Notational

Conversations with each other are the way children learn to have conversations with themselves, and learn how to be alone. Learning about solitude and being alone is the bedrock of early development, and you don’t want your kids to miss out on that because you’re pacifying them with a device.

Large portions of this section were written in a hotel in Ban Hat Yai, Thailand, which is one of the information-transfer capitals of the planet regardless of whether you think of information transfer as bits propagating down an optical fiber, profound and complex religious faiths being transmitted down through countless generations, or genetic material being interchanged between consenting adults. Male travelers approaching Ban Hat Yai will have a difficult time convincing travel agents, railway conductors, and taxi drivers that they are coming only to look at a big fat wire, but the hacker tourist must get used to being misunderstood.

I’M ALWAYS PRONE to do things very quickly, which has distinct advantages - you leave all the mistakes in, and the mistakes always become interesting. The Velvet Underground, for example, are the epitome of mistake-filled music, and it makes the music very subtle and beautiful.

This is a brief summary of my thoughts regarding the discussion on mathematics in Alex Galloway’s paper as well as some of the recent instigations against mathematics by the likes of Laruelle. Needless to say, I’m all for a speculative realist-bashing festivity but in a climate where vague approximations and arguments by way of juxtaposition are not rules of the game. And of course this is just a facebook comment: My first problem with this paper is that it keeps conflating algorithmic structures / computer science with mathematics despite making clear that the latter is a ‘part’ of mathematics. First there is an asymmetry between mathematics and computational science. This asymmetry is not in terms of size but is in terms of foundations, structures and trajectories. Overextending the critique of computational science and algorithmic domain into a critique of mathematics – by being so oblivious to this asymmetry – is metaphysically inflated at best and parochially misinformed at worst. The asymmetry between mathematics and computational science lies in the what defines the trajectory of the former versus the latter. Mathematics is ‘construction principles’ (gestural combinatorics, geometry, abductive inference, modalization, concept-mobilities, invariance preservation and transformation, manipulative hypothesization, etc.) plus ‘proof principles’ (logics, axiomatics, formalism). Constructions are responsible for generativity of mathematics and proofs responsible for its effectivity. Now the global landscape of mathematics is demarcated by the combination of both constructions and proofs (two very different domains) while its overall trajectory is defined by the excess of construction over proof, generativity over effectivity.

Computational science with its algorithmic approach, on the other hand, is a systematically finitized math where construction principles of mathematics are completely controlled in favor of *certain modes* of proof principles. In other words, the horizon of computational science is delimited by proof principles (algorithms are simply systems for operationalization of certain proof principles), and its trajectory is defined by the strict finitization of construction principles, that is to say, by limiting the generativity of mathematics. For this reason, computer science exhibits a unidirectional shift from mathematical generativity to mathematical effectivity. Digital machines and computational algorithms fully reflect this shift to effectivity by means of a very tight control over construction principles (geometry in particular). Therefore, the implicit goal of these machines is to be effective (i.e. operationalizing the effectivity of certain mathematical proof principles). The asymmetry between mathematics and computer science (algorithms, etc.) is both a matter of the constitution of the domain (construction and proof versus operationalized proof) and a matter of the trajectory of the horizon (if it is driven by the excess of generativity over effectivity or if it is driven by pure effectivity by way of restricting the generativity).

This asymmetry is unilateral, one can go from the generic domain of mathematics toward computation in various directions, but you cannot reflect on mathematics through computational science, there is no logical, epistemological or ontological map that allows such a move. So to say that “Simply put, software is math.” and then ameliorating it by adding “Computer science is a division of mathematics.” is like reminding yourself that you don’t have a foot but going on to shoot yourself in the foot anyway. Software is NOT mathematics, it is an operationalized product of a particular dimension of mathematics (namely, proof principles) that neither synthesizes the entirety of the landscape of mathematics nor defines its global trajectory. To castigate and ahistoricize mathematics and its ambitions by way of such conflation is precisely in line with the ideological core of today’s monopoly of computation and by extension, its exploitation by global capitalism (transforming the effectivity of the program to its own programmatic efficacy): They both coincide in degrading mathematics to a program of pure effectivity, one by virtue of its programs whose goals entail damming the unreasonable trajectory of reason (best manifested in the unreasonable generativity of mathematics which is always in excess over its reasonable effectivity), the other by by virtue of a potentially ideologizable and dangerous conflation that obscures the global landscape and the overall trajectory of mathematics. More or less with the same degree but by taking different paths, both contribute to the status quo of the cult of capital.

It is perhaps helpful here to point out that Badiou’s mathematics and Meillassoux’s mathematics – two seemingly similar but principally different takes on mathematics – are merely functional and topographic fractions of the domain of mathematics. Mathematics is neither set theory nor solely a systemic discourse shaped around the empty sign (Meillassoux) even though the latter astonishingly unbinds a very broad scope of mathematics in which the generative mechanisms of mathematics – contingency and continuity – find their true expressions (cf. Peirce). Note that Meillassoux however in his recent paper on iteration and the free sign restricts the operation of the free and empty sign to contingency alone which again results in an entirely new set of shortcomings for outlining the landscape of mathematics and its true capabilities. As a discipline endowed with maximal conceptual stability in which both universal adjoints of conception – the conditioning of the concept by the real and the oblique and asymptotic traction of the concept on the real – are present, mathematics is the constitutive gesture of knowledge, a realm through which thought non-classically stabilizes itself. Insofar as mathematics is the constitutive ‘gesture’ of knowledge (yet not the totality of knowledge) and by the virtue of the primacy of knowledge over any imperative, mathematics cannot and should not be, by any means, ejected from the global structure of thought or praxis on any level. Also, from a different perspective, the unreasonable generativity of mathematics sublimated in various modes of geometrical inference where normativity does not essentially repeat the initial and boundary conditions of reason (i.e. being reasonable) is one of the most promising trajectories for programming the next paradigm of machines whereby the efficacy of capitalism (effective only insofar as it is narrow in scope) is supplanted by the improvisational competence or effectivity of geometric metis, a different trajectory of reason ultimately inassimilable for the programmatic kernel of capitalism.

However, in complete accord with Alex, we should not forget that there is always a temptation to turn mathematics into the calculus of dogmatism and imperial education of thought and philosophers. It is against these pigeonholed biases that people like Zalamea, Longo and Lawvere should be enthusiastically read and embraced.

Now on to Laruelle: I feel that resurgence of some of these currents against mathematics is strongly influenced by Laruelle’s general attitude toward mathematics, itself a pure overreaction to an admittedly restricted and partially biased philosophies of mathematics saturated by an overzealous Platonist interpretation of mathematics, rather than mathematics as a universal and irreconcilable tension space between Plato and Aristotle. This has pushed Laruelle to embrace a so-called alternative to the alleged dominion of mathematics: physics instead of mathematics. I will go into details in another post about all this but suffice to say that the prioritization of math over physics or vice versa reminds me of math and physics freshmen who cluelessly rant about the priority of their respected disciplines (Mine is the first science yours is shit!). There is an absolute and insurmountable entanglement between mathematics and physics (whether quantum or relativity) from the perspective of mathematical constructions. This is the complete imbrication of physics and mathematics on the level of mathematical structures. There is no physics without mathematics. The latter allows for the articulation of the intelligibility for the former. This is exactly the perspective of modern physics following physicists like Einstein, Schrodinger and Weyl: physics – both quantum and relativity – is “geometry in action” (Boi). It is because geometry (where the role of regularities of space and time in mathematics surpasses that of logics and formalism) is but construction principles and mathematical structures (products parametrized by invariances of spacetime) and as I said, modern physics is at the base, the domain of mathematical structures (geometry of affines, metrics and connections) and their operativity. The separation between math and physics takes place on the level of their respective proof principles: logics and formalistic calculi for mathematics and experience and observation for physics. But even on this level, one should be extremely cautious of the subtle micro-entanglements between physics and mathematics. Physics without math is merely a philosophical or folk theoretical myth. Likewise, mathematics abstracted and purified from physics is a cheap joke told over and over again at the expense of Plato. The gestural origins of mathematics highlights precisely the intrusion of physics into mathematics into physics into mathematics … all in an entangled disequilibrium that at each instance generates a more ample space of navigation for the propulsion of theoretical reason. The importance of Chatelet (following Oresme, Descartes, Newton and Maxwell) lies in the very fact that he performs a full-scale mythoclastic operation against the fiction of math purified from physics in his treatise ‘The Stake of the Mobile’.

Ok I don’t think this facebook post can take anymore. More later.

No problem should ever have to be solved twice.

Creative brains are a valuable, limited resource. They shouldn’t be wasted on re-inventing the wheel when there are so many fascinated new problems waiting out there.

To behave like an artist, you have to believe that the thinking time of other artists is precious – so much so that it’s almost a moral duty for you to share information, solve problems and then give the solutions away just so other artists can solve new problems instead of having to perpetually re-address old ones.

Boredom and drudgery are evil.

Artists (and creative people in general) should never be bored or have to drudge at stupid repetitive work, because when this happens it means they aren’t doing what only they can do – solve new problems. This wastefulness hurts everybody. Therefore boredom and drudgery are not just unpleasant but actually evil.

To behave like an artist, you have to believe this enough to automate away the boring bits as much as possible, not just for yourself but for everybody else (especially other artists).