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Writing Architecture #14

The Alphabet and the Algorithm

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Digital technologies have changed architecture--the way it is taught, practiced, managed, and regulated. But if the digital has created a "paradigm shift" for architecture, which paradigm is shifting? In The Alphabet and the Algorithm, Mario Carpo points to one key practice of the making of identical copies. Carpo highlights two examples of identicality crucial to the shaping of architectural in the fifteenth century, Leon Battista Alberti's invention of architectural design, according to which a building is an identical copy of the architect's design; and, in the nineteenth and twentieth centuries, the mass production of identical copies from mechanical master models, matrixes, imprints, or molds. The modern power of the identical, Carpo argues, came to an end with the rise of digital technologies. Everything digital is variable. In architecture, this means the end of notational limitations, of mechanical standardization, and of the Albertian, authorial way of building by design. Charting the rise and fall of the paradigm of identicality, Carpo compares new forms of postindustrial digital craftsmanship to hand-making and the cultures and technologies of variations that existed before the coming of machine-made, identical copies. Carpo reviews the unfolding of digitally based design and construction from the early 1990s to the present, and suggests a new agenda for architecture in an age of variable objects and of generic and participatory authorship.

184 pages, Paperback

First published February 4, 2011

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Mario Carpo

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Profile Image for Luke.
912 reviews5 followers
May 30, 2025
“Alberti's pursuit of identical copies is exactly coeval to the development of print technologies, and this parallel chronology is certainly not a coincidence. Alberti's insistence on an ideal, but drastic, authorial cutoff-the point at which all revisions stop and identical replication starts- curiously anticipates a practice that eventually became common in the printing industry, and survives to this day in the technical term bon à tirer (good to print).5° Originally, the author's bon à tirer (normally dated and signed) written on the last proofs validated the final version of his or her text, and
"authorized" its identical replication in print. Thenceforward, readers could expect exactly the same words in each copy as in the author's original, even though the author never printed, nor necessarily signed, any individual book. Thanks to the cultural and technical logic of mechanical replication, authorship was extended from the author's original to all identical copies of it.
For intellectual and ideological reasons, which should be seen in the context of the humanists' invention of modern authorship, and perhaps in the larger context of the humanists' contribution to the shaping of the modern self and of the notion of individual responsibility, Alberti anticipated this division between an author's work and its mechanical reproduction. But Alberti tried to impose this authorial paradigm within the ambit of a manual production chain, where no machine would deliver identical copies, and scribes could be reasonably expected to produce just the opposite-randomly changing, individual variations. Also, but crucially for the history of architecture, Alberti extended his precocious bon à tirer paradigm from literary to architectural authorship, asserting that the same conditions and the same consequences should apply. The fact that in most cases the architect's design should beget only one building (and not a series of cop-ies, as would a printing press, or a late medieval scriptorium) is irrelevant in this context. 5' What matters is the relation of identi-cality between the original and its reproduction. Alberti's entire architectural theory is predicated on the notational sameness between design and building, implying that drawings can, and must, be identically translated into three-dimensional objects.
In Alberti's theory, the design of a building is the original, and the building is its copy.”

“As Erwin Panofsky claimed in a celebrated and controversial essay, the apparently random drift of late medieval architectural and decorative visual forms was nevertheless derived from, and inscribed within, a set of fixed normative genera. Panofsky famously interpreted this pattern of "differences within repetition" as an isomorphism between Gothic architecture and Scholastic philosophy, both based on a genus-species relation between stable general categories and variable singular events. Equally famously and controversially, and almost at the same time, Richard Krautheimer examined the conspicuous and at times baffling variances between medieval monuments that were meant to be recognizable copies of the same famous archetypes, to conclude that their semantic function was eminently symbolic (or socially conventional, and unrelated to iconicity (or actual visual re-semblance) 3 Both analyses aptly describe the visual environment that is being shaped by contemporary digital media. Each objectile is an exactly transmissible but nonvisual notation: it is a fixed normative genus, which may engender infinitely variable visual species. All singular eventuations of the same algorithmic code will be different from, but similar to, one another. They will expect from their beholder a capacity to read and discern similarities, and to use this ancestral cognitive skill to recognize meaningful patterns in a stream of endlessly variable visual signs.
We have reason to worry about, and possibly lament, the forthcoming demise of traditional architectural authorship. The recent spasms of authorial conceit (always an indelible part of the architect's trade, but recently risen to unprecedented levels) further reinforce the perception of an incipient crisis. Evidently, even among practitioners less inclined to theoretical specula-tion, the nagging feeling that something today is not quite right with architectural authorship has made some headway. But the likely victim of today's upheavals may not be the general, timeless notion of architectural agency. Once an esoteric modernist theory, now an ordinary postmodern practice, the death of the author affects today but one, particular, time-specific category of authors: the author of identical, mechanical copies- the modern, Albertian author. Modern objects (authorial, authorized, and identically reproduced) might also disappear in the process.“

“both the object and the event are seen as essentially variable entities. But insofar as the objectile is, technically, an open-ended algorithm, and a generative, incomplete notation, the objectile's designer will
"authorize" some general norms to determine aspects common to a range of variable and individual events. Evidently, in an open-sourced environment, the algorithmic code itself may be open to aleatoric, nonauthorial variations, but this does not alter the bigger picture. Seen in terms of a genus-species hierarchy, objects are ontologically-specific, whereas the objectile is the general category to which they belong. Hence the objectile's designer is a "general," or perhaps a "generic," author. This is not an unprecedented authorial model. It was in use for centuries, before Alberti came by.”

“Behind Alberti's quest for unlimited identical reproducibility stood a powerful metaphysical aspiration. At the same time, the need for exact copies of texts, images, objects of art and indus-try, and nature was widespread and rising in the new culture of the Renaissance. Indeed, much of what Alberti aimed at would soon be delivered by another reproductive technology-one that Alberti curiously failed to take into account. In a sense, printed images and printed text would soon fulfill part of Alberti's pro-gram, providing exactly what Alberti needed, and-one may surmise-would have used, had he had the notion that he could do so. Alberti did not learn of print with moveable type until his last years, but all along he must have been familiar with relief and intaglio printmaking, which were already fairly common in Italy during his lifetime. Apparently Alberti never considered that these then marginal reproductive technologies could be put to task for technical or scientific purposes. Yet all that would have been necessary to print Alberti's map of Rome (instead of digitizing it) was already technically available at the time of his writing everything, that is, except the idea that a map could be printed. Only a few years later, the rise of print and of printed images marked the end of Alberti's digital experiments: Alberti's digital technologies dropped out of sight-for five centuries. 35
In hindsight, Alberti's experiments may appear to have been the wrong technical answer to a general cultural need-a need so general and widespread, in fact, that soon another technology would emerge that delivered most of what Alberti was looking for, but better, faster, and cheaper. Mechanical technologies would soon mass-produce what neither hand-making nor digital technologies in Alberti's time could deliver- identical reproductions.
Customizable proportional scaling was lost in the process, but evidently the gains more than offset that loss. And mechanical technologies kept producing exactly repeatable visual imprints of all kinds and sizes for the five centuries that followed: a process that was extraordinarily accelerated by the industrial revolution in the nineteenth century, and is only now coming to an end.
Yet, in spite of their untimeliness and quixotic inventiveness, some of Alberti's technocultural inventions famously thrived and, constantly revised and upgraded for the last five centuries, they have marked the history of Western art, architecture, and civili-zation. Alberti's optical definition of a new class of "photographic" images would not come to full fruition until the development of chemomechanical photography in the nineteenth century, hut his geometrical method for determining the intersections of the visual rays with the picture plane was the foundation of modern perspective, and is at the basis of central projections as they are still studied today (or were until recently).“

“As Deleuze had remarked, Leibniz's mathematics of continuity introduced and expressed a new idea of the object: differential calculus does not describe objects, but their variations (and variations of variations). Deleuze even introduced a new term to characterize this two-tiered definition of the object-the "objectile," a function that contains an infinite number of objects. 8 Each different and individual object eventualizes the mathematical algorithm, or objectile, common to all; in Aristotelian terms, an objectile is one form in many events.
Deleuze mentions Bernard Cache with regard to the mathematical definition of the objectile adding that it corresponds to a new concept of the technical object, no longer mechanically made and mass-produced but digitally made and based on variations). 39
Cache's book Earth Moves, in which these arguments are devel-oped, was published in English in 1995. The French manuscript, not published in French until 1997, was first drafted in 1983.3°
So we see how a quest for formal continuity in architecture, born in part as a reaction against the deconstructivist cult of the fracture, crossed paths with the computer revolution of the mid-nineties and evolved into a theory of mathematical continuity. By a quirk of history, a philosophical text by Deleuze accompanied, fertilized, and catalyzed some stages of this process.”

“The vertical integration of digital design and digital manufacturing, and the technical continuity between digital tools for visualization, notation, and fabrication, imply the elimination of most mechanical matrixes from the production process. That will spell the end of many basic principles of industrial economics. In the mechanical world, once a matrix is made, its cost must be amortized by using it as many times as possible. The economies of scale resulting from mass production are proportional to the number of identical copies that are obtained from the same mold: in mathematical terms, if the number of identical copies is infinite, the unit cost of the matrix is zero. The more you print, the less you pay per copy. Digital printing, however, does not work that way.
A laser beam must individually hit and mark all pixels on a printing surface every time anew, regardless of the printout that preceded it and of the one to follow. A metal plate that is used only once, to print one copy, will make for a very expensive print; but a laser printer can print one hundred identical copies of the same page, or one hundred different pages, at the same cost per page. The same principle applies to all kinds of mechanical im-prints, as well as to all processes where the identical repetition of the same sequence of actions, whether manual or mechanical, used to generate economies of scale. Under certain conditions, digital technologies can now deliver serial variations at no extra cost, and generate economies of scale while mass-producing series in which all items are different-but different within limits.
On the eve of the digital revolution, Deleuze had famously anticipated this technological shift in his studies of difference and repetition, and, as mentioned above, his dual notion of "objet" and "objectile"3? still aptly defines the basic principles of a nonstandard series.
A nonstandard series is defined not by its relation to the visual form of any constituent item, but by the variances, or differen-tials, between all sequential items in the series. A nonstandard series is a set in which each item has something in common with all others. In technical terms, all objects in a nonstandard series share some algorithms, as well as the machines that were used to process those algorithms and to produce the objects themselves.
In visual terms, a nonstandard series comprises a theoretically unlimited number of objects that can all be different but must also all be similar, as the digital tools that were used to make them leave a detectable trace in all end products.
Algorithms, software, hardware, and digital manufacturing tools are the new standards that determine not only the general aspect of all objects in a nonstandard series, but also the aspects of each individual product, which may change randomly or by design. 3 Unlike a mechanical imprint, which physically stamps the same form onto objects, an algorithmic imprint lets outward and visible forms change and morph from one object to the next.”

“A comparison between two instances of nonstandard series designed by two of the most alert interpreters of the new digital environment illustrates this point. Greg Lynn's series of ninety-nine teapots for the Italian luxury manufacturer Alessi, 39 and Bernard Cache's open-ended series Projective Tables, 4º feature individual items that are visibly different from, yet strikingly similar to, all the other items in the series. The peculiar stilus of each series derives in part from different technological platforms, but mostly from different adaptations of existing design software that were implemented by the two authors, each creating his own range of variabilities and his own set of self-imposed limits.
Lynn favors software based on differential calculus; Cache developed an interface based on projective geometry. Both choices are arbitrary: each can be justified but neither is inevitable. In both cases the figural result is unequivocally distinctive: Lynn's differential calculus begets smoothness and continuous surfaces;
Cache's projective geometry generates angular intersections of planes in three dimensions.
But the shift from mechanical to algorithmic reproduction also prefigures a parallel and equally crucial shift in our visual environment at large. We are leaving behind a universe of forms determined by exactly repeatable, visible imprints and moving toward a new visual environment dominated by exactly transmissible but invisible algorithms. To some extent, the recent discussions on the role of indexicality in contemporary architecture may in turn be a sign of the impending demise of identicality, on which much of our architectural and visual environments depend. 4 Most mechanically reproduced objects and forms are unmediated indices of the imprint that made them; most handmade works of the premechanical age, as well as most algorithmically generated items of the digital age, are not. 42 The erratic drift of manual copies may distort or confuse the sign of the original archetype and, as a result, conceal the identity of its author, or make it irrelevant; the unlimited variances of high-tech, digitally controlled differential reproduction may have similar consequences.
In the universe of mechanical Reproduzierbarkeit, the identification and, in turn, the meaning of forms depended on their identicality. In the new world of algorithmic, or differential, re-producibility, visual sameness is replaced by similarity. 43 Similarity and resemblance, however, are not scientific notions, and are notoriously difficult to assess and measure. The classical tradition, which was based on imitation, tried to nail down a workable notion of similarity almost from the beginnings of Western thought. Computer engineers and cognitive scientists today are trying to do the same-for the time being with less acumen than their classical and humanist predecessors.���

“Yet the range, scope, and theoretical import of seamless nonstandard seriality in a digitized environment should not be confused with the apparent multiplication of choice in a mechanical environment (often limited to marginal or cosmetic aspects of a product, such as color). The end of modernism, the end of industrial standardization, and the rise of neoconservatism occurred almost simultaneously with the rise of digital technologies and digital culture in the West; though it is difhcult to establish a direct causal relationship between these events, it is easy to see why many that have taken a stance against the digital turn now see all new information technologies as agents of evil-or of financial capitalism. Using multiple forms for the same function may be vain, antisocial, and waste-ful. Using the same form for multiple functions, on the contrary, is often ingenious, frugal, egalitarian, and virtuous. But in some cases it may also not work.”

“Indeed, Wikipedia would be a fascinating field of enquiry for medievalists. Both a medieval manuscript and a blog, or a wiki, are bidirectional, interactive, read-and-write information technologies: if you can read from them, you can write on them.?8
Wikipedia pages can morph and change more or less in the same ways as philologists claim vernacular literature did at the end of the Middle Ages. And the participatory nature of the design process that digital integration may now support and promote is equally evocative of the collective and often anonymous way of building that was common on medieval building sites before the humanists' revolution. As I have argued, contemporary digital technologies are in many ways closer to some cultural technologies that preceded the mechanical age than they are to the mechanical age we are now abandoning. The current debate on the distributed, participatory nature of the Web 2.0 singularly corroborates this argument.”
39 reviews5 followers
March 6, 2015
How fast do books get old? I have watched a couple of lectures of his, i think i prefer him speaking, he is not that uptight and austere when he speaks and when he gets offtrack he becomes really interesting. The book is very well written though it suffers from the same thing that "theory" books usually do: disappointing epilogues due to their "genericness", they dont take risks, they dont suggest or propose or anything and somehow end up to be too "scientific" but in the manner of the experiment that was really nicely set up but didnt produce any interesting results.
Profile Image for Dimitrie Stefanescu.
8 reviews24 followers
March 7, 2012
more than excellent. mario carpo provides an eloquent, historically grounded account of the deep theoretical and practical consequences of the "digital paradigm shift" in architecture.
amazingly accurate and perfectly balanced in tone. a must read for all digital enthusiasts (as well as passive practitioners) of computational architecture.
Profile Image for Phillip.
77 reviews5 followers
September 16, 2017
In this current Age of Information, those of us who are not “digital natives” tend to look back on the days we were first introduced to personal computers and wax philosophical about how the simple integration of a certain digital technology has so quickly and so profoundly transformed our culture and commerce, as well as whether such
transformations are bringing our society in the right direction. The Alphabet and The Algorithm is an architect’s version of that rumination. In it the reader is introduced to the authorial voice of Mario Carpo, an architectural historian and critic who also serves as professor of theory at University College, London, and then taken on a tour
through the story of authorship in architecture and how revolutions in methods and technology have spurred its evolution.

In its simplest form, Carpo’s main argument is that architecture has changed from an art of craftsmanship and on-site collaboration, where no work would ever have one true author; to one of notation and identicality
between plans and actual constructions, thus solidifying the architect’s role as sole designer; and now to an act of digital differentiation and mass customization, which has the charm of individual craftsmanship while retaining a new role authorship for the architect.

The transition to digital design technologies is inevitable; the benefits and demands far outweigh any perceived costs. The way we transition, however, is not. I believe Carpo is right about what the future holds for
design, but until the day we can all use software as naturally as we use pencil, paper, or clay, we must be prudent in
the role we let such software play in our process. Flashy new toys may augment the way we play, but they will never replace the imaginations that inspire us to play in the first place.

A good read that generates discussions we NEED to be having right now in the design disciplines.
Profile Image for Savio de Oliveira.
4 reviews
December 2, 2020
Mario explica pontos essenciais para entender o histórico da prática arquitetônica, evidenciando a gradual separação entre desenho e obra e os impactos disso no processo projetual e construtivo. Ele faz isso brilhantemente e ainda complementa investigando os impactos de uma arquitetura cada vez mais cibernética no futuro (e, em certa parte, no presente).
2 reviews1 follower
August 10, 2011
Writing architecture continues to be a great. Similar to the Princeton Pamphlet Architecture series but actually substantive. The discussion of how the "architect" was defined by the earlier renaissance and the issue of authorship which arises with the development of the ability to duplicate instead of imitating is fascinating. The inevitable transformation of architecture is laid out here. With the arise of digital means of production the profession has already begun to be transition out of the confines of the industrial revolution. Now we can only hope that the developments in both material and manufacturing science will be employed not just as a means to realize renderings.
Profile Image for Rallie.
274 reviews1 follower
December 2, 2015
For a book talking about changing modes of spatial production between modernity and "the digital age" (post-modernity) this book removes its argument completely from political economy, a lack of context that greatly hurts its argument. Somehow there's no reference to either Lefebvre or Harvey. If you're interested specifically in Alberti's law of architecture, this may be a book for you. Otherwise, there's better stuff out there.
3 reviews
July 9, 2012
Very well written history of design from pre industrial to post industrial. Mario Carpo gives context and words to better understand current trends in architecture and the art of making.
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