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Wentworth - Alumni Library

THE SECOND DIGITAL TURN DESIGN BEYOND INTELLIGENCE

MARIO CARPO

THE MIT PRESS

CAMBRIDGE, MASSACHUSETTS

LONDON, ENGLAND

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ames: Carpo, Mario. author.

Title: The second digital turn: design beyond intelligence/ Mario Carpo.

Description: Cambridge, MA: The MIT Press, 2017. I Series: Writing

architecture I Includes bibliographical references and index.

fdentifiers: LCCN 2016054313 I ISBN 9780262534024 (pbk.: alk. paper)

Subjects: LCSH: Architecture and technology. I Architecture- -Information technology. I Architecture- -Computer-aided design.

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CONTENTS

ACKNOWLEDGMENTS

INTRODUCTION

2 THE SECOND DIGITAL TURN

4 .1 Data-Compression Technologies We Don't

Need Anymore

4·4 Don't Sort: Search

4.3 The End of Modern Science

4.4 The New Science of Form-Searching

4 .5 Spline Making, or the Conquest of Free Form

4 .6 From Calculus to Computation: The Rise and

Fall of the Curve

4.7 Excessive Resolution

4 .8 The New Frontier of Alienation, and Beyond

3 THE END OF THE PROJECTED IMAGE

3.1 Verbal to Visual

3.4 Visual to Spatial

3.3 The Technical and Cognitive Primacy of

Flatness in Early Modern Art and Science

3.4 The Underdogs: Early Alternatives to

Perspectival Projections

3.5 The Digital Renaissance of the Third

Dimension

ix

9

99

111

4 THE PARTICIPATORY TURN THAT NEVER WAS

4.1 The New Digital Science of the Many

4.4 The Style of Many Hands

4.3 Building: Digital Agencies and Their Styles

5 ECONOMIES WITHOUT SCALE: TOWARD A NONSTANDARD SOCIETY

5.1 Mass Production, Economies of Scale, Standardization

5.4 The Rise and Fall of Standard Prices

5.3 The Digital Mass- Customization of Social Practices

6 POSTFACE: 2016

NOTES

INDEX

•

131

134

135 140

145

147 149

153

159

165

217

ACKNOWLEDGMENTS

While researching and writing this book I had to dabble in

an inordinate number of disciplines and subjects, including

some that are manifestly outside of my expertise. I am aware

of the risks this entails; specialists in each of those fields will

no doubt find errors of all sorts. As often 'happens, I could

only outline a more general picture to the detriment of lo-

cal detail; going against the logic of the artificial intelligence I

try to describe, I was often obliged to merge, neglect, or com -

press plenty of data in order to allow some visible patterns

to emerge. I am grateful in advance to the scholars and col-

leagues who will correct my arguments and flag my simplifica -

tions and omissions. I am also thankful to the many colleagues

and friends with whom I discussed the ideas in this book over

the course of the last three years, and who generously offered

tips and advice: in particular, Alisa Andrasek, Marjan Colletti,

Marcos Cruz, Christian Girard, Jeff Huang, Achim Menges,

Marco Panza, Gilles Retsin, Jenny Sabin, Patrik Schumacher,

Axel Sowa, and the faculty and students at the B-Pro program

at the Bartlett School of Architecture, with whom I had many

fruitful sessions and discussions. Almost weekly discussions

with Frederic Migayrou left an evident trace throughout chap-

ter 4, and Philippe Morel generously shared technical and

mathematical insights, particularly on the history of spline

making. A grant from the Bartlett School of Architecture al-

lowed me to purchase some reproduction rights, and to hire

Alexandra Vougia as a research assistant and Tina Di Carlo as a

slightly different ways, and sometimes without saying it in so

many words.

2.4 The New Science of Form-Searching

Recent technical developments in the extrusion and robotic

winding and weaving of very thin filaments have prompted ex-

citing and promising experiments-at the Institute for Computa -

tional Design (ICD) of the University of Stuttgart, at the Bartlett

(University College Lon1on), and elsewhereY In 4014, Achim

Menges and Jan Knippers published a groundbreaking techni-

cal article describing their use of fiber-reinforced polymers in

the thin shell of the experimental ICD/ITKE Research Pavilion

they built in 4014. 33 Structural calculations for the pavilion had

to take into account the complex geometry of the shell, as well

as the density and direction of each bundle and layer of carbon

• and glass fibers wound in it. The authors began with a geomet-

rical and material layout inspired by biological models; then

they simulated the structural behavior of this first model using

standard computational finite element analysis (FEA), a math-

ematical method for the calculation of deformation and stresses

within a continuous structure. 34 Based on the results of this first

simulation, some aspects of the design were tentatively tweaked,

altering both the geometry of the shell and the internal layout of

the fibers. The FEA simulation was then rerun on this second

model, and so on, and repeated (iterated) many times over until

the authors were pleased with the results.

In this process of heuristic (not mathematical) optimiia-

tion, 35 every simulated model that was tried and discarded corre-

sponded to a physical model that a traditional artisan would have

made, tested, and likely broken in real life. Using digital simula-

tions of structural performance, however, today we can make and

break on the screen in a few hours more full-size trials than a

traditional craftsman would have made and broken in a lifetime.

40 CHAPTER 2

2.8

Alisa Andrasek, Wonderlab, AD Research Cluster 1,

B-Pro M.Arch Architectural Design, The Bartlett UCL,

Liquid (2016). Robotic extrusion of filaments on a vectorial template derived from computational fluid dynamics. Tutors: Alisa Andrasek, Daghan Cam, Andy

Lomas. Robotics: Feng Zhou. Students: Zhuoxing Gu, Tianyuan Xie, Bingyang Su, Anqi Zheng. © Alisa Andrasek, AD Research Cluster 1, The Bartlett UCL.

41

42

2.9 Gilles Retsin, Manuel Jimenez-Garcia, AD Research Cluster 4, B-Pro M.Arch Architectural Design, The Bartlett UCL, CurVoxels, 3D Printed Chair (2015). A robotically extruded chair combining a curved toolpath with a voxel-based data structure. Students: Hyunchul

Kwon, Amreen Kaleel, Xiaolin Yi.

2.10 Gilles Retsin and SoftKill Design, Protohouse, Collection Centre Pompidou (2012). Structural optimization (by iterative removal and addition of material) aimed at obtaining minimal volume and uniform stress throughout a complex architectural envelope. SoftKill design team: Nicholette Chan, Gilles Retsin, Sophia Tang, Aaron Silver. Developed at the Architectural Association Design Research Lab in London.

43

44

2.11 ICD Institute for Computational Design (Prof. Achim Menges). ITKE Institute of Building Structures and

Structural Design (Prof. Jan Knippers), ICO!iTKE

Research Pavilion 2012, Robotic filament winding of carbon/glass fiber structure, University of Stuttgart, 2012. © ICD/ITKE University of Stuttgart.

2.12 ICD Institute for Computational Design (Prof. Achim

Menges). ITKE Institute of Building Structures and

Structural Design (Prof. Jan Knippers). ICD/ITKE

Research Pavilion 2012, Exterior view of pavilion, University of Stuttgart, 2012. © ICD/ITKE University of Stuttgart.

45

Artisans of pre-industrial times (as well as the ideal artisan of

all times recently romanticized by Richard Sennett) 36 were not

engineers; hence they did not use mathematics to predict the

behavior of the structures they made. When they had talent they

learned intuitively, by trial and error, by making and breaking as

many samples as possible. So do we today, using iterative digital

simulations. We may or may not intuit some pattern, regularity,

or logic inherent or embedded in the structure we are tweaking-

but that is irrelevant. By making and breaking (in simulation) a

huge number of variatibns, at some point we shall find one that

does not break, and that will be the good one.

Inspired by Frei Otto's method of physical form-finding-

which Menges was the first to implement digitally and to trans-

late into computational terms-this heuristic design process is

functionally equivalent to the big data, search- based alterna -

tive to modern science mentioned earlier. Whenever digital

•' tools allow us to collect, record, and process huge troves of data,

information retrieval (the search for a precedent) is more ef-

fective than the traditional, deductive application of scientific

formulas or any other law of causation. The 40q ICD/ITKE

Research Pavilion being an experiment without precedent,

no corpus of previous, comparable instances was available for

search and retrieval. In the absence of any such historical ar-

chive, however, Menges, Knippers, and their team could avail

themselves of the immense power of digital simulation to create

on the spot, virtually, _just the archive they would have needed.

They may not have seen it this way, but by simulation and it-

eration they generated a vast and partly random corpus of many

very similar structures that all failed under certain conditions;

and they chose and ultimately replicated one that did not. 37 This

is a far cry from how a modern engineer would have designed

that structure-which is one reason why no modern engineer

could have designed it.

46 CHAPTER 2

A modern engineer would have started with a set of formu-

las establishing causal relationships between loads, forms, and

stresses in the structure. Typically used to calculate the resis-

tance of a structure after it has been designed, these formulas

can also drive and inspire our first, intuitive design of it. This

is because causal laws make sense, somehow: by the causality

they express, they interpret and provide some understanding of

the physical phenomena they describe. Indeed, in the classical

scheme of things, causality is seen as a primary law of nature;

so the laws of mechanics, for example, are held to spell out in

mathematical terms the way beams, cantilevers, pillars, arches, ' or vaults function in reality, and the formulas of structural en -

gineering have a "meaning" which is held to be true to nature.

Indeed, this meaningfulness, and the structural theories from

which it derives, are visible iri all masterpieces of modern struc-

tural engineering, from Eiffel's tower to Nervi's vaults. If we look at these modern structures we understand the basic structural

principles their designers had in mind when they first sketched

them.

That does not apply to our current way of designing by form -

finding, or, as we'should perhaps say, to better demarcate the

nature of today's process from that of its physical precursor,

computational form -searching. The power of Big Data applied to

information retrieval, simulation, and optimization makes the

formulaic data compression at the core of modern structural en -

gineering as obsolete as the Yellow Pages-or as the logarithmic

tables mentioned above. Gilles Deleuze famously disparaged the

abstract determinism of modern science, to which he opposed

the heuristic lore of artisan "nomad sciences." 38 Once again,

Deleuze's view of our pre-mechanical past doubles as an eerily

cogent anticipation of our digital future. Through computational

form-searching we can already design new structures of un-

imaginable complexity. But precisely because it is unimaginable,

TIIE SECOND DIGITAi. TUI\N 47

this posthuman complexity belies interpretation and transcends

the small-data logic of causality and determinism we have in-

vented over time to simplify nature and conve1i it into reassur-

ing, transparent, human -friendly causal models. Why does one

so unimaginably complex structure work, and the thousands of

very similar ones we just ran through FEA simulation do not?

Who knows. But the point is that it works. And if that is the case,

then we must come to the almost inevitable conclusion that the

new science of search µiay soon replace the method of experi-

mental science in its entirety, simply because simulation and

search can solve problems that the formalistic approach of mod-

ern science could never tackle. Computers can search faster than

humans can sort.

Digitally intelligent designers may be more enthusiastic or

more outspoken than other early adopters, but the new science

• of search has already pervaded, in spirit if not in letter, many of

today's data -driven cultural technologies, and traces of the same

quantitative, heuristic use of data are evident, in some muted,

embryonic way, in other branches of the natural sciences, such

as weather forecasting. 39 And sure enough, some historians of

science have already started to investigate the matter-with

much perplexity and reservation, as one would expect; as the

postmodern science of big data and computation marks a ma -

jor shift in the history of the scientific method. 40 As mentioned

above, mathematical abstractions such as the laws of mechanics

or of gravitation, for example, or any other grand theory of cau -

sation, are not only practical tools of prediction, but also, and

perhaps first and foremost, ways for the human mind to make

sense of the world. But then, if abstraction and formalization

(that is, most of classical and modern science, in the Aristo-

telian and Galilean tradition) are also seen as contingent and

time-specific data-compression technologies, one could ar-

gue that in the absence of the technical need to compress data

48 CHAPTER 2

in that particular way, the human mind can find many other

ways to relate to, or interpret, nature. Epics, myth, religion, and

magic offer vivid historical examples of alternative, nonscien -

tific methods, and no one can prove that the human mind is, or

ever was, hard-wired for modern experimental science. Many

postmodern philosophers, for example, would strongly object

to that notion. And as so many alternatives to modern science

existed in the past, one could argue that plenty of new ones may be equally possible in the future.

The mere technical logic of the new science of searching

goes counter to core postulates and assumptions of modern sci -

ence. Additional evidence of an even deeper rift between the two

methods is easy to gather. Western science used to apply causal-

ity to bigger and bigger groups, or sets, or classes of events-and

the bigger the group, the mote powerful, the more elegant, the more universal the laws that applied to it. Science, as we knew

it, tended to universal laws-laws that bear on as many differ-

ent cases as possible. The new science of data is just the oppo-

site: using information retrieval and the search for precedent,

data-driven prediction works best when the sets it refers to are

the smallest. Indeed, searches are most effective when they can

target and retrieve a specific and individual case-the one we are

looking for.4' In that, too, the new science of data represents a

complete reversal of the classical (Aristotelian, Scholastic, and

early modern) scientific tradition, which held that individual events cannot be the object of scienceY

In social science and in economics, this novel data -driven

granularity means that instead of referring to generic groups, so-

cial and economic metrics can and will increasingly relate to in-

dividual cases. This presages a brave new world where standards

and averages will no longer be either required or warranted:

fixed prices, for example, which were introduced during the In-

dustrial Revolution in order to standardize retail transactions,

TIIE SFCOND DIGITAL fUHN 49

have already ceased to exist, as each retail transaction in a digital

marketplace today is an algorithmically customized one-off, de-

livered at zero processing costs, or almost. 43 Likewise, the cost of

medical insurance, calculated as it still is on the basis of actuarial

and statistical averages, could become irrelevant, because it may

be possible to predict, at the granular level, that some individu -

als will never have medical expenses, hence they will never need

any medical insurance,_ and some will have too many medical ex-

penses, hence no one will ever sell them any medical insurance.

The individual that is the object of this new science of granular

prediction will no longer be a statistical abstraction-it will be-

come each of us, individually. This may be problematic from a

philosophical and religious point of view, as it challenges tradi-

tional ideas of determinism and free will; but in more practical

terms, it is also incompatible with most principles of a liberal

society and of a market economy in the traditional, modern

sense of both terms.

Natural sciences, however, offer quite a different picture.

As recent works by Neri Oxman and others have shown, we can

now design and fabricate materials with variable properties at

minuscule, almost molecular scales; and we can detect, quan -

tify, and take into account the infinite, minute, and accidental

variations embedded in all natural materials-a capriciousness

that made natural materials unsuitable for industrial use, and

almost eliminated them from modern industrial design. 44 Ar- tisans of pre-industrial times did not have much choice: they

had to make do with whatever natural materials they could find.

For example, when Alpine farmers had to roof a new chalet, they

looked high and low (literally) for a tree that would be a good

fit for the ridge piece; sometimes the shape of the roof would

be tweaked to match the quirks of the best available trunk.

And cabinetmakers could (and the extant few still can) skill -

fully work around almost any irregularity they find in a plank of

50 CHAPTER 2

timber and make the most out of it. But industrial mass produc-

tion follows a different logic. To be used in an assembly line, or

pieced together by unskilled workers, timber must be processed

and converted into a homogeneous material compliant with in -

dustrial standards-as plywood, for example, which is a factory-

made industrial product, although derived from wood. Artisan

masons of old (and few survive in the so-called industrialized

countries) knew very well how to make concrete on site the

smart way, making it stronger, for example, in the angles and

corner walls (more cement), cheaper in some infill (more rub-

ble), thinner and more polished next to some openings (more

sand), etc. But for engineers, concrete had to be dumb, homo-

geneous, and standard, the same all over, because that was the

only material they could design with the notational and math-

ematical tools at their disposal. Even assuming an engineer

could calculate the structural behavior of variable property con -

crete (concrete with different performances in different parts

of the same structure), until recently there was no practical way

to produce those variations to specifications, either by hand or

mechanically. After all, reinforced concrete is only an elemen-

tary, two-property material,,yet it took several decades to learn

a consistent, reliable way to design, calculate, fabricate, and

deliver it.

In theory, and increasingly in practice, digital design and

fabrication tools are eliminating many of the constraints that

came with the rise of industrial standards. X-ray log scanning,

for example, is already used in forestry: trees are scanned prior

to felling, and the cutting of the boards is customized for each

trunk to minimize waste. The scan is discarded by the sawmill

after the planks are sold, but there is no reason not to envis-

age a full design -to-delivery workflow, in this case extended

to include the natural production of the source material-from

the forest to the end-product, perhaps from the day the tree is

l"IIF SECO~D DIGITAL TUil~ 51

planted (which would once again curiously emulate ancestral

practices of our pre-industrial past). 45 Each tree could then be

felled for a specific task: a perfect one-to-one match of supply

and demand that would generate economies without the need

for scale-which is what digital technologies typically do when

they are used the right way. Likewise, variable property ma-

terials can now be designeq. and fabricated at previously un-

imaginable levels or resolution, including concrete, which can

be extruded and laid ·by nozzles on robotic arms, so each volu -

metric unit of material can be made different from all others.

This is what artisanal concrete always was-which always scared

engineers to death, because they could not design and calculate

that. Today we can.

Much as modern science tended to more and more general

laws bearing on the largest possible sets of events, modern tech-

nology tended to the mass production of standardized materi-

als that were designed to be, as much as possible, homogenous

and isotropic. Industrial standards were meant to generate

economies of scale, but also, and crucially, homogenous materi-

als could be described and modeled using elegant mathematical

tools such as differential equations and calculus. 46 Calculus is a

mathematics of continuity, which abhors singularities: it is per-

fect, for example, to quantify the elastic deformation of any ho-

mogeneous chunk of continuous matter. That is why the modern

science of engineering can calculate the stress and deformations

of the Eiffel Tower, which is made of iron, but until recently the

same science could not calculate the resistance of a ten -foot-

high brick-and-mortar garden wall.

To the contrary, using digital simulation and data-driven

form-searching, we can now model the structural behavior

of each individual part in a hypercomplex, irregular, and dis-

continuous 3- D mesh. And using digital tools, we can fabri -

cate any heteroclite mess precisely to specs, on time and on

52 CHAPTER 2

2.13 Alisa Andrasek, Wonderlab, AD Research Cluster 1, B-Pro M.Arch Architectural Design, The Bartlett

UCL, Morphocyte (2016). Variable property materials designed and fabricated through the simulation of the biological process of cellular division. Tutors: Alisa

Andrasek, Daghan Cam, Andy Lomas. Robotics: Feng

Zhou. Projects/Students: Zuardin Akbar, Yuwei Jing, Ayham Kabbani, Leonidas Leonidou. © Alisa Andrasek,

AD Research Cluster 1, The Bartlett UCL.

53

budget: robots will see to that. Industrial materials were stan-

dardized so they could be calculated and mass-produced. Today

we can calculate and fabricate variations at all scales, and com-

pose with unlimited variations as needed or as found in nature.

Used this way, the new science of granular prediction does not

constrain but liberates, and almost animates, inorganic mat-

ter.47 And far from being a L9-ere, albeit powerful, inspirational

metaphor-which it has been since the start of the digital turn

in architecture-vitalism is already, in many cases, an actual and

perfectly functional strategy, underlying or already embedded in

many experiments, tendencies, and trends that populate today's

computational design.

Indeed, alongside the traditional, positivistic approach to the

digital design and fabrication of variable property materials-

which would push the resolution of predictive models and de-

sign notations to the highest level of granular detail compatible

with the task, materials, and technology at hand-another, quite

different option appears to be increasingly viable. As Menges

has shown, in some cases the easiest way to cope with unwieldy

or quirky materials is to devolve some capacity for adaptive im -

provisation to the last stage of robotic manufacturing, above and

beyond traditional margins of tolerance. 48 Given the ease and

speed of data collection by ubiquitous sensors during all phases

of production, robotic manufacturing can already include some

reactive, autonomous skills. Rega·rdless of all practical consid-

erations, this approach also reflects a certain idea of the physical

world and of the nature of matter: if inorganic matter is alive (as

some believe it is, regardless of etymology), then its behavior

is also to some extent unpredictable or indeterminable, and the

only way to deal with the inherent capriciousness of such "liv-

ing" materials is to react to their whims and volitions on the spot

and on the fly. This would once again vindicate the well - known,

pervasive analogy between computational fabrication and the

54 CHAPTER 2

"smooth" tooling of traditional craftsmanship: no artisan would

X-ray a piece of timber before working on it, but all good ar-

tisans would know how to make the best of whatever they find

in it when they start carving it. Likewise, many expert dentists

would refrain from advanced digital scanning of a tooth they

must treat, and would rather keep drilling it, tentatively, until

their hapless patient screams. A first and obvious technological

upgrade of this truculently heuristic method would be to have

the dentist 3-D scan the tooth to the highest possible resolution,

then calculate the best path for the drill on the model, before

surgery starts-thus turning the dentist into an engineer, and

in fact into a designer, as the whole surgery }Vould be designed

in full and in advance on a digital model of the operating the-

ater. This would be the approach of modern structural design,

and of design in general, as itrhas been known since the Renais-

sance: design is a predictive tool; it models something before

it happens. Yet while many patients today would undoubtedly

like their dentists to behave like designers, many avant-garde

designers seem to prefer their robots to behave like old - school

dentists-stopping when the material screams, so to speak.

And, oddly, this trial-and-error approach to adaptive and reac-

tive robotic fabrication is already yielding more promising and

more practical industrial applications than the traditional scan-

and-design approach. Whether we like it or not, the future of

robotics may be closer to popular quackery than to industrial

engineering.

2.5 Spline Making, or the Conquest of Free Form

All tools modify the gestures of their users, and in the design

professions this feedback often leaves a visible trace: when

these traces become consistent and pervasive across objects,

technologies, cultures, people, and places, they coalesce into

the style of an age and express the spirit of a time. The second

TIIE SECOND DIGITAi. TUI\N 55

56

2.14 Jenny E. Sabin, PolyBrick (2015-16). Polybrick 1- Unfired PolyBricks featuring 3-D printed high-fire

clay body. Principal investigator: Jenny E.·sabin. Design research team: Martin Miller, Nicholas Cassab,

Jingyang Liu Leo, David Rosenwasser. ©Sabin Design

Lab, Cornell University. Image courtesy: Cooper-Hewitt

Design Museum.

digital style, the style of a data-affluent society and of a nouveau

data- rich technology, is the style of the late ~010s. And, as often

happens in the history of technology, a good way to assess what

is distinctive in the things we make, and in the way they look, is

to look at the tools we have stopped using and take stock of the

things we have just stopped making. Nothing shows the small-

data logic of the first digital age in architecture better than the

history of its most distinctive and recognizable trait, the spline-

based curve.

As we now know, the first digital style in the 1990s turned

out to be one of curves-or, as designers like to say, of "spliny"

curves, in reference to the mathematics of continuous curves,

or splines-which was one of the novelties of early CAD/CAM,

computer graphics, and animation software. Yet one would be

hard pressed to find any overarching or long- lasting reason to

explain why computers should be primarily-or indeed, almost

exclusively-used to make sinuous lines and curving surfaces, as

they were in the 1990s. In fact, the theory of digital mass cus- tomization, as it was known back then, would suggest just the

opposite. 49 Starting from the early 1990s, the pioneers of digi-

tally intelligent architecture argued that variability is the main

distinctive feature of all things digital: within given technical

limits, digitally mass-customized objects, all individually differ-

ent, should cost no more than standardized and mass-produced

ones, all identical. As c01:r~puters and robots do not articulate

aesthetic preferences, using CAD/CAM technologies we should

be able to design and make boxes as well as blobs, as need be,

at the same unit cost. Digital curvilinearity began to emerge as

a theoretical trope in the mid to late 1990s, when it was seen as

a side effect of sorts of the so-called Deleuze connection in ar-

chitecture, in particular through the influence of Deleuze's book,

The Fold: Leibniz and the Baroque.50 But the theory of the objec- tile (better known today as digital parametricism), as outlined

THE SECOND DIGITAi. TUHN 57

by Deleuze and Bernard Cache in that book, spoke for digital

variability as a general tenet of nonstandard mass production,

unrelated to any specific visual form. Deleuze's "fold" itself was

indeed a mathematical curve, which Deleuze related to continu -

ous functions and to Leibniz's invention of differential calculus;

but the early digital avant-garde preferred to interpret even the

Deleuzian "fold" as an angular crease, in the tradition of Pe-

. ter Eisenman's deconstructivism (and Eisenman himself was

central to this part of the story) .5' In short, nothing predes-

tined the first wave o'f digitally intelligent designers to become

streamliners. Nothing, that is, except the ease of use of the new

spline-modeling software that became available in the early

1990s. Spline modelers are those magical instruments, now em -

bedded in most software for computer graphics and computer-

aided design, that can script free-form curves of any kind, and

translate every random cluster of points, every doodle or uncer-

tain stroke of a pencil, into perfectly smooth and curving lines.

This apparently inexorable program of universal polishing of

the man-made environment (which is in fact a contingent side

effect of the mathematical tools at our disposal for its notation

and representation) derives from a complicated genealogy of

mechanical, mathematical, and computational developments,

each offering a particular take on the matter: sometimes aimed

at finding the smoothest line through some arbitrary points;

sometimes at the design of a randomly continuous curve; some-

times at its approximation through recursive subdivisions, and

so forth. 52

The most important component of today's curve-generating

software derives from studies carried out in the late 1950s and

early 1960s by two French scientists, Pierre Bezier, an engineer

by training, and mathematician Paul de Casteljau, working for the

Renault and Citroen carmakers, respectively. A few years apart,

58 CHAPTER 2

de Casteljau and Bezier found two different ways to write down

the parametric notation of a general, free-form, continuous

curve (or of more such curves joined together). The two methods

eventually merged, and although it is now known that de Castel-

jau's work came first, Bezier was first to publish his findings (as

of 1966). As a result these curves are known to this day as Bezier

curves; recent literature distinguishes between Bezier's curves

and the de Castel j au algorithm still used to calculate them. 53 N ei -

ther Bezier nor de Casteljau used the term "spline," and there

is evidence that Bezier perceived his own mathematical break-

throughs as conceptually independent from the mechanical and

mathematical tradition of spline making. 54 The term "spline"

derives from the technical lexicon of shipbuilding, where it de-

scribed slats of woods that were bent and nailed to the timber

frame of the hull. 55 The slats had to join those structural points

in the smoothest possible way to avoid turbulence in the stream-

line (the line of contact between the water stream and the hull)

and to limit drag. Later on, similar operations were performed

by hand in other branches of engineering for similar aerody-

namic reasons; the term equally refers to flexible rubber strips

that technical draftsmen used until recently for drawing smooth

curves between fixed points (drafting or draughting splines; or

lofting splines when executed in full size). A spline is thus the

smoothest line joining a number of fixed points, but there seems

to have been no scientific definition of it before 1946, when the

mathematician Isaac Jacob Schoenberg used the term to desig-

nate a new function he invented to calculate interpolations in

statistical analysis. Basis Splines, or B-Splines, as these math-

ematical functions were then called, were eventually upgraded

to include Bezier curves, and further generalized under the

name ofNURBS (for Non-Uniform Rational B-Splines): NURBS

are today the most common notation for free-form curves in

all branches of digital design and manufacturing. 56 Recursive

THE SECOND DIGITAi. TUHN 59

•

subdivisions, another method of curve generation, can approxi-

mate and parameterize existing shapes and volumes as found,

and for that reason, subdivision - based CAD software is largely

used by the animation industry. 57 When animation software first

became largely available, in the late 1990s, designers often saw

subdivisions as an alternative, more "naturalistic" approach to

f~ee-form, unbounded by the engineering constraints of early

CAD/CAM software; the mathematical premises of subdivi -

sion algorithms are also very different from those of splines and

Bezier curves. Yet for 'the last ten years or so, "Subs," or "Sub-

Ds," as students sometimes call them, have been mostly used as

different means to the same end-namely, to generate smooth

parametric curves and surfaces. Regardless of the mathemat-

ics used to notate them, or of the software used to draw them,

splines, NURBS, Bezier curves, and Subs generate high-tech,

sleek, streamlined images and objects from which each sign of

human intervention-the wavy, uncertain trace of the gesture of

the human hand and its analog, variable tools (angles, junctions,

gaps)-have all been removed.

The original purpose and task of Bezier's and de Casteljau's

math was, indeed, to eliminate precisely that kind of manual ap-

proximation from the design process. As Bezier and de Castel -

jau both recount in their memoirs, the mathematical notation

of curves and surfaces was meant :o increase precision, reduce tolerances in fabrication, and save the time and cost of making

and breaking physical models and mock-ups. 58 We can see why

carmakers in the 1950s and 196os-particularly French ones-

would have been interested in that technology: streamlining

(aerodynamics) was then popular in car design, but the molds

to cast dies for the metal presses had to be individually hand -

made by artisan model-makers, as were all the prototypes before

production; the final design of a car, for example, was not a set

of drawings but a 3- D master model made in hardwood, from

60 CHAPTER 2

which blueprints and their measurements would be derived as

and when needed. The famously aerodynamic Citroen DS was

designed in Paris in the years immediately preceding de Castel -

jau's studies-and entirely by hand; which is probably one reason

why de Casteljau, a young mathematician then just back from his

military service in Algeria, was hired by a research department at

Citroen called "determination mathematique des carrosseries"

(mathematic determination of bodywork), headed by a Mr.

Vercelli, about whom nothing more is known. 59

Bezier's and de Casteljau's research, at the start, appears to

have been primarily motivated by the mathematical ainbition to

translate general free-form curves into equations. Digital fab-

rication must have seemed a less urgent prospect back then:

Bezier's first experiments in i:_iumerically controlled milling ma-

chines were abandoned in 1960, and the first computer-driven

drafting machines he built from scratch in the years that fol -

lowed must have seemed so unpromising, in commercial terms,

that the Regie Renault, then state owned, allowed Bezier's team

to publish a series of scholarly papers where the new technology

was described in full. 60 Thus Bezier' s research was at the basis

of the CAD/CAM system that Renault kept developing and later

adopted, called UNISURF, but also of competing proprietary

technologies developed by other companies, such as the aircraft

maker Dassault. On the other side of town, de Casteljau's team

was bound to secrecy for longer. De Casteljau recently wrote

that, due to a prolonged strike of wood modelers, the templates

for the Citroen GS were the first to be produced entirely by ma -

chines, but it is not clear to what extent the bodywork itself was

designed on screens rather than in clay and wood: the GS started

production in 1970, and its design was developed throughout the

196os. 61

Of course, this was not an exclusively Gallic story. At the same

time as de Casteljau's and Bezier's studies on free-form curves,

TIIE SECOND DICITALTUllN 61

research on B-Splines was being carried out at MIT, Boeing, at

the British Aircraft Corporation, and particularly by Carl de Boor

at General Motors, which developed its own CAD/CAM system

in the 1960s; in 1981 Boeing was among the first adopters (or

perhaps the inventor) of NURBS, which in the same year were

endorsed by the Initial Graphic Exchange Standard (IGES), a

consortium of industry and government bodies. 60 Yet Bezier of-

t~n recounted that, as Iate as 1971, after one of his presentations,

a manager at Renault objected, "If your system were that good,

the Americans would ~lready have invented it! "63 In 1969, Robin

Forrest, whose work on Bezier's curves would contribute to the

generalization of B-Splines to NURBS, had to travel from Cam-

bridge, England, to the GM Research Laboratories in Detroit

to be shown "the crazy way Renault designs surfaces." 64 And in

July 1991, when the office of Frank Gehry in Los Angeles started

to look for a suitable CAD/CAM technology for the design of a

building in the streamlined shape of a fish ( which would become

the Barcelona Fish, still prominently floating over Barcelona's

Olympic Marina), through a succession of phone calls and the

intercession of Bill Mitchell at MIT and of Rick Smith at IBM,

Gehry's office was eventually referred to Dassault's headquarters

in Paris. The role of Dassault's CATIA software in contemporary

architecture is, to this day, better known than its industrial his-

tory before and after its architectural reincarnation. 65

Few of today's designers wouid have become keen spline-

makers if they had had to make each spline by hand, bending

slats of wood, or if they had had to slog through all of Bezier's

math with paper, pencils, and a slide rule. This is one reason

why free-form curves were seldom built in the past, except when

absolutely indispensable, as in boats or planes, or in times of

great curvilinear exuberance, such as the baroque, or the Space

Age in the 1950s and 1960s. But, as it happens, in one of those

only apparently serendipitous encounters that mark the history

62 CHAPTER 2

of technological change, mathematics and technology here kept

crossing paths. As computers became smaller and cheaper,

CAD software migrated from corporate mainframe computers

to workstations to desktop personal computers; AUTOCAD, the

first CAD tool designed for MS-DOS, was released in 198~.66 As

of the early 1990s affordable commercial software for computer-

aided design started to include powerful spline modelers that

made Bezier's math easily accessible through graphic user inter-

faces: control points and vectors that anyone could easily edit,

move, and drag on the screen with the click of a mouse. This game

turned out to be faster and more intuitive than the mathematics

on which it was based, and digital designers started to play it with

gusto. Form-Z, the most influential of these early packages, was

developed at Ohio State University, apparently with the complic-

ity of Peter Eisenman, and rel~ased in 1991. 67

Bezier's curves, B-Splines, and NURBS are pure mathemati-

cal objects, based for the most part on differential calculus; their

smoothness, which we perceive as a visual and tactile quality

when splines are built, is a quantifiable entity throughout the

design and production process, defined by one or more deriva -

tives to the function of the first curve. Mathematical objects do

not fit with the phenomenological world we inhabit; designers

using spline modelers "model" reality by converting it into a

stripped-down mathematical script, and the continuous lines

and uniform surfaces they draw or make in physical reality are

ultimately only a discrete, material approximation of the math-

ematical functions they use to notate them and computers then

use to calculate as many points belonging to them as needed. 68

Of course, not every digitally intelligent designer in the 1990s

was a pure spline-maker: Greg Lynn and Bernard Cache ex-

plicitly claimed to use calculus as a primary tool of design, 69

while Frank Gehry (for example) famously used computers

to scan, measure, notate, and build the irregular, nongeometric

THE SECOND DIGITAL TURN 63

three-dimensional shapes of his handmade maquettes. 7° From

its inauguration in 1997, Gehry's Guggenheim Bilbao (designed

from 1991 to 1994) was hailed as a global icon of the new digitally

driven architectural style, but as most digital designers at the

time used curve-generating software to even out, somehow, all

final lines and surfaces, the divide between free-form, subdivi-

~ions, and mathematical splines is often a tenuous one, and not

easy to perceive: regardless of the process (based on mathemat-

ics from the start, as in the case of Cache and Lynn, or derived

at least in part from ~atural accidents, as in the case of Gehry),

what one sees if one just looks is, simply, a landscape of sweep-

ing, spliny curves. This is the visual aspect that was mostly noted

at the time, and defined the style for which the first digital age

became famous, for better or worse. Fast-forward to ~016. The Internet boom famously busted

in ~001, but the spline-dominated, curvilinear style now often

associated with the "irrational exuberance" of the digital 1990s

lived on, still successfully practiced by some of the early pioneers

and handed down to a new generation of younger digital design-

ers. With technical progress, many visionary predictions from

the digital 1990s are now becoming a reality. Big, streamlined

surfaces can now be built at more affordable prices, and recent

projects by Zaha Hadid and others deploy this sinuous language

at ever bigger and bolder scales, with a level of technical and

formal virtuosity that would have· been unimaginable only a few

years ago. Today this style is often called "parametricism," 7' and

at its core mathematical splines and NURBS are its most dis-

tinctive notational and technical tool. Mathematical splines, in

turn, are based on analytic geometry and calculus: Newton's and

Leibniz's calculus is, to this day, the best instrument to describe

continuous lines that are characterized by variations, and varia -

tions of variations. The mathematics of free-form is thus the

zenith and culmination of a historical process that started with

64 CHAPTER 2

Descartes, Leibniz, and Newton: Baroque mathematics found a

way to use equations to replace the drawings of some simple geo-

metrical figures-straight lines and conics; using basically the

same tools, with only marginal upgrades, today we can notate any

curve whatsoever. Bezier, so to speak, finished the job that Des-

cartes and Leibniz had started. Yet once again, if we look at the

history of mathematics in terms of pure quantitative data analy-

sis, it is hard not to see calculus-just like logarithms, another

great invention of baroque mathematics-as another, but even

more astounding small-data technology: perhaps the ultimate

small-data technology of modern science.

2.6 From Calculus to Computation: The Rise and Fall of

the Curve

Consider the mathematical notation of any continuous line in the

well - known format y = f(x). How many points does any such no - tation include and describe? Plenty: an infinite number of them.

In practice, that script contains all the points we would ever need

in order to draw or produce that line at all possible scales. But

let's assume, again, to the limit and per absurdum, that we can

have access to unlimited, zero-cost data storage and process-

ing power. In that case, freed from the need to skimp on data, we

could easily do away with any synthetic mathematical notation

and record instead an inordinately long, dumb log: the list of the

positions in space (x-, y-, z- coordinates) of as many points of that line as necessary. The resulting cluster of points would not

appear to follow any rule or pattern, nor would it need to, so long

as each point is duly identified, tagged, and registered-ready for

use, so to speak. This is exactly the kind of stuff humans don't

like, but computers do well. That mathematical script (they =

f(x) functional notation) is a compact, economical, small-data

shorthand we use to replace what is in fact an extraordinarily

long list of numbers. As the list itself would be too long for our

THE SECOND DIGITAi TUR~ 65

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robot control of cyber physical fiber placement system,

University of Stuttgart, 2015. © ICD/ITKE University

of Stuttgart.

small-data skills, we convert it into a very short formula. That

formula is much easier for us to manipulate, process, and re-

member than the list itself would be; just like any of the modern

classification systems discussed above, an equation or function

also, miraculously, allows us to retrieve all the events it refers to

(in this instance, to recalculate the coordinates of all the points

it indexes), whenever needed. Thus an equation compresses, al-

most miraculously, an infinite number of points into a short and

serviceable alphanumerical script.

That works very well for us; which is why we still celebrate the

names of Descartes, Leibniz, and Newton and we still study ana-

lytic geometry and calculus at school-in fact, this is why all the

math we study at school, starting from the age of six, is aimed

and finalized at getting there-at mastering differential calcu -

lus more or less by the time we reach adulthood. But computers

do not work that way. When fed a raw, unstructured list, log, or

inventory of any size, computers can just keep it as it comes-in

its pristine sequence or any other, even if random or haphazard.

Computers can search and retrieve each item in any list, regard -

less of the way that list is or is not ordered, because this is what

computers do best: unlike us, and just like Gmail, computers can

search without any prior sorting.72 That list may be unimagin -

ably long, but computers don't care; and the computer's big data

logic makes perfect economic sense, if data cost nothing. A list

where raw data are kept unsorted does not make any sense to us,

but computers do not care about that either. We humans need

to sort (organize, classify, formalize, order, structure) a list to

make it usable (so we can retrieve the items in it) and to make it

meaningful (so we can organize ideas and things by hierarchies

or orders of causation). Computers are not in the business of

finding meanings and can use any huge, messy, untreated, and

unprocessed random inventory just fine: they can search with-

out sorting; hence they can predict without understanding. And,

THE SECOND DIGITAL TU11N 67

apparently, in many cases computers can already predict that

way better than we can in our own, traditional, small - data way-

which was that of modern science.

The calculus-based spline is a quintessential small-data tool.

As a design figure, splines are space-age technology; they belong

with the Beatles and flared jeans. Let's be honest: if we only look

at forms, or style, and we for-get about the technology, the digital

~pline of the 1990s was a revival. Computers made streamlining

cheaper and better; easier to design and make-but streamlin -

ing was certainly not a new idea, and in the last decade of the

twentieth century the spline was certainly not a new form. By

providing computational tools and graphic user-interfaces to

Bezier's math, digital spline modelers gave streamlining a new

lease on life. That was a very good idea twenty years ago, when

computers, processing power, and data were expensive. In that

context, it made perfect sense to use computers to emulate and

replicate the small -data logic of modern mathematics-in a

sense, to make computers imitate us. But in today's big data en-

vironment that mimetic effort is no longer necessary-indeed, it

is no longer warranted. Computers can work better by following

their own logic. We can make computers sort before searching,

the way we do. But computers already achieve much better re-

sults when we let them search without sorting, the way we don't

and can't do. Revolutions in manufacturing· tend to happen first at a small

scale, and scaling up may sometimes be late in coming. In this

instance, digital splines revolutionized graphic design one de-

cade before they changed the history of world architecture. It all

started with laser printing. Mechanical printers can only print

from a limited library of built-in metal fonts: think of a type-

writer. The interchangeable typeballs or daisy wheels in the

electric typewriters of the 1960s and 1970s allowed typists to

switch between a few styles of fonts, but replacing the typeballs

68 CHAPTER 2

or wheels took time. 73 Laser printers, to the contrary, can print

all kinds of fonts (and indeed any rasterized image), seamlessly

and from the same machine; so, when affordable laser printers

became available, in the mid-198os, word processors started

to upgrade their library of fonts, adding new styles and sizes.74

Following the traditions of typography, each font (for example,

Times) should then have been designed anew for each size (Sp,

1op, 1~p ... ), and each glyph digitized as a rasterized map of

pixels; but this would have created graphic files far too big for

the limited memories and processors of early personal comput-

ers. The solution came with Adobe's PostScript software, first

released in 1984. 75 PostScript notated the design of each glyph

mathematically, as a combination of straight lines and Bezier

curves. The advantage was that the same script would fit all

sizes, because the same formula would generate the same draw-

ing (say, the lowercase a in Times font) at every scale the avail-

able software and hardware would support, on the screen as well

as in print, and each of these scalable signs would look the same

(hence the acronym, then so popular, WYSIWYG, for "what you

see [on the screen] is what you get [in print])." Thus, thanks

to the math of free-form curves (Bezier's, etc.), a vast and un-

wieldy graphic library was compressed into a file so small that

it could run on most PCs of the time (which incidentally also

led to the desktop publishing revolution of the late 1980s and

1990s).

Once again, however, that entire strategy would be unwar-

ranted in today's computational environment. Processors and

storage devices are now so cheap and powerful that huge graphic

libraries of all kinds can now be kept and processed almost ev-

erywhere without the need for any sophisticated compression

technologies. For example: if we wanted to, we could redesign

each glyph to allow for design variations specific to each size of a

font (as was the case in traditional typography), and we could do

l'llf SECOND DIGITAL TUK~ 69

that for an inordinate number of different fonts. That would cre-

ate a very large inventory of bitmaps-but again, today that would

hardly be a problem. Of course, no matter how big that _in~en-

tory, the number of available bitmaps would always be limited,

and as bitmaps are not scalable, chances are that sooner or later

someone would fail to find a font in the exact size or resolution

needed. Using splines that would never happen: that is indeed

the great notational and, in a sense, ontological advantage of the

mathematics of continuity against all arithmetics of discrete - ' ness, old and new alike: an advantage which, in this instance,

we would deliberately relinquish. Would that matter? Today, we

might Google the font we need and find out that it already exists

somewhere. Someone could be tasked to add the missing parts

of the design when the time comes. Or we might let a few pixels

show in all of their coarse discreteness for a while, until some-

one, or something, interpolates, or fills the gaps. This is what

some designers of the second digital age are now doing.

2.7 Excessive Resolution In different ways, today's digital avant-garde has already started to use Big Data and computation to engage somehow the messy

discreteness of nature as it is, in its pristine, raw state-without

the mediation or the shortcut of elegant, streamlined math-

ematical notations. The messy_ point-clouds and volumetric

units of design and calculation that result from these processes

are today increasingly shown in their apparently disjointed

and fragmentary state; and the style resulting from this mode

of composition is often called voxelization, or voxelation. The

Computational Chair Design Studies by Philippe Morel of EZCT

.Architecture & Design were among the earliest demonstrations

of this approach,7 6 and the ~013 .A.rchiLab exhibition in Orlea~s,

France, reveals this new formal landscape at a glance (see, for

example, works by Alisa Andrasek and Jose Sanchez, Marcos

70 CHAPTER 2

Cruz and Marjan Colletti, Andrew Kudless, David Ruy and Karel

Klein, Jenny Sabin, and Daniel Widrig). 77 Subdivisions-based

programs, originally used to simulate continuous curves and

surfaces, today are often tweaked to achieve the opposite ef-

fect, and segments or patches are left big enough for the sur-

face to look rough or angular. Discreteness is also at the basis

of the method of finite elements (seen above) ,78 now embedded

in most software for structural design, and which represents

in many ways an early example of "agnostic" science, 79 where

the prediction of structural behavior is separated from causal

interpretations.

More examples could follow, but the spirit of the game is the

same: in all such instances, designers use the power of today's

computation to notate reality_ as it appears at any chosen scale,

without converting it into simplified and scalable mathematical

formulas or laws. The inherent discreteness of nature (which,

after all, is not made of dimensionless Euclidean points or of

continuous mathematical lines but of distinct chunks of matter,

all the way down to molecules, atoms, electrons, etc.), is then

captured and, ideally, kept as it comes, or in practice as close to

its material structure as needed, with all of the apparent ran -

domness and irregularity that will inevitably show at each scale

of resolution. Evidently, the abstract continuity of the spline

does not exist in nature: we can write down splines as mathemat-

ical formulas and imagine them as a seamless flow of Euclidian

points, but in physical reality we can only make most of them by

discrete pieces, by pixels or voxels-which can only be as small

as the maximum resolution supported by the display, printer, or

physical interface we are using. 80 The manufacturing tool which

best interpreted the spirit of continuity of the age of spline mak-

ing was the CNC milling machine, a legacy subtractive fabrica-

tion technology that, using computer-controlled drills, could at

its best simulate the sweeping, smooth, and continuous gestures

THE SECOND DIGITAL TURN 71

176 NOTES

is often done by letting the program randomly try out a number of different

options (within a given range of variations for each chosen variable), then

identifying clusters of values for which that set of variables generates the best

results (i.e., the best values in a given field for the function that is being op-

timized). The program then refocuses on those ranges of variations, drop-

ping (or "killing") all others, and generating new random trials within their

ambit: then choosing the best results from within that new range, and so on,

ad infinitum. \Vhenever the program is stopped, the designer can see the best

result among all those tried until then, but with no certainty that a better so-

lution may not be found with the next iteration, or with any additional one:

this method cannot find the best solution, only one that is as good as it gets:

in fact, the designer can choose one solution that he deems "good enough"

for his purposes at any time. Such evolutionary methods of optimization are

often described in biological, or even Darwinian, terms: see the description

of Galapagos, a Grasshopper plug-in. by its author, David Rutten, accessed

February 11, 2016. http://www.grasshopper3d.com/group/galapagos. A simi-

lar "survival of the fittest,'' evolutionary method of optimization by random

variations is known in web design under the name of NB testing: see Mario

Carpo, "Digital Darwinism," Log 26 (2012): 97-105. For evolutionary opti-

mization in structural engineering. see Grant P. Steven and Yi Min Xie, "A

Simple Evolutionary Procedure for Structural Optimization," Computers &

Structures 49, no. 5 (1993): 885-896, and Grant P. Steven and Yi Min Xie, Evo-

lutionary Structural Optimization (Heidelberg: Springer, 1997). Evolutionary

Structural Optimization (ESO) gradually removes material from a structure

as it is being designed. Mark Burry fa'.1'ously used Evolutionary Structural

Optimization methods in his work for the continuation of Gaudi's Sagrada

Familia in Barcelona: see Mark Burry. Yi Min Xie, et al.. ''Form Finding for

Complex Structures Using Evolutionary Structural Optimization Method,"

Design Studies 26, no. 1 (2005): 551 2. See also the so-called Dynamic Re-

laxation Method, known for having been used by Norman Foster for the de-

sign of the roof of the Great Courtyard of the British Museum in 2000. (I owe

some of this information to the unpublished master's thesis of my student

Christos Koufidis, Master in Architectural History, 2015, the Ba11lett. UCL).

The principles of evolutiona1y algorithms were first studied by John Holland

(Adaptation in Natura! and Artificial Systems: An Introductory Analysis with

Applications to Biology, Control, and Ar-tifi.ci.al intelligence [Ann Arbor: Univer-

sity of Michigan Press, 1975]). See also notes 98, 100.

36. See fuchard Sennett, The Craftsman ( ew Haven: Yale University Press,

2008).

37. Even the existing methods and software for structural optimization follow

essentially the same heuristic. trial-and-error procedure: as they do not

deduct results from formalized premises, but simply carry out massive, au-

tomated. and open-ended testings of a theoretically unli1nited range of ran-

domly variable design hypotheses-with some incremental, or "evolutionary"

targeting included in this recursive process: see note 35.

38. The rejection of modern science as a science of universals is central to

the postmodern philosophy of Gilles Deleuze and Felix Guattari. In Milles

Plateaux, in particular, Deleuze and Guattari opposed the ·'royal science" of

modernity, based on discretiza(.ion ("striated space") to the ·•smooth space"

of •·nomad sciences," based on "non.metric, acentered. rhizomatic multi-

plicities that occupy space without counting it and can be explored only by

legwork." which "seize and determine singularities in the matter, instead

of constituting a general form ... they effect individuations through events

or haecceities, not through the object as a compound of matter and form."

Deleuze and Guattari saw the model of nomad sciences in the artisan lore of

medieval master builders, and they had no foreboding of the then nascent

new technologies that would inspire digital makers one generation later. See

Gilles Deleuze and Felix Cuattari.A Thousand Plateaus, trans. Brian Massumi

(London and New York: Continuum, ~004), chap. ,~. "Treatise on Nomad-

ology." 406-409 and 450-451 (first published Minneapolis: University of

Minnesota Press, 1987; first published in French as Milles Plateaiix [Paris:

Les Editions du Minuit. 1980]).

39. Weather forecasting has traditionally included predictive mathematical

modeling (known as Numerical Weather Prediction, or NWP) alongside sta-

tistical data on local or global weather patterns, unrelated to the mathemati-

cal description of the physical phenomena themselves (this latter approach

also known as Model Output Statistics, or MOS). 1 n recent times, however.

the spike in data input (collected from ubiquitous sensors, crowdsourcing,

~OIES 177

i,

etc.) and in data processing capabilities has led to expectations of better Nu-

merical Weather Prediction. and to fewer and more timid attempts at using

weather data recording for the retrieval of statistically meaningful precedents

(as per the heuristic, "search-based" predictive method being discussed

here): see for example A. R. Ganguly, E. A. Kodra, A. Agrawal et al., "To-

ward Enhanced Understanding and Projections of Climate Extremes Using

Physics-Guided Data MiningTech,niques," Nonlinear Processes in Geophysics z1

(zo14): 7771 95. accessed February 11, zo16, http://www.nonlin-processes

-geophys.net/zi/777/zo14/npg-~1-777-zo14.html; on the historical mod-

eling of weather patterns evolving in time, E. Kalnay, Atmospheric Modeling.

Data Assimilation and Predictability (Cambridge: Cambridge University Press,

~ooz).

40. See D. Napoletani, M. Panza, and D. C. Struppa, "Agnostic Science: Towards

a Philosophy of Data Analysis," Fot1n.dations of Science 16, no. 1 (zou): 1--20;

"Artificial Diamonds Are Still Diamonds," Foundations of Science, 18, no. 3

(zo13): 591-594; "ls Big Data Enough? A Reflection on the Changing Role of

Mathematics in Applications," Notices of theAmerican Ma.thematical Society 61,

no. 5 (zo14): 485-490.

41. As search always starts with, and aims at, one individual event. the science of

search is essentially a science of singularities, but the result of each search is

always a cluster of many events, which must be compounded, averaged, and

aggregated using statistical tools. Thus, there are no lower limits to the level

of ·'precision" of a search (a lower level of precision, i.e., less intension. will

generate more bits, i.e., a larger extension in the definition of the set).

42. See note 16. On this aspect of Aristoteljan science, see Carlo Diano, Forma

e evento. Principi per ,ma interpretazione del mondo greco (Venice: Neri Pozza,

195z).

43. See chapter 5, and Mario Carpo, "Micro-Managing Messiness," M Files 67

(zo13): 16-19. An earlier version published as ·'Micro-Managing Messiness:

Pricing, and the Costs of a Digital Non-Standard Society," in James Andra-

chuk. Christos C. Bolos, Avi Forman, and Marcus A. Hooks. eds., "Money,"

special issue. Perspecta 47 (zo14): z19-zz6.

44. See Neri Oxman, "Programming Matter:· in Achim Menges. ed., "Material

Computation: Higher Integration in Morphogenetic Design," special issue

178 NOTES

(AD Profile z16), Architectural Design 8z, no. ~ (-.::01z): 88-95, on variable

property materials: Achim Menges, "Material Resourcefulness: Activat-

ing Material Information in Computational Design," in Architectural Design

8z, no. 2 (zoq): 34-43, on nonstandard structural components in natural

wood.

45. Menges.·· Material Resourcefulness," 4z.

46. As Dennis Shelden, chief technology officer of Gehry Technologies, re-

marked: ·'The purpose of materials processing-the industrial operations

that render trees into zx4s and ore into metal sheet-is to lower the world·s

complexity and align its behavior to those geometries for which we have trac-

table models and numerical solutions." Shelden, "Information Complexity

and the Detail," in Mark Garcia, ed., "Future Deta.lls of Architecture," spe-

cial issue (AD Profile 230),Architectural Design 84, no. 4 (zo14): 94. Shelden

continues: ·'The detailing strategies of today are developed parametrically

precisely to package, replicate~ and reduce information complexity" (96).

47. This vindicates the premonitions of Ilya Prigogine, another postmodern

thinker whose ideas were a powerful source of inspiration for the first gen-

eration of digital innovators in the 1990s. See in particular Ilya Prigogine and

Isabelle Stengers, Order Out of Chaos: Mans New Dialogue with Natt,re (New

York: Bantam Books, 1984); first published in French as La Nouvelle Alliance:

metamorphose de la science (Paris: Gallimard, 1979).

48. Menges, "The New Cyber-Physical Making: Computational Construction," in

Achim Menges, ed., "Material Synthesis: Fusing the Physical and the Compu-

tational," special issue (AD Profile z37),Architectural Design 85, no. 5 (2015):

z8-33. ·'But what happens if the production machine no longer remains just

the obedient executor of predetermined instructions, but begins to have the

capacity to sense, react, and act; in other words, to become self-aware?" (z9).

Menges continues: ·'Predictive modeling. both as geometric notation and nu-

merical simulation, may eventually be replaced by real-time physical sens-

ing and computational analysis, material monitoring, machine learning, and

continual (re)construction" (3~).

49. Earlier ideas of mass customization arose in the context of the postmodern

pursuit of customer choice, which initially led to a demand for variations

compatible with the modes of mechanical mass production then available.

NOTIS 179

180 NOTES

The typical expression of early mass customization was the multiple-choice

model, based on a finite number of conspicuous but often purely cosmetic

product variations. See Stanley M. Davis, Puture Perfect (Reading. MA: Ad-

dison-Wesley. 1987). where the expression "mass customization" may first

have occurred; Joseph B. Pine, Mass Customization: The New frontier in Bttsi-

ness Competition., foreword by Stan Davis (Boston: Harvard Business School

Press. 1993). At some point in the course of the 1990s it became evident

that digital design and production tools (then called CAD/CAM. or "file to

factory" technologies) allow for the mass production of endless variations.

theoretically at no extra cost. I nsof'ar as it does not employ casts or molds or

dies, digital fabrication does not need to amortize the upfront cost of me-

chanical matrixes, hence in any given cycle of digital fabrication the marginal

cost of production is always the same: more identical copies do not make

copies cheaper, and variations in the series do not make any new item more

expensive. In a sense, digital mass-customization provided a technological

answer to a long-standing post modern quest for product variations: but His

not clear when and how technological upply and cultural demand may have

first crossed paths.

The term mass wstomiza.tion. was first brought to the attention of digital

designers by William Mitchell in the late 1990s. See William J. Mitchell, "An-

ti tectonics: The Poetics of Virtuality." in The Virtttal Dimension. Architecture.

Representations. and Crash C11lture, ed. John Beckmann (New York: Princ-

eton Architectural Press, 1998), 205-217, in particular "Craft/Cad/Cam,"

210-212: William J. Mitchell, E-topia: Urban Life. Jim-But Not As We Know It

(Cambridge, MA: MIT Press, 1999), see esp. "Mass Customization," 150-152. But both the term and the notion of mass-customization were conspicuously

absent from Mitchell's groundbreaking and inspirational City of Bits (Cam-

bridge, MA: MIT Press. 1995), which was mostly devoted to the social, spatial.

and architectural implications of the migration of activities and functions

from physical space to "cyberspace." The idea of mass customization was at

the core of the mathematical and teclrnical notion of Deleuze's and Cache's

objectile, but it does not appear that Bernard Cache. Greg Lynn, or other pio-

neers of the first digital turn in the 1990s ever adopted the term "mass cus-

tomization'' itself. Starting with his seminal book Earth Moves. first published

in 1995 (but originally written in 1983), Bernard Cache often used the term

"nonstandard" with the same meaning (Cambridge, MA: MIT Press, 1995),

esp. 88. Similar notions (but without the use of any of these terms) were also

foreshadowed by Lynn in the now famous AD 63, ''Folding in Architecture''

(Greg Lynn, ed., "Folding in Architecture,'' special issue [AD Profile 102].Ar-

chitectllral Design 63, nos. 3-4, (1993], see in pai1icular Lynn's essay on Shoei

Yoh, "Shoei Yoh, Odawara Municipal Spo1ts Complex,'' 94-97, esp. 95). The

term "nonstandard" was then popularized by the eponymous exhibition in

Paris ("Arch.itectures non standard," Centre Pompidou. Paris, December 10,

2003-March 1, 2004, curated by Frederic Migayrou and Zeynep Mennan).

On the mass production of variable parts at the ame cost of standardized.

identical ones, see in particular the essays by Migayrou, Lynn, and Cache in

the exhibition catalog:Architectures non standard, eds. Frederic Migayrou and

Zeynep Mennan (Paris: Editions du Centre Pompidou, zoo3). 28, 90, and

138, respectively. See Mario Carpo, "Ten Years of Folding," introclucto1y essay

to the reprint of "Folding in Architecture" (London: Wiley-Academy, 2004).

14-19. esp. 16-18; "Pattern Recognition." in Kurt W. Forster, ed.,Metamorph:

Catalogue of the 9th International Biennale dArchitettura, Venice ~004-, 3 vols.

(Venice: Marsilio, 2004). 3: 44-58; 'The Demise of the Identical: Standard-

ization in the Age of Digital Reproducibility," paper presented at REFRESH.

First International Conference on the Historie of Media Art, Science and

Technology Banff New Media Institute, September 28-October 1, 2005.

accessed February 11. 2016, http://www.mediaarthistory.org/wp-content/

uploads/2011/05/Mario_Carpo.pdf, and several times reprinted: ''Tempest in

a Teapot," Log 6 (zoo5): 99-106: TheAlphabet and theAlgorithm, 93-106; Chris

Anderson, Makers: The New Industrial Revolution (New York: Random House,

201z), 71-88. On the marketing and psychological implications of multiple

choice (without reference to digital technologies), see Barry Schwartz, The

Paradox of Choice ( ew York: HarperCollins, 2004). Curiously, today's idea of

digital mass customization is prefigured, almost verbatim, in a brief passage

at the very end of the first edition of Marshall McLuhan's Understanding Media

(1964). McLuhan refers to variations in the mass production of automobile

tailpipes. which, he claims, are made possible by new computer-controlled

"automatic machines." Using such machines, McLuhan claims, "it is possible

\O'f l·S 18t

182 NOTES

to make eighty different kinds of tailpipes in succession, as rapidly, as easily,

and as cheaply as it is to make eighty of the same kind." (Marshall McLuhan,

Understanding Media: The Extension of Man [New York: McGraw-Hill, 1964],

314). McLuhan briefly describes the digital manufacturing devices he has in

mind, which appear more similar to today's industrial robots than to the nu-

merically controlled milling machines he could have observed back then (see

note 81). McLuhan even,goes on to note that "the characteristic of electric

automation is all in this direction of return to the general-purpose handicraft

flexibility that our own hands possess" (ibid.). McLuhan revisited and singu-

larly amplified the same argument in a 1967 article devoted to education and

technological change:

Just as the old mechanjcal production line pressed physical materials

into preset and unvarying molds, so mass education tended to treat

students as objects to be shaped, manipulated ... That age has passed.

More swiftly than we can realize, we are moving into an era dazzlingly

different. Fragmentation. specialization and sameness will be re-

placed by wholeness, diversity and. above all, a deep involvement.

Already, mechanized production lines are yielding to electronically

controlled, computerized devices that are quite capable or producing

any number of varying things out of the same material. Even today,

most U.S. automobiles are, in a sense, custom produced. Figuring

all possible combinations of styles, options and colors available on a

certain new family spo1ts car, for exampJe, a computer expert came

up with ~5 million different versions of it for a buyer. And that is on.ly

a beginning. When automated electronic production reaches full po-

tential, it will be just about as cheap to turn out a million differing

objects as a million exact duplicates. The only limits on production

and consumption will be the human imagination. (MarshalJ McLuhan

and George B. Leonard, "Tl)e Future of Education, The Glass of ,989,"

Look. 30 [February ~1. 1967]: ~3-~5: French translation in McLuhan,

Mutations 1990 [Tours, Mame, 1969]).

Yet, until recently, nobody seems to have been aware of McLuhan's va-

ticinations. Charles Jencks has often referred to this eminent precedent in

his recent works (Charles Jencks, The Story of Post-Modernism [Chichester:

Wiley, ~on], 16~). Philippe Morel has frequently cited McLuhan's 1967 ar-

ticle in his lectures, including at the conference Digital Postmodemities at the

Yale School of Architecture in Febmary ~014. McLuhan also precisely pre-

dicted the technical logic of the Web ~-O ("At electric speeds the consumer

becomes the producer and the public becomes a participant role player":

Marshall McLuhan and Barrington Nevitt, Take Today: The Executive as Drop-

out [New York: Harcourt Brace Jovanovich, 197~]. 4), a prediction that, as

is often the case, went entirely unnoticed until well after it came tme. In

another quirky late-modern development, a 1969 essay by Reyner Banham

celebrates multiple choice and user interaction as the alternative of the fu-

ture to the "boredom" and alienation of industrial mass production. Banham

gushes over the American hot rod movement (automotive enthusiasts who

modified and customized their cars using industrial spare parts and catalog-

based components), and, not surprisingly, in the same essay he disparages

electronic technologies as a worrying, hostile development, and "computer-

isation" as an "invisible power system" that must be "diverted or dismpted."

Reyner Banham, "Softer Hardware," Ark 44 (Summer, 1969): ~-u. Ark was

the journal of the Royal College of Arts: number 44 was subtitled "is all about

mass production/customisation," but the term "mass customization" itself

was not yet used.

50. Carpo, "Ten Years of Folding," 14-19; Carpo, The Alphabet and the Algorithm,

83-93

51. See in particular Peter Eisenman, "Visions Unfolding: Architecture in the

Age of Electronic Media," Domus 734 (199~): 17-~4; "The Affects of Singu-

larity," in Andreas Papadakis, ed., "Theo1y + Experimentation," special issue

(AD Profile 100) Architectural Design 6<, nos. 11-1< (199~): 4~-45; "Folding

in Time: The Singularity of Rebstock," in Architectural Design 63, nos. 3-4

(1993): 38-4~; Carpo, The Digital Tum inArchitecture, 15-<8.

52. The history of the notation, representation, and fabrication of free-form

curves straddles disciplines and competencies: some parts of it pertain to

the history of pre-industrial craft, others to the history of civil engineering

and industrial manufacturing; others still to the history of mathematics and

statistics, electronic computing, and software development; some are part

of corporate industrial history and are protected by patents and by indus-

trial and trade secrets. Reliable scholarly sources are few and far between;

many-including corporate websites-list facts and dates that are patently

contradictory or anecdotal. Sometimes the only source is Wikipedia, which.

contrary to its terms of service, but faithful to its spirit, serves in this instance

NOTES 183

184 NOTES

as an aggregator of oral traditions (mostly, one may infer, contributed by the

protagonists themselves or people close to them). Among the sources most

frequently used here, see in particular: Gerald Farin, "A Histo1y of Curves

and Surfaces in CAGD," in Gerald Farin, Josef Hoschek and Myung-Sao IGm,

Handbook of Computer Aided Geometric Design (Amsterdam and Oxford: Else-

vier, 2002), 1-,4; Georges Teyssot, with Olivier Jacques, "Faire parler les al-

gorithms: Les nuages virtuels du Metro pol Parasol (Seville) (Algorithms Can

Talk: The Virtual Clouds of Metro pol Parasol [Seville])," and Georges Teys-

sot, with Samuel Bernier-Lavigne, Pierre Cote, Olivier Jacques, and Dimi-

tri Lebedev, "Des splines aux NURBS: aux origines du design parametrique

(From Splines to Nurbs: The Origins of Parametric Design)," Le Visiteur,

Revue Critiq1,e dArchitecture 14 (2009): 101-121 and 122-123; Georges Teys-

sot, with Samuel Bernier-Lavigne, "Forme et Information. Chronique de

J'Architecture Numerique," in Action Architecture, ed. Alain Guiheux (Paris:

Editions de la Villette, 2011), 49-87; Alastair Townsend, "On the Spline. A

Brief Histo1y of the Computational Curve," Jonathan Anderson and Meg

Jackson, eds., "Applied Geometries" issue, International Journal of Interior

Architecture + Spatial Design 3 (2014): 48-60, accessed Febma1y ll, 2016,

http://www.alatown.com/spline-history-architecture. See also: Malcolm

Sabin, "Sculptured Surfaces Definitions: a Historical Survey," in Techniques

for Computer Graphic, ed. David F. Rogers and Rae A. Earnshaw (New York:

Springer, 1987), 285-338; David F. Rogers, An Introduction to NURBS: With

Historical Perspective (San Francisco: Morgan Kaufmann, 2001); Philippe Mo-

rel, "From e-Factory to Ambient Factoiy (or What Comes After Research?),"

in GameSetAndMatch II: On Computer Games, Advanced Geometries and Digital

Technologies, transactions of the Conference, TU Delft, Netherlands, March

29-April 1, 2006, ed. Kas Oosterhuis and Lukas Feireiss (Rotterdam: Epi-

sode Publishers, 2006), 532-544; 'A Few Precisions on Architecture and

Mathematics," Mathematica Day, Henri Poincare Institute, Paris, January 31,

2004; '·Geometrie polymorphe et jeux de langages formels: sur !'usage de la

geometrie et des model es dans !'architecture contemporaine," in Modeliser &

simuler: Epistemologies et pratiques de la modelisation et de la simulation, Tome 2,

ed. Franck Varenne, Marc Silberstein, Sebastien Dutreuil, and Philippe Hun-

ema (Paris: Editions Materiologiques, 2014), 293-335; "Some Geometries:

Polymorphic Geometries and Formal Language Games," in Morel, Five Essays

on Computational Design, Mathematics and Production (Sidney: Sidney Univer-

sity Press, 2008). 87-144. Other sources cited below.

53. For a full bibliography of Bezier's publication, see Christophe Rabut, "On

Pierre Bezier's Life and Motivations," Computer-Aided Design 34, no. 7 (June

2002): 493-510. An abridged biography in David F. Roger's obituary, "Pierre

Etienne Bezier, 1910-1999," in the same issue of CAD, 489-491; see also the

editorial introduction to Computer-Aided Design 22, no. 9 (November 1990),

a special issue honoring Pierre Bezier on his eightieth birthday; Pierre-Jean

Laurent and Paul Sablonniere, "Pierre Bezier: An Engineer and a Math-

ematician," Computer Aided Geometric Design 18, no. 7 (September 2001):

609-617. Bezier·s math was first published in Bezier, "Definition numeri-

que des courbes et surfaces," Automatisme 11, no. 12 (1966): 645-634, and

Automatisme 12. no. 1 (1967): 17-21: its application to CAD/CAM technology

in Bezier, "How Renault Uses rumerical Control for Car Body Design and

Tooling," Paper 6800010, Society for Automotive Engineers (Detroit, Januaiy

1968), Bezier, "Procede UNlSURF de Definition Numerique de Courbes Non

Mathematiques," Mecanique Electricite 1968: 219, and various subsequent

scholarly papers (1968. 1969, etc.; including, in 1971, in the Proceedings of

the Royal Society (Mathematical and Physical Sciences 321, no. 1545 (1971):

407-218). The chronology of de Casteljau's findings is more controversial:

"At Citroen, Paul de Casteljau defined the 'Bezier Curves' in a geometric and

algorithmic way, by using the 'de Casteljau algorithm,' in late 1958 and 1959;

he used Bernstein's polynomials soon afterward, much before Pierre Bezier.

This has been presented in internal Citroen reports (such as: de Casteljau, P

de F, SADUCSA manual, 1. Courbes a Poles; 4. Surfaces a Poles. Citroen [no date given]); was taught in the internal drawing school of Citroen from 1963;

has been mentioned to the lnstitut de la Propriete lndustrielle in March 1959

and June 1963; and has been kept secret by Citroen for a long time. Pierre

Bezier was aware of this and used to fully recognize that his work was posterior

to, though completely independent from, that of Paul de Casteljau.'' (Rabut,

CAD 34. no. 7 (2002]: 508). According to Farin the first public mention of

de Casteljau's algorithm, although not including a mention of the inventor,

is in J. Krautter and S. Parizot, "Systeme d'aide a la definition et a J'usinage

NO l'f.S 185

•

des surfaces de carrosserie," in P. Bezier, ed., "La commande umerique" is-

sue.Journal de la SIA 44 (1971): 581-586. "W. Boehm was the first to give de

Casteljau recognition for his work in the research community. He found out

about de Casteljau's technical reports and coined the term 'de Casteljau algo-

rithm' in the late 1970s." (Farin, "A History of Curves and Surfaces in CAGD,'"

see in particular section 1.3, "De Casteljau and Bezier," 4-6.) See Hanns Pe-

ter Bieri and Hartmut Prautzsch. "Preface," Computer Aided Geometri.c Design

16, no. 7 (August 1999), special issue dedicated to Paul de Faget de Casteljau:

579-581 (contains the text of the Laudatio read on the occasion of the confer-

ral to de Casteljau of the Doctorate Honoris Causae by the University of Bern

on December 6, 1997). De Casteljau's autobiographical note in the same issue

is ente1iaining but does not provide a timeline (Paul de Faget de Casteljau,

"My Time at Citroen," CAGD 16. no. 7 [1999]: 583-586).

54. P. Bezier, Letter to P. Rabut (1999). in Rabut, "On Pierre Bezier's Life and

Motivations." CAD 34, no. 7 (2002): 504.

55. According to Farin, the term "spline" was first used in English in 1752 ("A

History of Curves and Surfaces in CAGD,'' see in particular section 1.2, "Early

Developments." 1-4, curiously citing as a source H. L. Duhamel du Monceau,

Elemens de !Architecture Navale ou Traite Pr-atique de la Constructions des Vais-

seux [Paris 1752]. which, however, being written in French. uses the term

courbes). The Oxford English Dictionary cites a first occurrence in 1756 (from a

book on beehives), deriving from East-Anglian dialects (OED entry last up-

dated in 1989).

56. I. J. Schoenberg, "Contributions to the Problem of Approximation of Equi- distant Data by Analytic Functions. Part A: On the Problem of Smoothing and

Graduation. A First Class of Analytic Approximations Formulae," Quarterly

Journal of Applied Mathematics 4, no. 1 (1946): 45-99; ··Part B, On the Prob-

lem of Osculatory Interpolation. A Second Class of Analytic Approximation

Formulae," Quarterly Journal of Applied Mathematics 4, no. 1 (1946): 112-137.

On the timeline of B-Splines and NURBS development, see Farin, 'A Histo1y

of Curves and Surfaces in CAGD," in pa1iicular section 1.6, "B-spline Curves

and NURBS," 9-10.

57. Farin, "A Histo1y of Curves and Surfaces in CAGD," section 1.8, ··subdivision

Surfaces," u-12. Chai kin's algorithm, the basis of today's software for surface

186 NOTES

subdivisions. was invented in 1974 (George M. Chaikin, ·An Algorithm for

High Speed Curve Generation," Comp1,terGraphic and Image Processing 3, no. 4

[December 1974]: 346-349. George M. Chaikin, 1944-2007, first trained as

an architect at The Cooper Union, then as a computer scientist, was an artist

and educator.) Chaikin's algorithm's begot Doo and Sabin's, and Catmull and

Clark's (both in 1978): see E. Catmull and]. Clark, "Recursively Generated

B-Spline Surfaces on Arbitrary Topological Meshes," Computer-Aided Design

10, no. 6 (November 1978): 350-355; Daniel Doo and Malcolm Sabin, "Be-

havior of Recursive Division Surfaces Near Extraordinary Points," CAD Io,

no. 6 (1978): 356-360. Philippe Morel has pointed out that a precedent for

these and otberrecursive methods can be found in a small recreational work

by the Swiss mathematician Georges de Rahm, "Un peu de mathematiques a propos d'une courbe plane," Elemente der Mathematik, Revue de mathematiques

elementaires, II, 4 (July 15, 1947): 73-88 (oral communication). Today's best-

selling subdivision-based animation software, Maya, is hugely influential in

the design community. and in schools of architecture around the world. For

a vivid example on the use of Maya in the design of an icon of contemporary

·'globular' design (the Metropol Parasol in Seville, designed by Jurgen Mayer

H., Berlin: competition 2004; inauguration 2011) see Teyssot. "Algorithms

Can Talk."" Le Visi.teur 14 (2009): 206-212; for a timeline of the development

of subdivisions algorithms, 21 o and footnotes. Maya was first released in

February 1998; it was developed by the company Alias/Wavefront (owned by

Silicon Graphics as of 1995; formerly AJias Systems Corporation, formerly

Alias Research, founded 1983; bought by Autodesk Inc., 2006): see the Wiki-

pedia entries for Autodesk Maya and Alias System Corporation. The Autodesk

corporate website does not provide any information on the histo1y and

development of the software.

58. P. Bezier. letter to C. Rabut (1999). "Les Method es de la Carrosserie in 1960,"

in Rabut, ··on Pierre Bezier's Life and Motivations," CAD 34, no. 7 (2002): 495: Paul de Faget de Casteljau, ··My Time at Citroen," CAGD 16, no. 7 (1999):

583-586

59. De Casteljeau, "My Time at Citroen," 583.

60. Pierre-Jean Laurent, Paul Sablonniere, "Pierre Bezier," CAGD 18, no. 7

(2001): 6io, 614: Bezier's team had a CAE (Compagnie d'Automatisme

~OTES 187

Electronique) 530 computer (8Kb RAM), bought second-band: "in spite of

so crude an equipment. relatively complicated curves could be obtained: in

order to demonstrate to financial backers the proficiency of his protolype,

Bezier had the signature of the head cashier of the Banque de France, as found

on any French bank note, retraced in big scale!" De Casteljau cites an Olivetti

Tectractys (de Casteljau, "My Time at Citroen," 584), which must be a practi-

cal joke. as the Tectractys was an electromechanical calculator of the same

class as those I described above (section~- 1).

61. De Casteljau, "My Time at Citroen," 585. On the development of U !SURF at

Renault, see Pierre-Jean Laurent, Paul Sablonniere, "Pierre Bezier,'' 614.

62. Farin, "A History of Curves and Surfaces in CAGD," section 1.6. According to

Farin, the first systematic treatment of NURBS goes back to K. Versprille's

PhD thesis in 1975. According to Townsend, '·On the Spline. A Brief Histo1y

of the Computational Curve,'· International Journal of Tnterior Architecture +

Spatial Design 3 (~0,4), the term NURBS was introduced by Boeing in ,981

(no source given). Developments at Boeing are cited by Farin ("A Histo1y

of Curves and Surfaces in CAGD") but by none of the authors contributing

autobiographical notes to David F. Rogers,Anlntroduction to NURBS: With His-

to1ical Perspective: Robin Forrest, Rich Riesenfeld, Elaine Cohen, Tom Lyche,

Lewis Knapp, Ken Versprille, David Rogers.

63. David Rogers, "Biography: Pierre Bezier," in Rogers, An ln.troduction to

NURBS,36.

64. Robin Forrest, "Bezier Curves,'' in Rogers.An Introduction to NU RBS, 13.

65. Interviews with Frank Gehry, Tensho Takemori, Rick Smith, in Greg Lynn,

ed.,Archaeologyof theDigital, Catalogue ofth_e Exhibition held at the Canadian

Centre for Architecture, Montreal, Quebec, May ~013 (Montreal: Sternberg

Press, ~013): ~5, 3~, 38-39. Gehry had started to model the Barcelona Fish

using Alias (an early animation software); Gehry's team was referred to IBM,

then to Dassault by Bill Mitchell, then dean of the MIT School of Architecture

(ibid., 39). The idea was that the design of a big sculpture in the shape of a

fish would pose problems of streamlinjng similar to those tackled in aircraft

design, an intuition that appears more than warranted by the technical and

etymologic origin of splines in shipyard technology. Dassault's corporate

websites state that CATIA was launched in 1981 (and adopted, among others,

188 NOTES

by Boeing in 1984): accessed February 11, ~016, http://www.3ds.com/about-

3ds/hist01yh981-1997. CATIA may have been developed and used internally

by the Dassault aircraft company (then called Avions Marcel Dassault-Breg-

uet Aviation) from 1977 to ,981, with the name of CATI, before the software

was renamed CATIA to be marketed by the newly created subsidiary Dassault

Systemes ("CATI.A:' ent1y, Wi.kipedia).

66. Autodesk corporate website, accessed February 11, ~016, http://usa.autodesk

. com/ adsk/ servlet/item? id= 1 ~01 ~348&site ID= 1~311z.

67. Timeline from the website of the software's publisher, AutoDesSys, accessed

Februa1y 11. ~OJ6, http://www.formz.com/home/aboutus.html. On the de-

velopment of Form-Z by Chris Yessios and others at Ohio State University in

the late 1980s, and the involvement of Peter Eisenman in the early phases of

the project, see Greg Lynn, ed., Archaeology of the Digital, 55. "Chris Yessios

would also claim that I had asked for something to model things in 3-D, and

that he developed FormZ for our needs. We had special rights to FormZ for

years. We were the guinea pigs." According to Lynn, Eisenman might have

used an early version of FormZ, called Archimodos, for his Frankfurt Biozen-

trum project, submitted in 1987 (ibid., 57). Eisenman denies that (16). See

also Pierluigi Serraino, History of Fonn *Z (Basel: Birkhauser, ~ooz; and Turin:

Testa e lmmagine, zoo~); and Luca Galofaro, Digital Eisenman. An Office ~f the Electro,iic Era (Basel: Birkhauser, 1999). On the role of spline-based mod-

eling software in the history of digitally intelligent architecture, see Malcolm

McCullogh, "~o Years of Scripted Space," in Mike Silver, ed., ·'Programming

Cultures," special issue (AD Profile 18~) ,Architectu.ral Design 76, no. 4 (~006):

q-15. Rhino version 1.0 was released in October 1998. For a Rhino time line,

see the website of the software development company, McNeel, http:/ /wiki

.mcneel.com/rhino/rhinohistory (accessed March ~4. zo16).

68. It should be noted that not all that is digitally notated must be digitally pro-

duced-Le., fabricated or otherwise physically materialized using discrete,

number-based processes from start to finish. Images on today's computer

screens are rasters of discrete pixels, and so is almost eve1ything printed

on paper using laser or ink-jet peripherals, for example. But many may re-

member the drafting plotters of the last centu1y, where drawings were made,

line by line, by the mechanical movements of a pen. Such machines could

NOTES 189

•

69.

draw an arc of a circle by pivoting an arm around a center, thus in a sense

imitating the gesture of the hand of an artisan, instead of calculating and

then printing out a raster of very small dots or pixels, as today's printers do.

Mechanical plotters need very little vectorial information to do so, whereas

today's rasterized printouts use plenty of data, and need a different bitmap

for each scale or size of operations; to the limit, at maximum resolution the

number of pixels needed to rasterize a circle is infinite, whereas the equa-

tion (or the program for the movement of the mechanical arm of the plot-

ter) needed to draw that circle is always the same: the drafting plotter was

still a small-data tool. a data-compression technology using mathematics to

translate a long list of points into a short line of script. Drafting plotters

have almost entirely disappeared. but many similarly analog strategies per-

sist in today's 3-D robotic fabrication, or whenever robotic arms are tasked

to perform gestural operations that are digitally calculated but mechanically

operated.

Bernard Cache, "Objectile: The Pursuit of Philosophy by Other Means," in

"HypersurfaceArchitecture II." ed. Stephen Perella, special issue (AD Profile

141),Architectural Design 69, nos. 9-10 (1999): 67 ("mathematics has effec-

tively become an object of manufacture"); for centuries. architects have been

measuring their drawings with algebra, but now, "CAD software enables ar-

chitects to draw and sketch using calculus." Greg Lynn, Animate Form (New

York: Princeton Architectural Press, 1999), 16-18.

70. One of the best accounts to date ol' Gehry's early digital processes is in Alex

Marshall, "How to Make a Frank Geh1y Building," New York Times Magazine,

April 8, zoo 1. See also Coosjie Van Bruggen, Frank 0. Gehry. Guggenheim Mu-

seum Bilbao (New York: Guggenheim Museum, 1997), 135-140; Bruce Lind-

sey. Digital Gehry: Material Resistance, Digital Construction (Basel: Birkhauser.

zo01), 4z-47, 65-69, and Alberto Sdegno, "E-architecture, L'architettura

nell'epoca de! computer," Casabella 691 (zoo1): 58-67.

71. The term was forcefully reinstated in architectural discourse by Patrik

Schumacher, and thanks in particular to the reach and popularity of his re-

cent writings, parametricism is now often used as a synonym for digitally

intelligent architecture in general. Schumacher first used the term in a lec-

ture at the Smart Geometry conference in Munich in zoo7, and in print in

190 NOTES

two contributions to the catalog of the 11th Venice Architecture Biennale the

following year, "Parametricism as Style-Parametricist Manifesto" and "Ex-

perimentation Within a Long Wave of Innovation," in O!tt There: Architect-,.re

Beyond Building: Catalogue of the 11th International Biennale d'.4rchitettura,

Venice ~008, 5 vols., ed. Aaron Betsky (Venice: Marsilio, zoo8), esp. vols. 3

and 5. See also Patrik Schumacher, "Parametricism: A New Global Style for

Architecture and Urban Design," in Neil Leach. ed., "Digital Cities," special

issue (AD Profile 200), Architectural Design 79. no. 4 (zoo9): 14-z3. In de-

sign literature, parametricism is often meant to refer to the generic nota-

tion of a curve, which, for example, when planar. is written as a function of

two variables and several coefficients (as in: y =ax'+ bx+ c). The variation

of the coefficients (a,b.c) between certain limits generates a variable family

of curves (in that instance, parabolas). This notion of parametricism in design

culture may be traced back to Gilles Deleuze's and Bernard Cache's definition

of the objectile as a generic (parametric) object (see note 49). In mathemat-

ics, however, a parametric function more specifically defines the translation

of an explicit function (as the one WTitten above) into a system of equations

rewritten as functions of an external parameter. Most of the mathematics

of free-form curves and surfaces use parametric. not explicit notations of

functions, as these are more convenient to describe curves as functions of

angles, for example. As a consequence, "parametricism" in design can also

more specifically refer to the use of software based on splines, B-Splines,

NURBS, Bezier curves, and subdivisions. Schumacher may have had both

meanings in mind when he relaunched the term in zoo7-08. See the online

version of his Parametricist Manifesto of zoo8 (accessed February 11, zo16.

http://www. patrikschumacher. com/Texts/Pa rametricism %zoas 0/ozoStyle

.htm): "Contemporary avant-garde architecture is addressing the demand

for an increased level of articulated complexity by means of retooling its

methods on the basis of parametric design systems. The contemporary archi-

tectural style that has achieved pervasive hegemony within the contemporary

architectural avant-garde can be best understood as a research programme

based upon the parametric paradigm. We propose to call this style: Para-

metricism." In today's design parlance the terms may refer both to the use of

parametric software for the design of free-form curves and surfaces (NURBS,

\OHS 191

splines, etc.), and to the general variability inherent in all parametric nota-

tions, regardless of form and style.

72. But see note z6.

73. IBM's Selectric typewriter first introduced the "typeball,'' or golf ball in

1961 (all websites accessed March z4, zo16, http://www-03.ibm.com/ibm/

history/ibm100/us/en/icons/selectric). Xerox developed the daisy wheel

printing technology as of 197z-73. On the development of the daisy wheel

printer, see the Wikipedia entry (https://en.wikipedia.org/wiki/Daisy_wheel

_printing); the Xerox Corporation website does not refer to the develop-

ment of the daisy wheel printer at all (http://www.xerox.co.uk/about-xerox/

history-timeli ne/ engb. html).

74. Laser printing was developed by Xerox's Palo Alto Research Center (PARC)

in 19711 z; see a brieftimeline on the PARC website (http://www.parc.com/

about). The first laser printers aimed at the desktop market were the HP

Laserjet (1984; http://www.hp.com/hpinfo/abouthp/histnfacts/museum/

imagingprinting/0018) and the Apple LaserWriter (1985). On the develop-

ment of the Apple LaserWriter, see the Wikipedia entry (https:/ /en. wikipedia

.org/wiki/LaserWriter) and http://www.macworld.com/article/1150845/

laserwriter.html, accessed Februraiy 11, zo16. The Apple corporate website

does not provide an official timeline.

75. The Adobe company was founded in 198z. Jn 1985 the Apple Laser Writer was

the first printer to ship with a built-in PostScript interpreter (the "inter-

preter" was needed to rasterize the PostScript files sent out by the computer).

Timeline from the Adobe corporate website: see in particular, accessed

Februa1y 11, zo16, http://blogs.adobe.com/typblography/files/typblography/

TT%zoPS%zoOpenType.pdf. See also Townsend, "On the Spline," Inter-

national Journal of I nteriorArchitecture + Spatial Design 3 (zo 14): 5z.

76. EZCT Architecture & Design Research, Philippe Morel with l-latem Hamda

and Marc Schoenauer, Studies on Optimization: Computational Chair Design

Using Genetic Algorithms. zoo4. First presented at Archilab zoo4 in Orleans

(France) and published in Philippe Morel, "Computational Intelligence:

192 NOTES

The Grid as a Post-Human Network.'' in Christopher Hight and Chris Perry,

eds .. "Collective Intelligence in Design," special issue [AD Profile 183],

Architectural Design 76, no. 5 (zoo6): 100-103. A prototype and drawings of

the "Bolivar" model are in the Centre Pompidou Architecture Collection.

77. Daniel Widrig, Degenerate Chair (zo1z); Jenny Sabin. eSkin (zoo7-13); Ruy-

Klein, Klex (zoo8); Alisa Andrasek and Jose Sanchez, Bloom Garnes (zoiz);

Andrew Kudless, Chrysalis II/ (20iz); Marcos Cruz and Marjan Colletti, Robot

Foaming (zo13) in Marie-Ange Brayer and Frederic Migayrou, eds., Natu-

ralise,· !'architecture (Naturalizing Architecture), Catalogue of the Exhibitions

Archil.ab zo13, Orleans, FRAC, Fonds Regional d'Art Contemporain, Sep-

tember 14, zo13-Februa1y z. zo14 (Orleans: Editions HYX, zo13): 91, 143,

149, zo7, z19, z67.

78. See note 34.

79. See note 40.

80. See note 68, on the analog implementation of digital notations. and other

exceptions: not all that is digitally designed must be physically materialized

using discrete. number-based processes from start to finish.

81. Before the development of' electronic computers, NC (Numerical Control)

milling machines were driven by electromechanical calculators, punched

cards, or punched tapes. The first prototypes were developed by John T. Par-

sons (1913-zoo7, engineer, industrialist) for the US Air Force, then by the

Servomechanisms Laborato,y at MIT in 1949-5z. As in the case of the indus-

trial history of Bezier's curves ten years later, Parsons's research was origi-

nally triggered by the need to mass-produce splines (in this instance, the

airfoils of helicopter blades); for his contributions to the field of numerical

control Jobn T. Parsons was the first recipient of the Numerical Control So-

ciety Jacquard Award in 1968. The first commercial NC unit was marketed in

1954-55 by the Bendix Corporation (James Benes, "Microprocessor Magic,"

American Machinist 140, no. 8 [August 1996): 1z4-13z). For a slightly dif-

ferent timeline, see William Pease, "An Automatic Machine Tool," Scientific

American 187, no. 3 (195z): 101-115, and the corporate website of CMS No1ih

America, accessed February 11, zo16, http://www.cmsna.com/blog/zo13/

01/histo1y-of-cnc-machining-how-the-cnc-concept-was-born. NC ma~

chines started to include transistors in 1960 and integrated circuits in 1967

(Benes, "Microprocessor Magic," 124); it is not known when the expression

"CNC" (Computer Numerical Control) was first introduced. As late as 1996,

NOTES 193