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? 

Metamythics

The myth shows itself in the incompatibility of formal with informal (irrational) systems.  The human mind, in dealing with pure formal logic, will break down; and the machine, when grappling with self-reference, will do the same.  The search for absolute truth in mathematics will break the human mind, and it will also break mathematics.

Dangerous Knowledge, or, the prehistory of π.  The myth is not a new one.

Metamythics: a step outside of the myth, the level-jumping of self-awareness so important to the constitution of the math-myth.  Mise en abyme – the story within the story; here, the inner is also the outer.  The figure is also its own ground—math en abyme.  Turtles all the way down.

The figure of the accident is self-reference, the point where logic is pushed into convulsion and refraction, overflows its bounds into a new logic.  The problem of infinite repeatability, the figure of the grid; there’s only space for metastatic extension, not for overflow past limit at the point of logical hemorrhage.

The figure of self-reference doesn’t directly present itself at Pruitt-Igoe.  This is appropriate, since the problem here is the formalism of mathematics; it shouldn’t be expected to supply a solution, especially since it’s a key component of disaster in the myth.  Pruitt-Igoe was a disaster of formalism and mathematics, but applied formalism and mathematics; self-reference, in π and Gödel incompleteness, arises out of more abstract mathematical endeavors.  Nonetheless, disaster arises from the application of mathematics to problems of human beings.  I feel like this will probably be useful in approaching the myth-logic as a contrast.

As seen in Mythematics III, the human and the technology are intertwined at Pruitt-Igoe; the mathematical architecture requires human agency to achieve its self-destruction.  We can see this also in Max’s relationship with Euclid.  In pure mathematics, we’re seduced into thinking that the problem is inherently there; but it took incredible acts of human creativity to set the conditions and bring the accident about.  Technology’s entelechy progresses toward disaster, with our help it finds its limit.

Focusing on the object’s circulation is too ego-centric; rather, shouldn’t we be paying more attention to how things circulate around the object?  Does Max’s number circulate amongst the characters, or do the characters circulate through the number?  Isn’t the Pruitt-Igoe disaster defined, not by the circulation of objects, but the circulation of the social relative to the object, supplying the all-important speed?  Didn’t Gödel allow mathematics to circulate within itself, and leave us to figure it out?

The voice of the object: “You’re all egotistical—that’s ok, I can work with that.  Here’s something shiny.  Isn’t that nice?  Life can be shiny too—you can live in the future, just stick with me.  Say, have you ever heard of Plato?”

The accident shows us ourselves.  (Achtung, baby: spoilers.)  A preference for applied research over pure research, practicality over creativity for creativity’s sake.  The humanistic study is self-destructing.  Cultural studies, theory, aims at elucidating and improving the cultural clusterfuck in which we find ourselves.  But here, we fall back on infinite repeatability—let’s apply Marx the same way we apply Newton—turtles all the way down, stripped of qualitative novelty, ready to slip quietly into the archive’s grid. 

Plato and Play-Doh: the persistence of consistency versus the fun of essential mutability.  Wouldn’t you rather sculpt than use a mold?

Mythematics III - Pruitt-Igoe

Pruitt-Igoe expresses the infinite exchangeability of housing as a commodity—little boxes in a row, each interchangeable with the next, all meant for similar residents.  Resident and architecture, as ideally undifferentiated, strike back with speed.  Pruitt-Igoe lasted only 22 years, from first habitation to final destruction.

Modern architecture is seductive because of its mathematical utopianism—the elimination of individual quality in favor of mass homogeneity.  The commodity needs us, but doesn’t care about us.  Pruitt-Igoe, as an object, seduced residents to act as its self-destruction.  The object isn’t capable of self-reference, but the mathematical design of the projects expresses its self-destruction in its effects on the inhabitants.  Or, as two undifferentiated masses, residents and architecture become a single object.

The mathematical principle invaded sociality—the massive population prevented residents from being able to discern intruders.  This stems from literacy’s metaphysical fascination with math and science, permanence and stability.  The metaphysics of electracy—wellbeing, pleasure and pain—are at work in the social workings, but toward the opposite end from what Yamasaki expected.  The anticipated outcome was mass cooperation; mass homogenization instead produced the opposite result, a predisposition to defect from the social good.  It acted as a strange attractor for the organization of mutual defection, rather than cooperation.  More rational than rational, it slips into irrationality and disaster.

The projects would have eventually decayed on its own, especially thanks to shoddy building materials (a defection in the zero-sum game of finance).  Humans intensified its degradation, increased the speed—and this resulted from the same conviction in mathematics, scientific technology, the children of literacy, that powers the apparatuses of electracy.  The object resists knowing through the intervention of the subject.  It foregrounds the obscenity of mathematics, where it overflows its boundaries, in trying to order human life according to aqualitative logic.  If electracy is about entertainment value, math fails because it seeks to eliminate all quality, all possibility of novelty and entertainment.

Mythematics II - Gödel Incompleteness

In the early years of the 20^th 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.]