A concentration essay in 5 parts · March 2021 · annotated 2026
Computation Becomes Geometry
The March 2021 statement of intent where it started: computers do two jobs, calculating and putting things in order, and every interface is an apology for the gap between the machine's time and ours. Written to justify a self-designed degree at NYU Gallatin; Pulling Rabbits Out of Hats is named here first.
- By
- Jade Flowers
- Reading
- ~15 min
- Figures
- 5, all live
- Notes from 2026
- being written
How to read thisThe 2021 text stands as written. The 2026 layer, notes and scores, sits beside it and turns off with the switch at the top. Every figure is something to do rather than watch.
The argument in four moves
- iCalculation is not ordination.L'ordinateur: the one who puts things in order. Calculation queues tasks against resources and needs an interface to meet us in real time. Ordination is real-time response, and needs none.§ i ¶ iv
- iiMatter that reorders itself.Ordination's one first-class citizen is recursion, which, as Perlis put it, trades description for time: a five-line rule, a hundred and twenty-seven branches. Its frame is our frame.§ ii ¶ ii
- iiiImmersion becomes recursion.A program is crystallized thought, and thought is an act in space, not time: it unfolds out of what's already there rather than being assembled from nothing. Read through Sloterdijk, Alexander and Bratton.§ iii ¶ iv
- ivHold both eyepieces together.From two-point perspective to Simula to naked objects: a theory of computing has to keep the representation and its physical instance in one view.§ v ¶ i
A longer line of thought
March 2021 · you are here
Computation Becomes Geometry
Calculation vs ordination, and computing as a space-forming effect.
Later in 2021
Pulling Rabbits Out of HatsSkeuomorphism, the controller, the case against discoverability.
2021 · second edition 2026
The Periodic Table of the Interactions118 interactions, laid out by dimension, time, discoverability, and agency.
The One Who Puts Things In Order
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¶ i
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- 1
“The Two Types of Computing,” Bret Victor: 1. asymptotic complexity theory; 2. control theory (signal processing, cybernetics). ACT designed for batch jobs (deck of punchcards); CT designed for real-time response (aircraft and artillery). ACT has no concept of time, only a measure of how operating count scales with dataset size. CT has an explicit time variable, which is often real time. Today, most of our computing is in a realtime context (via simulated pseudo-physical interfaces) but hardware and software designed around the ACT view of computing.
- 2
I’m referring to Open AI’s GPT-3, of course: https://arxiv.org/abs/2005.14165
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Matter That Reorders Itself, Order That Re-Matters Itself
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¶ i
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- 1
Marshall McLuhan, from Understanding Media: “Instead of being concerned with separate machines, cybernation looks at the production problem as an integrated system of information handling.”
- 2
A phrase of Herbert Simon’s, from his “Elements of a Theory of Human Problem-Solving” (http://digitalcollections.library.cmu.edu/awweb/awarchive?type=file&item=33573 [archived])
- 3
This is referencing a famous “epigram” on computing by computer scientist Alan Perlis: “Recursion is the root of computation since it trades description for time.” (http://www.cs.yale.edu/homes/perlis-alan/quotes.html [archived])
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- 1
Amorphous Computing, Abelson et. al. (http://worrydream.com/refs/Abelson%20-%20Amorphous%20Computing.pdf [archived])
- 2
Apple’s Indoor Mapping Data Format (https://register.apple.com/resources/imdf/ [archived])
- 3
Jean Baudrillard’s book for those who need a citation.
- 4
However, I do believe Baudrillard’s framework to be especially relevant to analyzing our current computation-as-calculation state of affairs, as it is well-suited as a framework for understanding why interfaces are necessary within that paradigm.
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My Own Transformation
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¶ i
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In the course of the narrative, it should become clear why classical philosophy took form as macrospherology, as contemplation of the greatest orb and most encompassing immune structure. Wherever philosophical thought after Plato was at the necessary level, the two epitomes of totality, the world and God, were envisaged as an all-enclosing spheric volume in which countless subordinate world shells, value spheres and energy circles are concentrically embedded...Existence is characterized by immersion in a final element...2...If "life" has a boundlessly manifold space-forming effect, this is not only because every monad has its own individual environment, but more significantly because they are all intertwined with other lives and consist of countless units...What is decisive here, however, is that it always produces the space in which it is and which is in it in the first place...3...wherever human life is found, inhabited orbs appear which, in a sense, are rounder than anything that can be drawn with compasses.4
- 1
Spheres Vols. I-III, Peter Sloterdijk
- 2
Ibid. Vol 3, p.17
- 3
Ibid. Vol 3, p.23
- 4
Ibid, Vol I, p.11
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I focus on the idea that a living process always has enormous respect for the state (and morphology and form) of what exists, and always finds a next step forward which preserves the structure of what exists, and develops and extends its latent structure as it creates change...2The emergence of new structure in nature, is brought about, always, by a sequence of transformations which act on the whole, and in which each step emerges as a discernible and continuous result from the immediately preceding whole.[Each of Alexander's Fifteen Fundamental Properties] will, in general, tend to occur again and again, throughout nature, within three-dimensional systems. This question involves a level of morphological thinking which has no familiar language in contemporary mathematics.3The practical crux of unfolding, the essence of every living process is that it is above all a geometric process. That is surprising, and not widely understood. The unfolding is geometrical in its essence. Although there are many side features to living proces, it is fundamentally the unfolding of coherent geometric form.4
- 1
The Nature of Order Vols. I-IV, Christopher Alexander
- 2
Vol. I, p.128
- 3
Vol II, p, 18
- 4
Ibid. p.178
viii
We are very used to thinking of wholes as composed by parts. That is, a whole is generated by gathering the necessary parts (which, crucially, already exist) and putting them together in some way such that a thing is made from the parts. In this view, wholes are “built up” from parts.But the modern mind misses that in the organic and living unfolding of the world, wholes are generated by and out of other wholes, and the parts we observe are very often descended from the elaboration and internal differentiation of a whole whose existence precedes them.
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A known initial state plus a known morphism equals a predictable result. This equates to the deliberate composition and manipulation of formal systems. This process is also known as computation. Specific types of morphisms may also be employed to translate a representational state from one physical medium to another. ... any representational medium is inherently a computational medium. The machines we recognize today as computers constitute an efficient, yet extremely narrow interpretation of this idea.Alexander achieves [a broader application of this concept], as he uses the current representational—that is to say, geometric—state of the system, on the ground, to compute the next step in the construction process, itself a recursive application of a carefully-selected set of fundamental morphisms.
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The Stack makes space by occupying it; it does so by surveying abstraction, absorbing it, and virtualizing it, which is how it is even possible to consider whether or not it expresses a nomos at all...2...This accidental megastructure, this machine that is also a "state," is not the result of some master plan, revolutionary event, or constitutional order. It is the accumulative residue of contradictions and oppositions that arose to address other more local problems of computing systems design...3...The Stack is at once a machine that becomes a state, and a political geography that derives and is derived from the structure of that machine. The Stack includes all the various planetary computational technologies we now build with fanfare, but its significance is its reflection of the totality that emerges unintentionally...4...The Stack is an engine for thinking and building. The architectural metaphor may suggest an exclusive design for one given site, but it should direct us instead toward a geometry in which different things occupy the same site at the same time and cohere into a stable system because of this co-overlapping. The Stack is built of real things, but how we conceptualize its totality depends on powers of aesthetic abstraction.5
- 1
The Stack, Benjamin Bratton
- 2
Ibid. p.33
- 3
Ibid. p.8
- 4
Ibid. p.65
- 5
Ibid. p.64
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- 1
Ibid. p.66
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xvi
- 1
Ibid. p.61-62
- 2
Ibid. p.85
- 3
Ibid. p.87
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A Context for Research
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¶ i
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Traditionally, words have been privileged as the proper mode of explanation, as the tool of thought. Images [read: geometry] have, on the other hand, long been sequestered to the realm of spectacle and aesthetics, sidelined in serious discussions as mere illustration to support the text—never as equal partners.The source of this historical bias can be traced to Plato, who professed a deep distrust of perception, citing its illusory nature...For Plato, human life was a pilgrimage from the world of appearance [geometry] in the cave to the reality of pure forms—of truth....Descartes took this distrust of the senses a step further, as he considered that all he pierced might be a deception...By reducing the body to parts, he felt he would arrive at the mind, which he saw as being “entirely indivisible.”2
- 1
Unflattening, Nick Sousanis
- 2
Ibid. p.54-55
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The factual character of modern science – what we call its objective nature – arises chiefly from the fact that its results can be shared......[Descartes's] mechanistic idea tells us very little about the deep order we feel intuitively to be in the world. Yet it is just this deep order which is our main concern...In principle, rational discussion about building should be impossible.1
- 1
The Nature of Order Vol II, Christopher Alexander, p. 16-17
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...Galileo also changes sensations that seem to endanger Copernicus. He admits that there are such sensations, he praises Copernicus for having disregarded them, he claims to have removed them with the help of the telescope. However, he offerers no theoretical reasons why the telescope should be expected to give a true picture of the sky.1
- 1
Against Method, Paul Feyerabend, p.74
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In a way, Gödel got around [Russell and Whitehead] by building the first “meta-circular evaluator” — a language that interpreted itself.1
- 1
“What Godel Discovered”, (https://stopa.io/post/269 [archived])
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Since simulation is the method of analysis most commonly to be used for the systems in which we are interested, SIMULA is a dynamic language: It is designed to describe sequences of actions, not permanent relationships.1
- 1
“The Development of the SIMULA Languages,” p.248 (http://cs-exhibitions.uni-klu.ac.at/fileadmin/template/documents/text/The_development_of_the_simula_languages.pdf [archived])
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- 1
Naked Objects, Jacob Pawson
- 2
Ibid. p.9
- 3
In particular, he proposes novel ways of overcoming the limitations inherent in the paradigm of direct manipulation, and seeks to develop methods of performing actions that lack clear physio-spatial referents without resorting to foisting excessive abstraction on the user. Some of my research I hope to complete in my senior project extends this line of research into a paradigm I’m labeling “Pulling Rabbits Out of Hats,” and some early tests have already proven such a perspective’s promise.
Closing
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¶ i
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If we remain at the level of the visual aspects only, we fall back into a series of weak clichés or are led into all sorts of fascinating problems of scholarship far away from our problem; but, on the other hand, if we concentrate on the agonistic situation alone, the principle of any victory, any solidity in science and technology escapes us forever. We have to hold the two eye pieces together so that we turn it into a real binocular.1
- 1
Visualization and Cognition: Drawing Things Together, Bruno Latour, p.5
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List of works
adds a historical perspective adds a cultural, political or geographical context
Concentration
- Spheres Vols. I–III · Peter Sloterdijk
- The Nature of Order Vols. I–IV · Christopher Alexander
- The Stack · Benjamin Brattonadds a cultural, political or geographical context
- Augmenting Human Intellect · Douglas Engelbart
Humanities
- Understanding Media · Marshall McLuhan
- Against Method · Paul Feyerabendadds a historical perspective
- Unflattening · Nick Sousanis
- Technical Ekphrasis in Greek and Roman Science and Literature · Courtney Robyadds a historical perspective
Social & Natural Sciences
- Seeing Like A State · James Scott
- Data and Reality · William Kent
- 99 Variations on a Proof · Phillip Ording
Pre-Modern & Early Modern
- Allegory of the Cave · Platoadds a historical perspective
- On The Heavens · Aristotleadds a historical perspective
- Celestial Spheres illustration from Livre Du Ciel Et Du Monde · Nicole Oresme
- Chinese Bronze Object, Shang Dynasty, 1500 B.C.adds a cultural, political or geographical context
- De pictura · Leon Battista Albertiadds a historical perspective
- La Géométrie · René Descartesadds a historical perspective
- Monadology · Gottfried Leibniz
Papers
- Naked Objects · Richard Pawson
- The Anti-Mac Interface · Don Gentner and Jakob Nielsen
- Cognitive Dimensions for Cognitive Technology · A.F. Blackwell et al.adds a cultural, political or geographical context
- Visualization and Cognition: Drawing Things Together · Bruno Latour
- Knowledge In Pieces · Andrea diSessa
- Notes for a Modelling Theory of Science & Cognition · David Hestenes
Software
- Simula-67 · Ole-Johan Dahl and Kristen Nygaard
- Smalltalk-80 · Alan Kay, Dan Ingalls, Adele Goldberg
- Project Cybersyn · Stafford Beer et al.adds a cultural, political or geographical context