metaphysical & metaphorical musings : art, architecture, and arithmetic
Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Wednesday, April 20, 2011

Prezoject



Advance Praise

“I don’t speak Greek” – Epimenides, paradoxician [translated from the original Greek]

“…the least factual, most accurate account.” – Frank Mankiewicz, journalist

“…soft and spongey—like a Twinkie.  Like a Twinkie.” – Morgan Freeman, narrator

“Your film…one thing in two words: fucked up…very fucked up.  Okay three words, four words, who the hell cares…very very fucked up.  What I’d call a bad trip…I was so upset I even threw my friend’s fishtank at their china cabinet.  Ugly, very ugly.  Salt water, dead fish everywhere, me screaming ‘so very very fucked up.’  Five words.”
- Hunter S. Thompson, doctor of divinity [interview with Karen Green, qtd. in Danielewski]

“It’s like a koala bear crapped a rainbow in my brain.” – Hazel Murphy, captain

“surprisingly adequate” – Harold Bloom, logorrhetic sesquipod

“That’s Numberwang.” – Bertrand Russell, human

Tuesday, April 19, 2011

CATTt+astrophe

[strophe - a turn or division]


It finally happened.  There I was, minding my own business (well, my own beer), when I finally had an epiphany of my very own.  It was bound to happen—it’s fatality, after all.

I’ve been agonizing for days over my Prezi.  (Todd can attest—he’s seen me sulking around top floor of Rolfs like the ghost of Hamlet Sr.)  I just couldn’t make the damn thing come together, find the logic of the immanent trope.  So there I was, hunched in agony (competition with the object—who will prove more resourceful?) over my computer, when I finally found a tropic tangent.

In the later days of Pruitt-Igoe, broken glass was a conspicuous feature: cascades of shattered beer bottles filled the ground that originally promised ‘a river of trees’; more significantly, one of the buildings’ most prominent features was its busted-out windows.  Broken windows—a sign of fatality.  We’re all intimately familiar with this phenomenon.  It’s the scourge of the personal computer—the fatal error—a sign that Microsoft Windows has tripped over its own formality.  Pruitt-Igoe as a signifying accident is the very same as the blue screen of death.  This, of course, leads marvelously into Lev Manovich’s theorization of the new media screen, providing a convenient inroad into digital technology, a persistent parallel to modern architecture in my blog.

I hypothesized, early on, that the disaster was the organization of space.  The notion that suspicion and defection were emergent properties of the layout seem to corroborate this.  Pruitt-Igoe promised the American Dream of the mid-century.  The project arose as a result of flight to the suburbs, to the white picket fences of middle-class America.  Pruitt-Igoe was an urbanized version of the white picket fence neighborhood—‘vertical neighborhoods for poor people’, to quote Architectural Forum (and the scary thing is, these were words of praise).  The social disintegration seems to me a form of mass brinksmanship; if this barren, inhospitable space masquerading under a human metric was the best that the American Dream was going to offer up, the only option was to call its bluff.

Wednesday, February 23, 2011

/Part1 : Fatal Strategy

“We’re living in the future.” – Orlando Cordero, roommate
“You need to be rich to live in the future.” – [yours truly]

The accident, as the sight of a new ontology, shows us something of the real—it shows us our own agency, removed from us, coming back to haunt us.  We give up our own agency in the form of our creativity in favor of technoscience and the better, more convenient, more comfortable future that it promises.  Investment in ‘objectivity’ promises that this future will be the same for us all.

In the case of Pruitt-Igoe, we want the future—an elegantly geometric future that expresses how far the old ontology of science has taken us.  Unfortunately, that metaphysics is no longer relevant; we have to figure out a new future, and come to grips with the fact that the object will lead us there, co-opting our agency to bring itself & ourselves out of the present and further into the new metaphysics.

“Some called him a ‘pretext’.  Others said he was a point-for-point microcosm.” – A Spokesman for the Counterforce
“That could be a building, that was so general.” – Ian Roberts, improv comic

In Pruitt-Igoe, the infinite exchangeability of the object—the commodity relationship of living in futurity, the desire for technoscientific utopia—breaks down and bites us like a carnivorous coffee table.  Or, rather, it bit the lower-class residents who lacked capital and thus the capacity to consummate (after all, it is seduction) a range or variety of commodity relationships with different objects.  The infinite repetition of living space fills in for the (missing) infinite exchangeability of capital.

The grid shows us a certain ideal, a world wherein everything is calculable and placeable, but this disregards the bending or deformation that is the grid’s force.  This deformation is the accident—in Pruitt-Igoe, in Game Theory, the logical approach hits a breaking point.  Instead of imposing the subjective logic of literacy’s metaphysics onto the object, we have to let the object dictate our new strategy.

En abyme, the grid subdivides itself into smaller and smaller increments, like the fine calculation of a curve, infinitely expandable and contractible.  The golden spiral of Modulor is more poetic, and though we find this pattern in nature, Le Corbusier’s scale makes man the measure of all such objects.  But what happens to these at Planck scale, when time and space purportedly break down?

“Man’s desires are limited by his perceptions; none can desire what he has not perceived.”
“He who sees the Infinite in all things sees God.  He who sees the Ratio only sees himself only.”
- Blake, “There is No Natural Religion” [a&b]

The case of Watson, of Wolfram|Alpha, is the desire to bend the object to our will.  Instead of letting the object speak in its own way, we want the object to speak to our own understanding.  This seems like it will take us further from being able to ‘speak machine’ and grasp the accident as a sign, from being electrate.  Not the fatality we’re looking for.

The image of graffiti on the bare walls of Pruitt-Igoe keeps coming back to me; the logical zero-sum game of funding left a blank canvas for inhabitants (not necessarily residents).  If human and technological enetelchies are intertwined, this is the object co-opting us to bring it to ecstasy, to make it what it already is.  Pruitt-Igoe replaced St. Louis slums with a vision of the future of architecture-as-human-habitat that came to be worse than what it replaced—more slum than slum.

The task now is to find the poetics of space.  To liberate the image from the aqualitative grid and let it become artistic.


“…in Eternity the Four Arts: Poetry, Painting, Music,
And Architecture which is Science: are the Four Faces of Man.
Not so in Time & Space: there Three are shut out, and only
Science remains thro Mercy: & by means of Science, the Three
Become apparent in time & space, in the Three Professions
Poetry in Religion: Music, Law: Painting, in Physic & Surgery:”
- Blake, Milton


Of course, the only way out (past limit) is through (and on into ecstasis--abyme, Eternity, infinity).

I've come across poetic renderings of self-referentiality (the cultural archetype or myth I've found) more than a few times: Blake does it obliquely on several occassions, and Mark Danielewski depicts it explicitly in House of Leaves when his protagonist finds a copy of the book itself; Shakespeare and Oscar Wilde make a similar gesture when they make play the subject of the play (in Shakespeare's case, it's usually overtly metatheatrical; Wilde is subtler).  Being placed en abyme is what breaks mathematics (Godel and Principia) and machines (Euclid and the 216-digit number).

Mise en Abyme en Abyme : ^n+1 ?



Tuesday, February 22, 2011

Deformation & Fetish Objects

Deformation’s been on my mind all semester.  A big part of this chronic fixation is my puppy-love for Jerome McGann’s book radiant textuality: literature after the world wide web.  (It’s a spectacular book.  Really.)  Deformation is McGann’s instruction; he advocates precisely the sort of image manipulation we started our semester with, and shares his experience messing around with Dante Gabriel Rossetti’s art that lead to new insights on his own part.  His dictum is that no text (or image, I suppose) is ever self identical—so why not bring the image (or text, I suppose) into its ecstasy by helping it along?  McGann uses the term deformation to foreground the function of criticism and interpretation.  Transformation works equally well, and sheds any negative connotations that deformation might carry.

In a response to one of Wendy’s emails earlier this semester, I wrote a little about the deformation of the accident as an event into the static, flattened image of the accident, the sign; and about the deformation into pixilation (which allows us to make all those fun transformations).  This is implicit in McGann, particularly his discussion of how a high-powerd scanner never produced the same facsimile twice.  ‘Pixelation’ is also implicit in Newton’s calculus, which divides a curve into numerous discreet segments that resemble the original curve, and the same with Cartesian arithmetic, which transforms an algebraic statement into a geometric form mapped onto a grid—my figure for the Pruitt-Igoe disaster.  The design of the buildings was heavily influenced by Le Corbusier’s philosophy of architecture (thanks, Todd!) which relies heavily on formal properties and geometric space.  Le Corbusier is a pseudonym, a transformation of the identity, which corresponds with Le Corbusier’s Modular scale, a transformation of the physical body—the human form—into a mathematical exemplar, a harmony of ratios.  Even the name, Le Corbusier, suggests the force of bending and deforming.

I’ve looked briefly at the fetish-object, the relation between dominoes and punched cards.  Part of that examination was the difficulty of deciding just how far back to trace in pursuit of the object.  Both of these are, of course, cases of transformation/deformation, but the dominoes seem more interesting to me as a transformation of aleatory play.  Dominoes were, allegedly, derived from dice; in a physical sense, the dice are flattened out in the transformation to dominoes, but the luck of the throw is transformed into the luck of the draw, which seems like a sort of flattening out (maybe Caillois will be able to help me with this).  Dominoes also have the added feature of physical extension, of creating an emergent structure, form from number just as Le Corbusier’s architectural philosophy extols.  The difference between the domino-structure and the Pruitt-Igoe grid is the difference between liberal-aleatory and conservative-utilitarian deployments of space.

What’s the difference between Pruitt-Igoe and a stack of dominoes?  The stack of dominoes has a better chance of staying upright.

Sunday, February 20, 2011

Singularity

Self-referentiality is the ecstasy of the object, the passing of a rational limit—math becomes more logical than logic can accommodate, Euclid becomes more intelligent than its systems can sustain.  Baudrillard’s dimension collapse.

The allure of the object in this case is the promise of the future; it seduces us with the possibility of becoming futurity.

These themes come together in the theoretical Singularity—the belief that technoscience’s exponential growth of capacity, and the diminishing time needed to achieve this growth, will culminate in a radical historical event that will usher in a new type of technology and civilization.  One possibility is that computers like Euclid would no longer have to worry about self-referential meltdowns; artificial intelligence would be the new standard of electronic technology.

[In physics, a singularity is a similar impossible event.  The event of technology reaching a point of infinite improvement at infinite speed is much like the time-space event of the black hole, a point of infinite density and infinite gravity.  Nature abhors a vacuum, but she abhors infinites even more—at least, according to physics, which does not allow for infinite values, unknowable quantities.  A popular theory is that a singularity was the source of our universe; or, in its ecstatic form, that singularities are the wombs of universes.]

All of this, of course, relies on acceleration, speed, a greater or even qualitatively new condition of circulation in the dromosphere.  At the moment, we still have the luxury of critical thought, but after the singularity (if it does indeed happen), unpredictability will be the condition of the moment; we’ll have no choice but to think at the speed of light.  We’ve got to be faster than Watson.

The principles of the International school of architecture gave Pruitt-Igoe this shine of the future.  Theorizing the singularity and attending the inauguration of Pruitt-Igoe are both anticipations of the future.  The commodity relationship in a techno-utopic culture, reliant on science and mathematics, is the promise of the future, today.

The end of duration?

But what if the myth holds?  Could the singularity turn out to be π all over again? 

Saturday, February 19, 2011

Corbusier & Corbusier

"Le Corbusier 
adopted his pseudonym in the 1920s, deriving it in part from the name of a distant ancestor, Lecorbésier. But in the absence of a first name, it suggests a physical force as much as a human being. It brings to mind the verb courber, to bend, and, of course, Le Corbusier was a great bender of townscapes to his own will. It also brings to mind le corbeau, the crow or raven, not a conventionally beautiful bird in plumage or song, but one that is simple and unornamental in both and therefore, metaphorically speaking, honest and undeceiving, as Le Corbusier claimed his architecture to be. In French, le corbeau has a further meaning: that of a bird of ill omen—and perhaps that is the architect’s little joke upon the world."


Da Vinci's Vitruvian Man
Le Corbusier's design was informed by his Modulor, a scale of proportions based on the ratios of the human body, a continuation of Da Vinci's project in the Vitruvian Man.  It relies on the golden ratio, another irrational mathematical constant like pi, and the Fibonacci sequence, an exercise in vertigo which produces the golden spiral whose growth is related to the golden ratio.  Da Vinci and found this ratio inherent to the human form, and it can be seen in other natural phenomena.  Le Corbusier's ambition was to use this ratio to create architecture and design suited precisely to human proportions, possible through the mathematical order of the universe.
Le Corbusier's Modular Man

The first Modulor Man was based on the height of the average Frenchman, but was later revised to accord with the standard height of attractive men in English detective novels.  At least in the second case the base was a professedly fictional standard.  The very name, "Modular", evokes "modular", or interchangeable, the very image of Pruitt-Igoe, the design of which was inspired by Le Corbusier's architectural principles.  He considered the Modulor scale to be one capable of uniting the Metric and Imperial scales, creating universal equivalency.


One of Le Corbusier's early projects was the Domino House.  It is a very simple, practical design, but also one in which interior layout is customizable within the overall form.  The name evokes the image of dominoes stacked and arranged to build a small structure, but also recalls the variety of ways dominoes can be combined and recombined within the overall structure or rules of the game--the very essence of modularity.

Perhaps we've found the fetish-object?

Friday, February 11, 2011

Mythematics II - Gödel Incompleteness

In the early years of the 20th century, Bertrand Russell and Alfred North Whitehead set about axiomizing mathematics—boiling math down to its fundamental principles, modeling Euclid’s geometry.  One of Russell’s main concerns was eliminating the paradox of self-reference.  Toward this end, he and Whitehead penned their Principia Mathematica in three imposing volumes.  A few decades later, Kurt Gödel showed up and ruined everything by showing that any formal system at a certain threshold of power can, in a sense, self-destruct.

Gödel’s proof has two key points: that certain mathematical statements can be interpreted as statements about mathematics itself (which should only be possible in meta-mathematics), and that these statements can be condensed into a single statement which speaks about itself.  Thus, any formal system of a certain sophistication carries the potential for self-reference, the very thing Russell was so eager to eliminate.

Don Ault likes to say that the Principia was a turning point in the respective careers of Russell and Whitehead:  Russell was only able to think before the Principia, and Whitehead was only able to think afterward.  Whitehead penned his major philosophical works, and Russell became the doddering old man we see in Prisoner’s Dilemma.

Mythematics I - Daren Aronofsky’s π

Aronofsky’s film follows a search for an unknown quantity, the 216-digit constant in the equation of the universe.  Max, like von Neumann, is looking for the key to the stock market.  Unlike the science of game theory, the approach is through mathematics—he doesn’t want a theory, he wants an equation with the ability to exactly predict the movements and fluctuations of the stock market.  Max believes that the stock market, as a system, operates organically, and understanding this microcosmic process will open up the logic of the universe.

Like Baudriallard says, “there is nothing worse than to utter a wish and to have it literally fulfilled” (152).

Max’s donor is Euclid, his computer; Max and Euclid both operate on a formal etiquette, an exchange of language, that of mathematics.  Euclid is like the Tit-For-Tat program in Prisoner’s Dilemma: it can only communicate through its actions.  Sol and Max can communicate to each other through language and math, but Euclid only communicates through math.  Max proves himself worthy through his manipulation of formal systems; Max’s benefactor is a machine because Max is a virtuoso of machine language.

We can see this better in contrast.  Max is not a social being; his interactions with other people are typically standoffish, even abusive.  Max has his neighbor, Devi, as a social donor, though after Max throws her out of his apartment, she disappears from the narrative.  He insults her, violates etiquette, just as he does with Sol, who also exits the narrative following a quarrel with Max.  Max is better with machines than with humans; none of the people in the story become Max’s donor because he has very little regard for symbolic and contractual relationships.  These characters do compete for Max, like potential donors—they each try to offer something to Max that will aid him.  Marcy and Lenny become violent, seem like antagonists, but this is too superficial; this is simply the nature of Max’s sociality.    Sol, Marcy, Lenny seem like competing donors; calling Marcy and Lenny antagonists seems overtly superficial.  It seems more likely the number is the antagonist—but it is also the gift object of symbolic exchange.

Euclid “spits out” the number near the start of the film.  The number accumulates value as it circulates amongst the characters: Sol confirms the significance of the number, Marcy verifies its efficacy when her attempts to deploy it cause a stock market crash (which Euclid predicts, showing that the number is self-aware and capable of accounting for its own influence), Lenny and the Hasidic Jews elevate the number to the spiritual realm and grant it transcendence as the true name of God (Max secularizes and immanentizes the transcendent qualities, abstracts the pure science from the economic applications; for him, the number is the key to understanding the chaos of nature and creation).

But the gift is also the source of accidents.  It is the product of an accident—Euclid crashes immediately after printing the number.  Sol thinks that this number allows computers to become self-aware, but only briefly, because this knowledge is fatal—a formal system cannot handle functioning at that level.

Max doesn’t fare much better.  The number seems woven into Max’s unconscious—he’s capable of using it, but never articulates exactly how to use the number.  Marcy and Lenny can’t do it, at least not properly—that’s why they need Max (and in this sense, the potential-donor relationship inverts).  Max’s comprehension of the number is a bit like saying that the human brain does a sort of natural calculus: when a baseball player dives for a ball, his brain naturally ‘calculates’, accounts for all the variables of the situation, and the player ends up with a solution that will put the ball firmly in his glove.  But a ball player couldn’t tell you how to do all those calculations—it comes naturally.  Max, once he’s comprehended the number’s value, performs this sort of mental math that allows him to see the hidden patterns.

Fiona Apple : (aside) “If there were a better way to go then it would find me /… Be kind to me or treat me mean / I’ll make the most of it”. Max is an extraordinary machine.

But Max eventually begins to break down.  His brain can’t handle this function; it exacerbates an existing mental condition caused by staring at the sun as a child—staring at the number too long has the same disastrous effect.  Sol suffers the same fate—he retired from his work after a stroke, and when he returns to it after his fight with Max, he shares Euclid’s fate.

It’s not about the number, but knowing how to use it.  Marcy attempted to use the number to play the market, resulting in financial disaster.   She knows the number, but Max understands it.  Max says that the key is not the number, but its “meaning, syntax”.  The Jews have an inappropriate hermeneutic—transcendence isn’t the answer.  “You’ve calculated every 216 digit number, you’ve intoned all of them, what has it gotten you?”  Utility isn’t the answer either—Marcy crashes the stock market when trying to control it.  The pursuit of pure understanding leads only to non-comprehension.

Max and Sol try to accommodate a formal system, while Euclid attempts to accommodate a removal from that system, an awareness of itself as constituted by the workings of its own formal system.  The only solution is to unknow quantity.  Sol and Euclid auto-terminate; Max self-trephinates, structurally deprives himself of the ability to deal with numbers, and is left only with the expression of the grand equation: the surface aesthetics of the natural pattern, that which arises from the numbers but is not the thing itself.

The universe as a fractal organic system.  The price for perfect knowledge, however, is disaster—pain, madness, fatality—for Max and the system, the stock market.  Euclid’s self-awareness gives us an insight object-cognition in the midst of an accident: that is, how does the object experience the disaster?  What is the object’s point of view?  In this case, how does the mechanical, the purely formal, react to the organic and irrational?  It self-destructs. (So does the organic when experiencing the pure insight of perfect mechanical logic—poor Max.)

The mechanical is purely formal, but the organic is irrational.  The organic circle, an undifferentiated unbounded curve defined by an irrational constant— π.

Mythematics

Myth – “A traditional story…which embodies and provides an explanation, aetiology, or justification for something…” In this case, a cultural conviction; an archetype.

Mytheme – after Lacan’s matheme; a symbolic representation of ideas and analyses.  In this case, the archetype or myth expressed in culture.

Thematic – “The subject of discourse, discussion, conversation, meditation, or composition; a topic.”

Mathematics – “Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations.”

[Quoted definitions are taken from Oxford English Dictionary Online.]