On Digital Architecture in Ten Books. Volume 1 On Digital Architecture in Ten Books: Vol. 1: Books I–III. 9783035626018, 9783035625981

Citation preview

LUDGER HOVESTADT ON DIGITAL ARCHITECTURE

BOOKS I–III BIRKHÄUSER ETH ZURICH

The ARCHITECT

VOLUME I

The ARCHITECT

The VISUAL

The AUDITIVE

The ARCHITECT

ON DIGITAL ARCHITECTURE IN TEN BOOKS

The VISUAL The AUDITIVE

APPLIED VIRTUALITY BOOK SERIES VOL. 19

The ARCHITECT

LUDGER HOVESTADT The VISUAL

ON DIGITAL ARCHITECTURE VOLUME I

BIRKHÄUSER ETH ZURICH

The AUDITIVE

BOOKS I–III

The ARCHITECT

THE TEN BOOKS

The VISUAL

The AUDITIVE

The ARCHITECT

OBSTACLE

VOLUMEI.I

The ARCHITECT

151–361 ↗

About the INCONCEIVABLE OBSTACLE and the RESPONSIBILITY the author takes.

The VISUAL

BOOK I

OBJECTIVITY

VOLUMEI.II

The COMPLEX PLANE of PERSPECTIVE PROJECTION BOOK II

The VISUAL

397–871 ↗

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 …

872–1168 ↗

The AUDITIVE

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

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

The ARCHITECT

ENCODING and the SACRED

VOLUME II ↗

Leaving home, reading and forgetting. RATIONALISATION. It is about the GRAMMAR, the ORTHOGRAPHIA, the TRAGEDY, the SACRED BUILDINGS, the ENCODING … BOOK V

CODING and the PUBLIC

VOLUME II ↗

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

VOLUME II ↗

NUMBERS and OPERABILITIY

VOLUMEIII

The VISUAL

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

AIR and ARTIFICIAL INTELLIGENCE

VOLUME III ↗

How to see the subject with today’s EYES. A mood board. It is about the GEOMETRY, the AIR, the COLOURING (Vitruvius), the VISUAL SENSE, the ARTIFICIAL INTELLIGENCE today … BOOK VIII

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 …

FIRE and DIGITAL ARTICULATION

VOLUME III ↗

How to model the subject in today’s terms. It is about the ASTRONOMY / LOGIC, the FIRE, the GNOMONICS (Vitruvius), the AUDITIVE ACT, the DIGITAL ARTICULATION … BOOK X

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 ↗

The AUDITIVE

BOOK IX

The ARCHITECT

BOOKSI–III

The VISUAL

The AUDITIVE

The ARCHITECT

PREFACE

VOLUMEI

The VISUAL

1 ↗ 7 ↗ 17 ↗ 23 ↗ 34 ↗ 42 ↗ 47 ↗ 56 ↗ 66 ↗ 77 ↗ 87 ↗ 94 ↗ 106 ↗ 112 ↗ 118 ↗ 121 ↗ 127 ↗ 138 ↗ 147 ↗

The AUDITIVE

DEDICATION VOICES NATURE SENSES SCREENS PRESENCE SUBJECTS TURN NUMBERS and the SUN CIRCLES RENAISSANCE INVARIANCES GOVERNANCE THREATS ARCHITECTURE INSTRUMENT LITERACY LEARNING FRITZ HALLER

The ARCHITECT

DEDICATION

2

The VISUAL

These books think about ARCHITECTURE as a public statement, a speech, a talk, a designation, a discourse, an oration …

1

> Plato, Cicero and Vitruvius. Google, ARCHITECTURE, RHETORIC, AGORA.

Not the emperor is talking today, he is killed. Not the princes, they are driven out. It is the abstract idea of a  PUBLIC  heading its  PEOPLE .

3

> Etymonline, PUBLIC.

The  PUBLIC  does not come with  PEOPLE  automatically.  PEOPLE  have to make an effort to establish a  PUBLIC .

4

Emilio Estevez, The Public, 2019.

The AUDITIVE

5

6

7

These books are dedicated to the PUBLIC and not to its PEOPLE. They argue towards an ARCHITECTURE which gives the PUBLIC a FACE.

VOICES

The ARCHITECT

8

This is an unusual enterprise, not carried by a common sense, and quite complicated to read. It requires taking a step back.

9

Not a theory, no definitions. No classical understanding. A scaffold of TERMS forming a BODY OF THINKING.

10

Written in a kind of vernacular, because these books feel alienated to language.

11

As they feel alienated to the digital world. And they try to find a new stand.

12

More like exercises on how to think a world in terms of quantum physics and category theory.

13

Where everybody can talk with anybody in ABSTRACTION of space, time, and language.

14

And VOICES which are PUBLIC VOICES spoken with different TONGUES.

15

There is no ORIGINAL ARTICULATION. They all and always need TRANSLATIONS.

16

NATURE I think of NATURE as a GIFT GIVEN. An OBSTACLE, beyond UNDERSTANDING.

17

The VISUAL

They all think in quantum physical terms. They are curious and learning.

18

19

And of ARCHITECTURE as a SACRIFICE to SHARE RESPONSIBILITY.

20

The AUDITIVE

NATURE, being born to a new world by Mother Earth.

21

Temple of Hephaestus, Athens, 415 BC.

22

23

ARCHITECTURE as a PACT, a CONTRACT with NATURE.

The ARCHITECT

SENSES

24

Hans Makart, The Five Senses, 1872–1879: Sense of touch, hearing, sight, smell, taste. 25

One’s self is born with EYES and EARS, and it SMELLS, TOUCHES, and TASTES.

26

The INTELLIGIBLE and the SENSIBLE.

27

PLAYING them, like a FUGUE, to make FRIENDS with NATURE.

28

Also HEARING things from all DIRECTIONS and focusing to FOLLOW one.

29

Playing the INTELLIGIBLES – global localities – in counterpoint to the SENSIBLES – local globalities –

30

The BODY  PICTURES  the MIND.

31

The MIND  IMAGINES  the BODY.

32

The VISUAL

LOOKING at things in straight LINES and going around to get a full PICTURE.

33

The AUDITIVE

Sandro Botticelli, The Birth of Venus, 1484–1486: Aphrodite born from the foam of the sea.

34

35

SCREENS The 20th century SCREENED NATURE with EYES of a new SCALARITY.

36

Apollo 17: Blue Marble, NASA, 17. 12. 1972.

The ARCHITECT

37

Human red blood cells.

38

IMAGES are REFLECTIVE. IMAGES think in straight LINES OF LIGHT. TRACES of things as PASSIVE OBJECTS. IMAGES kill the vivid things.

39

SCREENS are PROJECTIVE. SCREENS think in CIRCLES OF LIGHT. COLOURS of things as ACTIVE SUBJECTS. SCREENS embrace the vivid things.

40

An optical trick. With lenses, prisms, telescopes, and microscopes in the RENAISSANCE.

Cameras, sensors, processors, networks, and arrays of pixels TODAY.

2021 The LOSS OF IMAGES. FACING a planet on SCREENS:

42

43

The VISUAL

PRESENCE

41

44

Carbon dioxide concentration, NASA, 2006.

45

The AUDITIVE

the ENVIRONMENT the CLIMATE the CULTURES the ECONOMIES the GENDERS the HUMANS … as PROJECTIVE SCREENS as ACTIVE SUBJECTS.

46

With new eyes, things become active and smart.

47

SUBJECTS

The ARCHITECT

48

Everything shows up as SUBJECTS, INCONCEIVABLE, not as DEFINITE OBJECTS.

49

 OBJECTS  are unified by the SUBJECTIVITY of following LINES of LOVE.

50

 SUBJECTS  share the OBJECTIVITY of being CIRCULAR around TRUTH.

51

One can WONDER at SUBJECTS, these things so:

52

One can dress up as is customary and fashionable and speak towards a future unknown to all of us.

53

The VISUAL

precious surprising hesitant wroth enraged tough dangerous attractive graceful …

54

Peter Zumthor, Residential and Studio House, 2004.

55

The AUDITIVE

Kairavini Pushkarani, Chennai, 2021.

56

57

TURN Things are changing fast. They turn from LINES on EARTH to CIRCLES in the AIR. From OBJECTS to SUBJECTS:

58

The ARCHITECT

Paul Klee, Twittering Machine, 1926.

59

ENERGY needs turning from limited natural resources towards the sun, as nature does.

60

MATERIAL needs turning from the limits of the natural ground towards recycling, as nature does.

61

One can see a turn from thermodynamic REALITY towards the RATIO of quantum mechanics and computing.

62

One can see ALL LIVING in the helix of the DNAs exposed to an environment in natural communication.

63

One sees the danger of the ORTHODOX TYRANNY refusing to see the world of the new scalarity.

64

One sees the danger of the TERROR of the MODERNIST EMPERORS refusing to respect the inherited scalarities of the world.

65

NUMBERS and the SUN

The VISUAL

One can see a turn of GENDER originated in REALITY towards a HUMANISM as a RATIONAL contract.

66

67

In the last 100 years the world population grew by a factor of 5.

68

In the last 50 years global wealth has increased by a factor of 60.

69

In the last 50 years life expectancy has grown by 20 years.

70

In the last 50 years an extra 6 billion people became literate.

71

The AUDITIVE

The new SCALARITY shows up in numbers beyond all NATURAL proportions:

72

In the last 200 years the rate of homicides went down by 80%.

73

Today world energy consumption is around 600 EJ.

74

Nature’s photosynthesis produces 400 EJ.

75

Solar radiation impact to our planet is 3,900,000 EJ. …

76

The ARCHITECT

77

The reference is the SUN, not NATURE, not EARTH.

CIRCLES

78

Can one want to affirm that there is no way back to the intimacies of the old scalarities?

79

There is not enough space for all the footprints, not enough resources for the traditions, as they are.

80

Circles do not have a footprint. they are not about QUANTITIES. They do not take up space.

81

Circles are not about PROGRESS, not about TERRITORY, nor about the NEW.

82

Circles are not about a HISTORY as the logical SEQUENCE of important EVENTS.

83

Circles rotate around the PAST, they bring HERITAGE into CONSTELLATIONS.

84

Circles repeat. BIRTH and DEATH. LIGHT and MATTER. WATER, AIR, SUN, and EARTH.

85

The VISUAL

They just rotate faster, to increase numbers. Circles are about QUALITIES. And they need time.

86

The AUDITIVE

The water cycle.

87

RENAISSANCE

The ARCHITECT

88

A RENAISSANCE is not something NEW. It is a REBIRTH, a next GENERATION.

89

An architectural RENAISSANCE grows around its HERITAGE and its BODY OF THINKING proudly says: I want to be an ARCHITECT.

90

This thinking goes with the old masters: The ARCHITECT knows WHAT to TALK about [rationcinatio] and HOW to DO things [fabricas].

91

ARCHITECTURE meets what people, nature, economy, society can expect [utilitas].

92

It is well constructed and in today’s terms sustainable [firmitas].

93

And all its aspects are in good proportions and beautiful [venustas].

94

95

INVARIANCES These few abstract CATEGORIES do not change, they are INVARIANT. They are what one can trust in as a DIGITAL ARCHITECT.

96

All these terms are not abstract enough to be INVARIANT. They change over TIME.

97

As an architect, one also cannot talk in terms of:

98

the footprints, the limits, the growth, the origins, the intuitions, the diversities …

99

The VISUAL

Not in materials, not in constructions, not in craftsmanship, not in technology, not in infrastructures, not in projects, not in simulations, not in productions, not in sustainability, not in calculations, not in analysis, not in science, not in art, not in knowledge, not in common sense, not the economy, not in ecology, not in structures, not in ontologies, not in necessities, not in social life, not in empathy, not in culture …

The AUDITIVE

The ARCHITECT

100

They cannot address the challenges of today, which are of a different scalarity. As are:

101

the electric, the media, the communication, the logistics, the screens, the distinctions, the decisions, the synthesis, the new economy, the contingencies …

102

ARCHITECTONICS is talking with these challenges, is bringing them into a constellation and calibrates them.

103

Everybody knows the topics of today that one wants to face as an ARCHITECT:

104

sustainabilities green cities climate change migration digital humanities new materialism feminism …

105

ARCHITECTURE is a generous place to accomodate the world in a certain temperament.

GOVERNANCE

106

As ARCHITECTURE headed the LIBERAL ARTS in ancient times.

108

And ARCHITECTURE always has been around RHETORIC and about GOVERNANCE.

109

ARCHITECTURE gives SOCIETIES, its POWERS, a FACE.

110

Not a specification, not a decision, not a statement, not an opinion, not a call, not an education, not an understanding, not a manifest for agitation, not an answer to a question, not a solution for a problem … just prior to all this: a BODY OF THINKING and a PUBLIC FACE everyone can talk to.

111

The AUDITIVE

107

The VISUAL

ARCHITECTURE is not a DISCIPLINE. It is heading all disciplines.

112

THREATS

The ARCHITECT

113

If one looks around: societies losing their faces in the powerful stream of the new scalarity.

114

All cultures are exposed to the unrestrained modernism, of a generic URBANISM eating their fabrics.

115

They experience CULTURAL HERITAGE opening its doors for consumption by tourism.

116

They are flooded by systematic understandings, and well-meaning designs of the new scalarity.

117

Rem Koolhaas names it: JUNK SPACE or the GENERIC CITY. I would paraphrase this with the PARADOX: ‘you can’t improve by doing better’.

ARCHITECTURE

118

119

Societies need architectonic constitutions heading the good intentions to meet the differences of us 8 billion people and the precious nature on this beautiful planet.

120

INSTRUMENT

The VISUAL

The sciences, the technologies, the disciplines, the theories, the arts … are the INSTRUMENT, not the PLAYING. I want to learn to TUNE them and PLAY them well.

121

122

It needs additional reading of personal interest to grow into a fleshed-out body.

123

Look things up, play around and juggle, and find interesting places for all things you know and learn.

124

The AUDITIVE

This treatise is a mechanics, a skeleton, a scaffold.

125

Concepts or persons are not introduced or explained. They are just presented in constellations.

126

It is a text to work with freely. An INSTRUMENT you are invited to learn to play.

127

LITERACY

The ARCHITECT

128

Why the structure of a poem? There is no adequate language yet for what this treatise wants to explore.

129

A straight text would follow the lines of a given language.

130

These poems are more on rotations, on constellations, and symmetries.

131

More towards CODE. ALGEBRA: fixing broken bones.

132

Writing a conventional text never ends. Taking conventional images never touches the details.

133

CODE gets active and starts to run.

It frees the words from their conceptual ground. They get animated by your intellect.

134

135

COMMUNICATING.

136

Read them like a sudoku. No beginning or end, but symmetries and balances to explore in open space.

137

LEARNING

The VISUAL

The style is a balance of TEXT, CODE, and IMAGES.

138

139

Not primarily to get fluent in using digital tools, but to be able to talk about the digital profoundly.

140

To get a voice in the new media. To become an upright person. To stand up as an architect of today.

141

Being literate you will be able to pass by the experts and disciplines, and directly access them all:

142

The AUDITIVE

First then an appeal to the architect, to train your intellectual craft. To learn to read and write. To become literate in the digital.

The ARCHITECT

143

craftsmanship, machines, productions, talks, books, images, arts, sciences, medicine …

144

access them – not necessarily master them – in your own way in the stream of the plenty.

145

Having all this access you take a knowing step back, forget everything you learnt, rub your eyes and gain a benevolent view on the beauty out there.

146

You embody all this knowledge in the best humanistic tradition. You are an ARCHITECT in this new, digital world.

147

FRITZ HALLER

148

Fritz Haller: the general node and the structure of crystals.

149

The VISUAL

This is a photo of my master Fritz Haller (1924–2012). This little man, talking about the world. With few words in a low voice. And shy gestures so as not to drive things away. An architect not of heavy stones, but of structures, lightweight and fast. Not digging the ground, but embracing the world. Generous and fragile. Is there a problem out there? He would doubt it, even with all his concerns.

150

Horsehead Nebula.

The AUDITIVE

The ARCHITECT

VOLUMEI.II

OBSTACLE

The VISUAL

The AUDITIVE

The ARCHITECT

The ARCHITECT

BOOKI

The VISUAL

The RESPONSIBILITY of the Architect

The AUDITIVE

INVARIANCE SEDUCTION HUMANISM INTEGRATION THE ARCHITECTURAL SCALARITIES THE HUMAN SCALARITIES DEDICATION THE 20th CENTURY SCALARITY

151 ↗ 176 ↗ 227 ↗ 233 ↗ 260 ↗ 278 ↗ 292 ↗ 297 ↗

The ARCHITECT

INVARIANCE

151

152

The VISUAL

Luc Besson, Lucy, 2014, 1:17:40.

153

Of course I look at the  CIRCLE  of the SUN and I  COUNT  the LINE [sequence] of  DAYS  and  NIGHTS .

154

I also  COUNT  the plenty of  THINGS  and I go  AROUND  them to explore their  BOUNDS .

155

The  CIRCLES , the OUTSIDE and the INSIDE, the SUN, the THINGS, and ME, the LINES of  COUNTINGS  …

156

The AUDITIVE

I, the alienated PUBLIC, I imagine myself, some ten or fifty thousand years ago, with the same brain capacity as today … I am sitting there … relaxed …

157

I recognise these SYMMETRIES. I start to think my world around them.

158

It is complex, I admit. But thinking things as straight  OBJECTS  or  EVENTS  is simply not enough.

159

The ARCHITECT

Paul Klee, Notebooks Vol. 1, The Thinking Eye, 1961, Das bildnerlsche Denken, 1956. 160

When comparing the me today with the me then it is difficult not to think in terms of progress.

161

I take into account that the brain has not changed. It always and everywhere thinks about everything.

162

The worlds of all times and cultures are of the same richness and the same complications.

163

It would be boring otherwise.

164

It’s not my brain that changes, it’s the things around me that change.

I become a different person, if I learn:

166

to run, to talk, to swim, to play the piano, to touch, to love, to read, to speak your language, to use a mobile, a fire, or electricity, to grow food, or have kids …

167

All this is not complicated. I just make friends with things. And I become them.

168

I just trust them, get interested, if they are present and around.

169

I grow into my ENVIRONMENT of a certain TEMPERAMENT and SCALARITY.

170

‘The landscape thinks itself in me… and I am its consciousness.’

171

Maurice Merleau-Ponty, Cezanne’s Doubt, 1945.

The AUDITIVE

165

The VISUAL

It makes a difference whether I have a book or the Internet at hand. A sword or a gun. A mechanics or a quantum mechanics. …

172

I inhabit IT like a tree growing from AIR towards the SUN.

173

The INTELLECT is with the ENVIRONMENT. My BRAIN is INTELLECTUAL and grows into the intellect.

174

Michelangelo, The Fall and Expulsion from Paradise, 1512.

The ARCHITECT

175

176

With this intellect comes POWER. With this power I loose INNOCENCE.

SEDUCTION

177

Still sitting there … times ago … and … IT THINKS.

178

IT follows the circles of the SUN and counts the DAYS and NIGHTS. IT counts the plenty of THINGS with their circular BOUNDS.

179

The SUN circles in  TIME  around a HORIZONTAL  AXIS OF SPACE . My BODY circulates in  SPACE  around a VERTICAL  AXIS OF TIME .

180

SPACE

181

TIME

AXIS OF TIME

AXIS OF SPACE

The VISUAL

TIME as a CIRCULAR LINE, passing by. SPACE a LINEAR CIRCLE, that I can walk around.

In mathematics this is the COMPLEX PLANE with the  REAL AXIS  and  IMAGINARY AXIS , NOT to be read as a geometric plane.

182

It is of  SPACE  and  TIME , not an OBJECT in SPACE or an EVENT in TIME. It is both in one.

183

–i

R

–R

i

The AUDITIVE

184

The ARCHITECT

185

I am aware, that this reading of  TIME  and  SPACE  is following the temperament of an Indo-European environment.

186

In the Greek or Latin language for example the  NOUNS  are ‘bodies in space’ the  VERBS  ‘actions in time’. And I know the twelve tenses to colour the TIME of the verbs from the PAST to the FUTURE.

187

This is NATURAL to me.

188

In the Chinese language there are no tenses at all. It looks like Chinese thinking acts in space and not in time.

189

My thinking sheaves actions towards a direction. Chinese thinking is more like a surface of water animated in circles by falling raindrops. This is what they told me.

190

I go around  SPACE  and  TIME  is passing by. They go around TIME and SPACE is passing by.

191

My HORIZON is blocked by massive objects. My SKY is open and transparent. Their HORIZON must be transparent and their SKY massive.

192

193

But in any case there are  CIRCLES  and  LINES , Or in mathematical terms: the  REAL  and the  IMAGINARY . And there is the preservation of  AREAS  and the  ANGLES . Or in physical terms:  ENERGY  and  IMPULSE . Or in physiological terms:  EARS  and  EYES . …

194

These INVARIANCES are shared by all cultures and make things work everywhere:

195

The AUDITIVE

In fact their things are alien to me: Their walls, doors, windows, their floors, roofs, gardens, their spaces, objects, subjects …

The VISUAL

Moon gate, Couple’s Retreat Garden, Suzhou, 2009.

The ARCHITECT

196

a pillow a stair a window a water pipe a fireplace a mobile phone penicillin a scooter concrete scissors chewing gum a light bulb a solar panel …

197

All cultures like these things. They temper them differently, to a degree I almost do not understand anything, but they obviously like them. Every time and everywhere.

198

It’s so easy to play the things of the new scalarity.

199

This is not simple at all. These new things are so convincing, so seductive.

200

They are alienating everything I know. A promise from a foreign land. Just working, in ways unknown.

201

The VISUAL

Peter Paul Rubens, The Rape of the Daughters of Leucippus, 1618. 202

After a while I get used to these things. I understand them in my terms.

203

It must be like this with all  CULTURES , must have been with all  TIMES .

204

It just needs time, trust, in me as a person. In us, as a society. Us as humans.

205

These things of intellect grow in all colours as in a GARDEN.

206

The AUDITIVE

I had never seen things like that. I play around, ashamed. I know my betrayal of my habits. It’s so easy, so tempting.

207

They change my ENVIRONMENT to another FREQUENCY. A slide shift in SCALARITY.

208

Like the weather. It changes, it is everywhere. I am exposed.

209

And I tune my thinking to the temperament of the environment, changed.

210

The ARCHITECT

211

Over time with more things coming, frequencies rise, showing higher resolutions.

212

Paul Klee, Notebooks Vol. 1, The Thinking Eye, 1961, Das bildnerische Denken, 1956. 213

I look at the past 5000 years and see number ranges of different scalarities and powers for counting and measuring.

214

I can explicate the NUMBER of things with  NATURAL  numbers,

I can explicate the PROPERTIES of things with  REAL  numbers,

216

and I can explicate the VIVIDNESS of things with  COMPLEX  numbers.

217

I read these number scalarities, as a METAPHOR for CONSTELLATIONS in historical time.

218

This reading of numbers is in reference to Hermann Weyl’s CONTINUUM, and not to be confused with Brouwer, Frege, or Russell.

219

I take languages and the mechanics of writing as a further example:

220

On the scalarity of mechanics in the Bronze Age –  NATURAL  numbers – and the writing with hieroglyphic and cuneiform characters a specific ‘TALK’ could be stored, processed, and transmitted.

221

On the scalarity of mechanics in antiquity –  RATIONAL  numbers – and the writing with the phonetic alphabet all ‘TALKS’ within a single language (Greek) could be stored, processed, and transmitted.

222

The AUDITIVE

215

The VISUAL

I can explicate the PROPORTIONS of things with  RATIONAL  numbers,

The ARCHITECT

223

On the scalarity of classical mechanics –  REAL  numbers – and with the printing press all texts within any specific language could be stored, processed, and transmitted.

224

On the scalarity of quantum mechanics –  COMPLEX  numbers – and with computing and artificial intelligence all languages can be stored, processed, and transmitted.

225

On today’s scalarity everybody is able to talk in all languages about everything.

226

This is fascinating, gives us an enormous new power and obviously needs to be CIVILISED.

227

HUMANISM

228

In the Greek tradition the civilisation of a new scalarity is called HUMANISM.

229

HUMANISM never was about explicating  DIVERSITIES  of a common origin, never about a REVOLUTION or EQUALITY, never immediate to theory, understanding, or truth.

230

I abstract from everything I know and am comfortable with, to be a generous host to the inconceivable and unknown.

231

HUMANISM is an expulsion or a seduction from safe ground to a new scalarity.

232

INTEGRATION

The VISUAL

HUMANISM always was about being able to talk in a new tongue, integrating the unexpected  DIFFERENCES  showing up on a new scalarity.

233

234

ARCHITECTURE today is about facing nature, cultures, us humans, as inconceivable and rich in  DIFFERENCES .

235

The millennia-old competition between the WEST and ISLAM or the rising power of CHINA today:

236

They are too fast and too strong to find common ground for DIVERSITIES.

237

The AUDITIVE

ARCHITECTURE today is NOT about celebrating nature, other cultures, us humans, as of the same origin and  DIVERSE .

The ARCHITECT

238

But I can affirm the DIFFERENCES and start to talk about a common future in wealth.

239

ARCHITECTURE is not about  DIFFERENTIATION  or the  INTEGRAL . It is about  DIFFERENCES  and  INTEGRATION .

240

On today’s complex scalarity computing enables me for example to read and write all languages. Which is fantastic and new.

241

But I have to cross the border and sacrifice the INTEGRAL, the UNDERSTANDING of my LANGUAGE as my friend has to do too.

242

With these probabilistic translations we do not share our UNDERSTANDINGS, we share the DIFFERENCES of our TALKS, and we mutually have to give them MEANING.

243

I, as a European, cannot, for example, insist on HUMAN RIGHTS, because this is a Western concept of  DIFFERENTIATION .

244

This is not in tune with the constellation of today, which needs  INTEGRATION .

245

And it is also of the scalarity of  REAL  numbers and by far not powerful enough to meet the  COMPLEX  scalarity.

246

CIVIL RIGHTS would be the corresponding concept of  INTEGRATION  and in tune with today’s constellation.

Yes it is complicated. Nobody knows, and there is no solution.

248

These things cannot be decided. They stay open and they keep talking.

249

It is an AFFAIR.

250

But what to trust across all times and cultures? Besides the positivity of actual forces and powers?

251

MATHEMATICS. The uncorrupted one. No pragmatics. Across times and cultures.

252

Forget the cliches about her. She is not about numbers, control, and complicated formulas. She is the Royal Path to Knowledge.

253

She is able to indicate adequate ABSTRACTIONS to integrate and differentiate on all scalarities.

254

Leibniz, for example, at the end of the 17th century, developed the binary number system, we today refer to with the calculus.

255

He developed it with the explicit goal of establishing diplomatic relations with the Chinese emperor Kangxi. Which unfortunately did not work out at all.

256

The AUDITIVE

247

The VISUAL

But until now we have only known INTEGRATION on the scalarity of  RATIONAL  and  REAL  numbers.

257

Nevertheless computers today, they are running everywhere in all cultures.

258

And people love and hate them in their own ways.

259

Still, computers are running all the same.

260

THE ARCHITECTURAL SCALARITIES

The ARCHITECT

261

Finding the right ABSTRACTIONS is not a simple task. I suggest this SKELETON OF SYMMETRIES:

262

The ten books of Vitruvius (1st century BC) on the scalarity of  RATIONAL  numbers are about the characteristics of BUILDINGS using these six categories: ordinatio, dispositio, eurythmia, symmetria, decor, and distributio. Very strange for people today.

263

The ten books of Aberti (15th century) on the scalarity of  REAL  numbers are about the characteristics of BUILDING ELEMENTS using these six categories: locality, area, compartition, wall, roof, and opening. Very common for people today.

264

This book develops the categories around the HUMAN SENSES.

265

It takes OPTICS, the physics of space as a METAPHOR.

266

The OPTICS of ANTIQUITY is about  WHITE LINES  of light. This is how the notion of space is constituted with RATIONAL numbers. These lines are able to articulate sculptural elements.

267

The VISUAL

Today there is an architecture on the scalarity of  COMPLEX  numbers writing about the characteristics of PROPERTIES of BUILDING ELEMENTS, and this treatise is asking for six categories.

268

Temple of Hephaestus, Athens, 415 BC.

269

The AUDITIVE

The OPTICS of MODERNITY is about the curvature of lines of light. There are mechanics of lenses and spectra of colours. At the scalarity of REAL numbers space is not full of lines but of  COLOURS . These colours are able to articulate lines.

270

Leon Battista Alberti, Santa Maria Novella, Florence, 1470.

271

The ARCHITECT

The OPTICS since 1900 is about the curvature of colours of light. There are electromagnetic antennas, cameras, and screens. At the scalarity of COMPLEX numbers space is not full of lines or colours, but of  IMAGES . These images are able to articulate colours.

272

HdeM, Elbphilharmony in Hamburg, 2017.

273

These examples show, that the scalarities are not competing in space or time.

274

It is more about another resolution. One can see buildings with different EYES.

275

There is also no reason to forget the schemes of the other scalarities. They just show other FACES and talk differently.

276

Without the BODIES of the prior scalarities there would be nothing I could BUILD on.

277

THE HUMAN SCALARITIES

278

279

It is us HUMANS contracting NATURE.

280

This is not, exactly not, ANTHROPOCENTRIC.

281

This is not, exactly not, EUROCENTRIC.

282

Nevertheless, the WESTERN HUMAN showed up like this in the different scalarities:

283

The AUDITIVE

ARCHITECTURE is always proportioned around the human body.

The VISUAL

This is the reason why  CULTURAL HERITAGE  or, in Alberti’s term,  ARCHAEOLOGY  is of key importance.

284

The  SCULPTURAL  body in ANTIQUITY

285

Greek sculpture ‘in space’: Kritios Boy, c. 480 BC.

286

The  ANATOMICAL  body in MODERNITY

The ARCHITECT

287

Andreas Vesalius, De humani corporis fabrica libri septem, 1514–1564.

288

Parmigianino, Self-Portrait in a Convex Mirror, 1524.

The  PERCEPTIVE  body TODAY

289

290

The VISUAL

Protein ABO.

291

Hiroshi Ishiguro, Geminoid, 2007.

The CATEGORIES of ARCHITECTURE have always been in synchronicity with rhetoric and good governance:

293

Vitruvius on the  RATIONAL  scalarity addressed his treatise to the EMPEROR Augustus.

294

The AUDITIVE

DEDICATION

292

295

Alberti on the  REAL  scalarity to his colleagues and wealthy CLIENTS.

296

This text on the  COMPLEX  scalarity to students and SOCIETY.

297

The ARCHITECT

298

THE 20th CENTURY SCALARITY “In front of the door of the house built at the foot of alpine pastures, a little girl of three is playing; as a birthday gift yesterday, she received a cream pink doll with green pants. Behind her, the calm facade with stone lintels still shines with the ochre paint applied with a great deal of effort back when the hay harvest abounded seven years ago. Her grandfather built the metal shed to the left of the main building, itself constructed at the beginning of the last century on the ruins of an old windmill erected in the location of an ancient monastery set up long ago on the premises of a temple—whether Roman or Gallic, we have forgotten—in front of rocks moved by a thousand-year-old flood on the part of this dancing and malicious torrent whose course is dug into the Jurassic strata of the mountains enclosing the semicircular horizon beneath snows said to be eternal.” Serres, The Incandescent, 2003.

299

Around 1900, a new scalarity of space opened up. Best known by quantum physics, relativity theory, and spacetime.

300

It comes with a new mathematics, new thinking, and new techniques.

As always in times of a new scalarity of space the cultural challenge is to  CIRCULATE  REALITY .

301

302

The VISUAL

The dramatic inside view on the REAL scalarity. Herman Melville, Moby-Dick, 1851, illustration of the final chase, 1902.

303

The dramatic inside view on the REAL scalarity. Staircase of the Opéra Garnier, Paris, 1875. 304

Then, a Copernican Revolution: from the REALITY of linear circles on a massive GROUND towards the RATIO of circular lines in AIR and LIGHT.

305

The AUDITIVE

The late 19th century with its wild inner turbulences: Sherlock Holmes, Sigmund Freud, Karl Marx …  OBJECTS  of  SUBJECTIVITY 

306

All things are of circulation now, they get their own MEMORY and they COMMUNICATE in CONSTELLATIONS.

307

An outside perspective on the COMPLEX scalarity. Square of the Republic, Belgrade, 2012.

The ARCHITECT

308

ACTIVE  SUBJECTS  of  OBJECTIVITY , not OBJECTS driven by SUBJECTIVITY.

309

By the way, this conception is exactly what Kant is emancipating from and what Hegel is fighting against.

310

I do not think they are wrong. But their writing is of long ago and today’s intellectual environment has changed to a phase of INVERSION.

311

I, the alienated PUBLIC, I read them with interest, but I turn their arguments inside-out.

312

And I am exposed to this STAGE of the new scalarity where these new active things PLAY around, where they all TALK with their own VOICES.

As there is the  COMPLEX  scalarity in SCIENCE: the quantum, the DNA, the X-rays, organic chemistry …

313

The  COMPLEX  elements of TECHNIQUES: the processors, the digital recordings, recycling …

315

The  COMPLEX  views on NATURE: the climate, the glaciers, the trees, the insects …

316

The AUDITIVE

317

The VISUAL

314

318

… The  COMPLEX  elements of CASUAL LIFE: the cars, the drugs, the chewing gum, the bikinis …

319

320

The ARCHITECT

I am not talking about TECHNOLOGY, this distant thing which is definite.

321

Mike Grist, Shimoda Beachites, Simoda, Japan, 2009.

322

I am talking about TECHNIQUES, which are around, which can become me.

323

I get used to techniques, I incorporate techniques, I become another person, I EMBODY techniques.

324

I, the PUBLIC, I am not any longer what I can DO. I am what I can THINK about.

325

They all show up in new colours. These vivid bodies begin to TALK.

326

327

The VISUAL

As a HUMAN I enter a new day in bright sunlight and meet the other SUBJECTS.

328

329

The AUDITIVE

These technical THINGS increasingly get powered by ELECTRICITY collected from the SUN.

330

331

Doping semiconductors to produce sensors or actuators, memories and processors, light emitters or photovoltaic cells. 332

The ARCHITECT

A flexible photovoltaic cell.

333

PROCESSORS run any function, they communicate wirelessly and worldwide.

334

Four Phase Systems, AL-1 processor, 1969.

335

All technical infrastructures of hard wires, pipes, and ducts are about to vanish, replaced by small smart devices.

336

All functions turn into APPLICATIONS and SERVICES.

337

The VISUAL

Electric wiring, Japan, 2009.

338

Mobile computing, 2013.

339

Things get sculptured in the imaginary light of a quantum technique.

340

The AUDITIVE

Look for example at the LIGHT: it is not a fire, it is not a bulb, or an optical machine any more. Light is just there by these tiny LEDs.

341

Mercedes Benz, ambient lighting, 2020.

It is the same with: sound air water safety security …

343

It does not matter whether it is: technical, natural, cultural, or casual.

344

Things get sculptured in light of a new scalarity.

The ARCHITECT

342

345

Growcer, indoor vegetable farm, 2020.

346

347

The VISUAL

Katja Novitskova, Approximation. The Apocalypse’s Many Horsemen, 2020.

Kyoto, Japan, 2012.

Things are just there in their colours beyond all reality without any reason.

348

Just because I say, I want it to be like that. In a contract with nature, not sourced by nature.

349

Naoshima, Japan, 2012.

The AUDITIVE

350

351

Peter Funch, Two to Tango, New York, 2010.

352

These bodies are powered by the radiation from the sun – again with quantum techniques – bypassing nature.

353

The ARCHITECT

Photovoltaics can be read as artificial photosynthesis bypassing nature in terms of energy.

354

No need to cut down trees, to burn coal or oil. Nature is nature.

355

These bodies are out of the natural cycles. They are running their own quantum cycles.

356

They are not using or consuming nature. HUMANS face nature, contract nature.

357

They tune their bodies towards HEALTH and become aware of the ENVIRONMENT.

358

There are not enough resources, there is not enough food, there is not enough space. The reality of nature is not enough.

359

I go natural.

360

361

The VISUAL

And I argue there is no way back. Because there are 8 billion like me on this tiny planet.

David Bowie in The Man Who Fell to Earth, 1976.

The AUDITIVE

The ARCHITECT

OBJECTIVITY

VOLUMEI.II

The VISUAL The AUDITIVE

The ARCHITECT

DOMAINS

BOOKSI–II

The VISUAL

The OBJECTIVITY of Architecture

The AUDITIVE

PREFACE

362 ↗

The ARCHITECT

PREFACE

363

Serres, The Incandescent, 2003.

I, the intricate PUBLIC, I close my EYES.

364

There is the  OUTER SUN . There is the  INNER ME .

365

The SUN is of LINEAR radiation and goes  AROUND . I have a CIRCULAR body and act in directed  LINES .

366

The VISUAL

At the end of the lane rising through the forest, positioned on a tall grassy hillock, surrounded by a torrent descending from the mountain, a farm and its annexes overlook a cirque dominated by glaciers. Beneath the morning sun and the motionless air, this view, this landscape, this scene reveal to me, in an ecstatic epiphany, the quiet presence of the things in their exact place. Transparent and wide, space here seems to swallow up time, suspended.

362

. I step out and MAKE an IMAGE of this CONSTELLATION. ComplexPlot[ z + �

367

368

,

z

369

The AUDITIVE

{z, –1.5 – 2 �, 1.5 + 1 �}]

370

The  LINEAR CIRCULARITY  and the  CIRCULAR LINEARITY , the everything, and not anything, in one coloured plane.

371

The SUN and the HUMAN. A METAPHOR of the COSMOS, the universal order. . ARCHITECTURE faces this order as the PLANE OF OBJECTIVITY.

373

ARCHITECTURE is a miniature of the world. .

374

It is challenging: a sacrifice, a martyrdom, a witness, memory, signature …

375

I can find this OBJECTIVITY everywhere:

The ARCHITECT

372

376

River Diagram of the Spontaneous Process of Heaven and Earth, Zhao Huiqian, Liu Shu Ben Yi, 1751. 377

“Everything is EMBEDDED in YIN and EMBRACES YANG.” Laozi, Chapter 42, 6th centrury BC.

“YANG refers to height, brightness, and the south side of a mountain.

378

YIN refers to a closed door, darkness, and the south bank of a river and the north side of a mountain.” Xu Shen’s Shuowen jiezi, 1st centrury BC.

379

. I face the COSMIC ORDER and place NATURE at the point of its outside. And ARCHITECTURE at the point of its inside.

380

The VISUAL

All times and cultures share this OBJECTIVITY.

381

ARCHITECTURE as miniatures of the cosmos to share responsibility.

382

. 383

He named the AXIS OF TIME, the circular linearity,  FABRICA .

384

And the AXIS OF SPACE, the linear circularity,  RATIOCINATIO .

385

RATIOCINATIO

FABRICA

386

The AUDITIVE

Talking to Vitruvius – the  RATIONAL  scalarity of space – in LINEAR light:

387

Talking to Alberti – the  REAL  scalarity of space – in COLOURED light:

388

He named the AXIS OF TIME, the circular linearity,  ORNAMENT .

389

And the AXIS OF SPACE, the linear circularity,  LINEAMENT .

LINEAMENT

ORNAMENT

390

Talking today – the  COMPLEX  scalarity of space – in IMAGINARY light:

392

I would name the AXIS OF TIME, the circular linearity, THE  VISUAL .

393

And the AXIS OF SPACE, the linear circularity, THE  AUDITIVE .

394

EAR

EYE

The ARCHITECT

391

395

Accordingly these two books raise the question of OBJECTIVITY:

396

 HOW to SEE  and  WHAT to SAY  as an ARCHITECT today.

The VISUAL

BOOKII

The VISUAL

397 ↗

Being DISTINCTIVE I SEE ALONG THE AXIS OF TIME The IMAGE and the PICTURE ARCHITECTURE SCAFFOLDS of TERMS MYTHICAL ENTITIES ABSTRACTION A LOOK at INFORMATION A LOOK at LANGUAGE

410 ↗ 420 ↗ 438 ↗ 449 ↗ 475 ↗ 497 ↗ 531 ↗ 546 ↗

The POWER of NUMBERS I SEE WHAT NUMBERS CAN SHOW The CALCULUS The FRAMING PROBLEM The ANALOGUE and the DIGITAL The IMAGE of CLASSIFICATION The ANALYTICAL VIEW The PHOTOGRAPHIC EYE PICTURE ANYTHING IMAGE of PRODUCTION

559 ↗ 581 ↗ 593 ↗ 608 ↗ 626 ↗ 639 ↗ 674 ↗ 687 ↗ 704 ↗

SEEING EVERYTHING FUNCTION vs EQUATION LIBERATION, ROTATION, and the COMPLEX PLANE THE ARTIFICIAL EYE and SCREENS

736 ↗ 774 ↗ 859 ↗

The AUDITIVE

The EYE

The ARCHITECT

The EYE

397

398

The VISUAL

Caravaggio, Boy Bitten by a Lizard, 1592.

399

analysis and science, forensics and crime, brain and scan, travel and selfie …

400

Not only IMAGES, all DATA is understood as something physical, as traces of evidence.

401

This is worrying: The flood of IMAGES, moving IMAGES, fake IMAGES …

402

suggestive, intuitive, involving, persuading …

403

The AUDITIVE

Only so as to try out: I trust my EYES:

404

This book is on HOW to SEE as an ARCHITECT with digital EYES.

405

An EYE is not an EYE.

406

Western people trust their EYES, they reason about the things they see. They do not trust these things out there. They trust their eyes. Even photos can be witnesses. But they do not trust the things. …

407

The ARCHITECT Hunayn ibn Ishaq, Book of the Ten Treatises of the Eye, 9th c., 12th c. 408

Just as a small counter-sketch: Islamic people think differently. Their optics is not about space, it is about the physiology of the eye. They did not build telescopes, they pioneered the surgery of the eye. Their truth is with the space, they do not trust the eye. …

409

A lot to talk about out there among migrants at the edge of the world.

The VISUAL

BOOKII

The VISUAL

Being DISTINCTIVE

The AUDITIVE

I SEE ALONG THE AXIS OF TIME The IMAGE and the PICTURE ARCHITECTURE SCAFFOLDS of TERMS MYTHICAL ENTITIES ABSTRACTION A LOOK at INFORMATION A LOOK at LANGUAGE

410 ↗ 420 ↗ 438 ↗ 449 ↗ 475 ↗ 497 ↗ 531 ↗ 546 ↗

I SEE ALONG THE AXIS OF TIME

410

411

Andy Warhol and his 20,000 Polaroids.

412

The ARCHITECT

I cannot SEE SPACE. SPACE spreads in all DIRECTIONS. My EYE CUTS SPACE in a single DIRECTION.

413 TIME

1 2 3 4 5 6

TIME cuts SPACE, spreading. 414

Looking in a specific DIRECTION, I see low FREQUENCIES as red, high FREQUENCIES as blue …

415

My EYE INTEGRATES these FREQUENCIES as COLOURS or TEMPERAMENTS.

O

R

750

Y

620

570

G

590

B

495

450

380

V

416

The visible spectrum as colours.

417

I remember STILL LIFES, and here they are: SPECTRA of TIMES, BIRTH and DEATH.

418

The VISUAL

COLOURS take TIME, not SPACE. My EYES SEE TIME, not SPACE.

419

Adriaen van Utrecht, Still Life with Bouquet and Skull, 1642.

421

Nicéphore Niépce, first photograph ever taken, 1826.

The AUDITIVE

The IMAGE and the PICTURE

420

422

The  IMAGE  TAKES a single shot, CUTS SPACE in a SPECIFIC DIRECTION.

423

I move my HEAD. Just a little, leave the IMAGE. I CUT SPACE in another DIRECTION.

424 t1 t0

1 2 3 4 5 6

By the DIFFERENCES of two IMAGES I MAKE a  PICTURE  of the SPACE around me.

426

 IMAGES  INTEGRATE SPACE by TIME.  PICTURES  DIFFERENTIATE TIME in SPACE.

427

428

SPACE PICTURE

TIME IMAGE

The ARCHITECT

425

An  IMAGE  takes a PRESENT point, it looks towards the PAST, and sees the HORIZON as the ORIGIN of things.

429

I  TURN  my head, I leave this point of presence and I MAKE my  PICTURE  of the WORLD around me.

430

With PICTURES my EYES are WANDERING AROUND and are welcoming things as FRIENDS.

431

PICTURES are OMNIDIRECTIONAL like SCULPTURES, like  SOUNDS .

432

The VISUAL

As there are: detailed MAPS, specific ONTOLOGIES, definite STRUCTURES … to KNOW where to go and what to think …

433

I  SEE  IMAGES in a SINGLE DIRECTION and I  HEAR  PICTURES of ANY DIRECTION.

434

With  IMAGES  I OPERATE in TIME. With  PICTURES  I MOVE in SPACE.

435

The AUDITIVE

Juan Gris, Guitar and Clarinet, 1920.

436

Robert Frank, Indianapolis, 1956. 437

438

 INSIDE   OUT 

ARCHITECTURE There are thousands and thousands of theories and manifestos. ARCHITECTURE is the ART of JOINING.

440

Not the ELEMENTS themselves, but the JOINING itself. The ELEMENTS are what they are. ARCHITECTURE affirms their DIFFERENCES.

441

I cannot  SEE  ARCHITECTURE. I just see the ELEMENTS. I THINK about the JOINING and I  HEAR  them PLAYING.

442

I cut the  ORIGIN  of ELEMENTS, cut them from  GRAVITY . I CONFIGURE them in the  LIGHT  of open  SPACE .

443

LIGHT

GRAVITY

The ARCHITECT

439

A CANON, a FUGUE that  SOUNDS  in space. Not an ORIGIN or a REASON that sticks to the  GROUND .

444

445

The VISUAL

Entrance gate of Dzogchen monastery, Tibet, 2018.

I am not interested, what the elements  ARE , I am LOOKING at what they are  SAYING .

446

DIFFERENT as they are, they are always within a CONSTITUTION. It would be a Babylonian confusion otherwise.

447

448

The AUDITIVE

Simon Stone, petrol station on the outskirts of Munich, 2020.

449

SCAFFOLDS of TERMS

450

To get used to my EYES of the  COMPLEX  scalarity I want to go out and have short CHATS with TERMS around ARCHITECTONICS.

451

 FORM  is not primary to joining.  STRUCTURE  is not primary to joining either. ARCHITECTONIC is both: formal structure and structural form.

FORM

The ARCHITECT

STRUCTURE

452

453

‘Form follows function.’ This thinks along the LINE of  STRUCTURES ,  SYSTEMS  …

454

 STRUCTURE  has no  FORM .  STRUCTURE  has a  SHAPE .  STRUCTURE  is of a FICTIONAL  FIGURE . But it has no  FORM .

455

STRUCTURES are  REAL . FORMS are  RATIONAL . STRUCTURES are  MOVED , FORMS  ANIMATED .

456

STRUCTURES are  OBJECTS  of  SUBJECTIVITY . FORMS are  SUBJECTS  in  OBJECTIVITY .

AXIOMS are PART  OF  a UNITY.  ONTOLOGIES . ATOMS are exposed  TO  not everything.  ETYMOLOGIES .

458

A  CIRCLE  is IRRATIONAL and of  UNITY . A  LINE  is RATIONAL and makes a  DIFFERENCE .

459

 NUMBERS  are OPERATING on OBJECTS IN  LOGIC . SUBJECTS are ARTICULATING with  CHARACTERS  of  ALGEBRA .

460

NUMBERS ORCHESTRATE  TIME , CHARACTERS DRAMATISE  SPACE .

461

 LINEAMENT  –  ORNAMENT   RATIOCINATIO  –  FABRICA   PROPORTION  –  MATERIAL   EURYTHMIA  –  SYMMETRIA  …

462

The idea is not to  UNDERSTAND  these TERMS. No need to fix them by  DEFINITIONS .

463

Just PUT them in a  CONSTELLATION  and TAKE A PICTURE.  TALK  with them.

464

This setup is very different from  STRUCTURALISM . Where STRUCTURE collapses to FORM.

465

The AUDITIVE

457

The VISUAL

STRUCTURES consist of FORMAL  PARTS . FORMS are CONSTITUTED by STRUCTURAL  ELEMENTS .

The ARCHITECT

466

Like an  IMAGE  of a butterfly. All the PARTS in beautiful details. Innocent, but dead.

467

My friends should stay vivid. Despite all  PRECISION  and  SOPHISTICATION  the FORMS should stay  MYTHIC  and the STRUCTURES  MAGIC .

468

Some more exercises on DIGITAL ARCHITECTURE:

469

ELEMENTS are  CONSTITUTED  and FORMS  CONFIGURED .

470

ELEMENTS are  STRUCTURAL . FORMS play in  SPACE .

471

ELEMENTS embody  CAUSALITY  FORMS are CAUSE and EFFECT at the  SAME TIME .

472

ELEMENTS have forgotten  EVERYTHING . FORMS make  DIFFERENCES .

473

ELEMENTS are of  NECESSITY . FORMS are about  CONTINGENCY .

474

ELEMENTS are  ANALYTICAL . FORMS play a  DRAMA . …

475

476

MYTHICAL ENTITIES ARCHITECTURE joins ELEMENTS to invite the WORLD to a formal DRAMA.

477

It was like this with stones in the EARLY TIMES,

478

with the arrangement of the speaking STATUES of the temples in  ANCIENT  time,

479

with the dramatised MOVEMENTS in the palaces and villas in  MODERNITY ,

480

and so with the staged VIVIDNESS of crystalline constellations of  TODAY .

481

The VISUAL

Stonehenge, Salisbury, c. 3000–2000 BC.

482

The AUDITIVE

Koolhaas, OMA, Casa da Música, concert hall, Porto, 2006.

As there are today: The QUANTA in physics, the nucleic acids of DNA, the computer networks …

483

484

MYTHICAL ENTITIES

485

Am I bothered with this notion of MYTH?

486

I look fascinated at my monitors, I believe the predictions about the future of our planet, I trust my smartphone every day, …

487

I rely on the searches in the Internet, the control circuits of the machines, the active ingredients of medicine, the logistics of food …

488

The ARCHITECT Elements of the Japanese railway system, 2011.

489

Is there anything of which I could not say it is a mythical entity?

490

Did I forget to marvel and believe that all these feats that I love, that I doubt, that I criticise, that I can’t think away …

491

Do I really think that they are given by nature?

492

493

As if by MAGIC. So elusive, energetic, probabilistic, light, fleeting, fast, precious …

494

More powerful than anything I know. Everything into nothing. Anything out of nothing.

495

The VISUAL

These formations: coming into being, growing, transforming, passing away.

496

The AUDITIVE

Lodhi Gardens, New Delhi, 2011.

497

ABSTRACTION

The ARCHITECT

498

I go on WANDERING AROUND with my new EYES, to PICTURE the world around me today.

499

1994 Rem Koolhaas the ‘generic city’ and ‘junk space’: ‘I can’t improve by doing better.’

500

1931 Kurt Gödel: we cannot think our world as  COMPLETE  and  CORRECT , only as incomplete and correct, or incorrect and complete.

501

The proof of Gödel’s theorem works like this famous paradox: A Cretan says: “All Cretans are liars.” Epimenides, 600 BC.

502

All domains of interest question themselves and end up in a paradox.

503

Marcel Duchamp, Fountain, Stieglitz, 1917. ‘Non Exhibition’, saying: this is art.

504

I SEE the post-structuralists, blinded by the logical performance of the electronic machines, not caring about  COMPLETENESS .

505

The  PARADOX  becomes  COMPLETE  in the  INFINITE . The  INFINITE  is  CORRECT  as  PARADOX .

506

1905 Albert Einstein’s relativity theory and the ABSENCE of MATTER:  MATTER  joins the  INFINITE ,  ENERGY  the  PARADOX .

507

Or go with  GRAVITY  paired with MATTER, and INVERT them to  LIGHT  as the ABSENCE of MATTER.

508

The VISUAL

Yet I SEE the logicists dreaming of complete, clean, and innocent  CORRECTNESS . As the structuralists do.

ENERGY LIGHT

MATER GRAVITY

509

510

PARTICLE

WAVE

511

The AUDITIVE

I can  GRASP  a PARTICLE, but not CONCEIVE it. I can  CONCEIVE  a WAVE, but not GRASP it.

The ARCHITECT

512

PARTICLES  INVENT  the RATIONAL and PARADOX as PICTURES.

513

WAVES  EXPLORE  the REAL and the INFINITE in IMAGES.

514

A  PARTICLE  is the  ELEMENT  of the REAL scalarity of SPACE in classical mechanics.

515

A  QUANTUM  is the  ELEMENT  of the REAL scalarity of SPACE in quantum mechanics.

516

QUANTA and PARTICLES are in SYMMETRY with each other. Both on the side of  PARADOXES , but QUANTA ABSTRACT PARTICLES.

517

 PARTICLES  in the 17th century are the ABSENCE of the Euclidean  REALITY . They talk about the DIFFERENCE as movements in the Cartesian space.

518

 QUANTA  in the 20th century are the ABSENCE of the Cartesian  REALITY . They talk about the DIFFERENCE as movements in the Riemann manifold.

519

Both,  PARTICLES  and  QUANTA , are in INVERSE CONSTELLATION to the 19th century  WAVES  in thermodynamics.

520

 PARTICLES  and  QUANTA  are of algebraic EQUATIONS of  WAVES , whatever they are. They set REALITIES into DIFFERENCE.

521

 WAVES  assume the logical EQUALITY of all  PARTICLES , wherever they are. They UNIFY all RATIONALITIES.

Like this my thinking goes in circles: from particles to waves to particles to waves …

522

523

524

The VISUAL

I now follow the idea that the infinitesimal levels of the wave and the paradoxical levels of particles mutually MERIDIATE each other.

525 QUANTUM

WAVE

PARTICLE

526

Via SYMMETRIES I can BEHAVE like the Old Masters. Via INVERSIONS I MERIDIATE between ABSTRACTIONS.

527

I do not get smarter playing this MECHANICS, but I gain beauty and power, to be careful with.

528

The AUDITIVE

On either side, the infinite or the paradoxical, I see the other side meridiated twice towards lower and higher ABSTRACTION.

529

I figure out these constellations free from narrowing definitions: The  PARADOX  becomes COMPLETE in the  INFINITE . The  INFINITE  is free of CONTRADICTIONS as  PARADOX .

530

And I apply it to ARCHITECTURE in contrast to Sullivan’s too simple ‘form follows function’:  STRUCTURES  CONSIST of FORMAL PARTS ==  ELEMENTS .  FORMS  ARISE from STRUCTURAL ELEMENTS ==  PARTS .

531

The ARCHITECT

532

A LOOK at INFORMATION 1948 Norbert Wiener: ‘Information is information, not matter or energy.’ Cybernetics or Control and Communication in the Animal and the Machine, 1948.

533

What to play on stage with this self-reference? Things should take a stand and talk with others.

534

Wiener’s world is pure, clear, and untouchable. It is omnipresent and sterile. A positive universal.

535

And in this game between INFORMATION and ENERGY I would assign the role of a figurator to MATTER. I also regard INFORMATION as a PARADOX.

536

537

The VISUAL

In contrast, I would think information with energy.  INFORMATION  ABSTRACTS  ENERGY , as the  QUANTA  ABSTRACT  PARTICLES .

INFORMATION

MATTER

ENERGY

With this I take a clear step out of the implicit conceptions of CYBERNETICS and Frege’s or Popper’s explicit third world or realm whose logical space is neither an inner nor an outer world.

538

Thoughts are neither things of the outer world nor ideas. A third realm (Reich) must be recognised.

539

Frege, The Thought, A Logical Inquiry, 1918. Popper, Three Worlds – The Tanner Lecture on Human Values, 1978.

540

And I am also not easy with the prophetic rites of SINGULARITIES. Yes, one can compare the QUANTITIES of this planet, but there is absolutely no QUALITY in these numbers.

541

The AUDITIVE

And I also distance myself accordingly from the misleading term OPEN SOCIETY, which, in the celebration of infinite self-reference, opens the doors to tyranny.

The  QUALITIES  are still, new again, and, as always, up for discussion.

543

 MACHINES  are without faults and incomplete. They have very little to say about the WORLD out there.

544

MACHINES do not help, they challenge. I, the ARCHITECT, want to take my stand.

545

 MACHINE  –  MECHANIC   DIVERGENCE  –  DIFFERENCE   EMANCIPATION  –  CATHARSIS   LITERATURE  –  POETICS   NOVEL  –  DRAMA   FINE ARTS  –  LIBERAL ARTS   GENERAL  –  ABSOLUTE   ENGINEERING  –  ARCHITECTURE   DESIGN  –  ARCHITECTURE  …

The ARCHITECT

542

546

A LOOK at LANGUAGE

547

Sentences are of SPACE and TIME, of the EARS and the EYES, they are of COMMUNICATION.

548

The  NOUN  is of SPACE, the  VERB  is in TIME:

549

The  apple  –  falls  down.

550

The  dog  –  barks .

551

There is no meaning in the NOUNS and VERBS themselves. The MECHANICS of a sentence constitutes meaning.

552

And I continue:

553

 ADJECTIVE  –  NOUN 

554

I HEAR a NOUN (SPACE) and I SEE an ADJECTIVE (TIME).

555

 ADVERB  –  VERB 

556

I SEE a VERB (TIME) and I HEAR an ADVERB (SPACE) …

557

This should be enough for the DRAMA of ARCHITECTURE: how to set TERMS in DIFFERENCE, how to TALK visually.

558

The VISUAL

I  HEAR  the NOUN, and I  SEE  the VERB:

The AUDITIVE

The ARCHITECT

The VISUAL

BOOKII

The VISUAL

The POWER of NUMBERS

The AUDITIVE

I SEE WHAT NUMBERS CAN SHOW The CALCULUS The FRAMING PROBLEM The ANALOGUE and the DIGITAL The IMAGE of CLASSIFICATION The ANALYTICAL VIEW The PHOTOGRAPHIC EYE PICTURE ANYTHING IMAGE of PRODUCTION

559 ↗ 581 ↗ 593 ↗ 608 ↗ 626 ↗ 639 ↗ 674 ↗ 687 ↗ 704 ↗

559

I SEE WHAT NUMBERS CAN SHOW

560

The sky at night.

The ARCHITECT

561

It is NIGHT.

562

Again I, the intricate PUBLIC, am lying on the GROUND, looking up to the SKY. To its LOGIC and UNITY.

563

What I SEE is so remote, there is nothing to TOUCH. But it is OMNIPRESENT and ABSOLUTE.

564

I get the  BOUNDS  and  ANGLES  from there. I do not get any  PROPORTION , or any  FORM .

565

Taking the  BOUNDS  from the SKY I COUNT in distinct PARTS:

566

The VISUAL

The stereographic projection of the night sky only preserves the angles.

567

These LINES of COUNTING are of an  ADDITIVE GROUP . There is ADDITION and SUBTRACTION, but no MULTIPLICATION and DIVISION.

568

Just a sequence in time.

569

Taking the  ANGLES  from the SKY I COUNT in CIRCLES:

570

571

572

Here I am with the NATURE of NUMBERS, they are of SPACE and TIME, of BOUNDS and ANGLES.

573

The AUDITIVE

These LINES of COUNTING are of a  MULTIPLICATIVE GROUP . There is ADDITION and SUBTRACTION, and there is MULTIPLICATION and DIVISION.

574

NUMBERS  IMAGINE  all ORDER, all EVOLUTION, all GROWTH, all SYSTEMS, all HIERARCHIES, all DIVERSIFICATION, all INDIVIDUATION …

575

But NUMBERS themselves are out of any ORDER, or rather, all ORDER is CHAOTIC by NATURE.

576

The ARCHITECT

The partitioning of a CIRCLE from 2 to 12 … 577

… in a plane layout …

578 … on a single line. 579

580

The SKY does not give any straight line or any form. It just gives the angles of partitions the NUMBERS operate on. {1} {2, 3} {11} {2, 2, 2, 2}

{2} {7} {2, 2, 3} {17}

{3} {2, 2, 2} {13} {2, 3, 3}

{2, 2} {3, 3} {2, 7} {19}

The prime factors of the numbers 1 to 20.

{5} {2, 5} {3, 5} {2, 2, 5}

The CALCULUS

581

582

My hands are a MACHINE on the  INTEGER  scalarity of numbers. I SEE the MYTH of the THINGS THEMSELVES.

583

The VISUAL

All CALCULUS is on circling jumps on this chaotic layout of numbers.

584

Finger positions in Luca Pacioli, Summa de arithmetica, 1494.

585

The abacus is a MACHINE on the  RATIONAL  scalarity of numbers. I SEE the MYTH of the PROPORTION OF THINGS.

586

The AUDITIVE

I follow the logical order of the SKY and embody the mobility of NUMBERS to be able to MEASURE things down here on EARTH.

587

An abacus.

588

The analytical engine plays on the  REAL  scalarity of numbers. I SEE the MYTH of the COLOURS OF THINGS.

589

The ARCHITECT

Charles Babbage, Analytical Engine, 1837.

590

Most of today’s software, written in the IMPERATIVE paradigm, mimics this  MACHINE  on the  REAL  scalarity of NUMBERS.

591

COMPUTING itself, despite all rhetoric today, is  ANALYTICAL  and not  LOGICAL , is not with  NUMBERS , but with  CHARACTERS .

592

COMPUTING is not a  MACHINE  driven by  REAL NUMBERS . It is a  MECHANICS  at the scalarity of  COMPLEX NUMBERS .

The FRAMING PROBLEM

593

594

I take these 4 parts for example:

595

The VISUAL

Because of the chaotic nature of numbers all CALCULATION on all scalarities runs into the problem of  COMBINATORIAL EXPLOSION .

596

They come in 24 possible combinations:

597

598

599

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

600

The Laplace Demon and the impossibility to fully predict the world. Pierre-Simon Laplace, A Philosophical Essay on Probabilities, 1814.

The AUDITIVE

With 6 parts I already get 720 combinations, 9 parts can show up in 362,880 combinations 32 parts can show up in 263,130,836,933,693,530,167,218, 012,160,000,000 combinations … And I ask the question: can something have any meaning, if it is arrived at with only 32 parts? Or to be fair to the real scalarity: if it is arrived at with only 32 parameters?

601

A good  DESIGN  is all about  EXCLUDING ELEMENTS , to keep a  SYSTEM  small and simple in its  COMBINATIONS .

602

SYSTEMS always play in the realm of LOGIC and  CORRECTNESS . They cannot be  COMPLETE .

603

As all science and technology in the 18th and 19th century is VISIBLE and CORRECT and, by necessity, not EXHAUSTIVE.

604

The ARCHITECT

J. Wolff, 1870. Culmann, Graphical Static, 1892. 605

There are the  POLYTECHNICS  within a visible  FRAME  of  LOGIC , and there are the  FINE ARTS  outside of this FRAME.

606

Portrait of Oscar Wilde, 1882.

The ANALOGUE and the DIGITAL

607

The VISUAL

Today I still SEE a lot of fights around the  FRAMING PROBLEM  inherited from the 19th century: intuition creativity emergence social life individualism diversity critique capitalism technology …

608

Things SHOW UP along the LINES of LIGHT.

609

At the scalarities of RATIONAL numbers one looks along  STRAIGHT  lines and SEES distant things as ONE and the same PROPORTION.

610

A

C

611

D

612

D

C

B A

Two points on a straight line thought as one in PROPORTION. Thales Theorem, ca. 600 BC.

The AUDITIVE

B

==

613

At the scalarity of REAL numbers one looks along  CURVED  LINES and SEES distant things as ONE and the same SYSTEM of PROPORTIONS.

614

pts = {{0, 1/2}, {4, 2}, {6, 3/2}, {8, 2}}; p = Expand@InterpolatingPolynomial[pts, x]

615

1 2

616

+

71 x 48

–

   25 x2

       11 x3       +   64     384

3 2 1

2

4

6

8

–1 Multiple points on a curved line thought as one as a SYSTEM. Lagrange Polynomial Joseph-Louis Lagrange, Mécanique analytique, 1788.

The ARCHITECT

617

A POLYLINE is  MULTIPLYING  PROPORTIONS, looking at them as ROTATIONS instead of as LINES of  ADDITION .

618

And one can SEE the FICTION of a CURVED LINE connecting any number of RATIONAL points in REALITY.

619

The OUTSIDE view to the fictional LINE. Charles Parsons, Niagara Suspension Bridge, 1856. 620

 CONTINUITY  is a  FICTION  in TIME an IMAGINATION within the LIMITS of LOGIC and the CALCULUS.

This is what is called the  ANALOGUE  and REALITY.

621

622

The VISUAL

The INSIDE view to the fictional LINE. Bultmann, Coorbis, Kodak employees in a penthouse on the roof of the State Street factory, 1890s.

ONE  IMAGINES  things in TIME.

623

SPACE DIGITAL

TIME ANALOGUE

624

TIME is  CONTINUOUS . The points themselves, the things in SPACE, are  DISCRETE ,  DIGITAL .

My EYES on an expedition, discovering REALITY. How to DISCOVER the BOUNDS of a SYSTEM?

626

627

The AUDITIVE

The IMAGE of CLASSIFICATION

625

628

Friedrich Georg Weitsch, Humboldt and Bonpland at the foot of Chimborazo Volcano, Ecuador, 1810.

629

Mother Earth, unknown. discovering things one can grasp with LOGIC derived from the SKY.

630

EXPEDITIONS TOURISM

The ARCHITECT

631

3 2 1

2

4

6

8

–1 To SEE a SYSTEM I have to select the parts I want to include.

632

It is all about SEEING the BOUNDS, including things within, dissecting things, excluding things not part of it, identifying a UNITY, taking a SYSTEM of THINGS out of the rest.

633

A SYSTEM always needs the assumption of LOGIC, of CALCULABILITY, of an ORIGIN, of TRUTH.

One needs to be EMPHATIC. It takes the SUBJECTIVITY of LOVE to be able to SELECT.

634

Because nothing can be EXHAUSTIVE in finite, calculable TIME.

635

The VISUAL

636

Natural History Museum, Vienna.

637

This is what is called: structure system engine image definition function species classification …

638

The AUDITIVE

Things have to be killed, to be fixed in time, within calculability to  IMAGINE  them.

639

The ANALYTICAL VIEW

640

Eadweard Muybridge, The Horse in Motion, 1872.

641

The ARCHITECT

I throw a die to get PARTITIONS 1/6, 4/6, 3/6 … of CIRCULAR COUNTING.

642 1

4

643

3

I circulate them along the axis of TIME and I SEE the FREQUENCIES of PARTITIONS.

644

645

646

With a few NUMBERS I SEE a random pattern.

pts = RandomInteger[{1, 6}, 24]

647

{1, 6, 5, 4, 3, 1, 5, 3, 3, 6, 6, 2, 1, 5, 3, 1, 2, 1, 5, 5, 1, 1, 2, 1}

648 649

1

6

2

5 3

4

650

Jacob Bernoulli, Law of Large Numbers, 1713. pts = RandomInteger[{1, 6}, 1000];

1

651 652

6

2

The VISUAL

The more numbers I take, the more the pattern of frequencies dissolves towards ‘nothing to SEE’. All NUMBERS have the same FREQUENCY.

5 3

4

With white noise there also is ‘nothing to SEE’:

653

654

As with the Brownian Motion:

655

656

Brownian Motion, 1827.

The AUDITIVE

White Noise.

657

All SYSTEMS SHOW UP as ‘something to see’.

658

This is a SYSTEM of three numbers connected by addition:

659

pts = RandomInteger[{1, 6}, {12, 3}]

660

{2, {3, {6, {5, {5, {1, {1, {5, {4, {5, {2, {4,

2, 5, 2, 6, 4, 3, 6, 1, 3, 2, 6, 4,

6} 3} 2} 4} 3} 3} 4} 3} 2} 6} 5} 6}

sum = Plus @@@ pts

662

{10, 11, 10, 15, 12, 7, 11, 9, 9, 13, 13, 14}

663

In large numbers it SHOWS UP as a SPECTRUM of the NORMAL DISTRIBUTION of FREQUENCIES of NUMBERS. Now there is ‘something to see’.

The ARCHITECT

661

Gauss, 1801.

664

4

3

2

1 18

17

16 15

5

14

6

13 12

7

8

9 10

11

Normal distribution on a rotating disk.

665

4

6

8

10

12

14

16

18

Normal distribution, numbers, sorted by their frequencies.

666

The more pointed the curve is, the more directed, concentrated, precise, perfect … the SYSTEM is.

667

No SYSTEM is PERFECT. There always is a VARIANCE of its INSTANCES. Every SYSTEM is an IDEAL.

668

Darwin for example DEFINED his HIERARCHIES of SPECIES by measuring their properties and looking for distinct distributions.

669

The VISUAL

Normal distribution of points on a plane.

670

The AUDITIVE

A B

How to CLASSIFY a POPULATION of INDIVIDUALS in A and B.

The EYES of the ENLIGHTENMENT look at the very DETAIL in high CONTRAST to distinguish INDIVIDUALS by precise DEFINITIONS of their TYPES.

671

672

A nineteenth-century illustration showing the morphology of the roots, stems, leaves, and flowers of the rice plant Oryza sativa.

673

The ARCHITECT

674

I SEE genotypical SCHEMES of LINES of how things evolve in TIME derived from a population of individuals in sharp contrast to other kinds.

The PHOTOGRAPHIC EYE

675

Otto Pfenninger, single shot colour photo, 1906.

676

A photograph works in an interesting way different from the analytical view and its lines of high contrast.

A photo is not a MAPPING of the SAME in DIVERSITY. It disinterestedly SEES DIFFERENCES and MOVEMENTS.

678

The ANALYTICAL EYE measures populations of things by an unchanged process in TIME and EMANCIPATES things from SPACE.

679

The PHOTOGRAPHIC EYE measures perspectives of space by a chemical process in TIME and EMANCIPATES SPACE itself.

680

The objects SEEN on a photograph are not explicit GENOTYPES, being analysed and understood by an analytical machinery.

681

The objects of a photograph are implicit. They just come with the light. The camera does not understand anything but SPATIALITY.

682

A  CAMERA  inverts  OPTICS , the physics of space, into an ARTIFICIAL EYE.

683

A chemical MACHINE produces MAPS of intensities of light of any perspective.

684

All OBJECTS then are meridiated by the  EMANCIPATED  SPACE. They  LIBERATE  themselves from ANALYSIS and TIME.

685

They become SUBJECTS in SPACE.

686

The AUDITIVE

677

The VISUAL

The figures of a photograph are liberated from their evolutionary bounds in time, they move freely in space, they talk and become persons.

687

PICTURE ANYTHING

The ARCHITECT

688

In the ENLIGHTENMENT in the 18th and 19th centuries INDIVIDUALS became wealthy healthy beautiful refined delicate … in a measure of abstraction and power never seen before.

689

However, when it comes to: nature the human the psyche … REGIMES easily become brutal and ugly: humans get classified by colour or proportion, abnormal behaviour gets graded as mad …

690

Nazi officials use calipers to measure an ethnic German’s nose, 1941.

 SYSTEMS  are always  CORRECT  and never  COMPLETE .

692

With the EYES of the  ENLIGHTENMENT  there is always EXCLUSION for the sake of being INCLUSIVE.

693

This is not the case with  PICTURES . They give up CORRECTNESS and gain COMPLETENESS.

694

PICTURES, being EXHAUSTIVE, affirm everything, and, most inconvenient: the bad as well as the good.

695

PICTURES withhold violence and death, as well as beauty and life … colonialism, exploitation, racism, eugenics …

696

Not as good or bad, but as a constitutive and right or wrong of the world one is exposed to.

697

“There is nothing either good or bad but thinking makes it so.”

698

William Shakespeare, Hamlet II.2, 1602.

The BODY OF THINKING would be incomplete. It would suffer with no hope for cure.

699

The AUDITIVE

691

The VISUAL

If one thinks in SYSTEMS there is no way to abandon injustice for the extremes and the abnormal.

700

Caravaggio, Judith Beheading Holofernes, ca. 1600.

The ARCHITECT

701

With these eyes I look around and SEE incomplete PICTURES of perpetrators feeling like their victims to be good.

702

And I SEE incomplete PICTURES of victims acting like their perpetrators to compensate the bad.

703

I also SEE the dangerous dreams of the technocrats that the LOGIC OF COMPUTATION might redeem humanity from the bad. …

704

705

IMAGE of PRODUCTION The power of SYSTEMS is not in the ANALYSIS, but in the  PRODUCTION  of new INSTANCES.

706

707

The VISUAL

Some 19th century products and how they are presented.

A 19th century factory.

708

These for example are 1000 numbers measuring 1000 instances of the same:

709

{12, 6, 16, 7, 9, 6, 10, 15, 12, 9, 15, 11, 5, 17, 6, 10, 11, 14, 7, 15, 11, 8, 9, 14, 8, , 11, 12, 11, 13, 3, 13, 6, 9, 12, 14, 6, 13, 12, 13, 12, 17, 9, 14, 12, 10, 9, 5, 8, 12, 8}

710

The AUDITIVE

A  MACHINE : DERIVES new INSTANCES of specific CLASSES, CREATES new INDIVIDUALS of specific SPECIES, GENERATES new PRODUCTS with specific MACHINES, CALCULATES new VALUES with specific FUNCTIONS, PREDICTS the FUTURE event by an ANALYSIS of the PAST, TAKES PICTURES of any PERSPECTIVE of SPACE …

711

These are their MEAN VALUE and STANDARD DEVIATION.

712

mean = N@Mean@instances sDev = N@StandardDeviation@instances

713

10.482

714

2.98103

715

With these two values I SPECIFY a FICTIONAL  MACHINE :

716

machine = PDF[NormalDistribution[mean, sDev], x]

717

0.133827 �-0.0562647

2

(-10.482+x)

The ARCHITECT

718

This MACHINE of extraordinary simplicity and elegance is able to PRODUCE new INSTANCES of the same  KIND :

719

production = Round@RandomVariate[NormalDistribution[mean, sDev], 1000]

720

{10, 9, 14, 12, 10, 11, 6, 13, 12, 10, 11, 9, 11, 14, 8, 10, 13, 14, 13, 7, 11, , 13, 9, 9, 9, 14, 12, 9, 15, 8, 10, 9, 5, 6, 11, 6, 8, 18, 7, 9, 16, 13}

721

To prove this, they show up with almost the same analytical numbers:

722

mean = N@Mean@production sDev = N@StandardDeviation@production

723

10.474

724

2.97963

725

I do not know what the SYSTEM is, I just take the numbers of measurement, build this generic MACHINE, and am able to PRODUCE new things with the same numbers of measurement.

726

This beautiful generic machine can produce anything. It therefore EMANCIPATES from the MATERIALITY of things.

727

Liberté, égalité, fraternité.

728

All analytics, all classical science, all technology, all industry, all institutions, all infrastructure, all linguistics, all literature, all images … are about: SUBJECTIVITY producing OBJECTS.

729

The VISUAL

It IMAGINES the PAST and PREDICTS the FUTURE of everything with the same MACHINE. This is what I would call: SUBJECTIVITY PRODUCES OBJECTS.

730

To show this more intuitively within recent schemes of visualisation: This is the PRODUCTION, or SIMULATION of INDIVIDUAL trees, specified by two PARAMETERS: the length and the angles of their branching:

731

The AUDITIVE

A 19th century advertisement.

732

733

734

The ARCHITECT

735

Another SYSTEM with a slightly different SPECIFICATION of just angles and length PRODUCES INSTANCES of a different KIND.

The VISUAL

BOOKII

The VISUAL

SEEING EVERYTHING

The AUDITIVE

FUNCTION vs EQUATION LIBERATION, ROTATION, and the COMPLEX PLANE THE ARTIFICIAL EYE and SCREENS

736 ↗ 774 ↗ 858 ↗

736

FUNCTION vs EQUATION

737

The  ANALYTICAL  VIEW of the 18th and 19th century  EMANCIPATES  from the body of things in  SPACE .

738

A  FUNCTION  for example PRODUCES an  IMAGE  of a circle by NUMBERS, LOGIC, and ARITHMETIC.

739

CIRCLE[a_] := {Cos[a], Sin[a]} ParametricPlot[CIRCLE[φ], {φ, 0, 2 π }]

740

1.0

The ARCHITECT

0.5 0.0 –0.5 –1.0 –1.0

–0.5

0.0

0.5

1.0

741

The EYES of FUNCTIONS are SYSTEMATIC, always CORRECT, but never COMPLETE.

742

A functional circle not a circle as a visible object. It is an approximation to an IDEAL.

743

744

It suggests that all things are in control of a total regime called Cartesian space.

745

But these eyes of logic do not know circles. They only know renderings of circles.

746

The  ALGEBRAIC VIEW  of the 20th century is different: It  LIBERATES  from  TIME , production, and control.

747

Here the circle is articulated with an  EQUATION  SYMBOLISING two ELEMENTS, whatever they are.

748

x2 + y2 == 1

749

It CONSTITUTES a  PICTURE  as a circle by CHARACTERS, ALGEBRA, and GEOMETRY.

750

The AUDITIVE

Take for example the short movie ‘Powers of Ten’, 1968: A super zoom with the EYES OF LOGIC along all known scales of space.

The VISUAL

Charles and Ray Eames, Powers of Ten, 1977.

751

ContourPlot[ x2 + y2 == 1, {x, –1, 1}, {y, –1, 1}]

752

1.0 0.5 0.0 –0.5 –1.0 –1.0

–0.5

0.0

0.5

1.0

The ARCHITECT

753

With the EYES OF ALGEBRA a circle is read like this: A PROPORTION of space x to time x equals the PROPORTION of time y to space y.

754

These algebraic eyes can move differently, they can take any perspective by multiplication and rotation. y ==

755

756

1 + x2

With these EYES one can, for example, step out by 1 and SEE the UNITY of SPACETIME: of  SPACE  ROTATED by  TIME  and  TIME  LINEARISED by  SPACE .

757 6

4

2

–4

–2

2

4

758

759

The VISUAL

One can take the perspective of the South Pole, rotate the head and SEE all the HEMISPHERE with the North Pole at the centre.

760

Poincaré disk.

761

The whole world on a single disk.

762

No PERSPECTIVE excluded. It is a PERSPECTIVITY, a LOCAL GLOBALITY.

763

The AUDITIVE

SPACE is EMBRACED by TIME and TIME EMBEDDED in SPACE.

764

Miroslaw Rogala, Lover’s Leap, 1995.

The ARCHITECT

765

Moving here is different from the crystalline Cartesian space:

766

A LOCATION is SEEING its WORLD … the WORLD rotates … and another LOCATION is SEEING its WORLD …

767

There is a lot to talk about between the two local views of one and the same world.

768

The ALGEBRAIC VIEW is not about the LINEAR SPACE, about CORRECTNESS and CONTROL, it is about the CIRCULAR SPACETIME, about COMPLETENESS and COMMUNICATION.

769

This distinction is of most importance with BIG DATA and ARTIFICIAL INTELLIGENCE today.

770

Today’s technical implementations operate in  CARTESIAN SPACE  and need a lot of computing power to  CONTROL  things as rendering.

771

This is the challenge of today: the powerful ALLIANCE OF CONTROL by economy, technology, institutions, didactics, media coverage, citation indexes, correctness, gender balances … they all ‘take breath’ to be PRODUCTIVE and CORRECT.

772

There remains nothing to SAY.

773

The VISUAL

It would be an act of  LIBERATION  if users could take their PERSPECTIVE with ALGEBRAIC EYES in SPACETIME and start to  TALK .

LIBERATION, ROTATION, and the COMPLEX PLANE

774

775

It is of a NECESSITY. An OBJECTIVITY.

776

The AUDITIVE

The  LIBERATION  from  TIME  to open SPACETIME is not an esoteric idea.

The ARCHITECT

777

In mathematics LIBERATION from TIME is just called  MULTIPLICATION  in contrast to  ADDITION , or  ROTATION  in contrast to  TRANSLATION .

778

LIBERATION from TIME has always taken place and become CONSTITUTIVE in a RENAISSANCE.

779

The  RENAISSANCE  of the RATIONAL PLANE in antiquity SHOWS MULTIPLICATION by the ROTATION of OBJECTS to PICTURE PROPORTIONAL LINES in  EUCLIDEAN  SPACE.

780

The  RENAISSANCE  of the REAL PLANE in 1500+ SHOWS MULTIPLICATION by the ROTATION of OBJECTS of LINES to PICTURE PROPORTIONAL MOVEMENTS in  CARTESIAN  SPACE.

781

782

FP–1

FP–2

783

I was taught how the PERSPECTIVE of the Renaissance works in the  REAL  plane. My computer mimics it with ease.

784

Now I am searching for the corresponding MECHANICS of the PERSPECTIVE of today in the  COMPLEX  plane.

785

The VISUAL

The  RENAISSANCE  of the COMPLEX PLANE in 1900+ SHOWS MULTIPLICATION by the ROTATION of OBJECTS of MOVEMENTS to PICTURE PROPORTIONAL CONDUCT in  RIEMANN  MANIFOLDS.

786

Y

X

Translation in Cartesian space.

787

 SCALING  in  CARTESIAN  SPACE is done by a  MULTIPLICATION  of  REAL  numbers.

788

IMAGES can be TRANSLATED and SCALED. They stay within the CARTESIAN SPACE.

789

The AUDITIVE

A  TRANSLATION  in  CARTESIAN  SPACE is done by an  ADDITION  of  REAL  numbers.

790

 ROTATION  cannot be done within the  CARTESIAN  SPACE. As  MULTIPLICATION  cannot be done within  RATIONAL  SPACE.

791

ROTATION can be approximated by a recursive sequence of TRANSLATIONS and SCALINGS. But there is NO ROTATION in CARTESIAN SPACE.

792

Y

X

The ARCHITECT

There is no rotation in Cartesian space.

793

If I  ROTATE , I 1 leave my SPACE [encoding], 2 do the rotation out of my SPACE [coding], and 3 come back to my SPACE [decoding] if I want.

794

 IMAGES  cannot be ROTATED.  PICTURES  leave SPACE, they ROTATE and they come back. They are from outer space.

795

Like a call with my mobile: My voice leaves my space – encoding – rotates in outer space – coding – and comes back somewhere else – decoding – As if out of nothing.

796

The  COMPLEX  SPACE ABSTRACTS the  REAL  CARTESIAN SPACE.

797

In  COMPLEX  SPACE there is a  REAL AXIS  representing a LINEARITY I am used to think of as SPACE, where CHARACTERS  TALK  GEOMETRY.

798

And there is an  IMAGINARY AXIS  representing a CIRCULARITY, I prefer to think of as TIME where NUMBERS  DO  ARITHMETIC.

799

Both AXES work with REAL NUMBERS, but the IMAGINARY AXIS introduces the UNIT � with these circular characteristics

800

�0 = 1, �1 = �, �2 = –1, �3 = –�, �4 = 1, �5 = �, …

801

to establish a COMPLEX ARITHMETIC:

802

z1 = a + b� z2 = c + d� z1 + z2 = (a + c) + (b + d)� z1 x z2 = (ac + bd�2) + (ad + bd)� = (ac – bd) + (ad + bd)�

803

The VISUAL

‘Leaving home’, ‘sitting at the edge of the world’, ‘coming back home’.

The AUDITIVE

804

A point in the COMPLEX plane in SPACETIME is written as:

805

2 + 3 �

806

i

R

Translation on a complex plane.

The ARCHITECT

807

An  ADDITION  on the COMPLEX plane of SPACETIME can be rendered as a TRANSLATION:

808

(1 + 2 �) + (2 + 1 �)

809

3 + 3 �

810

i

R

Addition translates on a complex plane.

This is a  MULTIPLICATION  on the COMPLEX plane of SPACETIME showing up as ROTATION and SCALING,

811

(2 + 1 �) (–3 + 1 �)

812

–7 – �

813

i

814

The VISUAL

R

Multiplication rotates and scales on a complex plane.

815

The Euler number � establishes the LINEARITY and the GEOMETRY of the COMPLEX PLANE.

816

The DERIVATION is the VELOCITY (TIME) at a certain LOCATION in CARTESIAN REAL SPACE.

817

D[2 x, x]

818

2

819

D[x2, x]

820

2 x

821

D[2x, x]

822

2x Log[2]

823

The AUDITIVE

The � establishes the CIRCULARITY and the ARITHMETIC of the  COMPLEX  PLANE.

824

There is a singular expression whose DERIVATION is the expression itself. It BRIDGES SPACE and TIME as the Archimedean spiral does.

825

D[�x, x]

826

�x

827

The Euler number � is an IRRATIONAL number like π and can be calculated with this infinite sequence:

828

� = 1 +

1 1

+

1 1×2

+

1 1×2×3

+

1 1×2×3×4

∞

+ ··· = k=0

1

k!

The ARCHITECT

829

N[�, 100]

830

2.718281828459045235360287471352662497757247093699959 574966967627724076630353547594571382178525166427

831

This BRIDGE of SPACE and TIME can specify a UNIT CIRCLE, the IDENTITY of SPACE and TIME in  COMPLEX  SPACE.

832

��π == –1 Euler identity, 1748.

833

ParametricPlot[ReIm[��φ], {φ, 0, 2 π }]

834

i

–1 1

–i

835

If I apply this expression to the COMPLEX plane I can ROTATE the CARTESIAN SPACE without DISTORTION:

And I am able to do ARITHMETIC on ANGLES:

836

��π/4 ��π/12 ��π/4 + �π/12 N@%

837

838

   �π �   3

839

840

0.5 + 0.866025 �

i

841

The VISUAL

   �π �   3

R

Multiplication of the natural exponential rotates on a complex plane.

I keep in mind that this ROTATION is done on the COMPLEX plane.

842

Not a vector, but the CARTESIAN SPACE itself is being ROTATED.

843

The natural exponential rotates space in time, not objects in space.

The AUDITIVE

844

845

In fact all CAD systems ROTATE OBJECTS on a COMPLEX PLANE using QUATERNIONS.

846

CAD systems mimic rotating objects. They actually operate with algebra in spacetime.

847

The ARCHITECT

Rotation of the Cartesian space in the complex domain by quaternions. 848

This is what happens to the objects: they leave the screen [encode], get ROTATED in COMPLEX SPACETIME [code] and come back to the screen [decode].

849

As an array of pixels as if from nowhere.

850

These FORMS are LIBERATED, taken off screen, by ROTATION.

851

I’d like to SEE a LIBERATED WORLD like this: A Poincaré disk, a ROTATING  PICTURE  of the WORLD on the COMPLEX plane, showing up in changing colours of SPACETIME.

852

Not as an  IMAGE  of fixed values CONTROLLING SPACE.

853

T1 T0

854

This is also a metaphor for a BIT in computing: not a NUMBER of the most simple CALCULUS on 0 and 1. Not a TRANSLATION.

855

A BIT is more about �, switching state in ROTATION. A ROTATING POINT opening up SPACETIME.

856

Can a thousand angels dance on the tip of a needle? One should not discredit this question.

857

The AUDITIVE

It is all about leaving CARTESIAN CONTROL [encode], talking about a ROTATION in SPACETIME [code], and coming back home to CARTESIAN SPACE [decode], as if out of nothing.

The VISUAL

The latitude or the equator of the planet is of rotation and time (clock), the longitude or the meridian is of translation and space (map).

SCREENS

858

On a technical level an analogue-to-digital converter works exactly as described: a circular partition of a certain resolution (TIME) counts an analogue level of linearity (SPACE).

859

860 K₁

= &

Ue

Q₀ Q₁

C

K₂

Qn counter

Ur

The ARCHITECT

sawtooth generator

square wave generator

861 5

4

4

5

6

8

Digital-to-analogue converter and scheme of operation. 862

On any SCREEN this CIRCULAR LINEARITY shows up in colours, as vivid pixels.

863

A pixel and a spectrum of colours.

864

865

The VISUAL

Pixels of an LCD screen.

Tokyo, train station, 2011.

866

Wong Kar-Wai, In the Mood for Love, 2000.

867

A new FACE of the ACTIVE SUBJECTS in symmetry and abstraction to the FACE of the Renaissance.

868

The AUDITIVE

This is what the  PERSPECTIVE EYE  SEES in terms of the  COMPLEX  scalarity.

869

Parmigianino, Vision of Saint Jerome, detail, 1527.

870

Where the PERSPECTIVE EYE established the VIEW of the  REAL  scalarity so common today. ***

The ARCHITECT

871

This is the FABRICA, these are the ORNAMENTS, this is what I can  SEE  today.

The AUDITIVE

BOOKIII

The VISUAL

872 ↗ 892 ↗ 902 ↗ 936 ↗ 956 ↗ 985 ↗ 1037 ↗ 1046 ↗ 1051 ↗ 1058 ↗ 1065 ↗ 1090 ↗ 1105 ↗ 1138 ↗ 1148 ↗ 1158 ↗

The AUDITIVE

The EAR I HEAR THE AXIS OF SPACE I SAY WHAT CHARACTERS CAN HEAR COMMUNICATION SOUND takes SPACE Turing Machine Von Neumann Architecture The Dominance of LOGIC The Dominance of ECONOMY The Dominance of the VISUAL Processing Interpreters and Compilers The Two Paradigms The SOUND of the 1960s The SOUND of the 1980s The SOUND of the 2000s

The ARCHITECT

The EAR

872

873

The VISUAL

A1 ENVIRONMENT

Le Corbusier, The Poem of the Right Angle, Le poème de l’angle droit, 1947, 1953.

874

The AUDITIVE

Men may affirm this beasts also and the plants perhaps And on this earth alone which is ours The sun master of our lives far off indifferent He is the visitor – an overlord he enters our house. In setting good evening he says to this mossy earth (oh trees) to these puddles everywhere (oh seas) and to our lofty wrinkles (Andes, Alps and Himalayas). And the lamps are lit up. Punctual machine turning since time immemorial engenders every instant of the twenty-four hours cycle the gradation the nuance the imperceptible almost providing a rhythm. Yet brutally he breaks it twice –– morning and evening. Continuity is his but he imposes an alternative – night and day – these two phases rule our destiny: A sun rises a sun sets a sun rises anew.

875

Wong Kar-Wai, In the Mood for Love, 2000.

876

The ARCHITECT

At  NIGHT , at home. I know all the things. They do not hide. These are my things in their right place. Counted by numbers, running in circles. I SEE everything at home. Nothing to TALK about. Quiet. I like them. Most of them. I like it. It is my place. …

877

Paun, India, 2020.

878

The sunrise of a new  DAY . OUTSIDE I hear the SOUND of another WORLD. …

879

At home, that was my REALITY. Stepping out I am among OTHERS, REALITIES alien to me.

880

881

The VISUAL

I open the door, take a breath, wait a little, step outside, and feel strange.

Cairo, 2012.

882

At home I could  SEE . Out here, I can’t.

883

I start to LISTEN … and begin to  TALK .

884

TALK with this WORLD out here.

885

TALK with other REALITIES as complicated as mine.

886

The AUDITIVE

It is an overwhelming world out here. I am exposed to it. I am a MIGRANT like the others.

887

The ARCHITECT

888

A COPERNICAN REVOLUTION. Switching  INSIDE   OUT . from the  EYE  to the  EAR .

889

 NIGHT  –  DAY ,  LINE  –  CIRCLE ,  TIME  –  SPACE ,  REAL  –  RATIO ,  ORNAMENT  –  LINEAMENT . …

890

My EYES, IN there, struggled with  INFINITY : what I SAW was always CORRECT, but it was never COMPLETE. Because my EYES have a DIRECTION.

891

My EARS, OUT here, struggle with the  PARADOX  that I can TALK about anything (COMPLETE) but it is never CORRECT, because I have to take a STANCE.

I HEAR THE AXIS OF SPACE

892

893

The VISUAL

Apollo 17, gnomon [“the one who knows”, “the discerner”] on the Moon, 1972.

I am OUT here, under the SUN, as a MIGRANT. Like all others.

894

895

The rotating globe as a clock (latitude) and a meter (longitude) 896

The AUDITIVE

We all cast shadows specific to our location in SPACE and TIME, to our  LONGITUDE  and  LATITUDE , MERIDIAN and EQUATOR.

897

Perspective projection and the preservation of the area of space and time.

898

We  SCREEN  the WORLD, ROTATE and FORGET the  IMAGES , MEMORISE them around the AXIS OF TIME.

899

–i The ARCHITECT

–R R

i The rotation of time and space on the complex Poincaré disk. 900

MEMORIES, of every time, of every culture, of every location …

901

All different. But anyhow: this is a new DAY under this singular SUN.

I SAY WHAT CHARACTERS CAN HEAR

903

The VISUAL

At  NIGHT  the IMAGES showed up in the SKY with different CHARACTERISTICS. Their NUMBERS run the  FUTURE .

902

904

The CONSTELLATIONS visible in the northern hemisphere.

In the  DAY  OUT here, under the SUN, I take a DISK of CHARACTERS as a KEY to TALK about anything.

905

Alberti, cipher disk, 1467.

I put this disk into my pocket. Memorising the SKY of the last NIGHT, memorising the things at HOME I KNOW, not here.

907

The AUDITIVE

906

908

Now I am able to TALK about anything, which is not there, OUT here in the DAY.

909 PAST MEMORY

INSIDE

OUTSIDE

DAY

NIGHT

FUTURE IMAGINATION

The ARCHITECT

910

At  NIGHT , IN there, I assume I understand EVERYTHING.

911

But in REALITY my things never have been PERFECT.

912

In the  DAY , OUT here, I affirm I do not know ANYTHING.

913

I can REASON about anything, but in detail I am always WRONG.

914

There is either DAY or NIGHT. There is nothing else.

 NUMBERS  are on EARTH at NIGHT,

916

 CHARACTERS  are in the AIR in the DAY.

917

I take a breath and start to TALK:

918

A ‘p’, then an ‘e’ then an ‘a’ …

919

I can turn the world over and assemble anything. I am able to ARTICULATE: peach peace pearl peano peacock …

920

This TALK to the OUTSIDE R is only a slit in the rotating disk on the complex plane:

921

922

–i CHARACTERS

R

NUMBERS

i

–R

The AUDITIVE

915

The VISUAL

DAY and NIGHT make things like me.

The ARCHITECT

923

I IMAGINE the FUTURE �, UNDERSTAND PRESENCE –R, MEMORISE the PAST –�, to ARTICULATE my PRESENCE R.

924

I cannot ARTICULATE without MEMORY, without UNDERSTANDING, without IMAGINATION.

925

I need to ROTATE this COMPLEX DISK.

926

 NUMBERS  IMAGINE the FUTURE to UNDERSTAND PRESENCE.

927

 CHARACTERS  MEMORISE the PAST to ARTICULATE my PRESENCE.

928

This is what characterises TIME and SPACE:

929

INSIDE and OUTSIDE are PRESENT in SPACE and exterior of TIME.

930

FUTURE and PAST are HERE in TIME and exterior of SPACE.

931

I  SHOW  my physical presence to IMAGINE the FUTURE. I LISTEN to my IMAGINATION to get an IDEA of the PRESENCE.

932

I  LOOK  at my IDEAS of PRESENCE to MEMORISE the PAST. And I TALK about my MEMORY to ARTICULATE my PRESENCE.

933

TALK

SHOW

SEE

HEAR

IDEA of SPACE

PICTURE of SPACE

MEMORY of the PAST

This is what I HEAR (blue slit) when Burroughs SAYS (red slit):

934

“A paranoid is someone who knows a little of what’s going on. A psychotic is a guy who’s just found out what’s going on.”

935

The VISUAL

VISION of the FUTURE

William S Burroughs, Friend magazine, 1970.

COMMUNICATION

936

937

If I ignore TIME things die to SPACE. If I ignore SPACE things vanish in TIME.

938

The AUDITIVE

All COMMUNICATION needs SPACE and TIME.

The ARCHITECT

939

All these things around me under the SUN are, like me, of SPACE and TIME: of a BODY of IMAGINATION, of IDEAS, of MEMORIES, and ARTICULATIONS. They are INCONCEIVABLE and vivid.

940

COMMUNICATION cannot be about targeting PROBLEMS in TIME or SPACE.

941

I learn to welcome the things OUT here, as DIFFERENT as they are, like FRIENDS do.

942

To COMMUNICATE with a friend I ROTATE time and space, this and that, again and again. We both like it most of the time. Our friendship stays INVARIANT. It has nothing to do with PROBLEMS to solve. It involves something like OBSTACLES or GIFTS, something I respect and want to live with. It is about CONTRACTING a COMMON FUTURE unknown to any of us.

943

TALK

SHOW

SEE

HEAR

IDEA of SPACE

PICTURE of SPACE

MEMORY of the PAST

944

The SENSES: HEARING and SEEING, and the ACTUATIONS: TALKING and SHOWING.

945

There is also the LINEAR: SEEING and SHOWING, and the CIRCULAR: HEARING and TALKING.

946

In the DAY I am ACTIVE and move to the OUTSIDE. At NIGHT I am SENSITIVE and move to the INSIDE.

947

A full rotation on the COMPLEX PLANE BRIDGES LINE to CIRCLE to LINE to CIRCLE.

948

A BRIDGE from CIRCLE to LINE, from CHARACTERS to NUMBERS, is a STEREOGRAPHIC projection, it preserves the  ANGLES  under the SKY at NIGHT and uses the  EXPONENTIAL .

949

The AUDITIVE

This BODY OF THINKING is of two SYMMETRIES:

The VISUAL

VISION of the FUTURE

The ARCHITECT

950

A BRIDGE from L ­ INE to CIRCLE, from NUMBERS to CHARACTERS, is a PERSPECTIVE projection, it preserves the  AREAS  under the SUN and uses the  LOGARITHM .

951

The disk itself is of the COMPLEX PLANE, is using the EXPONENTIAL, is complete but not correct: It is not a BODY or an IDEA in SPACE. It is a MEMORY of the PAST or a VISION of the FUTURE.

952

This should be the level of abstraction to COMMUNICATE with other times, cultures, and nature.

953

They are different but they can talk the same way on this level of communication that is natural.

954

COMMUNICATION is not addressing problems or working on solutions. It is about learning, being patient, staying abstract, and taking responsibility in coexistence.

955

Leon Theremin with his first music synthesiser, 1924.

SOUND takes SPACE

956

957

The VISUAL

Etienne-Jules Marey, zoetrope with ten sculptures of different phases of the flight of a gull, 1887.

Things cover space by rotating the COMPLEX PLANE: IMAGE, IDEA, MEMORY, ARTICULATION. I SEE the slit of ARTICULATION, I HEAR the full CIRCLE in-between.

958

959

960

The AUDITIVE

A grid of cameras in a subway station, Seoul, 2013.

I cannot SEE SPACE, I can HEAR its SOUND.

961

962

A subway station, Tokyo, 2011.

963

The things around, they are talking about their memories, their ideas, and imaginations.

964

And they are talking about strange worlds.

The ARCHITECT

965

A product in space embodies its production in time.

966

Rubber boots memorise their production.

967

968

The VISUAL

Light Emitting Element, LED.

Gargoyle, Notre-Dame de Paris.

And architecture joins them to articulate spaces, to talks of characteristic temperaments.

969

970

The AUDITIVE

Margarete Schütte-Lihotzky, Frankfurt kitchen, 1926.

These temperaments of talks differ over times and cultures.

971

This is the Western sound on different levels of abstractions and powers.

972

973

With the  SOUND  of the RATIONAL scalarity of space full of lines I turn the lines, of things around to communicate.

974

Scheme of a Greek temple, Peripteros, ca. 5th c. BC.

975

The ARCHITECT Pompeii, ca. 20 AD.

976

Pantheon, Rome, 1st c. AD.

With the  SOUND  of the REAL scalarity of space full of lines and colours, I turn the colours of things around to communicate.

977

978

The VISUAL

Bramante, St. Peter, 1505.

979

Caravaggio, Boy with Basket of Fruit, 1593.

Leon Battista Alberti, Santa Maria Novella, Florence, 1470.

The AUDITIVE

980

981

With the  SOUND  of the IMAGINARY scalarity of space full of lines, colours and images, I turn the images of things around to communicate.

982

Sharoun, Berlin Philharmony, 1963.

The ARCHITECT

983

Francis Bacon, Self Portrait, 1971.

984

realities:united, SPOTS, Berlin, 2005.

Turing Machine

985

986

Like all  SUBJECTS , it rotates VISION, IDEA, MEMORY, and TALK to ARTICULATE SPACE.

987

The VISUAL

The TURING MACHINE is a TECHNICAL model to rotate the complex plane. It also is a mathematical model of COMPUTABILITY, of what computers can do.

988

WRITE

SEE

SHOW

HEAR

INTERNAL STATE

EXTERNAL TAPE

PAST MEMORY

FUTURE VISION

989

The AUDITIVE

1 An EXTERNAL TAPE SHOWS the PRESENT ELEMENT to a SET of RULES (the FUTURE VISION). 2 An INTERNAL STATE LISTENS to the PAST of the FUTURE VISION. 3 A SET of RULES (the PAST MEMORY) SEES the changes of the INTERNAL STATE. 4 The PRESENCE of the EXTERNAL TAPE is CHANGED by a FUTURE STEP of the PAST MEMORY.

moving CPU

990

011

read/write device

1

0

1

1

0

0

1

memory tape The Turing machine in a classical illustration.

The ARCHITECT

991

This is an example:

992

1 I take an OUTER TAPE with 12 cells showing ‘0’.

993

turingTape = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};

994

2 The CODE or the FUTURE VISION and the PAST MEMORY consists of IF-THEN RULES like this:

995

{1, 1} → {0, 0, –1}

996

IF the inner state is 1 and the outer element on the tape is 1 THEN set the inner state to 0, change the outer element to 0, and make a movement to the left (–1).

997

My CODE is a set of rules:

998

999

1000

turingCode {1, 1} → {0, {1, 0} → {0, {0, 1} → {1, {0, 0} → {1, };

= 0, 1, 0, 1,

{ –1}, 1}, 1}, –1}

3 My INNER STATE is a list of two numbers: turingState = {1, 6};

1001

4 In this situation of IN and OUT rule 2 matches, is carried out, and results in a changed TAPE and STATE:

1002

{turingTape, turingState} = RunTuring[turingTape, turingState, turingCode]

1003

{{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 7}}

1004

And there is an endless rotation of this complex plane …

1005

{{0, {{0, {{0, {{0, {{0, {{0, {{0, {{0, {{0, {{0, {{0, {{0,

1006

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,

0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,

1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1,

0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0}, 0}, 0}, 0}, 0}, 0}, 0}, 0}, 0}, 0}, 0}, 0},

{0, {1, {0, {1, {0, {1, {0, {1, {0, {1, {0, {1,

7}} 6}} 5}} 4}} 5}} 6}} 7}} 8}} 9}} 8}} 7}} 6}}

… showing this TRACE in the outside slit of the actual presence over time. The past in the first line, the present in the last line.

The VISUAL

The machine has status ‘1’ and finds itself at position ‘6’ of the tape.

1007

1008

The AUDITIVE

A TRACE of COMPUTATION in TIME prominent as CELLULAR AUTOMATA.

This is not an IMAGE of COMPUTATION. It is an image of the RESULT of computation.

1009

The ARCHITECT

1010

I only SEE the single slit of a quantised PRESENCE of the rotating complex disk and its TRACES in TIME.

1011

I remember: I cannot SEE a ROTATION, I can HEAR it. I cannot SEE a SPACE, I can HEAR it.

1012

Which is complex to think.

1013

 SOUND  is OMNIDIRECTIONAL, and it does not COLLIDE with other sounds.

1014

SPACE is full of SOUNDS.

1015

Quite different from  THINGS of GRAVITY  around here. They COLLIDE in SPACE.

1016

I think SOUND, and with that of my EAR and TONGUE as a METAPHOR for the LIGHT of LINES on the  RATIONAL  scalarity.

1017

On the  REAL  scalarity I am thinking of LIGHT of COLOURS.

1018

On today’s  COMPLEX  scalarity I am thinking of IMAGINARY LIGHT. In technical terms this is ELECTROMAGNETISM.

1019

SPACE is full of LIGHT or rather ENERGY.

SPACE is OMNIPRESENT and TRANSPARENT. I cannot SEE it.

1021

Of course  LIGHT  collides with  MASS , but it does not collide with LIGHT.

1022

And of course MASS shows up in LIGHT.

1023

This is why I am able to have a phone call to China: 1 sound collides with the physical membrane of the microphone, 2 it is projected to electromagnetic waves, 3 transported almost at light speed in the global fibre network, 4 and projected back to the physical membrane of a speaker.

1024

That is the technical power of OMNIPRESENCE and TRANSPARENCE, of SPACE and LIGHT. And this is the new power of the COMPLEX SCALARITY of SPACE.

1025

The AUDITIVE

1020

The VISUAL

LIGHT is OMNIDIRECTIONAL. LIGHT does NOT COLLIDE with LIGHT. LIGHT spreads at light speed, it is OMNIPRESENT.

1026

One can identify two very common misreadings:

1027

1 The  TURING MACHINE  is not a  MACHINE . A MACHINE is built with moving and colliding PARTS. A MACHINE is MASSIVE. A TURING MACHINE is programmable, it is an  ANY MACHINE . It is not VISIBLE, it does not collide. It is a  MECHANIC , a QUANTUM MECHANIC. A MECHANIC is of LIGHT, it ACTS in SPACE.

1028

The ARCHITECT

–i MECHANIC

R

–R

MACHINE

i 1029

2 One can make the same distinction on the level of software.

1030

The  CALCULUS  works with NUMBERS to IMAGINE (EYE) an IDEA of the FUTURE. The CALCULUS drives a MACHINE. It is MASSIVE.

 COMPUTING  acts with CHARACTERS to ARTICULATE (EAR) my MEMORY of the PAST. COMPUTING acts as a MECHANICS. It is of LIGHT.

1031

COMPUTING CODE

R

–R

The VISUAL

1032

–i

CALCULUS PROGRAM

i 1033

COMPUTING is DIGITAL or rather it is about quantisation of SPACE at DAY.

1034

Pascal, Leibniz, Boole, Babbage … are about the CALCULUS, Even Frege or Russell.

1035

They are NOT about COMPUTING and the new scalarity of SOUND in the WORLD.

1036

The AUDITIVE

The CALCULUS is ANALOGUE or rather it is about continuity in TIME at NIGHT.

1037

1038

Von Neumann Architecture

The ARCHITECT

Computers are built exactly like this scheme by Turing. There are DATA either on a local device or on the global WORLD of the INTERNET. They can be ADDRESSED by a local BUS or a global URL. There is a PROCESSOR and there is CODE around the FUTURE VISION and the PAST MEMORY. And there is a CHANGE of DATA, again addressed via BUS or URL.

1039

How a CPU works.

1040

I think of them as  COMPUTING  subjects, not as  CALCULABLE  objects.

1041

On a technical level the ADDRESS localises and packs entities of this world: physical entities, data, or code. It does not matter. Things are just being packed. A VISION of the FUTURE.

1042

The VISUAL

I think of every SUBJECT out here as receiving, processing, and sharing information: me, my computer, the door, the dog, the tree, the insect, the stone, the glacier, the mountain, the planet …

A logistics centre, 2020.

The AUDITIVE

1043

The ARCHITECT

1044

The PRESENT thing is gone, the moment I close the package, as the slit of the outer presence of the complex plane p ­ asses by … there is PROCESSING, the MEMORY of the PAST … and the slit opens again and the delivery is unpacked:

1045

a phone call, a pair of shoes, a bank transfer, a glass of honey, an email, a Google request, an image changed by Photoshop, a laser print, a new track of music, a weather forecast …

1046

The Dominance of LOGIC

1047

Today’s thinking is dominated by  LOGIC  and the CALCULUS because this is so intuitive, so simple. It mimics old habits.

1048

It takes an intellectual effort to make this clear distinction:

1049

LOGISTICS is COMPUTING. It is of LIGHT. It is not of LOGIC and CALCULATION. It is not MASSIVE.

The Dominance of ECONOMY It is important to point out that the CALCULUS is with  ECONOMY , and COMPUTATION with  POLITICS . They circulate on the COMPLEX plane.

1050

1051

The VISUAL

Forgetting this distinction, I lose my VISION of the FUTURE, my MEMORY of the PAST. my package, my address, my code, my self … The SOUND of the WORLD becomes flat and monotone.

1052

1053

–i COMPUTING CODE

R

–R

CALCULUS PROGRAM

This again takes an effort:

1054

ECONOMY is about ­the correctness and the logical necessities of the NIGHT. ECONOMY IMAGINES the FUTURE from the PAST.

1055

The AUDITIVE

i

1056

POLITICS is about the completeness and the paradox contingencies of the DAY. POLITICS MEMORISES the PAST towards a FUTURE.

1057

The SOUND of the WORLD today is missing the public conversations of POLITICS. It is more about the ECONOMY of media, it is about CALCULATION.

1058

The ARCHITECT

The Dominance of the VISUAL

1059

It is also interesting that COMPUTING has the tendency to forget the SOUND and directly goes VISIBLE.

1060

There are these huge arrays of processors of the Graphical Processor Unit (GPU) to drive the colours of my screens with extreme, parallelised speed.

1061

I look at the pixels on my screen: they are rotating in time, as the processors of the GPUs run, as if there is no difference.

1062

The same parallel processors are very successful in the operations on large matrices for machine learning.

1063

Here again: I am looking at the traces and I am missing the SOUND.

1064

Processing

The VISUAL

Nvidia, Ampere GA102, a GPU with 28.3 billion transistors, 2020.

1065

1066

1 NUMBERS are packed into a sequence of bits.

1067

32 173

1068

{0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1}

1069

1070

The AUDITIVE

I take a short look into how PROCESSORS work, how they rotate the complex plane.

1071

CHARACTERS and texts are packed as sequences of numbers.

1072

“I am looking with your eyes”

1073

str = “I am looking with your eyes”; Characters@str; ascii = ToCharacterCode@str

1074

1075

{73, 32, 97, 109, 32, 108, 111, 111, 107, 105, 110, 103, 32, 119, 105, 116, 104, 32, 121, 111, 117, 114, 32, 101, 121, 101, 115} 0 1 0 0 1 0 0 1

0 0 1 0 0 0 0 0

0 1 1 0 0 0 0 1

0 1 1 0 1 1 0 1

0 0 1 0 0 0 0 0

0 1 1 0 1 1 0 0

0 1 1 0 1 1 1 1

0 1 1 0 1 1 1 1

0 1 1 0 1 0 1 1

0 1 1 0 1 0 0 1

0 1 1 0 1 1 1 0

0 1 1 0 0 1 1 1

0 0 1 0 0 0 0 0

0 1 1 1 0 1 1 1

0 1 1 0 1 0 0 1

0 1 1 1 0 1 0 0

0 1 1 0 1 0 0 0

0 0 1 0 0 0 0 0

0 1 1 1 1 0 0 1

0 1 1 0 1 1 1 1

0 1 1 1 0 1 0 1

0 1 1 1 0 0 1 0

0 0 1 0 0 0 0 0

0 1 1 0 0 1 0 1

0 1 1 1 1 0 0 1

1076

1077

The ARCHITECT

2 The LOGICAL operator ‘AND’ takes two sequences of bits and generates a new sequence.

1078

1079

1080

The ARITHMETIC operator ‘ADD’ takes two sequences of bits and generates a new sequence.

1081

123 + 16 = 139

1082

1083

1084

That’s it. A PROCESSOR turns everything into anything with LOGICAL and ARITHMETIC operations.

0 1 1 0 0 1 0 1

0 1 1 1 0 0 1 1

The first PROCESSOR was able to operate on packages of 4 bits with a frequency of 500 kHz.

1085

1086

The VISUAL

Intel, CPU 4004 with 2300 transistors, 1971. The first processor to turn everything into anything.

These operations are CODED with ASSEMBLY LANGUAGES. They directly symbolise the elements of the digital MECHANICS. This CODE adds two numbers:

1087

FIM P0, $A2; LD R0; ADD R1; XCH R1; DONE JUN DONE;

1088

Adding two numbers on an intel 4004 processor, 1971.

1089

The AUDITIVE

Initialise registers with bytes HEX: R0 = 2, R1 = A, load R0 into accumulator, add R1 into accumulator, and store in R1, DONE. Endless loop DONE as end of program.

1090

1091

Interpreters and Compilers Of course ASSEMBLY LANGUAGES are raw, good only for experts, and not very helpful or understandable for public discourse [TALKS].

1092

The ARCHITECT

Feurzeig and Papert, LOGO Turtles and educational robotics, 1967.

1093

HIGH LEVEL PROGRAMMING LANGUAGES configure the elementary commands according to certain ideas and pragmatics, such as readability or compactness.

1094

They symbolise abstractions of the FLOW of CONTROL and DATA TYPES.

1095

INTERPRETERS or COMPILERS translate code from a HIGH LEVEL LANGUAGE into an ASSEMBLY LANGUAGE, before it is executed by the processor.

1096

The role of INTERPRETERS and COMPILERS is to CIVILISE COMPUTING.

1097

7 forward turn left 5 forward turn left …

1098

can be translated into assembly language before showing results, like this:

1099

The VISUAL

Because PROCESSORS can do anything, they can for example constitute a computer language for kids, like running a turtle to make drawings with LOGO in 1967. These are some commands: turn left, turn right, pen up, pen down, step forward … Easy to imagine, a little complicated to do, is that these commands

1100

The AUDITIVE

I like to think of an architectural model as a public TALK, interpreted or compiled into a geometric model. It is of a symbolic computation.

1101

1102

Architecture is not an aggregate of geometric objects. There are thousands of them in stupid repetitions. Architecture is the sound of subjects in resonance. A public conversation articulated in a few lines of CODE of adequate symbolic words of a computable language.

1103

The ARCHITECT

Ludwig Mies van der Rohe, glass skyscraper, 1922.

1104

This argument should not to be confused with  PARAMETRICISM . Which is not talking at all, because it develops a symbolic language to mimic mechanical production and CONTROL.

The Two Paradigms

1105

Because processors can do anything, it is much easier and more intuitive to symbolise established habits: the machines we know, the economy we know, all the politics we know, the science we know, the arts we know … make them just go faster, to produce more, to go to more details with more colours, and more control.

1107

Today I see the thinking of the 19th century in high volume and high resolution.

1108

As a bold exaggeration: the global middle class today behaves like the small bourgeoisie of the 19th century.

1109

Like the dichotomy of the EYE and the EAR, the NIGHT and the DAY, NUMBERS and CHARACTERS, TIME and SPACE, there are two principal paradigms of computer languages:

1110

The AUDITIVE

1106

The VISUAL

And here I am with the key challenge of COMPUTING today.

1111

 IMPERATIVE PROGRAMMING  … Fortran, Ada, Pascal, C, JAVA, Python … follows the pragmatic path of symbolising the logical principles of the CALCULUS and accelerating the old emancipatory habits. These languages symbolise the FLOW OF CONTROL, they operate in TIME. They are always CORRECT but never complete, and they are easy to visualise. They are athletic. Von Neumann: First Draft of a Report on the EDVAC, 1945

1112

The ARCHITECT John von Neumann, Planning and Coding of Problems for an Electronic Computing Instrument, 1947. 1113

 DECLARATIVE CODING  … Lisp, Smalltalk, Mathematica … symbolises the algebraic or logistical principles of COMPUTING and liberates from pragmatism. These languages symbolise DATA TYPES and the SOUND in SPACE. They are COMPLETE and not CORRECT. They are adequate for a public TALK [discourse]. They are intellectual. Church, An Unsolvable Problem of Elementary Number Theory, 1936.

The set of free variables FV (T ) can be defined inductively over the structure of a λ-term T as follows:

1114

1 FV (�) = {�} if the term is a variable � 2 FV (T1 T2) = FV (T1) � FV (T2) for applications, and 3 FV (λ�.T ) = FV (T ) \ {�} if the term is an abstraction, its free variables of T are other than � . The set of bound variables B (T ) of a term T is computed also inductively: 1 B (�) = 0, if the term is a verifiable � .

The VISUAL

2 B (T1 T2 ) = B (T1 ) � B (T2) for applications, and 3 B (λ�.T ) = B (T ) � {�} if the term is an abstraction, its bound variables are the bound variables of T unified � . By means of the definition of free and bound variables, we can now the notion of (free) variable substitution (insertion) can be inductively defined by: 1 � [x ← T ] = � if variable x is not equal to �. 2 � [� ← T ] = T 3 (T1 T2)[x ← T ] = (T1[x ← T ]T2[x ← T ]) 4 (λ�.T' )[� ← T ] = (λ�.T' ) 5 (λ�.T' )[x ← T ] = (λ�.T' [x ← T ] if variable x is not equal to � and if FV (T ) is disjoint from B (λ�.T' ). The set of algebraic rules constituting the Lambda Calculus. 1115

PROGRAMS of  IMPERATIVE LANGUAGES  are  DECLARATIVE .

1116

CODES of  DECLARATIVE LANGUAGES  are  IMPERATIVE .

1117

 IMPERATIVE PROGRAMMING  is about the LOGICAL CONTROL OF FLOW. It SPECIFIES step by step  HOW  a  PROGRAM  should  PROCEED .

1118

The AUDITIVE

I keep in mind that  LANGUAGE  and  PROGRAMMING  are INVERSE:

The ARCHITECT

1119

 DECLARATIVE CODING  is about the ALGEBRAIC SYMBOLISATION of DATA. It ARTICULATES  WHAT  a  CODE  should  SAY .

1120

 IMPERATIVE PROGRAMMING  is easy to learn. Like how to use new words in your language.

1121

 DECLARATIVE CODING  is hard to learn. Like learning a new language, for example Chinese.

1122

If I ask for example an  IMPERATIVE LANGUAGE  how to add two numbers, I’ll get a lot of step by step  TUTORIALS  on  HOW  to  DO  it.

1123

A Java tutorial on how to add two numbers. 1124

If I ask the same question to a  DECLARATIVE LANGUAGE  I’ll get  DICTIONARY  of  WHAT  I can also  SAY .

1125

The VISUAL

A Mathematica dictionary on the entry ‘Plus’.

1126

The  COMBINATORIAL EXPLOSION  is CHALLENGED by the SITUATION that if you TALK about the WORLD you cannot find an end in detail.

1127

The  FRAMING PROBLEM  STRUGGLES with the FACT that if you want to DO things CORRECTLY you have to FRAME a PROBLEM.

1128

 IMPERATIVE LANGUAGES  FACE the COMBINATORIAL EXPLOSION.  IMPERATIVE PROGRAMS  HAVE the FRAMING PROBLEM.

1129

 DECLARATIVE LANGUAGES  HAVE the FRAMING PROBLEM.  DECLARATIVE CODE  FACES the COMBINATORIAL EXPLOSION.

1130

 IMPERATIVE LANGUAGES  are like POETRY. VESSELS to EXPLORE the WORLD.

1131

The AUDITIVE

Correspondingly there are two principal challenges in computing:

The ARCHITECT

1132

 IMPERATIVE PROGRAMS  are like PROSE. INSTRUCTION MANUALS for a PRODUCTION LINE.

1133

 DECLARATIVE LANGUAGES  are like PROSE. INSTRUCTION MANUALS for a PRODUCTION LINE.

1134

 DECLARATIVE CODE  is like POETRY. VESSELS to EXPLORE the WORLD.

1135

With von Neumann  PROGRAMS  I have a GENERAL PROCEDURE and I  SOLVE  PROBLEMS.

1136

With  CODE  of the LAMBDA CALCULUS I have an ABSTRACT MACHINE and I  WRITE  about the WORLD.

1137

These are the two invariant axes of programming languages on the complex plane of objectivity. Programming languages came to be successful and disseminated by a rotation on this plane.

1138

The SOUND of the 1960s

1139

HIGH LEVEL LANGUAGES symbolise the mechanics of the processor, the INNER FLOW OF CONTROL.

1140

The  CODE  learnt to CHARACTERISE any FORM and any STRUCTURE.

1141

FORM and STRUCTURE stayed crystalline to STAGE liberated public TALKS.

1142

These TALKS sound like the mechanics of Newton.

1143

1144

The VISUAL

This was the time of the ‘first wave of artificial intelligence’, the golden years, and it faced the problem of COMBINATORIAL EXPLOSION.

Ludwig Mies van der Rohe, Seagram Building, 1958.

1145

1146

Screen of a mainframe computer, 1960.

The AUDITIVE

Open office space, ca. 1970.

1147

1148

There were approximately 100,000 mainframe computers and there were EXPERT makers of these symbolic mechanics.

The SOUND of the 1980s

The ARCHITECT

1149

OBJECT-ORIENTED languages symbolised DATA TYPES.

1150

The  PROGRAMS  learnt to emancipate FORM and stay with the SYMBOLISATION of STRUCTURE.

1151

This was the time of the ‘second wave of artificial intelligence’ and expert systems, and it faced the FRAMING PROBLEM.

1152

STRUCTURE stayed crystalline, FORM became expressive to STAGE and SUPPORT the public TALKS.

1153

These TALKS sound like the machines of Carnot.

1154

Foster + Partners, HSBC Building, Hong Kong, 1985.

1155

1156

The VISUAL

Cubical office space, ca. 1990.

StarOffice, 1993.

There were approximately 100,000,000 personal computers. There are still the EXPERTS of the mechanics of the stage, but there are also t­ he CREATIVES, understanding and helping towards a comfortable life.

1158

MARKUP LANGUAGES symbolise the OUTER FLOW OF CONTROL, the activities of the world.

1159

The  CODE  has learnt to emancipate from STRUCTURE and FORM.

1160

The AUDITIVE

The SOUND of the 2000s

1157

1161

This is the time of artificial intelligence today, deep learning, and it is facing the question, WHAT TO SAY, if anything can be DONE.

1162

There are expressive STRUCTURES and FORMS to STAGE, SUPPORT, and CONTROL public TALKS.

1163

These TALKS sound like the mechanics of Heisenberg.

1164

The ARCHITECT Foster + Partners, 30 St Mary Axe, London, 2003.

1165

Google office, 2013.

1166

There are approximately 100,000,000,000 things of the internet. There are still the EXPERTS of the mechanics, there are still the CREATIVES with the understanding, and there are now also the PROPHETS of a better life.

1167

The VISUAL

The interfaces of the Internet of Things, 2020.

*** This is the RATIOCINATIO, this is the LINEAMENT, this is what I can  SAY  today.

1168

The AUDITIVE

The ARCHITECT

APPENDIX

VOLUMEI

The VISUAL The AUDITIVE

INDEX OF WORDS SOURCES FOR IMAGES AND GRAPHICS COLOUR CODE

1169 ↗ 1170 ↗ 1171 ↗

The ARCHITECT

INDEX OF WORDS

1169

A

BEHAVE527 BIG DATA 769 BIRTH 85, 418 BIT856 BODY 31, 32, 180, 277, 939, 951 BODY OF THINKING 9, 89, 111, 699, 944 BOUNDS 155, 178, 564, 566, 573, 627, 632 BRAIN173 BRIDGE 824, 831, 948, 949, 950 BUILD277 BUILDING262 BUILDING ELEMENTS 263, 264

The AUDITIVE

B

The VISUAL

ABSENCE 507, 508, 517, 518 ABSOLUTE 545, 563 ABSTRACT797 ABSTRACTION 13, 254, 261, 497, 526, 527 ABSTRACT MACHINE 1136 ACT1027 ACTIVE947 ACTIVE SUBJECT 39, 45, 308, 868 ACTUATION945 ADDITION 568, 572, 617, 777, 787, 807 ADDITIVE GROUP 568 ADDRESS 1038, 1042 ADJECTIVE 554, 555 ADVERB 556, 557 AFFAIR250 ALGEBRA 131, 460, 750 ALGEBRAIC EYES 771 ALGEBRAIC SYMBOLISATION 1119 ALGEBRAIC VIEW 747, 768 ALLIANCE OF CONTROL 772 ALL LIVING 62 ANALOGUE 608, 621, 1033 ANALYSIS 474, 591, 685, 705, 708 ANALYTICAL EYE 679 ANALYTICAL VIEW 639, 737 ANATOMIC286 ANCIENT479 ANGLE 194, 564, 570, 573, 836, 949 ANTHROPOCENTRIC281 ANTIQUITY 267, 284 ANY DIRECTION 434 ANY MACHINE 1027 ANYTHING912 APPLICATION337 ARCHAEOLOGY276 ARCHITECT 89, 90, 103, 146, 396, 404, 544 ARCHITECTONICS 102, 450, 451 ARCHITECTURE 2, 6, 20, 22, 91, 105, 107, 108, 109, 110, 118, 234, 235, 239, 279, 293,  372, 373, 379, 381, 438, 439, 440, 476, 530, 545, 558 AREA 194, 950 ARITHMETIC 738, 815, 836, 1080, 1084 AROUND 155, 364 ARTICULATE SPACE 987 ARTICULATION 460, 920, 923, 924, 927, 932, 939, 958, 1031, 1119 ARTIFICIAL EYE 683 ARTIFICIAL INTELLIGENCE 769 ASSEMBLY LANGUAGE 1087, 1091, 1095 ATOM458 AXIOM458 AXIS800 AXIS OF SPACE 385, 389, 393 AXIS OF TIME 384, 388, 392, 898

C

The ARCHITECT

CALCULABILITY633 CALCULABLE1041 CALCULATION 594, 708, 1049, 1057 CALCULUS 581, 582, 620, 855, 1030, 1033, 1035, 1047, 1052, 1111 CAMERA683 CANON444 CARTESIAN SPACE 770, 781, 787, 788, 789, 790, 791, 797, 817, 835, 843, 854 CASUAL LIFE 318 CATEGORY 95, 293 CATHARSIS545 CAUSALITY471 CAUSE471 CENTURY SCALARITY 297 CHALLENGE1127 CHANGE 989, 1038 CHAOTIC575 CHARACTER 460, 461, 591, 750, 905, 917, 927, 949, 950, 1031, 1071, 1110,  1140, 1172 CHARACTERISTICS903 CHARACTERS TALK GEOMETRY 798 CHAT450 CHINA236 CIRCLE 57, 77, 154, 156, 194, 459, 570, 889, 948, 949, 950, 958 CIRCLES OF LIGHT 39 CIRCULAR 50, 301, 364, 946 CIRCULAR COUNTING 641 CIRCULARITY 799, 815 CIRCULAR LINE 179 CIRCULAR LINEARITY 369, 862 CIRCULAR SPACETIME 768 CIVIL226 CIVILISE COMPUTING 1096 CIVIL RIGHTS 246 CLASS708 CLASSIFICATION626 CLIENT295 CLIMATE45 CODE 131, 133, 135, 994, 997, 1038, 1087, 1102, 1117, 1119, 1136, 1140, 1160 COLLIDE 1013, 1015, 1020 COLOUR 39, 269, 387, 415, 417, 1017 COLOURS OF THINGS 588 COMBINATION601 COMBINATORIAL EXPLOSION 594, 1127, 1129, 1130, 1141 COMMON FUTURE 942 COMMUNICATION 136, 306, 547, 768, 936, 937, 940, 942, 952, 954 COMPILER 1095, 1096 COMPLETE 500, 506, 529, 602, 692, 741, 890, 891, 1113 COMPLETENESS 505, 694, 768 COMPLEX 217, 224, 245, 264, 271, 296, 313, 315, 316, 318, 391, 450, 785, 804, 807, 811,  835, 842, 851, 867, 1018, 1052, 1173 COMPLEX ARITHMETIC 802 COMPLEX DISK 925 COMPLEX NUMBERS 592 COMPLEX PLANE 182, 774, 783, 815, 816, 845, 948, 951, 958 COMPLEX SCALARITY 1025 COMPLEX SPACE 797, 798, 831 COMPLEX SPACETIME 848 COMPUTABILITY986 COMPUTATION 1009, 1052 COMPUTING 591, 592, 1031, 1034, 1036, 1041, 1049, 1059, 1106, 1113 CONCEIVE510 CONFIGURE442 CONSTELLATION 84, 218, 306, 366, 464 CONSTITUTION 447, 457, 469, 750, 778 CONTINGENCY473 CONTINUITY620 CONTINUOUS625 CONTINUUM219 CONTRACT 22, 942 CONTRADICTION529 CONTRAST671 CONTROL 768, 770, 1094, 1104, 1162 CONTROLLING SPACE 852 CONTROL OF FLOW 1118, 1139 COPERNICAN REVOLUTION 888 CORRECT 500, 506, 603, 692, 741, 772, 890, 891, 1111, 1113, 1128 CORRECTNESS 504, 602, 694, 768 COSMIC ORDER 380 COSMOS370 COUNT 154, 155, 156, 566, 568, 570, 572 CREATE708 CREATIVES 1157, 1167 CULTURAL HERITAGE 115, 276 CULTURE 45, 204 CURVED LINE 613, 618 CUT SPACE 423 CUTS SPACE 422 CYBERNETICS538

D

The VISUAL

DATA 401, 1038, 1119 DATA TYPES 1094, 1113, 1149 DAY 154, 178, 947, 1172 DEATH 85, 418 DECLARATIVE1116 DECLARATIVE CODE 1113, 1119, 1121, 1130, 1134 DECLARATIVE LANGUAGE 1117, 1124, 1130, 1133 DEDICATION 1, 292 DEFINED669 DEFINITE OBJECTS 48 DEFINITION 463, 671 DERIVATION 708, 817, 824 DESIGN 545, 601 DETAIL671 DICTIONARY1124 DIFFERENCE 230, 235, 238, 239, 242, 425, 440, 459, 472, 517, 518, 520, 545, 558, 678 DIFFERENT 447, 941 DIFFERENTIATION 239, 243 DIGITAL 608, 625, 1034 DIGITAL ARCHITECT 95 DIGITAL ARCHITECTURE 468 DIRECTION 29, 412, 414, 423, 890 DISCIPLINE107 DISCOVER627 DISCRETE625 DISK905 DISTORTION835 DIVERGENCE545 DIVERSE234 DIVERSIFICATION574 DIVERSITY 229, 237, 678 DIVISION 568, 572 DONE 1089, 1161 DRAMA 474, 476, 545, 558 DRAMATISE SPACE 461

E

The AUDITIVE

EAR 25, 194, 547, 891 EARLY TIMES 478 EARTH 57, 76, 85, 585, 916 ECONOMY 45, 1051, 1052, 1055, 1057 EFFECT471 ELECTRICITY330 ELECTROMAGNETISM1018 ELEMENT 440, 441, 442, 469, 470, 471, 472, 473, 474, 476, 514, 515, 530, 748 EMANCIPATION 545, 679, 680, 685, 726, 737 EMBODY323 EMBRACED761 EMPEROR294 EMPHATIC634 ENERGY 59, 194, 507, 536, 1019 ENGINEERING545 ENLIGHTENMENT 671, 688, 693 ENVIRONMENT 45, 170, 173, 207, 357 EQUALITY 229, 521 EQUATION 520, 736, 748 EQUATOR896 ETYMOLOGIES458 EUCLIDEAN SPACE 779 EUROCENTRIC282 EURYTHMIA462 EVENT 83, 158, 183 EVERYTHING 472, 910 EVOLUTION574 EXCLUSION 601, 693 EXHAUSTED 603, 635, 695 EXPEDITION630 EXPERT 1147, 1157, 1167 EXPLORE 1131, 1134 EXPONENTIAL 949, 951 EXTERNAL TAPE 989 EYE 25, 35, 194, 274, 362, 399, 404, 406, 431, 450, 498, 547, 627, 671, 693, 741, 756, 890 EYE CUTS SPACE 412 EYE INTEGRATES 415 EYES OF ALGEBRA 753 EYES OF LOGIC 744 EYES SEE TIME 417

F FABRICA 384, 462, 871 FACE 6, 110, 275, 868, 1129, 1130 FACING43 FACT1128 FICTION 618, 620 FICTIONAL FIGURE 454 FICTIONAL MACHINE 715 FINE ARTS 545, 605 FLOW1094 FLOW OF CONTROL 1111 FOLLOW29 FORGET898 FORM 451, 454, 455, 456, 457, 465, 467, 470, 472, 473, 474, 564, 850, 1140, 1142,  1150, 1152, 1160, 1162 FORMAL PARTS 457, 530 FORMS ANIMATED 455 FORMS ARISE 530 FORMS CONFIGURED 469 FRAME 605, 1128 FRAMING PROBLEM 593, 607, 1128, 1129, 1130, 1151 FREQUENCY 207, 414, 415, 643, 650, 663 FRIEND 27, 431, 941 FRITZ HALLER 147 FUGUE 27, 444 FUNCTION 708, 736, 738, 741 FUTURE 186, 708, 728, 903, 923, 926, 930, 931, 951, 989, 1030, 1042, 1050, 1055, 1056 FUTURE VISION 989, 994, 1038

G

The ARCHITECT

GARDEN206 GENDER 45, 63 GENERAL545 GENERAL PROCEDURE 1135 GENERATE708 GENERATION88 GENERIC CITY 117 GENOTYPE681 GEOMETRY 750, 816 GIFT18 GIFTS942 GOVERNANCE 106, 109 GRASP510 GRAVITY 442, 508, 1015 GROUND 305, 444, 562 GROWTH574

H HAVE 1129, 1130 HEAD423 HEALTH357 HEAR 29, 441, 550, 555, 557, 934, 945, 946, 958, 961, 1011 HEAR PICTURES 434 HEAR THE AXIS OF SPACE 892 HEMISPHERE759 HERE930 HERITAGE 84, 89 HIERARCHY 574, 669 HIGH LEVEL LANGUAGE 1093, 1095, 1139 HISTORY83 HOME I KNOW 907 HORIZON 191, 428 HORIZONTAL AXIS 180 HUMAN 45, 280, 325, 356, 370 HUMANISM 63, 227, 228, 229, 230, 232 HUMAN RIGHTS 243 HUMAN SENSES 265

I IDEA 931, 932, 939, 951, 958, 987, 1030 IDEAL 668, 742 IDENTITY831 IMAGE 38, 135, 271, 366, 401, 402, 420, 422, 423, 425, 428, 435, 466, 513, 626, 704,  738, 789, 794, 852, 898, 903, 958, 1009 IMAGES INTEGRATE 426 IMAGINARY 194, 391, 981 IMAGINARY AXIS 182, 799, 800

The VISUAL

IMAGINARY LIGHT 1018 IMAGINATION 620, 924, 931, 939 IMAGINE 32, 623, 637, 728, 923, 926, 931, 1030, 1055 IMPERATIVE 590, 1117 IMPERATIVE LANGUAGE 1116, 1122, 1129, 1131 IMPERATIVE PROGRAMMING 1111, 1118, 1120, 1129, 1132 IMPULSE194 INCLUSIVE693 INCONCEIVABLE 48, 939 INDIVIDUAL 671, 688, 708, 731 INDIVIDUATION574 INFINITY 506, 507, 513, 529, 890 INFORMATION 531, 536 INFORMATION ABSTRACTS ENERGY 535 INNER ME 363 INNER STATE 999 INNOCENCE175 INSIDE 156, 929, 947 INSIDE OUT 437, 888 INSTANCE 668, 705, 708, 718 INSTRUCTION MANUAL 1132, 1133 INSTRUMENT 119, 121, 126 INTEGER583 INTEGRAL 239, 241 INTEGRATION 233, 239, 244, 246, 247 INTELLECT173 INTELLIGENCE 26, 30 INTERNAL STATE 989 INTERNET1038 INTERPRETER 1095, 1096 INVARIANCE 94, 95, 97, 151, 195, 942 INVERSE 508, 519, 1115 INVERSION 310, 527 IRRATIONAL 459, 827 ISLAM236 IT THINKS 177

J JAVA1111 JOINING 439, 440, 441 JUNK SPACE 117

K KIND 718, 733 KNOW429

L

The AUDITIVE

LAMBDA CALCULUS 1136 LANGUAGE 241, 546, 1115 LATITUDE896 LEARNING138 LIBERAL ARTS 108, 545 LIBERATION 685, 747, 771, 774, 775, 777, 778, 850, 851 LIGHT 85, 305, 339, 442, 508, 609, 1016, 1017, 1019, 1020, 1022, 1023, 1025, 1027, 1031, 1049 LIMIT620 LINE 28, 49, 57, 154, 156, 194, 364, 453, 459, 568, 572, 609, 617, 673, 781, 889, 948,  949, 950, 1016 LINEAMENT 389, 462, 889, 1168 LINEAR 364, 383, 946 LINEAR CIRCLE 179 LINEAR CIRCULARITY 369 LINEARITY 798, 816 LINEAR SPACE 768 LINES OF LIGHT 38 LISTEN 884, 931 LITERACY127 LITERATURE545 LOCAL GLOBALITY 763 LOCATION 766, 817 LOGARITHM950 LOGIC 562, 602, 605, 620, 629, 633, 738, 1046, 1047, 1049 LOGICAL 591, 1077, 1084 LOGIC OF COMPUTATION 703 LOGISTICS1049 LOGO1097 LONGITUDE896 LOOK 531, 546, 932 LOOKING 28, 446 LOSS OF IMAGES 43 LOVE 49, 634

M MACHINE 543, 544, 545, 583, 586, 590, 592, 684, 708, 718, 725, 728, 1027, 1030 MAGIC494 MAKE 366, 425, 430 MAPPING678 MAPS 429, 684 MARKUP LANGUAGE 1159 MASS 1022, 1023 MASSIVE 1027, 1030, 1049 MATERIAL 60, 462 MATERIALITY726 MATHEMATICS252 MATTER 85, 507, 508, 536 MEANING242 MEAN VALUE 711 MEASURE585 MECHANIC 528, 545, 552, 592, 785, 1027, 1031, 1087 MEMORISE 898, 900, 923, 927, 932, 939, 1056 MEMORY 306, 924, 932, 951, 958, 987, 1031, 1044, 1050 MERIDIAN 524, 896 MERIDIATE527 METAPHOR 218, 266, 370, 1016 MIGRANT 882, 894 MIND 31, 32 MODERNIST EMPERORS 65 MODERNITY 269, 286, 480 MOVE435 MOVEMENT 455, 480, 678, 783 MULTIPLICATION 568, 572, 777, 788, 790, 811 MULTIPLICATIVE GROUP 572 MULTIPLYING PROPORTIONS 617 MYTH 467, 485, 583, 586, 588 MYTHICAL ENTITIES 475, 484

The ARCHITECT

N NATURAL 67, 187, 214, 221 NATURE 17, 18, 22, 27, 76, 280, 316, 379, 573, 575 NECESSITY 473, 776 NIGHT 154, 178, 561, 876, 889, 903, 907, 910, 914, 915, 916, 947, 949, 1033, 1055, 1110, 1172 NORMAL DISTRIBUTION 663 NOUN 186, 548, 550, 552, 554, 555 NOVEL545 NUMBER 66, 214, 460, 461, 573, 575, 579, 585, 590, 591, 646, 650, 663, 738, 855, 903, 916,  926, 949, 950, 1030, 1067, 1110, 1172 NUMBERS DO ARITHMETIC 799 NUMBERS IMAGINE 574

O OBJECT 49, 57, 158, 183, 304, 308, 456, 685, 729, 779, 781, 783 OBJECTIVITY 50, 308, 375, 377, 395, 456, 776 OBJECT ORIENTED 1149 OBJECTS IN LOGIC 460 OBSTACLE18 OBSTACLES942 OMNIDIRECTIONAL 432, 1013, 1020 OMNIPRESENCE 563, 1020, 1021, 1025 ONTOLOGY 429, 458 OPEN SOCIETY 540 OPERATE 435, 460 OPTICS 266, 267, 269, 271, 683 ORCHESTRATE TIME 461 ORDER 574, 575 ORIGIN 428, 442, 444, 633 ORIGINAL ARTICULATION 16 ORNAMENT 388, 462, 871, 889 OTHERS880 OUTER FLOW OF CONTROL 1159 OUTER SUN 363 OUTER TAPE 992 OUTSIDE 156, 878, 921, 929, 947

P PACT22 PARADOX 117, 506, 507, 512, 516, 529, 536, 891 PARAMETER731 PARAMETRICISM1104 PART 466, 530, 566, 1027

The VISUAL

PARTICLE 510, 514, 516, 517, 519, 520, 521 PARTICLES INVENT 512 PARTITION 641, 643 PART OF 458 PASSIVE OBJECTS 38 PAST 84, 186, 428, 708, 728, 923, 927, 930, 932, 951, 989, 1031, 1044, 1050, 1055, 1056 PAST MEMORY 989, 994, 1038 PEOPLE 3, 4, 6 PERCEPTIVE289 PERFECT 668, 911 PERSPECTIVE 708, 763, 771, 784, 785, 950 PERSPECTIVE EYE 867, 870 PERSPECTIVITY763 PHOTOGRAPHIC EYE 674, 680 PICTURE 28, 31, 420, 425, 430, 431, 432, 435, 498, 512, 694, 695, 696, 701, 702, 750,  781, 783, 794 PICTURE ANYTHING 687 PICTURE PROPORTIONAL LINES 779 PICTURES DIFFERENTIATE 426 PLANE OF OBJECTIVITY 372 PLAY 27, 119, 312, 441 POETRY 545, 1131, 1134 POLITICS 1052, 1056, 1057 POLYLINE617 POLYTECHNICS605 POWER 110, 175 PRECISION467 PREDICT 708, 728 PRESENT 42, 428, 923, 927, 929, 931, 932, 989, 1010, 1044 PRESENT ELEMENT 989 PROBLEM 940, 942, 1128 PROCEED1118 PROCESSING1044 PROCESSOR 333, 1038, 1066, 1084, 1085, 1097 PRODUCE 718, 725, 738 PRODUCES INSTANCES 733 PRODUCT708 PRODUCTION 704, 705, 731 PRODUCTION LINE 1132, 1133 PRODUCTIVE772 PROGRAM 1116, 1118, 1135, 1150 PROGRAMMING1115 PROGRESS82 PROJECTIVE39 PROJECTIVE SCREENS 45 PROPERTY 216, 264 PROPHET1167 PROPORTION 215, 462, 564, 610, 613, 753 PROPORTIONAL CONDUCT 783 PROPORTIONAL MOVEMENTS 781 PROPORTION OF THINGS 586 PROSE 1132, 1133 PUBLIC 3, 4, 6, 153, 311, 324, 362, 562 PUBLIC FACE 111 PUBLIC VOICES 14

Q

R RATIO 61, 305, 889 RATIOCINATIO 385, 462, 1168 RATIONAL 63, 215, 222, 247, 262, 267, 294, 383, 455, 459, 512, 521, 586, 610,  618, 973, 1016, 1173 RATIONAL PLANE 779 RATIONAL SPACE 790 REAL 194, 216, 223, 245, 247, 263, 269, 295, 387, 455, 513, 514, 515, 588, 590, 613,  784, 787, 788, 870, 889, 977, 1017, 1173 REAL AXIS 182, 798 REALITY 61, 63, 301, 305, 517, 518, 520, 618, 621, 627, 880, 886, 911 REAL NUMBERS 592, 800 REAL PLANE 781 REASON 444, 913 REBIRTH88 REFLECTIVE38 REGIME689 RENAISSANCE 40, 87, 88, 89, 778, 779, 781, 783 RESPONSIBILITY20 RESULT1009

The AUDITIVE

QUALITY 81, 541, 542 QUANTA ABSTRACT PARTICLES 516, 535 QUANTITY 80, 541 QUANTUM 483, 515, 516, 518, 519, 520 QUANTUM MECHANIC 1027 QUATERNION845

REVOLUTION229 RHETORIC109 RIEMANN MANIFOLDS 783 ROTATE 793, 794, 835, 843, 848, 898, 925, 942 ROTATE OBJECTS 845 ROTATING PICTURE 851 ROTATING POINT 856 ROTATION 617, 774, 777, 779, 781, 783, 790, 791, 811, 842, 850, 854, 856, 1011 RULE989

S

The ARCHITECT

SACRIFICE20 SAME678 SAME TIME 471 SAW890 SAYING446 SAYS934 SAY WHAT CHARACTERS CAN HEAR 902 SCAFFOLDS449 SCALARITY 35, 67, 170, 207 SCALING 788, 789, 791, 811 SCHEME673 SCIENCE313 SCREEN 34, 39, 43, 858, 862, 898 SCREENED NATURE 35 SCULPTURE 284, 432 SEDUCTION176 SEE 504, 505, 550, 555, 557, 563, 583, 586, 588, 643, 646, 673, 702, 876, 958 SEE ALONG THE AXIS OF TIME 410 SEE ARCHITECTURE 441 SEE IMAGES 434 SEEING 610, 613, 632, 678, 681, 766, 867, 945, 946, 989 SEE SPACE 412, 961 SEE WHAT NUMBERS CAN SHOW 559 SELECT634 SENSES 23, 945 SENSIBLE 26, 30 SENSITIVE947 SEQUENCE83 SERVICE337 SET989 SHAPE454 SHARE20 SHOW 931, 989 SHOWING 945, 946 SHOWS MULTIPLICATION 779, 781, 783 SHOW UP 609, 657, 663 SIMULATION731 SINGLE DIRECTION 434 SINGULARITY541 SITUATION1127 SKELETON OF SYMMETRIES 261 SMELL25 SOCIETY 110, 296 SOLVE PROBLEMS 1135 SOPHISTICATION467 SOUND 432, 444, 878, 956, 961, 973, 977, 981, 1013, 1014, 1016, 1036, 1050, 1057, 1059,  1064, 1113, 1138, 1148, 1158 SPACE 179, 180, 183, 185, 190, 412, 417, 425, 426, 435, 442, 470, 514, 515, 547, 548,  555, 557, 573, 625, 679, 686, 708, 737, 756, 761, 793, 794, 798, 831, 859, 889, 896,  928, 929, 930, 937, 938, 939, 940, 951, 956, 1011, 1014, 1015, 1019, 1021,  1025, 1027, 1034, 1110, 1113, 1172 SPACE ROTATED 756 SPACETIME 756, 771, 775, 804, 807, 811, 851, 854, 856 SPATIALITY682 SPECIES 669, 708 SPECIFICATION733 SPECIFIC DIRECTION 422 SPECIFY 715, 1118 SPECTRUM 418, 663 STAGE 312, 1142, 1152, 1162 STANCE891 STANDARD DEVIATION 711 STATE1002 STATUES479 STEREOGRAPHIC949 STILL LIFES 418 STRAIGHT610 STRUCTURAL470 STRUCTURAL ELEMENTS 457, 530 STRUCTURALISM465 STRUCTURE 429, 451, 453, 454, 455, 456, 457, 465, 1140, 1142, 1150, 1152, 1160, 1162 STRUCTURES CONSIST 530 STRUCTURES MAGIC 467 STRUGGLES1128 SUBJECT 47, 48, 50, 51, 57, 325, 456, 460, 686, 987, 1040 SUBJECTIVITY 49, 304, 308, 456, 634, 729 SUBJECTIVITY PRODUCES OBJECTS 728

SUBTRACTION 568, 572 SUPPORT 1152, 1162 SYMBOLISATION 748, 1150 SYMMETRIA462 SYMMETRY 157, 516, 527, 944 SYSTEM 453, 574, 601, 602, 613, 627, 632, 633, 657, 658, 667, 668, 691, 692, 705, 725, 733 SYSTEMATIC741

T

The VISUAL

TAKE422 TAKE A PICTURE 464 TAKES PICTURES 708 TALK 90, 221, 222, 242, 312, 326, 464, 558, 771, 876, 884, 885, 886, 891, 905, 908, 918, 921,  932, 987, 1091, 1101, 1113, 1127, 1142, 1143, 1152, 1153, 1162, 1163 TALKING 945, 946 TAPE1002 TASTE25 TECHNIQUE 315, 322, 986 TECHNOLOGY320 TEMPERAMENT415 TEMPERAMENTS170 TERM 9, 449, 450, 463, 558 TERRITORY82 TERROR65 TEXT135 THE ARCHITECTURAL SCALARITIES 260 THE AUDITIVE 393 THE HUMAN SCALARITIES 278 THEN RULES 994, 996 THE VISUAL 392 THINGS 155, 156, 178, 330, 632, 1015 THINGS THEMSELVES 583 THINK441 THINKING324 THREATS112 TIME 97, 179, 180, 183, 185, 186, 190, 204, 417, 418, 426, 435, 547, 548, 555, 557, 573, 620,  623, 625, 635, 643, 673, 679, 680, 685, 747, 756, 761, 775, 777, 778, 799, 817, 824, 831,  859, 889, 896, 928, 929, 930, 937, 938, 939, 940, 1010, 1033, 1110, 1111, 1172 TIME EMBEDDED 761 TIME LINEARISED 756 TODAY 41, 289, 481 TONGUE 14, 1016 TOUCH 25, 563 TOURISM630 TRACE 38, 1007, 1010 TRANSLATION 16, 777, 787, 789, 791, 807, 855 TRANSPARENCE 1021, 1025 TRUTH 50, 633 TUNE119 TURING MACHINE 986, 1027 TURN 56, 430 TUTORIAL1122 TYPE671 TYRANNY64

U

V VALUE708 VARIANCE668 VELOCITY817 VERB 186, 548, 550, 552, 556, 557 VERTICAL AXIS OF TIME 180 VESSELS 1131, 1134 VIEW870 VISIBLE 603, 1027, 1059 VISION 951, 987, 1042, 1050 VIVIDNESS 217, 481 VOICE 7, 14, 312

The AUDITIVE

UNDERSTANDING 18, 241, 242, 463, 924 UNDERSTAND PRESENCE 923, 926 UNIFY521 UNIT800 UNIT CIRCLE 831 UNITY 458, 459, 562, 632, 756 URBANISM114

W WATER85 WAVE 510, 519, 520, 521 WAVES EXPLORE 513 WEST236 WESTERN HUMAN 283 WHAT 90, 396, 1119, 1124 WHAT TO SAY 1161 WHITE LINES 267 WONDER51 WONDERING AROUND 431, 498 WORLD 430, 476, 543, 766, 851, 878, 885, 898, 1036, 1038, 1050, 1057, 1127,  1131, 1134, 1136 WRITE1136 WRONG913

1170

SOURCES FOR IMAGES AND GRAPHICS

The ARCHITECT

5 https://www.realchangenews.org/sites/default/files/styles/article_image_full/public/The% 20Public%20movie%20review.jpg?itok=BMojT7yL 19 https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/10/Rainforest_2880x1920.jpg 21 https://live.staticflickr.com/2580/3967158874_56370ec16c_b.jpg 24 https://upload.wikimedia.org/wikipedia/commons/2/22/Makart_Fuenf_Sinne.jpg 33 https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Sandro_Botticelli_-_La_nascita_di_Venere_-_Google_Art_Project_-_edited.jpg/1200px-Sandro_Botticelli_-_La_nascita_ di_Venere_-_Google_Art_Project_-_edited.jpg 36 https://upload.wikimedia.org/wikipedia/commons/thumb/9/97/The_Earth_seen_from_Apollo_ 17.jpg/1280px-The_Earth_seen_from_Apollo_17.jpg 37 https://img.nzz.ch/2020/8/17/062afd59-2613-4a34-b59d-f62698befdbe.jpeg 44 https://www.youtube.com/watch?v=x1SgmFa0r04 46 https://upload.wikimedia.org/wikipedia/commons/0/08/Tarota_%28Casia_toral%29_plant_ with_raindrops.jpg 54 https://i.pinimg.com/originals/50/fb/81/50fb81f8ffa1bc43ea00c6e13b12f74b.jpg 55 https://1.bp.blogspot.com/-_F72LMYUNFA/YaDcForgqiI/AAAAAAABGq0/p790VSkhK1EKf3SI5jGmtRSobHUs2h9QCLcBGAsYHQ/s2048/kulam%2B1%2B%2528Copy%2529.JPG 58 https://upload.wikimedia.org/wikipedia/commons/0/09/Die_Zwitscher-Maschine_%28 Twittering_Machine%29.jpg 86 https://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Diagram_of_the_Water_ Cycle.jpg/1600px-Diagram_of_the_Water_Cycle.jpg?20160321145531 148 https://www.srf.ch/static/cms/images/1280w/04b47b.jpg 150 https://www.espacioprofundo.com/adjuntos/monthly_2020_02/341526455_received_ 1824422997689155(1).jpg.ce1e0e748e5037f5d0b79333ec3a577e.jpg" 152 https://de.wikipedia.org/wiki/Lucy_(2014) 159 https://monoskop.org/images/1/15/Paul_Klee_Notebooks_Vol_1_The_Thinking_Eye.pdf 181 https://upload.wikimedia.org/wikipedia/commons/6/67/Michelangelo_Sündenfall.jpg 198 https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/20090905_Suzhou_Couple%27s_ Retreat_Garden_4442.jpg/2560px-20090905_Suzhou_Couple%27s_Retreat_Garden_4442.jpg 210 https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Peter_Paul_Rubens_%26_ Jan_Wildens_-_De_ontvoering_van_de_Dochters_van_Leucippus.jpg/800px-Peter_Paul_ Rubens_%26_Jan_Wildens_-_De_ontvoering_van_de_Dochters_van_Leucippus.jpg 268 https://www.archdaily.com/917977/paul-klees-bauhaus-notebook-is-now-online/5ced15e 1284dd1e7030002c8-paul-klees-bauhaus-notebook-is-now-online-photo?next_project=no 270 https://live.staticflickr.com/2580/3967158874_56370ec16c_b.jpg 272 https://lh3.googleusercontent.com/proxy/mPk9pXNmeUZLquwEJ22SsGnVbjfQsqhbZuyJ0M CppWLXL_ivwjBBVpZ6xP6fOoTcqXb-atX0nMPx5UX2pEHNsPtXpO0DlT--d9AVn9KdF r358CSTwuRUcoXY1lPHysMdEFOigeerZkj6VLjjBsiI0dB9 285 https://www.baunetzwissen.de/imgs/2/1/2/9/4/0/3/elbphilharmonie_c_sophie_wolter_2400fca25acc0383f.jpg 287 https://i.pinimg.com/originals/91/c4/34/91c434b12b4d01b65724314af622a0f3.jpg 288 https://i0.wp.com/www.raptisrarebooks.com/images/57034/de-humani-corporis-fabricalibri-septem-andreas-vesalius-first-edition.jpg?fit=1427%2C2590&ssl=1 290 https://upload.wikimedia.org/wikipedia/commons/a/ab/Parmigianino_Selfportrait.jpg 291 http://www.geminoid.jp/projects/kibans/Images/m001.jpg 302 https://upload.wikimedia.org/wikipedia/commons/8/8b/Moby_Dick_final_chase.jpg 303 https://i.pinimg.com/564x/38/a5/44/38a544579dc6efae25af20b1ca333d71.jpg 307 https://cdn.pixabay.com/photo/2017/06/27/14/34/belgrade-2447500_960_720.jpg

The VISUAL The AUDITIVE

314 http://www.sbadandrmc.com/s/cc_images/cache_3926876404.jpg 317 https://static.visitestonia.com/images/3489697/-1_-1_false_false_f988ee70ed3e993f8e0 cad91d9a7fc09.jpg 319 https://de.messeshop-deutschland.de/fotos/haushaltsartikel_spuelmittel_pril_pro-naturesensitive-calendula-500ml_2_1800x1800.jpg 321 https://www.michaeljohngrist.com/wp-content/uploads/2008/09/beach-kids-play.jpg 327 https://pixnio.com/free-images/2017/11/18/2017-11-18-20-29-55.jpg 328 https://www.sierraclub.org/sites/www.sierraclub.org/files/styles/flexslider_full/public/sierra/ articles/big/SIERRA%20Seedling%20WB.jpg?itok=znJwNKDC 334 https://images.computerhistory.org/siliconengine/1971-2-1.jpg 338 https://i.blogs.es/5b9ced/anuncioiphone/1366_2000.webp 341 https://pbs.twimg.com/media/ElnK7V3WkAAvvyE.jpg 345 https://img.luzernerzeitung.ch/2020/10/10/97f0deb4-dd4a-4844-ba57-88e464f22d65.jpeg? width=1080&height=720&fit=crop&quality=75&auto=webp 346 https://artlogic-res.cloudinary.com/w_1200,c_limit,f_auto,fl_lossy,q_auto/artlogicstorage/ kraupatuskanyzeidler/images/view/4767d0e39c2c986a240611f56434f81ej/kraupa-tuskany zeidler-katja-novitskova-approximation-the-apocalypse-s-many-horsemen-2020.jpg 351 https://api.time.com/wp-content/uploads/2011/09/babeltales-twototango.jpg 361 https://m.media-amazon.com/images/M/MV5BMTU2MTQxNTE4OV5BMl5BanBnXkFtZTgw NzU1NTU5MTE@._V1_.jpg 376 https://buckinghamhsiao.files.wordpress.com/2017/03/fig-3-river-diagram-of-the-spontan eous-process-of-heaven-and-earth-from-zhao-huiqian-liu-shu-ben-yi-1751-wenyange-editionlouis-fig-12.jpg 398 https://4.bp.blogspot.com/-n8mhkvilf3k/V7nW1e2MMTI/AAAAAAAAGq4/pWoY2KU3LAU zctzEOKt0JC-tFf7_78NBwCLcB/s640/CaravaggioBoyBittenbyaLizard1594-96.jpg 407 http://www.tipacilar.com/wp-content/uploads/2016/01/46_89de53aa-ceb8-4b01-87dbd694e8380583jpg.jpg 411 https://peacockplume.fr/sites/default/files/Andy%20Warhol%20Polaroid%20Foundation.jpg 416 https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Linear_visible_spectrum.svg/ 2560px-Linear_visible_spectrum.svg.png 419 https://blog.sevenponds.com/wp-content/uploads/2015/06/768px-Adriaen_van_Utrecht-_ Vanitas_-_Still_Life_with_Bouquet_and_Skull.jpg 421 https://i.redd.it/yp2lwd7wi2071.jpg 433 https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/JuanGrisGuitarwithClarinet Kuntsmuseu.jpg/640px-JuanGrisGuitarwithClarinetKuntsmuseu.jpg 436 https://lh5.googleusercontent.com/o-tdlm_SujlKTbmRJtHDCRZVRfQhU3TuRSeSYOOFPrWR AkQAlS2xaUWj6B-igtY91FMOlM6N42_DpsWZ55bGXgzbrcMoZLPKoyHJkb_XW1U79Pna9_ xquAzq5pg4AJHktAncK_FN 445 https://live.staticflickr.com/1974/30036614337_bd85a90df8_b.jpg 448 https://media1.faz.net/ppmedia/aktuell/1785145034/1.7546601/format_top1_breit/moeglichstviel-reden-um-die.jpg 477 https://www.olympus.de/company/media/content/news/ssd/210209-olympus-stonehengeorigins/stonehenge_image_2-credit-andre-pattenden_english-heritage_img_1200.jpg 482 https://mir-s3-cdn-cf.behance.net/project_modules/fs/c2277328734383.55cf6e0c5787b.jpg 503 https://upload.wikimedia.org/wikipedia/commons/f/f6/Duchamp_Fountaine.jpg 525 https://upload.wikimedia.org/wikipedia/commons/4/41/Earth_Rotation_%28Nepal%2C_ Himalayas%29.jpg?20151005185332 577 https://ia803102.us.archive.org/BookReader/BookReaderImages.php?zip=/33/items/summa dearithmeti00paci/summadearithmeti00paci_jp2.zip&file=summadearithmeti00paci_jp2/ summadearithmeti00paci_0092.jp2&id=summadearithmeti00paci&scale=1&rotate=0 578 https://canadabayheritage.asn.au/wp-content/uploads/2021/07/Basic-Chines-Abacus.jpg 580 https://www.eamesoffice.com/wp-content/uploads/2014/02/1968_Babbage_s-CalculatingMachine-scaled.jpg 589 https://zenodo.org/record/1628613#.Yv3mYy8RqgQ 596 https://s3-eu-west-1.amazonaws.com/b2bstorage.arte.tv/photos/0515250-cropped.jpg 598 https://live.staticflickr.com/5587/14777215676_8006505a51_b.jpg 606 https://upload.wikimedia.org/wikipedia/commons/5/56/Rail_Road_Suspension_Bridge_ Near_Niagara_Falls_v2.jpg 612 https://i.guim.co.uk/img/static/sys-images/Guardian/Pix/pictures/2012/1/19/1326965512213/ 1890s-Kodak-employees-on--013.jpg?width=1920&quality=85&auto=format&fit=max&s=f7 affbfc7c0b1c6c1fd251a25cd0c700 619 https://amerika21.de/files/a21/styles/page-grid-6-flexible-height/public/img/2019/humboldtbonpland_chimborazo.jpg?itok=zow6jCp624 https://www.nhm-wien.ac.at/jart/prj3/nhm-resp/images/cache/bd0d48661fc61b24ce7991 5862b487b6/0x588CD1027D92146E8722E2B400689E91.jpeg 656 https://decoryourhome.store/wp-content/uploads/2019/12/il_fullxfull.1961467438_761nscaled.jpg 664 http://internationalphotomag.com/wp-content/uploads/2017/12/OttoPfenninger_Early_Color_ Photos_1906_PhotogrVphy_Magazine_03.jpg 665 https://th-thumbnailer.cdn-si-edu.com/ZHAJfj6y3SyPlwaQt8P5OlTszag=/1000x750/filters: no_upscale():focal(942x790:943x791)/https://tf-cmsv2-smithsonianmag-media.s3.amazon aws.com/filer/6b/51/6b510bda-3f1d-438e-806c-af38a51897aa/gettyimages-613497858.jpg 666 https://image.geo.de/30030228/t/Ga/v3/w960/r0/-/caravaggio5-pop-jpg--9652-.jpg 670 https://pbs.twimg.com/media/FOm8Jm-WQAQ3d1x?format=jpg&name=large 672 https://wpr-public.s3.amazonaws.com/wprorg/styles/resp_orig_custom_user_wide_1x/s3/ segments/textile%20Workers%2C%20Mississippi%2C%20image%20by%20National%20 Archives%20and%20Records%20Administration.jpg?itok=CiGLUvzt 675 https://i.pinimg.com/originals/fe/e8/08/fee80860a4520468345a52d2273c56d9.jpg 706 https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQUUY064cLyePC2Z6lzOd7fDfs 5ySTQc8qq1QyM4zIBqzNY3xgt3ePTp9zCGH9PD_N0iTs&usqp=CAU 730 https://iconeye.com/wp-content/uploads/2013/06/Icon120-Powersof10-inside.jpg 735 https://pbs.twimg.com/media/CnXGU8-UMAAol85.jpg 743 https://v2.nl/archive/works/lovers-leap/leadImage_large 757 https://www.kunstkurs-online.de/Seiten/perspektivisch-zeichnen/bilder-perspektive/wuerfel2FP-44b.png 814 https://www.youtube.com/watch?v=d4EgbgTm0Bg 814 https://3b1b-posts.us-east-1.linodeobjects.com/images/about/channel.png 841 https://reference.wolfram.com/language/workflow/AccessGPIOOnRaspberryPi.html 847 https://cdn57.androidauthority.net/wp-content/uploads/2017/09/S8-Infinity-Display-AMOLEDunder-microscope-gds-aa-1080p-2nd.jpg 860 https://www.showroomworkstation.org.uk/pictures/programme/2/2/7/.22734/~~EDjpbm7l/ In_the_Mood_for_Love_3.jpg

The ARCHITECT

861 https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Parmigianino%2C_visione_ di_san_girolamo_03.jpg/1920px-Parmigianino%2C_visione_di_san_girolamo_03.jpg 874 https://en.wikipedia.org/wiki/Poem_of_the_Right_Angle 875 https://www.daskino.at/fileadmin/user_upload/WKW_Poster_InTheMoodForLove_originalscaled.jpg 877 https://r1imghtlak.mmtcdn.com/5305c4e86d3111eba6ca0242ac110003.jpg 895 https://s26162.pcdn.co/wp-content/uploads/2016/09/Apollo-17-Photo-Courtesy-NASA-01.jpg 899 https://cdn.mos.cms.futurecdn.net/zDHiTCNw6TDUC8XEt4GHWj-1024-80.jpg.webp 904 https://upload.wikimedia.org/wikipedia/commons/7/70/Alberti_cipher_disk.JPG 943 https://upload.wikimedia.org/wikipedia/commons/7/71/Leon_Theremin.jpg 955 https://upload.wikimedia.org/wikipedia/commons/f/f4/Murey.jpg 962 https://www.parlonspeinture.com/wp-content/uploads/2017/07/potter-1139047_1280-1-1080 x675.jpg 965 https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Rubber_boots.jpg/1280pxRubber_boots.jpg 966 https://i5.walmartimages.com/asr/813c8efa-4122-45d3-9780-db4f4fb43ad0_1.cdfdb59be 548260cfaa29af31c820466.jpeg?odnHeight=2000&odnWidth=2000&odnBg=ffffff 968 https://i.pinimg.com/564x/3f/60/09/3f60091e07c681641a02ca99cca8279b.jpg 970 https://media.architectuul.com/architecture/4e50da0a-4efc-4b7f-9a30-2e186d7b5f76_ large.jpg 974 https://www.history.com/.image/c_limit%2Ccs_srgb%2Cq_auto:good%2Cw_1240/MTY1NTIx MTIwOTMyNDA2ODIy/parthenon-gettyimages-122340023.webp 975 https://upload.wikimedia.org/wikipedia/commons/thumb/8/85/Meister_des_Porträts_des_ Paquius_Proculus_001.jpg/1200px-Meister_des_Porträts_des_Paquius_Proculus_001.jpg 976 https://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Pantheon_%28Rome%29__Right_side_and_front.jpg/1490px-Pantheon_%28Rome%29_-_Right_side_and_front.jpg? 20220327200016 978 https://www.jstor.org/stable/44988075 979 https://retrospektiven.files.wordpress.com/2020/03/michelangelo_caravaggio_062.jpg?w =660 980 https://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Santa_Maria_Novella_Florence_ façade.jpg/2560px-Santa_Maria_Novella_Florence_façade.jpg 982 http://scharoun-gesellschaft.de/wp-content/uploads/2020/11/SC1956_fil00-3.jpg 983 https://scontent-vie1-1.xx.fbcdn.net/v/t1.6435-9/122841936_4030892616927893_379935 3112533911029_n.jpg?_nc_cat=106&ccb=1-5&_nc_sid=730e14&_nc_ohc=GFjy4lvXlcIAX-kJ 25y&_nc_ht=scontent-vie1-1.xx&oh=36079a7baa93ae3be66dd1b4b06c116b&oe=6190B0D4 984 https://www.hs-wismar.de/storages/hs-wismar/_processed_/c/8/csm_PM_130407_01_ realities_united_BIX_Graz_f85404dbd2.jpg 1039 https://sourceforge.net/projects/johnnysimulator/ 1043 https://www.ssi-schaefer.com/resource/image/46438/landscape_ratio8x4/1575/750/bf37 1660bbdf96d3b8d08bd42fb96d96/uZ/palettenregale-dam-image-de-1027-.jpg 1062 https://static.techspot.com/articles-info/2151/images/2020-12-03-image.jpg 1086 https://zonait.ro/wp-content/uploads/2015/11/intel404img.gif 1092 http://cyberneticzoo.com/wp-content/uploads/mindstorms_turtle-x640.jpg 1103 https://en.wikiarquitectura.com/wp-content/uploads/2017/01/Rascacielos_de_vidrio.jpg 1112 https://upload.wikimedia.org/wikipedia/commons/6/64/Flow_chart_of_Planning_and_ coding_of_problems_for_an_electronic_computing_instrument%2C_1947.jpg?2015042 1140848 1123 https://beginnersbook.com/2017/09/java-program-to-add-two-numbers/ 1125 https://reference.wolfram.com/language/ref/Plus.html 1144 https://archeyes.com/seagram-building-new-york-mies-van-der-rohe/seagram-building-miesvan-der-rohe-ezra-stoller-photographer-er2-1958/ 1145 https://api.time.com/wp-content/uploads/2014/03/time-life-building-60s-don-draper-02.jpg 1146 https://user-images.githubusercontent.com/5091582/172979587-9d895255-9087-429e92e8-9094eedd9318.png 1154 https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/HK_HSBC_Main_Building_ 2008.jpg/480px-HK_HSBC_Main_Building_2008.jpg 1155 https://www.billi-uk.com/wp-content/uploads/2019/06/90s-office.jpg 1156 https://de.libreoffice.org/assets/Uploads/Timeline-pics/_resampled/ResizedImageWzQ5 NywzNzNd/Starwriter-compact-2.png 1164 https://i.pinimg.com/originals/5a/eb/99/5aeb996bc9a6baec86c77bf95c41e5b3.jpg 1165 http://petermorrisonmosaic.com/wp-content/gallery/commercial-other/Google-Heaquarters.jpg 1166 http://microsoftportal.net/uploads/posts/2014-02/1391418350_windows-8.jpg

COLOUR CODE

1171

1172

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

1173

in  MAJOR  tuning in  MINOR  tuning

1174

The VISUAL

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

The AUDITIVE

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 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, kalkgrau 115 g/m2 Surbalin glatt, kalkgrau 115 g/m2 Salzer EOS 80 g/m2 TYPEFACE MH Archetype by Matthieu Huegi LIBRARY OF CONGRESS CONTROL NUMBER 2022946354 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.

The ARCHITECT

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. ISBN 978-3-0356-2598-1 e-ISBN (PDF) 978-3-0356-2601-8 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

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.

The VISUAL

The AUDITIVE