

RM A H

IMAGE

O

LI A

E

VALUE i

The AUDITIVE HARMONY, or: How to FORGET ANY CHARACTER by NUMBERS.

298

A picture is worth a thousand words.

299

The IMAGE HARMONISES the INVARIANCE of the INNER ANYWHERE to be REALISED by the SYNCHRONICITY of the OUTER EVERYWHERE.

300

DECODING and the PRIVATE

The IMAGE is HEARD | HARMONISED and not visual yet. It is passive and sensory.

CODING and the PUBLIC

RE

296

ENCODING and the SACRED

IMAGE – HEALTH

295

MATTER

302

The IMAGE is DIRECTIONAL to SHOW REALITY. There is no inside and no outside. The IMAGE is out of SPACE, has no INSIDE, no OUTSIDE, but a beginning and an end. The IMAGE connects the PAST with the FUTURE.

303

As an IMAGE the PUBLIC ENCODES the ASPECT of a LEARNING ORGANISM.

304

ENCODING of IMAGES

305

The IMAGE is ENCODED as LISTS of NUMBERS.

306

LISTS of NUMBERS ENCODE SOUNDS in TIME.

307

{…, 0.207104, 0.24021, 0.271317, 0.25902, 0.247392, 0.233065, 0.222868, 0.213599, 0.225833, 0.235563, 0.231672, 0.264051, 0.24108, …}

IV

301

V

308

0.5 –0.5 0

309

310

VI 311

1

2

3

4

5

6

7

LISTS of LISTS of NUMBERS ENCODE IMAGES on a computer screen. {1 →

, 2 →

, 3 →

, 4 →

}

312

313

LISTS of NUMBERS ENCODE SIGNIFICATIONS to CLASSES, DEFINITIONS, or CONCEPTS as ‘COLOURS’. → → → →

“Window” “Door” “Wall” “Cat” …

315

316

CODING and the PUBLIC

1 2 3 4

314

ENCODING and the SACRED

ARRAYS of NUMBERS ENCODE sensor values from somewhere in the world.

YOLO multi-object detection and classification, 2019.

317

DECODING and the PRIVATE

London terror attack 07/07/05.

318

These CONCEPTS as SIGNIFYING NUMBERS can be sorted …

319

Sort[{“A”, “C”, “B”}]

320

{A, B, C}

IV

321

322

… gathered …

323

Gather[{a,b,c,a, c,b,b}]

324

{{a,a},{b,b,b},{c,c}}

325

V Elements of architecture curated by Rem Koolhaas at Venice Biennale, 2014. 326

… or counted.

327

Counts[{a,b,c,a,c,b,b}]

328

329

ARRAYS of NUMBERS, or IMAGES ENCODE datasets or records.

VI

age

sex

survived

1st

29

female

True

1st

1

male

True

1st

2

female

False

1st

30

male

False

1st

25

female

False

48

male

True

1st

330

row 1–6 of 1309

331

On the RATIONAL scale the ORDER of THINGS is shown by physical PARTS.

332

333

CODING and the PUBLIC

IMAGES, like DATASETS, are about CLASSIFICATION i.e. REPETITION in TIME. They orchestrate the ORDER of THINGS around PREDICTABILITY and HEALTH.

ENCODING and the SACRED

class

Mosaic floor, Pompeii, 79.

334

DECODING and the PRIVATE

On the  REAL  scale the ORDER of THINGS is shown by physical PROPERTIES.

335

IV Filippo Brunelleschi, Cathedral of Santa Maria del Fiore, Florence, 1436.

336

On the  COMPLEX  scale the ORDER of THINGS is shown by VALUES changing physical properties.

337

V realities:united, SPOTS, Potsdamer Platz, Berlin, 2005.

338

339

ARRAYS of NUMBERS ENCODE CNNs (Convolutional Neural Networks). They RECORD the PAST, to ESTABLISH an ORDER of THINGS in TIME, for example for RECOGNITION. 8@128x128

24@48x48

24@16x16

8@64x64

Max-Pool

1x256 1x128

Convultion

Max-Pool

Dense

Dense

VI

The PUBLIC ENCODES the PRESENT SYNCHRONICITY by REALISING a TEXTURE: ARITHMETIC MINOR.

N

N D

R

TEXTURE

IS N

SE

RM A H

IMAGE

O

LI A

E

VALUE i

343

The TEXTURE SHOWS | REALISES and is not auditive yet. It is active and actual.

344

It is REALISED by HEALTH in a FUTURE VISION to UNDERSTAND the ENVIRONMENT as a MEMORY of the PAST.

345

GRAVITY AXIOM

346

DECODING and the PRIVATE

The VISUAL SYNCHRONICITY, or: How to PROPORTION EVERY SET of NUMBERS by CHARACTERS.

CODING and the PUBLIC

–R

RE

342

SE

A

LI

ST

A

ER

O

D

TI

N

RA

GRAMMAR

U –i

341

ENCODING and the SACRED

TEXTURE –  SYNCHRONICITY

340

A TEXTURE is DIRECTIONAL to CONSTITUTE a CONTRACT. The TEXTURE is out of TIME, it is not about the PAST, not about the FUTURE. The TEXTURE takes SPACE, it is the PRESENT OUTSIDE of ANY INSIDE.

348

As a TEXTURE the PUBLIC ENCODES the ASPECT of a GRAVITATIONAL BODY.

349

ENCODING of TEXTURES

350

VALUES ENCODE the omnipresent sensory world. TEXTURES ENCODE the synchronised actuated bodies.

351

VALUES ENCODE e.g. with analogue-digital-converters, TEXTURES ENCODE e.g. with digital-analogue-converters.

352

TEXTURES are ENCODED by a NOTATION of sorted discrete  INTEGER  entities in TIME.

IV

347

V 353

VI Sherbrooke Missal, ca. 1310 – ca. 1320.

They are converted e.g. by the fingerboard of a guitar on the  RATIONAL  scalarity.

354

ENCODING and the SACRED

355

Ron Akiyama, Jimmy Page, 1975.

356

On the  COMPLEX  scalarity I can find sequences of  REAL  numbers as samples of any sound.

357

{…, 0.207104, 0.24021, 0.271317, 0.25902, 0.247392, 0.233065, 0.222868, 0.213599, 0.225833, 0.235563, 0.231672, 0.264051, 0.24108, …}

358

1.5μH

22μF 6.3V

10pF 10nF 97.6kΩ

ADP1613

VDD

D

SI4346DYT1-E3

359

110nH 1μF 50V

2.2μF 50V

COMP

SS

8

FB

FREQ

7

3

EN

VIN

6

4

GND

SW

5

1

1μF

2

S

G

16

3 4 5 6

R_SEL CLR SYNC SCLK SDI SDO LDAC DGND 7

VOUTA

12

0V TO 30V

VOUTB

11

0V TO 30V

VOUTC

10

0V TO 30V

VOUTD AGND

9

0V TO 30V

8

AD5504

Sequences of real numbers need a digital-analouge converter to be rendered to reality.

TEXTURES ENCODE ACTUATORS to CHARACTERISE SPACE on the COMPLEX SCALARITY.

360

DECODING and the PRIVATE

TO MICROCONTROLLER

0.1μF 50V

14

VLOGIC VDD

VDD 13

10nF

VDD

0.1μF 50V

1 2

140kΩ 5.62kΩ

1N5819HW-7-F

10Ω

09608-001

VDD

CODING and the PUBLIC

On the  REAL  scalarity these have been notated with  RATIONAL  numbers to constitute a polyphone well tempered tuning.

361

The LIST of NUMBERS is SHOWN e.g. by the movements of the membrane of a SPEAKER,

362

IV RCA, first commercial moving-coil cone loudspeaker, 1926.

363

or the coloured light emitted by the movements of ELECTRONS.

364

V 365

366

These ACTUATORS – sound, light, temperature, moisture … – project frequencies or colours, synchronised in all directions and changing over time.

VI

367

368

369

370

371

372

Blender 2.80 animation, 2020.

DECODING and the PRIVATE

On the  COMPLEX  SCALARITY TEXTURES ENCODE or REALISE the SYNCHRONICITY by ordered things of movement of VALUES for example on computer screens.

CODING and the PUBLIC

TEXTURES ENCODE the REALISATION of any FORM.

ENCODING and the SACRED

I SEE these synchronised colours in space as TEXTURES. They spread in space to be SEEN with the EYES of the FUTURE.

373

IV Microsoft Windows 10 OS start screen, 2015.

374

TEXTURES project SORTED THINGS of TIME to a PRESENT EXISTENCE in urban SPACE on the  COMPLEX  SCALARITY.

375

V Tokyo subway station.

376

TEXTURES project SORTED THINGS of TIME to a PRESENT EXISTENCE in SPACE onto, for example, frescoes on the  REAL  SCALARITY.

377

VI Andrea Palladio, Villa Rotonda: frescoes from the 1590s correspond little to Palladio’s intentions.

The PUBLIC ENCODES its ENVIRONMENTAL CONDITION by UNDERSTANDING its GRAMMAR: LOGOS MINOR.

380

N

N

SE

A

LI

ST

A

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O

D

TI

N

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GRAMMAR

U D

–i

R

TEXTURE

IS N

SE

RM A H

IMAGE

O

LI A

E

VALUE i

381

The GRAMMAR ARTICULATES | UNDERSTANDS and is not yet visual. It is active and actual.

382

The GRAMMAR is UNDERSTOOD by the SYNCHRONICITY of the OUTER EVERYWHERE to be RATIONALISED by the INVARIANCE as the INNER ANYWHERE.

383

DECODING and the PRIVATE

The AUDITIVE ENVIRONMENT, or: How to INCLUDE EVERY NUMBER by CHARACTERS.

CODING and the PUBLIC

–R

RE

379

ENCODING and the SACRED

  GRAMMAR –  ENVIRONMENT

378

MASS

385

The GRAMMAR is SPHERICAL to EVALUATE the RATIONAL. The GRAMMAR is out of SPACE, has no INSIDE, no OUTSIDE, but a beginning and an end. A GRAMMAR connects the FUTURE with the PAST.

386

As a GRAMMAR the PUBLIC ENCODES the ASPECT of a TRAINING CONSTITUTION.

387

ENCODING of GRAMMARS

388

A GRAMMAR is ENCODED as RULES of SYMBOLIC CHARACTERS

IV

384

V 389

a :→ b a is followed by b

390

This is what the PUBLIC understood from all the characteristics of the past.

391

GRAMMARS ENCODE the UNDERSTANDING of the unfolding of a spatial layout in 2D or 3D.

392

Initial shape:

H

Rule 0

B

B H

VI

F H Rule 1

F

R B

B

X R

X

H R

R

X = F or B

S’

Rule 12

393

S

B G

Rule 13

F’

G F

G G X’

X

X = F or S

Ulrich Flemming, the grammar of Queen Anne houses, 1987.

An  ENCYCLOPAEDIA  ENCODES a ‘general course of instruction’ as a GRAMMAR and is of CHARACTERS.

394

ENCODING and the SACRED

Rule 17 B’

395

CODING and the PUBLIC

Diderot and d’Alembert, Encyclopédie, title page, 1772.

396

Correspondingly a  GRAMMAR  is of SYMBOLS and CATEGORIES. An  IMAGE  of SIGNIFICATIONS, SETS, and CLASSIFICATIONS.

397

A GRAMMAR ENCODES the classical order as an UNDERSTANDING of the PAST to RATIONALISE an INVARIANCE and not as an IMAGE of a PRODUCTION.

398

DECODING and the PRIVATE

In contrast to a  DICTIONARY  – a ‘collection of words and phrases’ – which would be an IMAGE and be of NUMBERS.

399

IV Ephraim Chambers Cyclopædia, The Five Orders of Architecture, 1728. 400

With today’s Artificial Intelligence Recurrent Neural Networks (RNN) UNDERSTAND the PAST and establish a GRAMMAR to RATIONALISE the INVARIANCE e.g. of a TRANSLATION of two languages or a spoken to a written language, speech to text. The PUBLIC encodes TRANSLATION as RNNs.

V 401

O W V

Ot₁

Unfold …

h U X

Ot

W V

ht₁ U Xt₁

Ot+₁

W V

ht U Xt

W V

ht+₁ U Xt+₁

Scheme of a recurrent neural network, 2022.

V

…

VI

ENCODING and the SACRED

BOOKIV

ENCODING and the SACRED CODING and the PUBLIC

EPILOGUE

408 ↗ 426 ↗ 437 ↗

DECODING and the PRIVATE

EPILOGUE ON COLOURS ON IMAGES ON DRAWINGS

This book is about the SACRIFICE of the REALITY at home.

403

 ENCODING  is about the  MAJOR  circle of  CHARACTERS  and the  MINOR  circle of  NUMBERS .

404

ENCODING itself is symbolised by CHARACTERS and at the same time symbolises all ENCODING.

405

Because of this self reference I cannot think of ENCODING as a  MACHINE  processing  OBJECTS .

406

I sacrifice my thinking in specification, in problems, in objects … There is the WORLD, there are the temperaments, there is ENCODING, there is me … and I tune into a body of thinking of a different scale.

407

Hence the metaphor of learning to ride a bike, as an embodiment of bike riding.

IV

402

V VI

There is for example the physical colour spectrum of Newton by a prism in sunlight in  MAJOR  tuning in the DAY.

409

410

And there is the physiological colour scheme of Goethe by a slit in a dark room in  MINOR  tuning at NIGHT.

411

412

Both are on the  REAL  scale. On this scale colour is either physical OR physiological. One needs to decide.

413

DECODING and the PRIVATE

Colour spectrum of a camera obscura.

CODING and the PUBLIC

Colour spectrum of a prism.

ENCODING and the SACRED

ON COLOURS

408

On the  COMPLEX  scale the PUBLIC does not need to decide. ENCODING or SYMBOLISATION works perfectly the same either way.

415

With Newton I ENCODE the physics of colours {red, green, blue} with three numbers

416

RGBColor[{1,0,0}]

IV

414

417

418

With Goethe I ENCODE the physiology of colours {hue, saturation, brightness} also with tree numbers.

419

Hue[{1,1,1}]

420

421

V

There is no difference on the symbolic level. The distinction between physical and physiological, projective and reflective, energy and matter, particle and wave, between the inner and the outer circle, sacrificed, symbolised, memorised in numbers.

VI

422

ENCODING and the SACRED

I just give them a name and they are gone, I can talk about them by their names. I can operate on them by their numbers. They by themselves are gone, out of reality, sacrificed … but … they come back on a new scale in details and brightness I have never seen before.

The RGB and HUE colour space in a physical rendering. 424

CODING and the PUBLIC

423

The colour space in a physiological rendering. 425

DECODING and the PRIVATE

But that’s about DECODING and COMING HOME. This book is about LEAVING HOME and getting exposed to the COSMOS at the edges of the world.

426

ON IMAGES Finally some exercises in seeing IMAGES with changing EYES:

428

1 This is an ENCODING of a physiological IMAGE on the REAL scale covering a PICTURE towards VISION.

IV

427

429

430

V Johann Heinrich Wilhelm Tischbein, Goethe in the Campagna, 1787.

431

VI

432

2 An ENCODING of a physiological IMAGE on the REAL scale covering a VISION towards an omnipresent POINT.

433

3 An ENCODING of a physical PICTURE on the COMPLEX plane covering the invariance of VALUES towards the LINES of MEMORY.

434

436

CODING and the PUBLIC

435

ENCODING and the SACRED

Claude Monet, Coquelicots, 1873.

Natural landscape, 2020.

DECODING and the PRIVATE

437

ON DRAWINGS Or: more about getting an EYE on seeing the DRAWINGS changing:

439

The RATIONAL CONSTITUTION GRAMMAR | LINE on the  REAL  scalarity, a MEMORY of the PAST to TALK towards the FUTURE.

IV

438

440

441

V Giambattista Nolli, plans of Rome, 1748.

442

443

A CONSTRUCTION in REALITY VISION | IMAGE on the  REAL  scalarity, a VISION of the FUTURE anchored in the PAST.

VI

444

Or again a RATIONAL CONSTITUTION GRAMMAR | LINE on the  COMPLEX  scalarity, a MEMORY of the PAST to TALK towards the FUTURE.

445

ENCODING and the SACRED

Camillo Sitte, The Art of Building Cities, 1889. As inversion to Nolli.

446

CODING and the PUBLIC

447

Leon Krier, ca. 1980. With a larger scalarity than Nolli and in inversion to Sitte.

… DECODING and the PRIVATE

IV

V

VI

CODING and the PUBLIC

BOOKV

ENCODING and the SACRED CODING and the PUBLIC

EPILOGUE – SCAENOGRAPHIA

448 ↗ 513 ↗ 526 ↗ 532 ↗ 539 ↗ 547 ↗ 592 ↗ 638 ↗

DECODING and the PRIVATE

PREFACE CODE MECHANICS and MACHINES ARCHITECTURE and ENGINEERING PROCESSORS 1900+ The technical LANGUAGES of 1930+ The technical LANGUAGES of 1960+ The technical LANGUAGES of 1980+ The technical LANGUAGES of 2000+

IV

V

VI

449

Jacques Callot, Les grandes misères de la guerre 17 – La revanche des paysans, 1633.

ENCODING and the SACRED

PREFACE

448

450

451

DECODING and the PRIVATE

It is a mess back there in 1648. War at home. 30% killed. Everybody exhausted. I, the PUBLIC, leave this home, keeping it in my MEMORY. I join the others at court, this abstract place off reality. And I start to talk, to negotiate. In CODED forms, detached.  RATIONAL  not to have  REAL  fights at home.

CODING and the PUBLIC

Peter Greenaway, The Draughtsman’s Contract, 1982.

At the EDGE OF THE WORLD I SACRIFICED everything.

453

I look back and MEMORISE all FORMS and I KNOW all  STRUCTURES .  SPACE  and  TIME .

454

I symbolise  FORMS  – GEOMETRY  MAJOR  – and reason about  STRUCTURES  – LOGOS  MINOR  –

455

I prepare a stage for a  LIBERATED  talk to represent my interest as a symbolic  MEMORIAL .

456

This is how I understand for example the Baroque court: this is not for pleasure but an existential challenge.

457

Today PEOPLE say: this was a decadently luxurious elite at the 17th century court. I doubt it was fun.

458

Liberté, égalité, fraternité and the  EMANCIPATED  bourgeoisie Yes, it was only them, but nevertheless.

IV

452

V 459

VI Ferdinand Urbahns, upper class salon, 1895.

460

461

ENCODING and the SACRED

The  LIBERATION  of the white middle class by the symbolisation of all FORMS. And again: it was only them.

Ray K. Metzker, Berlin, the 1920s.

462

463

CODING and the PUBLIC

The  EMANCIPATION  of the global middle class by the symbolisation of all STRUCTURES, to support PEOPLE as equals.

Michael Ochs, Berlin, 1980s.

464

the world wars, the cold war, the end of history, the clash of cultures, the migrants, income inequality, the limit of growth, the climate crisis …

465

DECODING and the PRIVATE

A lot of changes in PUBLIC, still a lot of trouble at HOME:

Yes,  PEOPLE  should complain about their condition.

467

Yet the  PUBLIC  cannot. Because, whatever it is, it is in charge.

468

It takes a lot of effort for the PUBLIC to  LIBERATE  from its PEOPLE.

469

Today’s struggles are analogous to the temperament of the 19th century called  THERMODYNAMICS , in physical terms.

470

With all good intentions PEOPLE at home learn, work, and perform. They continuously try to do better.

471

But there is no improvement without focus and exclusion. What is good at home is very often bad for the others.

472

Necessarily so. On a global scale nobody can improve by doing better.

473

The PUBLIC affirms this paradox as a  QUANTUM MECHANICAL  condition. It does not decide at home, it negotiates with the others.

474

At HOME  ECONOMY  shows HOW to DO things to be GOOD.

IV

466

V VI

476

STRUCTURES emancipate from FORMS, FORMS liberate from STRUCTURES. As the CIVIL emancipates from the COMMON, the COMMON liberates from the CIVIL. As URBANISATION emancipates from the CITY, the CITY liberates from URBANISATION. As NUMBERS emancipate from CHARACTERS, CHARACTERS liberate from NUMBERS. As PROGRAMS emancipate from CODE, CODE liberates from PROGRAMS. …

477

Coming back HOME. I remember these words that made strong contracts. They show up in surprising propositions:

478

URBANISATION is about ECONOMY, NUMBERS and CONTROL. The CITY is of POLITICS.

479

EMANCIPATION frees from genealogical control, to explicate every control of spatial bounds.

480

LIBERATION frees from physical bounds to explicate any boundaries in the flow of time.

481

DECODING and the PRIVATE

At court in PUBLIC I listen to the play of these words: All these circulations, not to be wrong, embracing anything, deciding nothing:

CODING and the PUBLIC

475

ENCODING and the SACRED

In PUBLIC  POLITICS  asks WHAT to SAY not to be WRONG.

EMANCIPATION criticises the PURE RATIO and prioritises the VISUAL REALITY of IMAGES and CONTROL.

483

CHARACTERS play in the AUDITIVE realm. Their RATIO LIBERATES from the ‘mess’ of REALITY.

484

Today things at HOME have become super VISUAL, super controlled, and super powerful.

485

At first glance this is GOOD for the PEOPLE at home, but it gets increasingly toxic for the PUBLIC out there.

486

The VISUAL does not negotiate. Today the VISUAL conquers. In PUBLIC it is an impatient WAR MACHINE driven by NUMBERS and NECESSITIES.

487

Today’s ADMINISTRATIONS take CARE. They are GOOD to their PEOPLE. But their decisions follow NECESSITIES, they do not take RESPONSIBILITY.

488

They are GOOD, but not RIGHT. An excess of ECONOMY and a lack of POLITICS. Things run out of PROPORTION.

489

A PUBLIC LIBERATES from the overwhelming access of necessities implemented as URBANISM.

490

A PUBLIC talks about the CITY and negotiates in new CODES.

IV

482

V VI

CODING and the PUBLIC

BOOKV

ENCODING and the SACRED CODING and the PUBLIC

CODE

513 ↗ 526 ↗ 532 ↗ 539 ↗ 547 ↗ 592 ↗ 638 ↗

DECODING and the PRIVATE

MECHANICS and MACHINES ARCHITECTURE and ENGINEERING PROCESSORS 1900+ The technical LANGUAGES of 1930+ The technical LANGUAGES of 1960+ The technical LANGUAGES of 1980+ The technical LANGUAGES of 2000+

491

IV Dirck van Delen, Dirck Hals, An Interior with Ladies and Cavalier, 1629.

V

492

I remember ARCHITECTURE as the ART of JOINING elements, of what things of all TIMES and habits can agree on in SPACE. ARCHITECTURE as a PUBLIC CONSTITUTION.

493

Renaissance architecture constituted the  REAL  scalarity of space, the COLOUR of LIGHT, or the PROPERTIES of THINGS.

494

Today I, the PUBLIC, am looking for a constitution of the  COMPLEX  scalarity of space, the IMAGINARY LIGHT or the changing properties, the vividness, the VALUES of THINGS.

495

This is what I can find:

496

CRISTALLOGRAPHY is the 20th century SCIENCE of JOINING elements.

497

001 101

VI

111

1 111

100 110

100

101

110

001

010

111

Spherical projection of normals to crystal faces.

498

499

ENCODING and the SACRED

A powder X-ray diffractometer in motion.

Comparison of observed and calculated diffraction patterns. 500

501

–l

k

×i –i

×j –j

l j

–k

i

×k Complex quaternion to rotate objects in 3D space in CAD systems. 502

DECODING and the PRIVATE

In the architecture of the REAL scalarity I have ELEMENTS like stones, clay, wood, fabrics, iron, glass …

CODING and the PUBLIC

COMPUTING is the 20th century TECHNIQUE of JOINING elements.

503

IV Semper orchestrates the construction of a building along the concepts of textiles, ceramics, tectonics, stereotomy, and metallurgy. Caribbean hut, The Style, 1851.

V

Today new ELEMENTS show up in PUBLIC, memorising or incorporating their specific habits and powers.

505

As there are the super materials like concrete, foam, chrome, or plastic …

506

As there are pipes and drains for water or ducts for ventilation or valves for heating …

507

There are also electrical wires for light, speakers for audio, wireless connections for screens …

508

All these new players are joining the architectural scene, and they want to be proportioned to qualify the spaces of today.

509

They start to talk in a common language, a CODE, to TALK in PUBLIC.

VI

504

510

ARCHITECTURE IS OF COMPUTING.

511

And here ARCHITECTURE meets its old friends: the techniques, the arts, the mechanics, the crafts …

512

514

 MECHANICS  are SUBJECTS. They CONSTITUTE ‘SKELETONS’ ANIMATED by an OBJECTIVITY.

515

DECODING and the PRIVATE

A windmill to pump water.

CODING and the PUBLIC

MECHANICS and MACHINES

513

ENCODING and the SACRED

This is why computers are not tools to be used in architecture. Computing takes part in the PUBLIC TALKS.

They project a LINEARITY of any DIRECTION to a stable CIRCULARITY.

517

They MOVE within the FLOW of AIR or the DIRECTIONAL LIGHT in the DAY.

518

MECHANICS act in an ENVIRONMENT, if they are RIGHT.

IV

516

519

V A machine or motor.

VI

520

 MACHINES  are OBJECTS. They CONSTRUCT a BOUNDARY DRIVEN by SUBJECTIVITY.

521

They project a stable CIRCULARITY to a LINEAR OPERATION of a specific DIRECTION.

522

They WORK with the INNER FORCES of GRAVITY under the ROTATING SKY of the NIGHT.

523

524

MACHINE

MECHANICS

525

ENCODING and the SACRED

MACHINES are HEALTHY, if they work WELL.

–i

MECHANICS

–R MACHINE

i

ARCHITECTURE and ENGINEERING

526

527

DECODING and the PRIVATE

ARCHITECTURE and ENGINEERING LIGHT and GRAVITY DAY and NIGHT MAJOR and MINOR MECHANICS and MACHINE … are mutually dependent, are of different sound and vision.

CODING and the PUBLIC

–R

528 ARCHITECTURE

–i

TALK

–R

IV

SHOW

SEE

–R

HEAR

i ENGINEERING

ARCHITECTURE as a MECHANICS and  MAJOR  tuning goes counterclockwise: is SEEN and TALKING , is SHOWN and LISTENING.

530

ENGINEERING as a MACHINE and  MINOR  tuning goes clockwise: is HEARD and SHOWS, is TALKED about and SEES.

531

Needless to say that I cannot ARTICULATE architecture if engineering cannot SHOW it, that nothing can be SEEN in LIGHT, if MASS does not SHOW up, that a WIREFRAME cannot be touched, if there is no TEXTURE, …

V

529

VI

533 2000+ 1980+ 1960+ 1930+ 1900+

ENCODING and the SACRED

PROCESSORS 1900+

532

534

CODING and the PUBLIC

Marcel Duchamp, The Bride Stripped Bare by Her Bachelors, Even, 1915–1923.

535

DECODING and the PRIVATE

Duchamp the artist, Turing the mathematician, PROCESSORS the technology … they give me an idea of an ANY- MACHINE , an ANY-OBJECT, an OBJECTIVITY, to be ready to constitute a SUBJECT a  MECHANICS , to be ready to CODE the  COMPLEX  scale.

536

IV Aleksandr Rodchenko, Shukhov, Shabolovskaya telecentre, Moscow, 1922. 537

PROCESSORS are CONSTITUTED like a MECHANICS. They project any LINEAR OPERATION into a stable CIRCULARITY.

538

In terms of IT: PROCESSORS are CONSTITUTED with REGISTERS, BUSSES, and LOGICAL UNITS.

V

539

The technical LANGUAGES of 1930+

540 2000+ 1980+ 1960+ 1930+ 1900+

VI 541

ASSEMBLY LANGUAGE

PROCESSOR

They project the stable CIRCULARITY of the LOGICAL UNIT to the LINEARITY of OPERATIONS.

543

They SIGNIFY ADDRESSES to REGISTERS and BUSSES to EMANCIPATE the SEQUENCE of CONTROL of the LOGICAL UNIT.

544

Their PROGRAMS CONTROL the SEQUENCE of COMMANDS.

545

They are MASSIVE, VISUAL, ECONOMIC, and they need TIME.

546

CODING and the PUBLIC

542

ENCODING and the SACRED

The first level of technical languages are  ASSEMBLY LANGUAGES . They CODE PROCESSORS as a  MECHANICS  to PROGRAM MACHINES.

DECODING and the PRIVATE

547

IV

The technical LANGUAGES of 1960+

548 2000+ 1980+ 1960+ 1930+ 1900+

549

ASSEMBLY LANGUAGE

HIGH LEVEL LANGUAGE

V The second level of technical languages are  HIGH-LEVEL LANGUAGES . They PROGRAM ASSEMBLY LANGUAGES as  MACHINES  to CODE MECHANICS.

551

HIGH-LEVEL LANGUAGES SYMBOLISE the FLOW of CONTROL to LIBERATE SEQUENCES of COMMANDS of ASSEMBLY PROGRAMS.

552

They project the LINEARITY of the FLOW OF COMMANDS to the CIRCULARITY of STANDALONE PROGRAMS.

553

Their CODES are ENERGETIC, AUDITIVE, POLITICAL, and they take SPACE.

VI

550

554

555

556

CODING and the PUBLIC

Halogen lamp, 1970s.

ENCODING and the SACRED

Electric fuse box, 1960s.

Fiat 500 L, 1968–1972.

557

DECODING and the PRIVATE

Hamburg, 1975.

558

IV Marlon Brando, Torrance, California, 1963.

V VI

559

FUNCTIONALISM – POP – 1960+

560

A SYMBOLIC LIBERATION of FORM on the REAL scalarity of classical mechanics.

561

‘TALKS like NEWTON’

562

Learning to TALK in  MAJOR  tuning.

563

On a technical level these ‘TALKS like NEWTON’ are PROGRAMS implemented on MAINFRAMES.

564

Their FORMS and COLOURS are elementary, atomistic, rational, exposed, explorative. Their STRUCTURES and MATERIALS are embodied, axiomatic, transcended.

565

566

Here I do not TALK about the IDEA of a PRESENT SELF. I SEE all these ideas percolated to the MEMORY OF THE PAST. With this memory I am able to articulate my PRESENT BODY. But this is not what I am doing here.

567

James R. Page, Vancouver, 1970s.

569

PICTURE – PRESENCE TALK about how to TALK

570

571

DECODING and the PRIVATE

In terms of IT: ITERATION CONDITIONAL RECURSION

CODING and the PUBLIC

568

ENCODING and the SACRED

LINE – POEM TALK about what can be SEEN

572

IV

Here I do not SEE the MEMORY of the PAST. My voice projects this memory as my PRESENT BODY. This body cannot be SEEN, it has to be SHOWN to the IMAGINATION of the FUTURE first. But this is not what I am talking about here.

573

Dario Bartolini, Archizoom Associati, Superonda, 1967.

574

V Citroën DS, 1955–1967.

575

VI ‘Light my Lucky’, advertisement, 1980s.

576

GRID – NOVEL TALK about how to be SHOWN

577

578

579

580

CODING and the PUBLIC

Here I cannot HEAR the VOICE of the PRESENT BODY. It is SHOWN to me in PARTS to IMAGINE the FUTURE, to be HEARD by my INNER SELF. But this is not what I am SEEING here.

ENCODING and the SACRED

In terms of IT: ASSIGNMENT TYPIFICATION

581

DECODING and the PRIVATE

Feller, STANDARDdue, 1969.

582

IV Vico Magistretti, Eclisse, Artemide, 1965.

583

V

Helmut Bätzner, B1171 chair for Bofinger, 1960s.

584

585

In terms of IT: DEFINITION NESTING SCOPE

VI

586

587

Here I cannot SEE my IMAGINATION of the FUTURE. I LISTEN to it to get an IDEA of my INNER SELF. This INNER SELF can be SEEN by the MEMORY of the PAST, but this is not what I am DOING here.

588

ENCODING and the SACRED

POINT – OMNIPRESENCE TALK about what to HEAR

589

590

In terms of IT: ASSOCIATION LIST

591

DECODING and the PRIVATE

Miele Studio M, 1967.

CODING and the PUBLIC

Andreas Feininger, 1960s.

592

IV

The technical LANGUAGES of 1980+

593 2000+ 1980+ 1960+ 1930+ 1900+

594

OBJECTORIENTED LANGUAGE

IMPERATIVE LANGUAGE

V VI

595

The third level of technical languages are  OBJECT-ORIENTED LANGUAGES . They CODE HIGH LEVEL LANGUAGES as a  MECHANICS  to PROGRAM MACHINES.

596

OBJECT-ORIENTED LANGUAGES SIGNIFY HIERARCHIES of DATA TYPES to EMANCIPATE from DATA STRUCTURES of the HIGH-LEVEL CODE.

597

They project a stable CIRCULARITY of STANDALONE PROGRAMS to the LINEARITY of USER INTERACTIONS.

598

599

ENCODING and the SACRED

Their PROGRAMS are MASSIVE, VISUAL, ECONOMIC, and they need TIME.

Electric fuse box, 1980s.

600

601

DECODING and the PRIVATE

Fiat Panda, 1980–1986.

CODING and the PUBLIC

Compact fluorescent lamp, 1980s.

602

IV Karlsruhe, 1980s.

603

Sylvester Stallone, 1976.

STRUCTURALISM – POSTMODERN – 1980+

605

A SYMBOLIC EMANCIPATION of STRUCTURES from FORM on the REAL scale in DYNAMICS.

606

‘TALKS like CARNOT’

607

Learning to TALK in MINOR tuning.

608

On a technical level these ‘TALKS like CARNOT’ are APPLICATIONS implemented on PCs.

V

604

VI

609

GRAMMAR – ENVIRONMENT TALK about what to SEE

610

ENCODING and the SACRED

Their STRUCTURES and MATERIALS are explicit, defined, strong, real, supportive. Their FORMS and COLOURS are distinct, expressive, infantile, playful, historical, natural.

612

Here I do not TALK about the REALITY of SYNCHRONISED EXISTENCES. I UNDERSTAND all these THINGS OF REALITY to SEE the MEMORY OF THE PAST. With this memory I am able to RATIONALISE my OMNIPRESENT INVARIANCE. But this is not what I am doing here.

613

DECODING and the PRIVATE

UNDERSTAND the RECORD of the PAST.

CODING and the PUBLIC

611

614

IV Hans Hollein, Haus Haas, 1990.

615

Mirko Karsch, New York, 1990s.

In terms of IT: COROUTINES EVENTS

617

TEXTURE – SYNCHRONICITY TALK about how to be TALKED about

V

616

618

619

VI

Here I do not SEE the FUTURE IMAGE. It helps me to REALISE my SYNCHRONISED EXISTENCE in actual SPACE. To SEE this EXISTENCE I have to UNDERSTAND all these THINGS of REALITY. But this is not what I am doing here.

620

621

622

In terms of IT: INTERFACE

623

DECODING and the PRIVATE

‘Where a man belongs’, advertisement, 1980s.

CODING and the PUBLIC

Ford Cortina, 1982.

ENCODING and the SACRED

Apple IIci, 1989.

624

IMAGE – HEALTH TALK about how to SHOW

625

IV 626

Here I do not RATIONALISE the SOUND of my PRESENT INSISTENCE. I PARTICIPATE to SEE the FUTURE IMAGE of the ORDER OF THINGS. This PARTICIPATION will help me to REALISE my SYNCHRONISED EXISTENCE. But this would be another kind of TALK.

627

V OPENSTEP | NeXTSTEP operating system, 1985-1996.

628

VI

GIRA, S-Color, 1985.

629

ENCODING and the SACRED

David van Severen, Vitra, .03 Chair, 1998.

630

631

PIXEL – INVARIANCE TALK about what to HEAR

632

CODING and the PUBLIC

In terms of IT: ENCAPSULATION INHERITANCE

633

634

DECODING and the PRIVATE

Here I RATIONALISE the MEMORY of the PAST to an OMNIPRESENT INVARIANCE. I INSIST on this SOUND. To SEE this SOUND I need to PARTICIPATE in the FUTURE IMAGE of the ORDER of THINGS. But this is not what I am doing here.

635

IV Office cubicals, 1990s.

636

IKEA, Faktum, 1995.

637

V

In terms of IT: POLYMORPHISM

VI

639 2000+ 1980+ 1960+ 1930+

ENCODING and the SACRED

The technical LANGUAGES of 2000+

638

1900+

640

MARKUP LANGUAGE

641

MARKUP LANGUAGES SYMBOLISE global USER INTERACTIONS to LIBERATE from ONTOLOGIES of DATA of OBJECT-ORIENTED PROGRAMS.

642

They project the LINEARITY of USER INTERACTIONS to the CIRCULARITY of WEB APPLICATIONS.

643

Their CODES are ENERGETIC, AUDITIVE, POLITICAL, and they take SPACE.

644

DECODING and the PRIVATE

The fourth level of technical languages are  MARKUP LANGUAGES . They PROGRAM HIGH-LEVEL LANGUAGES as  MACHINES  to CODE MECHANICS.

CODING and the PUBLIC

OBJECTORIENTED LANGUAGE

645

IV Electric fuse box, 2010s.

646

LED stripes, 2010s.

647

V Fiat Panda, 2004-2012.

648

VI Karlsruhe, 2020.

649

 IMPERATIVE LANGUAGES  RATIONALISE / OUTLINE SPACE by ‘DIGITAL LINES’. MAJOR

650

ENCODING and the SACRED

Scarlett Johansson, 2017.

651

652

CODING and the PUBLIC

 DECLARATIVE LANGUAGES  REALISE / FILL OBJECTS by ‘DIGITAL COLOURS’. MINOR

653

654

With  BIG DATA   STRUCTURE  is your INVARIANCE. You forget ALL  STRUCTURE .

655

DECODING and the PRIVATE

With  HIGH-LEVEL LANGUAGES  the  DIGITAL  ABSTRACTS from FORM. With  OBJECT-ORIENTED LANGUAGES  the  DIGITAL  ABSTRACTS from STRUCTURE.

Not all  TYPES , not all  CREATION , not all  SENSE .  ORTHOGRAPHIA  

657

With  ARTIFICIAL INTELLIGENCE   FORM  is your INVARIANCE. You forget ANY  FORM .

658

Not any  MEMORY . not any  MAKING . not any  MEANING .  ICHNOGRAPHIA 

659

With  BIG DATA , or ORTHOGRAPHIA, you CIVILISE CULTIVATION.  CULTURAL HERITAGE 

660

With  ARTIFICIAL INTELLIGENCE , or ICHNOGRAPHIA, you CULTIVATE CIVILISATION  URBANISATION 

661

 IMPERATIVE SOFTWARE  is  ANIMATED  NOT by ALL the COMMANDS, but by a CLOCK.

662

 DECLARATIVE SOFTWARE  is  DRIVEN  NOT by ANY DATA, but by a USER.

663

INTERNET PUBLISHING  is  ANIMATED  NOT by ALL the USERS, but by TIME.

664

 BIG DATA  of the  INTERNET  uses MARKUP languages to  FORGET  all FORM of DATA by XML and to forget all STRUCTURE of DATA by XSL.

IV

656

V VI

665

The INTERNET has no  FORM , and any  STRUCTURE  there has no  MEANING  and no  SENSE .

666

667

668

A wireless computer with camera for 3$ and 14 mm × 20 mm. 669

670

iOS storyboards in Xcode, 2019.

DECODING and the PRIVATE

The INTERNET mimics any FORM and any STRUCTURE in all details.

CODING and the PUBLIC

SpaceX, Starlink Satellites, 2019.

ENCODING and the SACRED

It comes paired with algorithms of  ARTIFICIAL INTELLIGENCE  using  PROBABILISTICS  to  FORGET  any CONTROL OF FLOW.

671

IV A landscape of smartphone interfaces around real estate, 2021. 672

Bulthaup, b3, enclosed kitchen cabinets, 2020.

V

673

Berker, R.x series, 2012.

674

Today we PICTURE ARCHITECTURE without FORM and without any STRUCTURE.

VI

675

676

677

CODING and the PUBLIC

Urban office space, 2021.

ENCODING and the SACRED

Amazon distribution centre, 2021.

Diez, Chassis, 2008.

678

And like always in this constellation: you have to forget all STRUCTURE to establish FORMS of a new MECHANICS.

679

DECODING and the PRIVATE

An abundance of STRUCTURE and a lack of FORM.

You have to forget  LANGUAGE  to learn to TALK in your own  VOICE .

681

This VOICE is your INVARIANT axis, a MECHANICS turning YOUR world around.

682

To  SAY  things that have never been  HEARD  on EARTH.

683

And here we are with the TRIVIUM, the three linguistic subjects of the seven liberal arts.

684

GRAMMAR DIALECTIC RHETORIC

685

It is about  TALKING  in  PUBLIC ,  CIVILISING  the  URBAN , and  ARCHITECTURE .

686

ORTHOGRAPHIA ICHNOGRAPHIA SCAENOGRAPHIA

687

IMPERATIVE languages are a  MECHANICS  you can  EMANCIPATE  from. Their  PROGRAMS  are  ENGINEERING .

688

DECLARATIVE languages are  LANGUAGES  you can  RISE UP  from. Their  CODES  are about  ARCHITECTURE .

IV

680

V VI

689

You cannot  FORGET   PYTHON  as a LANGUAGE because it mimics a  CLASSICAL  MECHANICS.

690

You can  FORGET   MATHEMATICA  as a LANGUAGE to establish a new MECHANICS on a  QUANTUM  level.

691

ENCODING and the SACRED

 PYTHON  is the most prominent IMPERATIVE language.  MATHEMATICA  is the most prominent DECLARATIVE language.

CODING and the PUBLIC DECODING and the PRIVATE

IV

V

VI

BOOKV

CODING and the PUBLIC

ENCODING and the SACRED

CODING and the PUBLIC

    EPILOGUE – SCAENOGRAPHIA

DECODING and the PRIVATE

692

This book is about ARCHITECTURE as a PUBLIC TALK.

693

IV NASA, 2012.

694

V

The global PUBLIC shares the same technology. At home PEOPLE live in different conditions. A common CODE is able to proportion both: the same and the different.

695

Andreas Fuhrimann Gabrielle Hächler, Haus Alder, 2020.

696

VI Robin Hammond, Lagos, 2014.

697

698

ENCODING and the SACRED

A common CODE enables the PUBLIC to talk about a commonwealth of its PEOPLE, different as they are.

Valerio Olgiati, Das gelbe Haus, 1999.

Favela, Rio de Janeiro, 2005.

700

701

Kanye West, Kim Kardeshian, 2018.

DECODING and the PRIVATE

The smart and fast ones, … Bezos, Musk, Kardashian … these warlords show the irresistible power of the  DIGITAL  scale.

CODING and the PUBLIC

699

702

SCAENOGRAPHIA negotiates the COMMON and CIVILISES the PUBLIC.

703

IV Piazza del Campo, Siena, Italy.

704

These PUBLIC TALKS are around digital humanism, a digital Renaissance, and digital architectonics.

V VI

DECODING and the PRIVATE

BOOKVI

ENCODING and the SACRED CODING and the PUBLIC

705 ↗

ONE HEARING SPACE SEEING TIME The HUMAN PROPORTION

714 ↗ 722 ↗ 729 ↗

TWO AIR – LINEAMENT EARTH – ORNAMENT

755 ↗ 793 ↗

THREE The EYE of the LINEAMENT The EYE of the ORNAMENT

833 ↗ 899 ↗

FOUR The COMPLEX PLANE The HUMAN PROPORTION The SCALARITIES of SPACE The ARCHITECTURAL AFFAIR in MAJOR The ARCHITECTURAL AFFAIR in MINOR EPILOGUE

939 ↗ 944 ↗ 963 ↗ 971 ↗ 1058 ↗

DECODING and the PRIVATE

PREFACE

IV

V

VI

As the PUBLIC, I left home, ENCODED all things as MEMORY. Book IV

706

I also TALKED with the others at the edge of the world in PUBLIC CODES. Book V

707

ENCODING and the SACRED

PREFACE

705

708

709

DECODING and the PRIVATE

Now I am coming home. Step by step I DECODE the public talks. My things become sharper, they get tuned in their colours and synchronised with the world. My things prosper because they are safe at home on fertile ground. Like the other homes in all their differences.

CODING and the PUBLIC

Bong Joon-ho, Parasite, 2019.

IV

V

VI

DECODING and the PRIVATE

BOOKVI

ENCODING and the SACRED CODING and the PUBLIC

ONE

714 ↗ 722 ↗ 729 ↗

DECODING and the PRIVATE

HEARING SPACE SEEING TIME The HUMAN PROPORTION

I, the PUBLIC, ENCODED my world in two circles: The circles of the DAY and the circles of the NIGHT, of  MAJOR  and  MINOR  …

711

I SIGNIFIED all things by SETS of NUMBERS and gave them NAMES, written in CHARACTERS.

712

The TALKS at the edge of the world have been with these SYMBOLIC NAMES, not with the things themselves.

713

DECODING, coming back, knows the same two circles: the  MAJOR  circle of the DAY of WHAT TO SAY at home, and the  MINOR  circle of the NIGHT on HOW TO DO things at home.

IV

710

V 714

715

716

HEARING SPACE

VI

717

718

719

I called that: I HEAR SPACE, a PICTURE.

720

721

SEEING TIME

722

CODING and the PUBLIC

OMA, Casa da Música, Porto, 2005.

ENCODING and the SACRED

I ‘see’ the MAJOR circle of the DAY as PICTURES of SYNCHRONICITY showing TRANSPARENT SPACE.

723

Anton Yankovyi, The rotating northern night sky above the Nepali Himalayas, 2011.

DECODING and the PRIVATE

724

725

I SEE the MINOR circle at NIGHT as IMAGES of INVARIANCE showing MASSIVE TIME.

726

IV OMA, Casa da Música, Porto, 2005.

727

I called that: I SEE TIME, an IMAGE.

728

V 729

The HUMAN PROPORTION

VI

730

DAY and NIGHT PICTURE and IMAGE EAR and EYE are in PROPORTION.

731

I am aware that a PROPORTION is not a geometric setting, as I see it in all these drawings.

732

ENCODING and the SACRED

A proportional grid on the facade of: Leon Battista Alberti, Santa Maria Novella, Florence, 1470.

… 733

… Input

734

A PROPORTION BRIDGES these INCOMMENSURABLES.

735

Coming back from the edge of the world BRIDGES the CIRCULAR SYNCHRONICITY of the SKY with the LINEAR INVARIANCE on EARTH.

736

CODING and the PUBLIC

A PROPORTION is not between LINES and LINES. It is between CIRCLES and LINES the IRRATIONAL and the REAL between entities, which are INCOMMENSURABLE, as the  3  and the  2 .  SYCHRONICITY   INVARIANCE   MAJOR   MINOR   LINEARITY   CIRCULARITY   GRID   COLOUR   EAR   EYE   SEX   NAVEL   CHARACTER   NUMBER   LINEAMENT   ORNAMENT   PICTURE   IMAGE 

DECODING and the PRIVATE

737

IV Leonardo da Vinci, Vitruvian Man, ca. 1490.

The Vitruvian Man recentres from the NAVEL – centre of the CIRCLE == LINEARITY – the natural CREATION to the SEX – centre of the SQUARE == CIRCULARITY – the engendering INTELLECT.

739

A PROPORTION is about squaring the circle not the square as a circle. A PROPORTION is not a GEOMETRIC ENTITY. It BRIDGES the GEOMETRIC and the HARMONIC.

740

With Archimedes I have the CIRCLE of the SKY and the radius as a LINE on EARTH and I have the spiral as a BRIDGE between SKY and EARTH.

V

738

The Archimedean Spiral, 225 BC.

T

2πr

VI

O

r

P

741

742

N@GoldenRatio

743

1.618033988749895

744 745

746

747

CODING and the PUBLIC

On the  COMPLEX  scalarity of SPACE I find Le Corbusier’s Modulor.

ENCODING and the SACRED

I read the Vitruvian Man as a METHAPOR of the HUMAN PROPORTION BRIDGING SKY and EARTH on the  REAL  scalarity of SPACE.

Le Corbusier, Modulor (1942–1955).

The Modulor shows the SYNCHRONICITY of the SKY as a GRID on the COMPLEX scalaritiy according to the Archimedean spiral and the golden ratio.

749

750

DECODING and the PRIVATE

748

But I cannot find the INVARIANCE here, the COLOUR on the COMPLEX scalarity. The Modulor thinks the GRID as positive and GEOMETRIC. The Modulor is NOT a PROPORTION of CIRCLE and LINE.

752

Interestingly the Modulor is anchored to the INVARIANT NAVEL, not the SYNCHRONICITY of the SEX, which is simply missing.

753

The Modulor is not about the HUMAN PROPORTION it is about – as the name says – the MODULE, the BASE of a COLUMN, the INVARIANT OMNIPRESENCE of SPACE at the COMPLEX SCALARITY which I called the POINT.

IV

751

V VI

DECODING and the PRIVATE

BOOKVI

ENCODING and the SACRED CODING and the PUBLIC

TWO

755 ↗ 793 ↗

DECODING and the PRIVATE

AIR – LINEAMENT EARTH – ORNAMENT

754

Before I talk in architectural terms about WHAT TO SAY and HOW TO DO things, coming back home from the public talks, I want to characterise the two circles in more detail.

IV 755

756

AIR – LINEAMENT The  MAJOR  circle of the DAY is about WHAT to SAY, is about the ARTICULATION and the SYNCHRONISED PRESENCE in SPACE. BOOK III

757

V 758

The POINT

759

I start with the view of my inner self.

760

761

Here I have an IDEA of everything, the INVARIANT ATOM. This POINT is out of TIME, It is not all the PRESENCE of LIGHT, it is the OMNIPRESENCE of LIGHT.

VI

762

763

ENCODING and the SACRED

I keep this in mind and I give these POINTS of anything NAMES.

764

765

766

767

Here I am with the MEMORY as sequences of NAMES. LINES CHARACTERISE the MEMORY of the PAST. They are not OBJECTS, they are SEQUENCES of NAMES.

768

769

DECODING and the PRIVATE

I am turning from the inner self to the point of the past, facing the future.

CODING and the PUBLIC

The LINE

770

I keep this in mind and sort my MEMORY in lists and rules of anything around a vertical AXIS of TIME to be able to talk.

IV

771

772

The FACE

773

Now I am turning from the point of the past to the outer presence.

775

Here I present an actual PICTURE, taking space in LIGHT as SYNCHRONISED FACES of a PRESENT BODY.

V

774

776

777

VI 778

This PRESENCE is the SLIT I can HEAR which is in SYNC with my MEMORY and INVARIANT to my INNER SELF.

The VOLUME

779

I am turning again from the OUTER PRESENCE to the VISION of the FUTURE, driven by the PAST.

781

Here I go with the PRODUCTION of what I talked about. The LINES of PRODUCTION, the HEALTHY BODY. the REASONABLE VOLUME.

782

ENCODING and the SACRED

780

783

784

CODING and the PUBLIC

I keep this in mind and organise my doing along the lines of reason.

785

DECODING and the PRIVATE

786

The CIRCLE of the LINEAMENT

787

IV

The MAJOR circle of the DAY constantly rotates: … POINT LINE FACE VOLUME POINT LINE …

789

or in physical terms: … LOCATION VELOCITY GRAVITY WEIGHT LOCATION VELOCITY …

V

788

790

VI

791

In the next chapter the LINEAMENT meets the fertile ground of the ORNAMENT, the MINOR circle.

792

   EARTH –  ORNAMENT

793

794

795

796

Again, I start with the view of my inner self.

797

798

I am not the MASS of everything, I am the INVARIANT AXIOM. The ability to rotate and repeat.

799

DECODING and the PRIVATE

The VALUE

CODING and the PUBLIC

The  MINOR  circle of the NIGHT is about HOW to DO, is about the PRODUCTION and the OMNIPRESENT INVARIANCE in TIME. BOOK II

ENCODING and the SACRED

In terms of Alberti – the REAL SCALARITY of SPACE – I read about this circle as LINEAMENT.

800

This POINT is out of TIME, It is not all the PRESENCE of MATTER, it is the OMNIPRESENCE of MASS or MATERIALITY

IV

801 The ability of atoms to repeat rendered as a colour. 802

I keep this in mind and I assign these AXIOMS to NUMBERS.

803

The SPHERE

805

Now I am turning from the inner self to the point of the past, facing the future.

V

804

806

807

Here I am exposed to the ENVIRONMENT of all AXIOMS MEMORISING the PAST in circulations of connected NUMBERS.

808

VI The WIND of connected FREQUENCIES rendered as a ball.

809

810

The CYLINDER

811

I am turning from the point of the past to the outer presence.

812

ENCODING and the SACRED

I keep this in mind and SYNCHRONISE my MEMORIES with the WINDS of the AIR.

813

814

815

816

817

DECODING and the PRIVATE

This PRESENCE is the SLIT I can SEE. It is in SYNC with the ENVIRONMENTAL MEMORY and INVARIANT to the MATERIALITY

CODING and the PUBLIC

Here I present a massive body, taking space, by the PRESENT SKIN as SYNCHRONISED TEXTURES.

818

The ROTATIONAL AXIS

819

Finally I am turning from the OUTER PRESENCE to the VISION of the FUTURE, driven by the PAST.

IV

820

821

The PRODUCT, the MASSIVE IMAGE, the MATERIAL, a MACHINE, an energetic frequency.

822

V Mass becomes matter by rotation on the complex plane. 823

824

I keep this in mind and organise my doing along the lines of production.

VI

The CIRCLE of the ORNAMENT

825

827

828

CODING and the PUBLIC

The MINOR circle of the NIGHT constantly rotates: … VALUE ROTATION CYLINDER SPHERE VALUE ROTATION … or in physical terms: … ENERGY MATTER POTENTIAL MASS ENERGY MATTER …

ENCODING and the SACRED

826

DECODING and the PRIVATE

IV

V

VI

DECODING and the PRIVATE

BOOKVI

ENCODING and the SACRED CODING and the PUBLIC

THREE

833 ↗ 899 ↗

DECODING and the PRIVATE

The EYE of the LINEAMENT The EYE of the ORNAMENT

829

This book is about coming back home. Giving HUMAN PROPORTIONS to the RATIONAL circles of the SKY and the REAL lines on EARTH.

IV

830

831

Chapter TWO characterised the RATIONAL and the REAL in principle terms.

832

This chapter THREE will characterise them in Western architectural terms.

The EYE of the LINEAMENT

833

V

834

835

836

VI

837

838

The POINT

839

840

ENCODING and the SACRED

I close my EYES, I forget all these COLOURS and SEE the OMNIPRESENCE of LIGHT at my single POINT.

841

CODING and the PUBLIC

842

Cedric Price, Wish We Were Here, 1980s.

DECODING and the PRIVATE

843

The MEMORY

844

IV

845

846

I look at this facade with the EYES of SYNCHRONICITY

847

848

V

… and I SEE it as an ARRAY of RULES positioning WINDOWS in a FACADE

849

A rule memorising a sequence of elements of facades and windows. 850

This rule applied to the elements of the facade.

VI

851

These rules are out of SPACE, they establish memories of sequences in time, wherever they are in SPACE. It is a GRAMMAR, it is of OMNIPRESENCE, and it provides SYNCHRONICITY.

852

The PICTURE

853

854

ENCODING and the SACRED

In architectural design this technique is known as SHAPE GRAMMAR.

855

856

857

858

859

860

DECODING and the PRIVATE

In architectural design this technique is known as PARAMETRISM.

CODING and the PUBLIC

If I look at the same facade with the EYES of the PRESENCE, I SEE the ELEMENTS taking SPACE.

861

With the EYES of SYNCHRONICITY and the EYES of the PRESENCE I SEE all the different LAYERS of a BUILDING.

862

IV 863

The facade,

864

V 865

the construction,

866

867

the logistics and operation,

VI

868

ENCODING and the SACRED

all the technical services, …

869

870

871

The HEALTH

872

CODING and the PUBLIC

as a sculptural body.

873

With the EYES of the FUTURE VISION I SEE how things are DONE.

875

DECODING and the PRIVATE

874

876

IV In a factory,

877

878

in construction,

879

V 880

by robots,

881

882

? 1 In 1

UPPER Constant 1

VI

LOWER Constant 2 2 In 2

3 In 3 4 In 4

883

1D T(u) Table 1 2-D u1 T(u) u2 Table 2

> RelOp1

OR

mode

mode

< RelOp2 K1 Gain

1 — Z Delay

mode Data Store Read

by programs,

>0 Switch

1 Out 1

884

885

886

887

888

889

A HEALTHY BODY OPERATING in TIME towards the IDEA of INVARIANCE in PROPORTION to the HUMAN BODY.

890

DECODING and the PRIVATE

… to all devices.

CODING and the PUBLIC

distributed by infrastructures,

ENCODING and the SACRED

driving interfaces,

The EYE of the ORNAMENT

891

892

IV 893

894

The PIXEL

895

896

V 897

898

899

I close my EYES, I forget all these LINES and SEE the INVARIANCE of MATTER at my single POINT.

VI

900

ENCODING and the SACRED

Junya Ishigami, I’m Not Here, RIBA Journal, 2018.

The ENVIRONMENT

901

902

I look at buildings with the EYES of SYNCHRONICITY and SEE the air, the water, the fire, the heat, the traffic … flowing in particles, all the same.

904

CODING and the PUBLIC

903

905

DECODING and the PRIVATE

FetchCFD, air flow simulation, 2020.

906

IV Junya Ishigami, Invisible Architecture, RIBA Journal, 2018.

907

The TEXTURE

908

909

V 910

I look at the same facade with the EYES of the PRESENCE I SEE its PARTS as a massive skin in colours.

911

912

The play of the windows and the ORNAMENT of the facade,

VI

913

the textures, the reflections, the light,

914

ENCODING and the SACRED

MVRDV, Bulgari Bangkok, 2020.

915

916

917

the interfaces on streets,

918

Valerio Olgiati, Yellow House, 1999. 920

DECODING and the PRIVATE

919

the traces of time …

CODING and the PUBLIC

the interfaces on screens,

921

The IMAGE

922

923

IV 924

I look at the same facade with the EYES of the INVARIANCE, I SEE the massive PARTICLES appear in TIME.

925

V 926

The facade,

927

928

with its pixels of low resolution,

929

VI 930

on a screen,

931

932

933

934

935

CODING and the PUBLIC

as massive IMAGES of colours in TIME decoupled from SPACE,

ENCODING and the SACRED

on my device from any PERSPECTIVE,

Leonardo da Vinci, Perspective Study of The Adoration of the Magi, 1481.

936

DECODING and the PRIVATE

Like the massive LINES of the perspective drawings which had been decoupled from things in the RENAISSANCE …

IV

V

VI

DECODING and the PRIVATE

BOOKVI

ENCODING and the SACRED CODING and the PUBLIC

FOUR

939 ↗ 944 ↗ 963 ↗ 971 ↗ 1058 ↗

DECODING and the PRIVATE

The COMPLEX PLANE The HUMAN PROPORTION The SCALARITIES of SPACE The ARCHITECTURAL AFFAIR in MAJOR The ARCHITECTURAL AFFAIR in MINOR

IV

937

This chapter now introduces a more detailed vocabulary on WHAT to SAY and HOW to ACT when coming home.

938

It again uses Western metaphors and terms in a Renaissance-like constellation. How to communicate with other cultures and times will be discussed in Books VIII–X.

939

940

The COMPLEX PLANE

V

A key reference of these books are the PLATONIC SOLIDS and the COMPLEX PLANE of SPACE and TIME.

941

FIRE EARTH

AIR WATER

–SPACE

+SPACE

–TIME

+TIME

VI

942

They also apply the VISUAL and the AUDITIVE, the SENSORY and ACTUATORY to this scheme.

943

ENCODING and the SACRED

PAST FUTURE

SEE IN

OUT

TALK SHOW

HEAR

FUTURE PAST

945

946

Applying the human body to this scheme, these terms are used for the outer circle in MAJOR tuning:

947

CODING and the PUBLIC

The HUMAN PROPORTION

944

948

SEE SEX

PICTURE

TALK SHOW

HEAR

HEALTH

DECODING and the PRIVATE

MEMORY

To be read like this:

950

The PAST has SEEN all IDEAS.

951

The MEMORY ARTICULATES a SYNCHRONISED BODY.

952

The PICTURE SHOWS the VISION of the FUTURE.

953

HEALTH is CONSUMED by the INVARIANT inner SELF.

IV

949

954

955

And I am using these terms for the inner circle of MINOR tuning:

956

V 957

DISSOLVE

ORIENT

REFLECT

LEARN

NAVEL

IMAGE

ENVIRONMENT

IMAGINATION

VI

958

To be read like this:

959

The FUTURE is TRAINED by the NAVEL MATTER.

960

The actual PRESENCE REFLECTS the IMAGINATION.

961

The ENVIRONMENT DIRECTS the SUBSTANCES.

962

The SCALARITIES of SPACE

963

964

And I am arguing with three different scalarities of space in this Renaissance CONSTELLATION:

965

The  RATIONAL  scalarity of antiquity, the  REAL  scalarity of the RENAISSANCE and BAROQUE and the  COMPLEX  scalarity of today.

966

An ARTICULATION of the OUTER circle on the  RATIONAL  scalarity. Temple of Concordia, Agrigento, 5th century BC.

DECODING and the PRIVATE

967

CODING and the PUBLIC

I, the PUBLIC, look at today’s body of thinking in the constellation of a Renaissance, and correspondingly ARCHITECTURE does not develop along a line of HISTORICITY – this would be in the tradition from Laugiers to Semper – but as a miniature of the COSMOS.

ENCODING and the SACRED

The IMAGES DISSOLVE to the ENVIRONMENT.

968

IV An ARTICULATION of the OUTER circle on the  REAL  scalarity. Andrea Palladio, Villa Rotonda, 1571.

969

An early ARTICULATION of the OUTER circle on the  COMPLEX  scalarity. Le Corbusier, Villa Savoye, 1931.

V 970

A recent ARTICULATION of the OUTER circle on  COMPLEX  scalarity. OMA, Casa da Música, Porto, 2005.

VI

I now apply these schemes directly to the architectural elements like floor, wall, ceiling; and base, facade, and roof, as, in my reading, Alberti and Vitruvius did.

972

ENCODING and the SACRED

The ARCHITECTURAL AFFAIR in MAJOR

971

973

The OUTER circle of MAJOR tuning articulates the SYNCHRONICITY and POLITICS, and is applied to base, column, facade, and roof.

975

CODING and the PUBLIC

974

976

SHOW

SEE HEAR

GROUND ROOF

BASE

TALK

DECODING and the PRIVATE

FACADE

COLUMN

This outer circle ARTICULATES ARCHITECTURE in AIR, with LIGHT mediating the notion of SPACE, as OMNIPRESENT and COLLISION-FREE, ALWAYS COMPLETE and NEVER CORRECT, ephemeral, atomistic, and ARTICULATED by CHARACTERS.

978

SEX

IV

977

979

V VI

980

I start with the view from the INSIDE.

981

It BRIDGES WATER → AIR EAR → EYE, SENSIBLE → SENSIBLE. and active → passive.

982

I paraphrase it with: The SEX has SEEN all IDEAS, and I HEAR the PRIVATE SILENCE → to be SEEN by the MEMORY of the PAST, and with these EYES I SEE the OMNIPRESENCE of LIGHT, and I HEAR the GLOBAL OBJECTIVITY of SPACE and EXPLORE the INTELLECTUAL CONTINGENCIES of the WORLD.

983

I SEE the SPACE with the INSIDE view as  LINES , as  COLOURS , and as  IMAGINARY.

984

MEMORY

985

987

It BRIDGES AIR → FIRE, EYE → TONGUE, SENSIBLE → ACTUABLE. active → active.

988

I paraphrase it with: The MEMORY ARTICULATES a SYNCHRONISED BODY, and I SEE the MEMORY of the PAST → to be able to TALK to the PUBLIC, and with these EYES I SEE the SYNCHRONICITY of TIME, and I am AWARE of the CONTINGENCIES of the PAST and TALK about the RESPONSIBILITY in the FUTURE.

989

DECODING and the PRIVATE

I take the view form the PAST FUTURE.

CODING and the PUBLIC

986

ENCODING and the SACRED

On the RATIONAL scalarity this is ARTICULATED as the  BASE . On the REAL scalarity this is ARTICULATED as the  LINEAMENT . On the COMPLEX scalarity this is ARTICULATED as the  PROCESSOR .

IV

990

On the RATIONAL scalarity this is ARTICULATED as the  COLUMN . On the REAL scalarity this is ARTICULATED as  ARCHAEOLOGY . On the COMPLEX scalarity this is ARTICULATED as  DATA .

991

I see the PAST FUTURE as  SUBJECTS , as  DRAWINGS , and as  SPECTRA .

992

PICTURE

993

V VI

994

I take the view form the OUTSIDE.

995

It BRIDGES FIRE → EARTH, TONGUE → HAND, ACTUABLE → ACTUABLE, passive → active.

996

I paraphrase it with: The PICTURE SHOWS the VISION of the FUTURE, and I TALKED to the PUBLIC → to be able to SHOW my VISION of the FUTURE, and with these EYES I SEE the PRESENCE in LIGHT, and I EMBODY the LOCAL SUBJECTIVITY in SPACE and ACT along the LINE of NECESSITY on EARTH.

997

I see the OUTER SPACE as  BODIES , as  FACES , and as  FACETS .

998

HEALTH

999

ENCODING and the SACRED

On the RATIONAL scalarity this is ARTICULATED as a  FACADE . On the REAL scalarity this is ARTICULATED as a  CONSTITUTION . On the COMPLEX scalarity this is ARTICULATED as  CODE .

1000

It BRIDGES EARTH → WATER, HAND → EAR, ACTUABLE → SENSIBLE, passive → passive.

1002

I paraphrase it with: The HEALTH is CONSUMED by the INVARIANT inner SELF, and I get SHOWN the VISION of the FUTURE → to be HEARD by the PRIVATE SILENCE, and with these EYES I SEE the INVARIANCE of MATTER in TIME, and I am AWARE of the NECESSITIES of the FUTURE and I am DRIVEN by the ORIGIN in the PAST.

1003

DECODING and the PRIVATE

1001

CODING and the PUBLIC

I take the view from the FUTURE PAST.

IV

1004

On the RATIONAL scalarity this is ARTICULATED as the  ROOF . On the REAL scalarity this is ARTICULATED as the  MACHINE . On the COMPLEX scalarity this is ARTICULATED as the  PROGRAM .

1005

I see the FUTURE PAST as  OBJECTS , as  PROPERTIES , and as  VALUES .

1006

How to read the scheme

1007

V Leon Battista Alberti, Cipher Disk, 1467.

1008

All this sounds very cryptic. Yes it is written in a mechanical way. It is more a cipher than a text. How to read it?

1009

1010

VI 1011

I take for example the view from the OUTSIDE and look at the  FACADE  of a Greek temple.

1012

1013

If I look with  RATIONAL  EYES, I see a FACADE. If I look with  REAL  EYES, I see a CONSTITUTION.

1015

I look at the Palladian villa, see its CONSTITUTION with my REAL EYES. I need my RATIONAL EYES to look through the CONSTITUTION and SEE the FACADE.

1016

With the Greek temple I see the FACADE with my REAL and RATIONAL EYES. The CONSTITUTION cannot be explicated in EUCLIDEAN SPACE, it has to be IMAGINED in CARTESIAN SPACE.

1017

I do not claim to know, what a FACADE or a CONSTITUTION is. I bring these terms into interesting CONSTELLATIONS to stabilise and enrich them, leaving their definitions open.

1018

DECODING and the PRIVATE

1014

CODING and the PUBLIC

If I look at the  FACADE  of the Palladian villa, this proposition still seems to fit. But there is an additional flavour, which I suggested to name with the term  CONSTITUTION .

ENCODING and the SACRED

I find this proposition: With these EYES I SEE the PRESENCE in LIGHT This sounds quite adequate.

1019

IV

And I can go on like this with the COMPLEX scalarity: The Le Corbusier villa still seems to fit the proposition ‘the FACADE shows the PRESENCE in LIGHT’. But again it has an additional flavour, which has no established name yet, because it is the time of today. I would suggest to name it with the term  CODE .

1021

Reading Terms

1022

Using the term CODE might be surprising here, but it came up for reasons of symmetry and gives me the next level of explication to the PRESENCE in LIGHT for the COMPLEX scalarity of SPACE.

V

1020

VI

1024

2 With the Le Corbusier villa with COMPLEX EYES I expect to SEE CODE explicated.

1025

With the Palladian villa with COMPLEX EYES I expect to SEE implicit CODE.

1026

This contrast finds my attention. It especially implies: Masterpieces of 20th century architecture show up as CODE.

1027

In fact, nobody knows what CODE is. There is no definition of a concept which works satisfactorily, whatever people say.

1028

The suggested scheme of thinking about new terms to turn the table: As an architect I can find a lot of material to make friends with this complicated and powerful term named CODE.

1029

DECODING and the PRIVATE

1 I get an idea of how to think about CODE as an ARCHITECT: CODE is a CONSTITUTION, has a FACADE. CODE ARTICULATES a PRESENCE in LIGHT. Different from PROGRAMS, GRAMMARS, LANGUAGE, DATA … which can be seen with other EYES. With this architectural flavour I, the architect, can talk with other DOMAINS in PUBLIC.

CODING and the PUBLIC

1023

ENCODING and the SACRED

This is interesting in two directions:

Again: I am aware that this is not a THEORY, this is a TREATISE, a MECHANICS, an INSTRUMENT to THINK about ARCHITECTURE in today’s terms.

1031

It does not claim TRUTH, it is just fast, interesting, and claims to be COMPLETE. And of course this INSTRUMENT needs training to be tuned and played well.

1032

About ROTATION

1033

Giving credit to this instrument: its mechanics is of ROTATION.

IV

1030

V

1034

1035

VI 1036

The CONSTITUTION of the Palladian villa seems to be established by a ROTATION of the FACADE of the Greek temple around the vertical AXIS.

1037

1038

I know this technique of ROTATION by the perspective drawing, I remember Alberti’s ‘la pictura ’ and ‘la statua ’: PRESENCE in LIGHT.

1039

Leon Battista Alberti, linear perspective as a technical sculpturing of ‘going around’, 1450. 1041

If the  CONSTITUTION  of the Renaissance can be read as a ROTATION of  EUCLIDEAN  space, I can read the  CODE  of today as a ROTATION of  CARTESIAN  space.

1042

DECODING and the PRIVATE

I suggest to read the technique of the perspective projection as a ROTATION of EUCLIDEAN space towards the scalarity of the CARTESIAN space, as a ROTATION of EUCLIDEAN LINES towards CARTESIAN rotated lines or PROPERTIES.

CODING and the PUBLIC

1040

ENCODING and the SACRED

If a  FACADE   is a PRESENCE in EUCLIDEAN SPACE, the  CONSTITUTION  ROTATES this SPACE to a PRESENCE in CARTESIAN SPACE.

IV

1043

And I can read the  FACADE  of the Greek temple as a ROTATION of an  unnamed  space which should have been constitutive for Egyptian and Babylonian architecture.

1044

All of them can be read as PRESENCE in SPACE or as ROTATIONAL SPACE, a LOCAL SUBJECTIVITY.

1045

1046

These arguments took place with the most obvious rotation around the z-axis. But they work also around the horizontal x- and y-axis.

V

1047

1048

In EUCLIDEAN space the platform and roof of the temple are articulated precisely.

1049

VI 1050

After a ROTATION there is much more differentiation and articulation in the Palladian villa, however you read it.

1051

The EUCLIDEAN and the CARTESIAN space are just different worlds, which cannot communicate in rational lines, but in irrational rotations.

1052

Given that reading, the CODE of the Le Corbusier villa is almost directly a spherical rotation of the Palladian CONSTITUTION.

1053

ENCODING and the SACRED

One has to be careful: this is not a line of progress, there is not more or less sophistication. It is just another SCALARITY of SPACE to be seen with different EYES.

1054

As we can compare the different temperaments of the CODE of Le Corbusier in 1931 and for example OMA in 2005.

1056

1057

DECODING and the PRIVATE

1055

CODING and the PUBLIC

If the PUBLIC agrees on that ROTATION the PRIVATE can have different voices, talking about architecture without being detached in a post-structuralist manner.

1058

IV

The ARCHITECTURAL AFFAIR in MINOR

1059

1060

1061

V

Now it is time to complete my instrument with the symmetrical INNER circle in MINOR tuning, which is applied to materiality, the rotational symmetries of rooms, the walls, floors, and ceilings.

1062

DISSOLVE

ORIENT

REFLECT

LEARN

SUBSTANCE

WALL

CEILING ROOF

AXIS

1063

VI

This inner circle ARTICULATES ARCHITECTURE on EARTH with MASS mediating the notion of TIME, as SYNCHRONOUS and COLLIDING, NEVER COMPLETE and ALWAYS CORRECT, massive, axiomatic, and CALCULATED with NUMBERS.

1064

1065

1066

CODING and the PUBLIC

Andrea Palladio, La Rotonda, 1571.

ENCODING and the SACRED

Herculaneum, Casa di Nettuno e Amphitrite, n. 22, 79 BC.

Julius Shulman, Eames House, 1949.

Rem Koolhaas, Casa da Música, 2005.

DECODING and the PRIVATE

1067

1068

NAVEL

1069

IV

1070

The FUTURE is TRAINED by the NAVEL MATTER.

1071

I start with the view from the INSIDE.

1072

It BRIDGES AIR → WATER, EYE → EAR, SENSIBLE → SENSIBLE. and passive → active.

1073

V

In The OMNIPRESENCE SEEN by the MEMORY of the PAST → HEAR the PRIVATE SILENCE. The INVARIANT centre of all rotation. PIXEL | VALUE

VI

1074

 MATERIAL  |  ORNAMENT  |  INFORMATION  AIR to WATER. MATTER (SUBSTANCE of SPACE) is DIRECTED by the ENVIRONMENT (the future SPHERE around the PAST) and TEACHES the IMAGINATION (the PAST of the FUTURE).

1075

On the RATIONAL scalarity this is ARTICULATED as the  MATERIAL . On the REAL scalarity this is ARTICULATED as the  ORNAMENT . On the COMPLEX scalarity this is ARTICULATED as the  INFORMATION .

IMAGINATION

1076

I take the view from the FUTURE PAST.

1079

It BRIDGES WATER → EARTH, EAR → HAND, SENSIBLE → ACTUABLE. and active → active.

1080

FUTURE PAST HEARD by the PRIVATE SILENCE → SHOWN to the VISION of the FUTURE. It is HEARD by SILENCE to be SHOWN to the FUTURE. The PAST drives the FUTURE along lines of necessity. Space: the centre of the world. Time: the production of things IMAGE

1081

 AXIS  |  CONSTRUCTION  |  INFRASTRUCTURE  WATER to EARTH. The IMAGINATION (the PAST of the FUTURE) is TRAINED by the MATTER (SUBSTANCE of SPACE) and REFLECTED by the TEXTURES (SPATIAL IMAGES of THINGS).

1082

On the RATIONAL scalarity this is ARTICULATED as the  AXIS . On the REAL scalarity this is ARTICULATED as the  CONSTRUCTION . On the COMPLEX scalarity this is ARTICULATED as the  INFRASTRUCTURE .

1083

DECODING and the PRIVATE

1078

CODING and the PUBLIC

The actual PRESENCE REFLECTS the IMAGINATION.

ENCODING and the SACRED

1077

1084

TEXTURE

1085

IV

The IMAGES DISSOLVE to the ENVIRONMENT.

1087

I take the view from the OUTSIDE.

1088

It BRIDGES EARTH → FIRE, HAND → TONGUE, ACTUABLE → ACTUABLE. and active → passive.

1089

OUT SHOW to the VISION of the FUTURE → TALKED to the PUBLIC. The actual PRESENCE of an articulated BODY. The SYNCHRONICITY of all rotations. TEXTURE

1090

 WALL  |  SKIN  |  INTERFACE  EARTH to FIRE. The TEXTURES (SPATIAL IMAGES of THINGS) REFLECT the IMAGINATION (future AXIS to the past) and DISSOLVE into the ENVIRONMENT (the SPHERE around the PAST).

1091

On the RATIONAL scalarity this is ARTICULATED as the  WALL . On the REAL scalarity this is ARTICULATED as the  SKIN . On the COMPLEX scalarity this is ARTICULATED as the  INTERFACE .

V

1086

VI

ENVIRONMENT

1092

I take the view from the PAST FUTURE.

1095

It BRIDGES FIRE → AIR, TONGUE → EYE, ACTUABLE → SENSIBLE. and passive → passive.

1096

PAST FUTURE TALK to the PUBLIC → SEE the MEMORY of the PAST. The PAST talks towards a contingent FUTURE, politics. Space: the edge of the world. Time: the vertical axis of a rotating mechanics. Simulation | ENVIRONMENT

1097

 FLOOR/CEILING  |  MECHANICS  |  LANGUAGE  FIRE to AIR. The ENVIRONMENT (the SPHERE around the PAST) DISSOLVE the TEXTURES (SPATIAL IMAGES of THINGS) and DIRECT the MATTER (SUBSTANCE of SPACE).

1098

On the RATIONAL scalarity this is ARTICULATED as the  CEILING . On the REAL scalarity this is ARTICULATED as the  MECHANICS . On the COMPLEX scalarity this is ARTICULATED as the  LANGUAGE .

1099

DECODING and the PRIVATE

1094

CODING and the PUBLIC

The ENVIRONMENT DIRECTS the SUBSTANCES.

ENCODING and the SACRED

1093

IV

V

VI

BOOKVI

DECODING and the PRIVATE

ENCODING and the SACRED

CODING and the PUBLIC

EPILOGUE

DECODING and the PRIVATE

1100

This book is about WHAT to SEE and SAY about ARCHITECTURE with the EYES of today.

1101

IV Peter Greenaway, Prospero’s Books, 5:38, 1991.

It introduces quite a complex scheme. It is important that it stays implicit for it should work beyond every specific style and it can be used in any characteristic way.

1103

It especially is not about problem and solution. Which is almost inverse to PARAMETRISM whose technological PRAGMATISM forces things towards looking all the same.

1104

It is MECHANICS around INVARIANCES abstracting from DIFFERENCES, giving stability in talking about architecture without constraining it.

1105

The terms introduced and the mechanics used are not fully developed by far. But they are powerful and stable.

1106

It is intentionally designed like a PROGRAMMING LANGUAGE which is detached from everything, to be open to CODE anything.

1107

And it should be learnt like a programming language. It needs repetition, patience, and an actual context to practice.

V

1102

VI

1109

The mathematics and the mechanics are meant to stay the same, the terms and metaphors will develop differently.

1110

It also has a deep integration of computational terms and techniques, for the CODE can be evaluated in line with today’s techniques.

1111

There have been a few examples of what to see and talk about as an architect and what to learn from the old masters on today’s COMPLEX scalarity.

1112

To give more examples in all directions would be exhausting to read. This text is meant to motivate you to continue like this in your own terms.

1113

The questions of the practical HOW to do things today will be explicated in Books VII–X: artificial intelligence, natural communication, digital articulation, and cultural heritage.

1114

.

DECODING and the PRIVATE

No need to remind us again, that the terms and metaphors used are a continental Western rendering and can be read as examples for other cultures.

CODING and the PUBLIC

1108

ENCODING and the SACRED

If mastered, it promises COMMUNICATION across all times and cultures.

IV

V

VI

APPENDIX

VOLUMEII

ENCODING and the SACRED CODING and the PUBLIC

1115 ↗ 1116 ↗ 1117 ↗

DECODING and the PRIVATE

INDEX OF WORDS SOURCES FOR IMAGES AND GRAPHICS COLOUR CODE

IV

V

VI

A

CODING and the PUBLIC

ACTIVE SUBJECT 269 ACTUABLE 988, 995, 1002, 1080, 1088, 1096 ACTUATOR 365, 942 ADMINISTRATION487 ALGEBRA MAJOR 124 ALGEBRA MINOR 296 ALPHABET 171, 187 ALWAYS COMPLETE 977 ALWAYS CORRECT 1063 ANIMATED 515, 661, 663 ANY CHARACTER 298 ANY DATA 662 ANY FORM 657 ANY INSIDE 198, 347 ANY LIST 273 ANY MACHINE 535 ANY NUMBER 164 ANY OBJECT 535 ANY SET 126 APPLICATION608 ARCHAEOLOGY990 ARCHITECT1024 ARCHITECTURE 2, 492, 511, 512, 527, 529, 674, 685, 688, 692, 964, 977, 1030,  1063, 1100 ARITHMETIC63 ARITHMETIC MAJOR 214 ARITHMETIC MINOR 341 ARRAY 226, 312, 329, 338, 848 ARTICULATION 166, 195, 196, 199, 253, 382, 531, 756, 951, 977, 983, 989, 990, 997,  1004, 1024, 1075, 1083, 1091, 1099 ARTIFICIAL INTELLIGENCE 657, 660, 665 ASPECT 132, 169, 199, 221, 278, 303, 348, 386 ASSEMBLY LANGUAGE 542, 550 ASSEMBLY PROGRAM 551 ASSIGNMENT576 ASSOCIATION591 ATOM276 AUDITIVE 252, 253, 483, 553, 644, 942 AUDITIVE BEING 126 AUDITIVE ENVIRONMENT 381 AUDITIVE HARMONY 298 AUDITIVE PRESENCE 194 AWARE 989, 1003 AXIOM 346, 801, 806 AXIS 770, 1036, 1082, 1083, 1090

ENCODING and the SACRED

INDEX OF WORDS

1115

B

C CALCULATE1063 CARE487 CARNOT 606, 608 CARTESIAN 1017, 1037, 1041, 1042, 1052 CATEGORY 171, 397 CATHARSIS15 CEILING 1098, 1099

DECODING and the PRIVATE

BAROQUE966 BASE 753, 983 BIG DATA 655, 659, 664 BODY 199, 998, 1089 BOOK 15, 22, 29, 756, 794, 829 BOUNDARY520 BRANCHING283 BRIDGE 735, 736, 739, 740, 742, 981, 988, 995, 1002, 1072, 1080, 1088, 1096 BUILDING861 BUS 538, 544

IV V

CHARACTER 59, 114, 121, 122, 126, 164, 187, 194, 211, 263, 264, 273, 343, 381, 394,  403, 404, 477, 483, 711, 734, 977 CHARACTERISE SPACE 360 CIPHER 281, 283 CIRCLE 34, 99, 100, 101, 102, 734, 738, 740, 751, 786, 824 CIRCULAR LINE 59 CIRCULAR SYNCHRONICITY 736 CITY 477, 479, 490 CIVIL477 CIVILISATION 659, 660, 685, 702 CLASS314 CLASSICAL MECHANICS 690 CLASSICAL ORDER 55 CLASSIFICATION 331, 397 CLOCK661 CODE 20, 25, 44, 66, 74, 85, 86, 101, 104, 119, 211, 451, 477, 490, 509, 535, 553, 644, 688,  694, 697, 997, 1020, 1022, 1024, 1026, 1027, 1028, 1029, 1042, 1053, 1056, 1106, 1111 COLLISION 977, 1063 COLOUR 258, 314, 408, 493, 564, 609, 751, 840, 984 COLUMN 753, 990 COMEDY 22, 44, 66 COMING BACK HOME 10, 23, 31, 43, 72, 425 COMMAND 545, 551, 661 COMMON 477, 702 COMMUNICATION 86, 1108 COMMUNITY181 COMPLETE1031 COMPLEX 109, 110, 111, 336, 357, 414, 434, 445, 494, 535, 746, 749, 751, 966, 983,  990, 997, 1004, 1020, 1022, 1075, 1083, 1091, 1099, 1112 COMPLEX EYE 1025, 1026 COMPLEX PLANE 286, 940 COMPLEX SCALARITY 360, 371, 374, 753 COMPUTING 500, 511 CONCEPT 118, 314, 318 CONDITIONAL569 CONNECTION171 CONSTELLATION 118, 965, 1018 CONSTITUTION 248, 347, 515, 537, 538, 997, 1014, 1015, 1016, 1017, 1018, 1024,  1036, 1037, 1042, 1053 CONSTRUCTION 248, 442, 520, 1082, 1083 CONSUMPTION 953, 1003 CONTINGENCY 982, 989 CONTRACT347 CONTROL 479, 482, 544, 551 CONTROL OF FLOW 665 COORDINATE201 CORINTHIAN 66, 74 COROUTINE616 COSMOS 425, 964 COURSE214 CREATION 656, 738 CRISTALLOGRAPHY496 CULTURAL HERITAGE 659 CYLINDER 810, 826

D

VI

DATA 642, 664, 990, 1024 DATASET331 DATA STRUCTURE 596 DATA TYPE 596 DECLARATIVE 688, 689 DECLARATIVE LANGUAGE 652 DECLARATIVE SOFTWARE 662 DECODING 25, 43, 64, 72, 85, 86, 102, 104, 425, 709, 713 DEFINITION 314, 585 DIALECTIC 22, 684 DICTIONARY396 DIFFERENCE 251, 1104 DIGITAL 650, 652, 654, 700 DIRECT 198, 220, 302, 347, 962, 1074, 1094, 1098 DIRECTION 131, 253, 516, 521 DIRECTIONAL LIGHT 517 DISSOLVE 1098, 1090 DO 251, 588, 875 DOMAIN1024 DORIC 59, 60, 66, 70 DRAWING 437, 438, 991 DRIVEN 520, 662, 1003 DYNAMICS605

E EAR 34, 734 EARTH 249, 257, 261, 682, 736, 740, 742, 829, 995, 996, 1002, 1063, 1080, 1082, 1088, 1090 ECONOMY 474, 479, 488, 546, 598

FACADE 848, 997, 1010, 1014, 1015, 1016, 1017, 1018, 1020, 1024, 1036, 1037, 1043 FACE 772, 788, 998 FACET998 FIELD197 FILL652 FIRE 988, 995, 1088, 1090, 1096, 1098 FLOOR1098 FLOW 517, 551 FLOW OF COMMANDS 552 FORCE231 FORGET 164, 298, 664, 665, 690, 691 FORM 369, 453, 454, 460, 477, 560, 564, 605, 609, 654, 657, 664, 666, 669, 674, 678, 679 FUNCTIONALISM559 FUTURE 122, 131, 168, 187, 198, 214, 220, 233, 264, 277, 302, 347, 367, 385, 439,  442, 445, 572, 579, 588, 781, 818, 952, 959, 989, 996, 1003, 1070, 1074, 1081,  1082, 1089, 1097 FUTURE IMAGE 619, 626, 634 FUTURE PAST 1001, 1005, 1079, 1081 FUTURE VISION 122, 129, 196, 275, 345, 875

GEOMETRIC ENTITY 739 GEOMETRIC OBJECT 172 GEOMETRY 59, 739, 751 GEOMETRY MAJOR 162, 454 GEOMETRY MINOR 271 GIVE BALANCE 277 GLOBAL OBJECTIVITY 982 GOOD 474, 485, 487, 488 GRAMMAR 258, 268, 379, 382, 383, 385, 386, 387, 388, 394, 397, 400, 439, 445, 610,  684, 851, 1024 GRAPH 172, 181, 183, 185, 187, 189 GRAPHIC 201, 223 GRAPHS ENCODE MAPS 175 GRAPHS ENCODE MECHANICS 177 GRAVITATIONAL BODY 348 GRAVITY 197, 233, 346, 522, 527, 789 GRID 247, 248, 249, 251, 256, 734, 749, 751 GRID NOVEL 577 GROUND251

DECODING and the PRIVATE

G

CODING and the PUBLIC

F

ENCODING and the SACRED

EDGE 172, 201 EDGE OF THE WORLD 452 ELECTRON363 ELEMENT 502, 504, 856 EMANCIPATION 251, 261, 458, 462, 480, 482, 544, 596, 687 EMBODY996 ENCAPSULATION631 ENCODE FREQUENCIES 236 ENCODE IMAGES 309 ENCODE PICTURES 200 ENCODE SIGNIFICATIONS 314 ENCODE SOUNDS 306 ENCODING 13, 42, 60, 70, 83, 84, 85, 86, 99, 104, 121, 122, 134, 135, 136, 170, 171, 172,  189, 201, 222, 223, 241, 263, 264, 279, 280, 288, 304, 305, 312, 329, 338, 349,  352, 360, 387, 388, 403, 404, 405, 406, 414, 415, 418, 428, 431, 434, 706, 710 ENCRYPTION87 ENCYCLOPAEDIA394 ENERGETIC 553, 644 ENERGY 130, 827 ENGINEERING 527, 530, 687 ENVIRONMENT 129, 196, 275, 345, 518, 610, 806, 901, 961, 962, 1074, 1086, 1090,  1092, 1094, 1097, 1098 ENVIRONMENTAL CONDITION 379 ENVIRONMENTAL MEMORY 815 ENVIRONMENTAL TEMPERAMENTS 264 ESTABLISH338 EUCLIDEAN 1017, 1037, 1041, 1042, 1048, 1052 EVALUATION 265, 273, 274, 294, 385 EVENT 183, 616 EVERY CHARACTER 216 EVERY LIST 194 EVERY NUMBER 381 EVERY OUTSIDE 131, 277 EVERY SET 343 EXISTENCE619 EXPLORE982 EXPONENTIAL103 EYE 367, 427, 734, 840, 846, 856, 861, 875, 898, 904, 910, 924, 982, 989, 996,  1003, 1012, 1024, 1051, 1100

H

IV

HAND 995, 1002, 1080, 1088 HARMONIC 275, 296, 299, 300, 739 HARMONY220 HEALTH 129, 196, 264, 275, 296, 331, 345, 523, 872, 953, 999, 1003 HEALTHY BODY 782, 890 HEAR 129, 218, 220, 259, 299, 530, 579, 586, 632, 682, 777, 982, 1003, 1073, 1081 HEAR SPACE 714, 719 HIGH LEVEL CODE 596 HIGH LEVEL LANGUAGE 550, 551, 595, 641, 654 HISTORICITY964 HOME 464, 474, 478, 484 HOW TO DO 713, 754 HUMAN BODY 890 HUMAN PROPORTION 729, 742, 753, 829

I

V

ICHNOGRAPHIA 29, 34, 658, 660, 686 IDEA 122, 130, 567, 588, 761, 890, 950, 982 IMAGE 236, 266, 299, 300, 302, 303, 304, 305, 329, 331, 396, 397, 398, 426, 427,  428, 431, 442, 482, 725, 727, 730, 921, 934, 1081 IMAGE HEALTH 624 IMAGES DISSOLVE 961, 1086 IMAGINARY 111, 984 IMAGINARY AXIS 122, 264 IMAGINARY LIGHT 494 IMAGINATION 228, 231, 236, 572, 588, 960, 1074, 1076, 1078, 1082, 1090 IMAGINE 72, 256, 579, 1017 IMPERATIVE 687, 689 IMPERATIVE LANGUAGE 650 IMPERATIVE SOFTWARE 661 INCLUDE 216, 381 INCOMMENSURABLE 35, 734, 735 INFORMATION 1074, 1075 INFRASTRUCTURE 1082, 1083 INHERITANCE631 INNER1061 INNER ANYWHERE 166, 218, 300, 383 INNER FORCES 522 INNER SELF 579, 588, 777 INSIDE 111, 121, 168, 220, 263, 302, 385, 980, 984, 1071 INSIST634 INSTALL168 INSTRUMENT 1030, 1031 INTEGER352 INTELLECT 738, 982 INTERFACE 623, 1090, 1091 INTERNET 664, 666, 669 INTERNET PUBLISHING 663 INVARIANCE 166, 218, 294, 300, 383, 398, 400, 655, 657, 681, 725, 751, 777, 815,  890, 898, 924, 953, 1003, 1073, 1104 INVARIANT ATOM 761 INVARIANT AXIOM 799 INVARIANT EVALUATION 263 INVARIANT INSIDE 131 INVARIANT NAVEL 752 INVARIANT OMNIPRESENCE 753 IONIC 63, 64, 66, 72 IRRATIONAL734 ITERATION569

J JOINING 492, 496, 500 JPEG236

VI

K KNOW453

L LANGUAGE 119, 680, 688, 690, 691, 1024, 1098, 1099 LAYER861 LAYOUT185 LEARNING ORGANISM 303

ENCODING and the SACRED

LEAVING HOME 10, 11, 31, 42, 70, 425 LIBERATION 119, 251, 260, 455, 460, 468, 481, 551, 642 LIGHT 130, 233, 257, 493, 527, 531, 761, 775, 840, 977, 982, 996, 1012, 1020,  1022, 1024, 1039 LINE 33, 61, 165, 166, 168, 169, 170, 171, 172, 179, 187, 189, 247, 248, 249, 256,  268, 434, 439, 445, 734, 740, 751, 765, 782, 788, 898, 936, 984, 996 LINEAMENT 734, 786, 791, 792, 983 LINEAR252 LINEAR CIRCLES 63 LINEAR EQUATIONS 233 LINEAR INVARIANCE 736 LINEARITY 516, 543, 552, 597, 643, 738 LINEAR OPERATION 521, 537 LINE POEM 565 LINES CHARACTERISE 768 LINES ENCODE 181, 183, 185 LINES SEE 251 LIST 305, 306, 309, 314, 361, 591 LISTEN 124, 128, 253, 529, 588 LOCAL SUBJECTIVITY 996, 1044 LOCATION789 LOGARITHM103 LOGICAL UNIT 538, 543, 544 LOGOS MAJOR 192 LOGOS MINOR 379, 454

M

CODING and the PUBLIC

MACHINE 228, 231, 248, 405, 520, 523, 527, 530, 542, 550, 595, 641, 820, 1004 MAINFRAME563 MAJOR 42, 53, 70, 114, 121, 122, 257, 260, 403, 409, 527, 529, 562, 650, 710,  713, 717, 756, 788, 947, 975 MAKING658 MARKUP664 MARKUP LANGUAGE 641, 642 MASS 384, 531, 799, 827, 1063 MASSIVE 546, 598 MASSIVE IMAGE 820 MASSIVE TIME 725 MATERIAL 219, 564, 609, 820, 1074, 1075 MATERIALITY 799, 815 MATHEMATICA 689, 691 MATTER 301, 799, 827, 898, 959, 1003, 1070, 1074, 1082, 1098 MEANING 658, 666 MECHANICS 110, 117, 119, 189, 248, 515, 518, 527, 529, 535, 537, 542, 550, 595,  641, 679, 681, 687, 691, 1030, 1098, 1099, 1104 MEMORIAL455 MEMORISE 13, 453, 806, 808 MEMORY 129, 162, 167, 196, 275, 345, 434, 439, 445, 451, 572, 588, 634, 658,  706, 768, 770, 777, 843, 951, 982, 985, 989, 1073, 1097 MEMORY OF THE PAST 567, 613 METHAPOR742 MINOR 43, 53, 72, 115, 257, 261, 263, 264, 403, 411, 527, 530, 607, 652, 710, 713,  725, 734, 792, 794, 826, 956, 1061 MODEL258 MODULE753 MOVEMENT 179, 249, 251, 517

N

O OBJECT OBJECTIVITY OBJECT ORIENTED LANGUAGE OBJECT ORIENTED PROGRAM OMNIPRESENCE

100, 179, 405, 520, 652, 768, 1005 515, 535 595, 596, 654 642 254, 255, 761, 799, 840, 851, 977, 982, 1073

DECODING and the PRIVATE

NAME 13, 226, 711, 763, 768 NAVEL 734, 738, 1068 NECESSITY 486, 487, 996, 1003 NESTING585 NETWORK181 NEVER COMPLETE 1063 NEVER CORRECT 977 NEWTON 561, 563 NIGHT 122, 247, 411, 522, 527, 710, 713, 725, 730, 794, 826 NOTATION352 NOVEL122 NUMBER 63, 115, 121, 122, 126, 194, 211, 216, 226, 228, 236, 241, 263, 264, 280,  281, 298, 305, 306, 309, 312, 314, 329, 338, 343, 361, 396, 403, 477, 479, 486,  711, 801, 806, 1063 NUMBERS ENCODE 231, 233, 243, 294

IV

OMNIPRESENT INVARIANCE 613, 634, 794 OMNIPRESENT LISTENER 132 OMNIPRESENT OUTSIDE 198 OMNIPRESENT POINT 121 ONTOLOGY642 OPERATE890 OPERATION543 ORDER 331, 332, 334, 336, 338, 634 ORDER OF THINGS 626 ORIGIN1003 ORNAMENT 792, 824, 912, 1074, 1075 ORTHOGRAPHIA 15, 33, 656, 659, 686 OTHER34 OUTER975 OUTER EVERYWHERE 166, 218, 300, 383 OUTER PRESENCE 781, 818 OUTER SPACE 998 OUTLINE650 OUTSIDE 111, 121, 168, 220, 263, 302, 385, 994, 1010, 1087

P

V VI

PARAMETRISM 859, 1103 PART 332, 579, 910 PARTICIPATION 626, 634 PARTICLE924 PAST 13, 122, 129, 131, 162, 168, 196, 198, 220, 233, 264, 275, 277, 302, 338,  345, 347, 385, 398, 400, 439, 442, 445, 572, 588, 612, 634, 768, 781, 806, 818,  950, 982, 989, 1003, 1073, 1074, 1081, 1082, 1090, 1097, 1098 PAST FUTURE 987, 991, 1095, 1097 PEOPLE 13, 26, 76, 457, 462, 466, 468, 470, 485, 487, 694, 697 PERCEPTIVE SCREEN 169 PERSPECTIVE932 PICTURE 192, 195, 196, 198, 199, 201, 211, 253, 254, 255, 256, 267, 428, 434, 674,  717, 719, 730, 775, 853, 952, 992, 996 PICTURE IMAGE 734 PICTURE PRESENCE 570 PICTURES ENCODE 205, 207, 209 PIXEL 894, 1073 PIXEL INVARIANCE 632 PLANE 99, 102 PLATONIC SOLIDS 940 POEM 119, 122 POETRY189 POINT 124, 128, 129, 131, 132, 134, 135, 253, 254, 255, 256, 258, 265, 431, 753,  758, 761, 763, 788, 799, 836, 840, 898 POINT OMNIPRESENCE 586 POLITICAL 553, 644 POLITICS 475, 479, 488, 975 POLYMORPHISM637 POP559 POSTMODERN604 POTENTIAL 197, 827 PRAGMATISM1103 PREDICTABILITY331 PRESENT 254, 255, 761, 777, 799, 815, 856, 861, 910, 960, 996, 1012, 1020, 1022,  1024, 1037, 1039, 1044, 1078, 1089 PRESENT BODY 192, 567, 572, 579, 775 PRESENT EXISTENCE 374, 376 PRESENT INSISTENCE 626 PRESENT INVARIANCE 271 PRESENT OUTSIDE 347 PRESENT PICTURE 121 PRESENT SELF 124, 567 PRESENT SENSE 278 PRESENT SKIN 813 PRESENT SYNCHRONICITY 341 PRIVATE 31, 1055 PRIVATE SILENCE 982, 1003, 1073, 1081 PROBABILITY 183, 665 PROCESSOR 535, 537, 538, 542, 983 PRODUCE 228, 231, 236 PRODUCT820 PRODUCTION 398, 782, 794 PRODUCTIVE SCHEME 221 PROGRAM 477, 563, 598, 687, 1004, 1024 PROGRAM CONTROL 545 PROGRAMMING LANGUAGE 1106 PROJECTIVE247 PROPERTY 334, 493, 1005, 1041 PROPORTION 168, 194, 211, 343, 488, 730, 731, 734, 735, 739, 751, 890 PROPORTIONAL CONSTITUTION 66 PUBLIC 5, 9, 31, 70, 72, 74, 76, 250, 390, 400, 414, 451, 464, 467, 468, 473, 475,  476, 485, 486, 490, 494, 504, 509, 685, 694, 697, 702, 706, 710, 964, 989, 996, 1024,  1055, 1089, 1097 PUBLIC CODE 707 PUBLIC CONSTITUTION 492 PUBLIC ENCODES 124, 132, 162, 169, 192, 199, 214, 221, 271, 278, 296, 303, 341,  348, 379, 386

489 44, 74, 269, 510, 692, 704 119 482 689, 690

Q QUALITY288 QUANTITY264 QUANTUM691 QUANTUM MECHANIC 473

R

CODING and the PUBLIC

RATIO 260, 271 RATIO LIBERATES 483 RATIONAL 35, 332, 354, 356, 385, 451, 829, 831, 966, 983, 990, 997, 1004, 1075,  1083, 1091, 1099 RATIONAL CONSTITUTION 439, 445 RATIONAL EYES 1015, 1016, 1017 RATIONALISE 274, 275, 383, 398, 400, 613, 626, 634, 650 REAL 109, 111, 334, 356, 357, 413, 428, 431, 439, 442, 451, 493, 502, 560, 605, 734,  742, 829, 831, 966, 983, 990, 997, 1004, 1017, 1075, 1083, 1091, 1099 REAL AXIS 121, 263 REAL EYE 1015, 1016 REALISATION369 REALISE 257, 300, 341, 344, 345, 371, 619, 626, 652 REALITY 261, 402, 442, 483, 613, 619 REAL SCALARITY 376, 791 REASONABLE VOLUME 782 RECOGNITION338 RECORD 338, 612 RECURSION569 REFLECT 960, 1078, 1082, 1090 REFLECTIVE247 REGISTER 538, 544 RENAISSANCE 260, 936, 966 RENDERING223 REPETITION 249, 331 RESOLUTION283 RESPONSIBILITY 487, 989 REVOLUTION261 RHETORIC 29, 684 RIGHT 488, 518 RIGIDITY119 RISE UP 688 ROOF1004 ROTATE1037 ROTATING SKY 522 ROTATION 826, 1032, 1033, 1036, 1039, 1041, 1042, 1043, 1050, 1055 ROTATIONAL AXIS 817 ROTATIONAL SPACE 1044 RULE 388, 848

ENCODING and the SACRED

PUBLIC LIBERATES PUBLIC TALK PUBLIC VOICE PURE RATIO PYTHON

S DECODING and the PRIVATE

SACRED 13, 31 SACRIFICED 402, 452 SAME33 SATIRE 29, 43, 64 SCAENOGRAPHIA 22, 686, 702 SCALARITY1051 SCIENCE496 SCOPE585 SCREEN 70, 258 SEE 129, 165, 166, 256, 274, 367, 529, 530, 531, 565, 567, 572, 579, 588, 725, 848,  856, 861, 875, 910, 924, 950, 982, 984, 989, 1012, 1073 SEE CODE 1025 SEE LINES 162 SEE TIME 722, 727 SELF 953, 1003 SENSE 656, 666 SENSIBLE 981, 988, 1002, 1072, 1080, 1096 SENSOR288 SENSORY942 SEQUENCE 544, 545, 551, 768 SET 397, 711 SHAPE GRAMMAR 852 SHOW 196, 198, 217, 218, 259, 344, 361, 529, 530, 531, 572, 577, 579, 624, 952,  996, 1003, 1081, 1089 SHOW GRIDS 214 SHOW REALITY 302

IV V

SIGNIFICATION397 SIGNIFY711 SIGNIFY ADDRESSES 544 SIGNIFY HIERARCHIES 596 SIGNIFYING CHARACTERISTICS 280 SIGNIFYING NUMBERS 318 SILENCE1081 SIMULATION241 SKELETON515 SKIN 1090, 1091 SLIT 777, 815 SORTED THINGS 374, 376 SOUND 626, 634 SPACE 59, 61, 131, 168, 198, 211, 220, 277, 286, 302, 347, 374, 376, 385, 453, 492,  553, 619, 644, 650, 742, 746, 753, 756, 791, 851, 856, 934, 940, 977, 982, 984,  996, 1022, 1037, 1044, 1051, 1074, 1082, 1098 SPATIAL IMAGE 1082, 1090, 1098 SPEAKER361 SPECTRUM991 SPHERE 803, 826, 1074, 1090, 1098 SPHERICAL 131, 168, 277, 385 SQUARE738 STABILITY2 STANDALONE PROGRAM 552, 597 STOCHASTIC PARAMETER 243 STRUCTURALISM604 STRUCTURE 453, 454, 462, 477, 564, 605, 609, 654, 655, 664, 666, 669, 674, 678, 679 SUBJECT 515, 535, 991 SUBJECTIVITY520 SUBSTANCE 962, 1074, 1082, 1094, 1098 SYCHRONICITY734 SYMBOL397 SYMBOLIC CHARACTER 388 SYMBOLIC EMANCIPATION 605 SYMBOLIC LIBERATION 560 SYMBOLIC NAME 135, 712 SYMBOLISATION 414, 551, 642 SYMMETRY117 SYNC 777, 815 SYNCHRONICITY 166, 218, 300, 371, 383, 617, 717, 749, 752, 846, 851, 861, 904,  975, 989, 1089 SYNCHRONISED BODY 951, 989 SYNCHRONISED EXISTENCE 613, 619, 626 SYNCHRONISED FACE 775 SYNCHRONISED PRESENCE 756 SYNCHRONISED TEXTURE 263, 813 SYNCHRONOUS1063 SYNCHRONISE808 SYSTEM233

T

VI

TALK 74, 101, 187, 439, 445, 509, 529, 530, 561, 562, 563, 565, 567, 570, 577,  586, 606, 607, 608, 610, 613, 617, 624, 626, 632, 680, 685, 707, 712, 989,  996, 1089, 1097 TALKING IN PUBLIC 10, 16, 31 TEACH1074 TECHNIQUE500 TELL259 TEXT211 TEXTURE 258, 267, 341, 344, 347, 348, 349, 352, 360, 367, 374, 376, 531, 617, 907,  1082, 1084, 1089, 1090, 1098 TEXTURES ENCODE 350, 351, 369, 371 THEORY1030 THERMODYNAMIC469 THING 296, 331, 332, 334, 336, 338, 493, 494, 619, 634, 1082, 1090, 1098 THINGS OF REALITY 613 THREE832 TIME 63, 131, 198, 277, 286, 306, 331, 338, 347, 352, 374, 376, 453, 492, 546, 598,  663, 761, 770, 794, 799, 890, 924, 934, 940, 989, 1003, 1063 TONGUE 988, 995, 1088, 1096 TRAGEDY 15, 42, 60, 76 TRAINING 386, 959, 1070, 1082 TRANSLATION400 TRANSPARENT SPACE 717 TREATISE1030 TRIVIUM 1, 683 TRUTH1031 TUNING30 TYPE656 TYPIFICATION576

U UNDERSTANDING URBANISATION

345, 379, 382, 383, 391, 398, 400, 612, 613, 619 477, 479, 489, 660, 685

USER USER INTERACTIONS

662, 663 597, 642, 643

VALUE 271, 275, 277, 278, 279, 280, 336, 371, 434, 494, 796, 826, 1005, 1073 VALUES ENCODE 350, 351 VARIANT INSIDE 277 VELOCITY 167, 179, 789 VERTICE 172, 187, 201 VISIBLE100 VISION 217, 218, 220, 221, 222, 223, 226, 228, 231, 233, 236, 241, 243, 266, 428, 431,  442, 781, 818, 952, 996, 1003, 1081, 1089 VISUAL 223, 247, 252, 484, 486, 546, 598, 942 VISUAL ANALYSIS 216 VISUAL INVARIANCE 273 VISUAL MEMORY 164 VISUAL REALITY 482 VISUAL SYNCHRONICITY 343 VOCABULARY258 VOICE 579, 680, 681 VOLUME 779, 788

ENCODING and the SACRED

V

W

Y YOUR681

1116

4 https://i.pinimg.com/originals/fb/1f/a1/fb1fa1b05d99e6ecc8a8e3c42eab3b4f.jpg 12 https://i.pinimg.com/originals/7c/d7/ec/7cd7ecd6a63bd8aa935301e8bcb2d213.jpg 16 http://digi.ub.uni-heidelberg.de/diglit/serlio1609/0088 18 https://bauforumstahl.de/fileadmin/_processed_/4/5/csm_Civic-Architects---LocHal-Tilburg--Credits-Stijn-Bollaert---06_0b204ea7a5.jpg 22 http://digi.ub.uni-heidelberg.de/diglit/serlio1609/0087 25 https://arquitecturaviva.com/assets/uploads/obras/40235/av_91034.jpeg?h=098e5fa6 29 http://digi.ub.uni-heidelberg.de/diglit/serlio1609/0089 53 https://de-academic.com/pictures/dewiki/69/Eberhard_Weber_beim_MPS_Festival_1971_ %28Heinrich_Klaffs_Collection_18%29.jpg 58 https://upload.wikimedia.org/wikipedia/de/f/f6/Säulenordnung-2.jpg 62 https://upload.wikimedia.org/wikipedia/de/f/f6/Säulenordnung-2.jpg 65 https://upload.wikimedia.org/wikipedia/de/f/f6/Säulenordnung-2.jpg

DECODING and the PRIVATE

SOURCES FOR IMAGES AND GRAPHICS

CODING and the PUBLIC

WALL 1090, 1091 WAR MACHINE 486 WATER 981, 1002, 1072, 1074, 1080, 1082 WEB APPLICATION 643 WEIGHT 219, 789 WELL523 WHAT 74, 475, 756, 937, 1100 WHAT TO SAY 713, 754 WIND808 WINDOW848 WIREFRAME531 WORK522 WORLD 294, 406, 982 WRITING189 WRONG475

IV V VI

69 https://pbs.twimg.com/media/Dd0MKcbV0AIvE1x.jpg:large 71 https://pbs.twimg.com/media/EdnEX-rXoAAXdF_.jpg 73 https://epiteszforum.hu/uploads/images/2010/03/1920_722-zmn4kv-sanaa-christian-diorbuilding-omotesando-tokio-foto-hsuzuki-01.jpg 97 https://m.media-amazon.com/images/M/MV5BMTU2MTQxNTE4OV5BMl5BanBnXkFtZTgw NzU1NTU5MTE@._V1_.jpg 98 https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Home_made_Bento.jpg/ 1280px-Home_made_Bento.jpg 106 https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Small_bike%2C_big_road_ %2837289758876%29.jpg/2560px-Small_bike%2C_big_road_%2837289758876%29.jpg 108 https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Athen_BW_2017-10-09_1437-37.jpg/2560px-Athen_BW_2017-10-09_14-37-37.jpg 120 https://upload.wikimedia.org/wikipedia/commons/5/50/Beatrice_Cenci.jpg 154 https://www.kunstkopie.de/kunst/parmigianino/Turkish-Slave.jpg 176 https://www.custom-wallpaper-printing.co.uk/images/POS/wallpaper/tube-map-shadowlarge.jpg 178 https://www.researchgate.net/profile/Ofelia-Corbu/publication/237652349/figure/fig17/ AS:330783635066880@1455876372066/The-scheme-for-a-linear-hydraulic-engine-usageThe-component-parts-for-the-scheme-from.png 186 https://d3i71xaburhd42.cloudfront.net/b3806e22dcf5a79353ccdc344cf42b836a21b7e7/ 2-Figure1-1.png 188 http://photos1.blogger.com/img/18/1753/400/phoenician.jpg 208 https://i.pinimg.com/originals/98/1c/9e/981c9e69e8150da1a7bba5bfb3430fb6.jpg 210 https://wiki.openstreetmap.org/w/images/1/12/ScalableMapsLondonBW.png 212 https://archive.org/details/banco-rari-215_202101/page/n19/mode/2up 232 https://www.fosterandpartners.com/media/2632341/hero_0793_fp276124.jpg?width=3840 &quality=85 240 https://d5wt70d4gnm1t.cloudfront.net/media/a-s/articles/3242-828812449395/anatomyof-an-artwork-betty-1977-by-gerhard-richter-ORIG.jpg 262 https://moar-prod.imgix.net/5b563649-2908-4849-8d6a-57d2b1c2c7e9/IM.138.jpg?auto= compress%2Cformat&fit=min&fm=jpg&q=80&rect=0%2C0%2C2400%2C2897 290 https://asset.conrad.com/media10/isa/160267/c1/-/de/152977_BB_00_FB/image.jpg?x= 1000&y=1000&format=jpg&ex=1000&ey=1000&align=center 291 https://reference.wolfram.com/language/workflow/AccessGPIOOnRaspberryPi.html 292 https://upload.wikimedia.org/wikipedia/commons/thumb/7/70/AD570_571.png/2560pxAD570_571.png 316 https://learn.alwaysai.co/hs-fs/hubfs/object-dectection-4.jpg?width=1200&name=objectdectection-4.jpg 317 https://listverse.com/wp-content/uploads/2012/02/7_7_bombtriall_468x395.jpg 321 https://olddesignshop.com/wp-content/uploads/2017/10/Vintage-Dictionary-Page-Pump kin-OldDesignShop.jpg 325 https://archinect.imgix.net/uploads/n4/n4hkhcd4lwx85m0n.jpeg?fit=crop&auto=compress %2Cformat&w=1200 333 https://i.pinimg.com/originals/96/08/54/96085462d84f6d0fd5822904cb75c74b.jpg 335 https://images.squarespace-cdn.com/content/v1/53172b1be4b0cc8a5401db4a/161488 1660374-9FLYX6IZXPK6JZB62LWH/florence-along-dusty-roads-11.jpg?format=2500w 337 https://www.baunetz.de/talk/crystal/pdf/de/talk14.pdf 339 https://i.stack.imgur.com/K9lmg.png 353 http://hdl.handle.net/10107/4394695 355 https://www.premierguitar.com/media-library/image.jpg?id=25744309&width=600&quality=80 359 https://audio-advent.ghost.io/content/images/size/w600/2017/12/CN0193-00-1024.gif 362 https://upload.wikimedia.org/wikipedia/commons/9/91/Rice_Kellogg_loudspeaker_2.jpg 364 https://creators-images.vice.com/content-images/contentimage/no-slug/eb1aaced8fd45f 9d5684d4ee7d2d5580.jpg?crop=1xw:0.8450704225352113xh;center,center&resize=1200 368 https://cdn11.bigcommerce.com/s-gy4oo/images/stencil/1280x1280/products/5085/11386/ 12-Inch-PO-NO-TAPE__66861.1624993875.jpg?c=2 373 https://blog.kakaocdn.net/dn/31kPQ/btqDADnfxQT/Jw8fW7JxsmuS8NXQouyTy0/img.png 375 https://upload.wikimedia.org/wikipedia/commons/4/40/Tokyo_Metro·TOYO_Rapid_Railway_ Nishi-Funabashi_Station_Gates.jpg 377 https://64.media.tumblr.com/0347cccc9d354744c7ff3aea58d9b6f1/tumblr_owl6jsbKSg1 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ENCODING and the SACRED CODING and the PUBLIC DECODING and the PRIVATE

514 https://upload.wikimedia.org/wikipedia/commons/4/4e/Old_Windmill.jpg 519 https://i.pinimg.com/originals/18/67/b8/1867b8580e4a1995de285d5eccd78e10.jpg 534 https://arthive.net/res/media/img/oy1200/work/347/[email protected] 536 https://mkram.ru/wp-content/uploads/Aleksandr-Rodchenko.-SHuhovskaya-bashnya..jpg 554 https://t4.ftcdn.net/jpg/00/81/82/85/360_F_81828584_Nyt4xMqdrAHIoYkAZsFPoX3N1gj 2JcnX.jpg 555 https://upload.wikimedia.org/wikipedia/commons/c/c8/Halogen_lamp_operating.jpg 556 https://i0.wp.com/www.curbsideclassic.com/wp-content/uploads/2019/09/Lusso_dash.jpg? w=1024&ssl=1 557 https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Lange_Reihe_Blumen.jpg/ 2560px-Lange_Reihe_Blumen.jpg 558 http://cdn.shopify.com/s/files/1/0564/5405/4087/products/feinstein-06.jpg?v=1628726043 568 https://1.bp.blogspot.com/-96ExIrlDY2A/U7KigZPDcAI/AAAAAAAAtPo/hZmbQZtmwpY/s1600/ Vancouver,+Canada+in+the+1970s+(2).jpg 573 https://www.artribune.com/wp-content/uploads/2019/10/Archizoom-Associati-Superonda1969-72.-Edizione-Poltronova.-Photo-©-Studio-Branzi.jpg 574 https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/1967_Citroen_ID19B_pic3. 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IV V

732 https://i.pinimg.com/originals/39/b1/d0/39b1d0b7679675a5b4af8739ad4662c9.jpg 737 https://upload.wikimedia.org/wikipedia/commons/f/f1/Vitruvian_Man_by_Leonardo_da_ Vinci.jpg 741 https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Archimedean_spiral_circle_ squaring_triangle.svg/480px-Archimedean_spiral_circle_squaring_triangle.svg.png 747 https://www.dabonline.de/wp-content/uploads/2020/09/Ideal_Schneider.jpg 839 https://www.caimmo.com/fileadmin/_processed_/8/2/csm_Wien-Mariahilferstrasse-17Aussen-Nacht-2_32151adf71.jpg 842 https://cdn.wallpaper.com/main/styles/fp_grid_900x1050/s3/legacy/gallery/17052356/01_ cedricprice_jp040311.jpg 860 https://s3.envato.com/files/9d187273-5fae-4555-b4ca-8ccff3fc2aab/inline_image_ preview.jpg 864 https://architecturefarm.files.wordpress.com/2011/02/const-2-freitag.jpg 866 https://www.cemat.ro/wp-content/uploads/2018/12/qwedwq.jpg 868 https://img.nzz.ch/2016/9/22/ef32b33c-769f-4844-8eb6-33d590aa6d3c.jpeg 870 https://images.adsttc.com/media/images/540a/9260/c07a/808f/0a00/00a8/large_jpg/ 03.jpg 876 https://www.zwk.de/wp-content/uploads/2017/06/nassseite_2017_04.jpg 878 https://cdn.peri.com/.imaging/xxl/dam/cdcc7251-d5c6-468e-b1d8-788b1cbb7169/54 534/casa-da-música-the-concert-hall-is-pictured-here-after-structural-work-had-beencompleted.jpg 880 https://gramaziokohler.github.io/compas_fab/latest/_images/01_robot_model.jpg 882 https://www.mathworks.com/help/examples/ecoder/win64/ConfigureDataInterfaceFeatured Example_01.png 884 https://blog.cronn.de/img/posts/ios-swiftui-migration/swiftui-3-storyboard.jpg 886 https://img.freepik.com/premium-photo/high-rise-office-construction-with-open-ceilingsee-structure-system-work-glass-windows-take-aerial-view-buildings-city-empty-spacedeveloper-investment_43263-2613.jpg?w=2000 900 https://darkroom.ribaj.com/1200/e693fc08b513ff9168c9113f5624376c:1b0f59ff9e159c 1d2d43a1530545f4ff 905 https://s3-eu-west-1.amazonaws.com/fetchcfd/original/file-1483040927828.jpg 906 https://darkroom.ribaj.com/0/668/bea0519d518dd3257b727816d1babb2e:b74741f9f49fb1c 07fcebe1f5cb90faf/i-am-groot-the-vijversburg-visitor-centre-follows-its-same-old-paths 913 https://mvrdv.com/media/uploads/Main_Leisure_BulgariBK_WEBSIZE.jpg 915 https://www.jakehookermusic.com/images/youtube-Jake.jpg 917 https://oceanoutdoor.com/website/wp-content/uploads/fly-images/24825/lsqbillboard2000x900-c.jpeg 886 https://live.staticflickr.com/2122/5738607600_8cca7cf937_b.jpg 929 https://www.allaboutcircuits.com/uploads/articles/A_close_up_view_of_an_OLED_display.png 935 https://upload.wikimedia.org/wikipedia/commons/b/bd/Leonardo%2C_Studio_per_l%27 Adorazione_dei_Magi%2C_Uffizi.jpg 967 https://upload.wikimedia.org/wikipedia/commons/5/51/Agrigent_BW_2012-10-07_12-5227.JPG 968 https://img.fotocommunity.com/villa-rotonda-fdb3fcde-4c7a-42ef-a241-f8a4ce05cf55.jpg? height=1080 969 https://upload.wikimedia.org/wikipedia/de/a/af/Villa_Savoye_2015.jpg 970 https://iammone.files.wordpress.com/2017/12/rem-ko.jpg 1007 https://upload.wikimedia.org/wikipedia/commons/7/70/Alberti_cipher_disk.JPG 1040 https://scienceofcybersecurity.files.wordpress.com/2022/02/fig_15.jpg 1064 https://i.pinimg.com/736x/e2/43/f7/e243f7cd01306c61db28ab0a8d77e85d--pompeiiand-herculaneum-st-century.jpg 1065 https://www.inexhibit.com/wp-content/uploads/2021/01/Villa-La-Rotonda-Vicenza-AndreaPalladio-interior-5-Inexhibit.jpg 1066 https://static.vitra.com/media/asset/2962628/storage/v_fullbleed_1440x/41607420.jpg 1067 https://i2.wp.com/iwan.com/wp-content/uploads-iwan/2013/07/Porto-Casa-da-Musica5615-scaled.jpg?w=2560&quality=100&ssl=1

VI

1118

on the scalarity of the  FRACTIONAL  numbers on the scalarity of the  RATIONAL  numbers on the scalarity of the  REAL  numbers on the scalarity of the  COMPLEX  numbers

1119

in  MAJOR  tuning in  MINOR  tuning

1120

CODING and the PUBLIC

on the side of  DAY, SPACE,  and CHARACTERS  on the side of  NIGHT, TIME,  and NUMBERS 

ENCODING and the SACRED

COLOUR CODE

1117

DECODING and the PRIVATE

AUTHOR Ludger Hovestadt ACQUISITIONS EDITOR David Marold, Birkhäuser Verlag, Vienna, Austria CONTENT & PRODUCTION EDITOR Bettina R. Algieri, Birkhäuser Verlag, Vienna, Austria COPY EDITING / PROOF READING Sebastian Michael, London, UK

IV

LAYOUT AND COVER DESIGN Onlab: Vanja Golubovic, Matthieu Huegi, Thibaud Tissot, Geneva, Switzerland, www.onlab.ch IMAGE EDITING Andreas Gebhardt Reproduktion, Berlin, Germany PRINTING AND BINDING Holzhausen, die Buchmarke der Gerin Druck GmbH, Wolkersdorf, Austria PAPER Surbalin seda, steingrau 115 g/m2 Surbalin glatt, steingrau 115 g/m2 Salzer EOS 80 g/m2 TYPEFACE MH Archetype by Matthieu Huegi LIBRARY OF CONGRESS CONTROL NUMBER 2022940943 Bibliographic information published by the German National Library. The German National Library lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in databases. For any kind of use, permission of the copyright owner must be obtained.

V

ISBN 978-3-0356-2599-8 e-ISBN (PDF) 978-3-0356-2603-2 ISSN 2196-3118 © 2023 Birkhäuser Verlag GmbH, Basel P.O. Box 44, 4009 Basel, Switzerland Part of Walter de Gruyter GmbH, Berlin/Boston 987654321 www.birkhauser.com

VI Cradle to Cradle Certified® is a globally recognized standard for safe and recyclable products. The Salzer EOS paper used for this book was awarded C2C Certified® Silver-level certification.

ENCODING and the SACRED

CODING and the PUBLIC

DECODING and the PRIVATE