Sunday, March 8, 2009

Digitizing the Continuum

by Carlos Pedro Gonçalves

The reign of the digital imposes itself with the digitocracy over the continuum. The mathematical continuum, irreducible to the countable, is negated as interdict, as dangerous illegality.

Of mathematics, it is demanded a logocentered logicity, a reifying and imprisoning reduction that strives to reduce the semantic to the syntactic and, thus, extends the formal incompleteness to a semantics that does not possess it.

The mathematical intuition is substituted by the cold deduction that, incapable of scaling new horizons because it lacks imaginative capability, does not explore the mathematical idea and its apprehension by the mathematician that intuits it in a sensual immediateness produced by an imaginative synthesis, idea, itself, by nature, irreducible to a logical logocentrism, as Gödel proved it.

To scale new horizons… to think beyond the barriers of the code… dangerous activities… incompatible with a digitocracy extended to the mathematical activity itself. The formal language ceases being just an instrument of discursive organization and of formalization auxiliary to the proof, to become an instrument of thought control.

From abstractive auxiliars, the language and the formal system become instruments of alienation of the mathematical thinking itself, that, to think the formal, empty of semantics, loses its object of intentionality – the mathematical object, in itself, as abstract object of thought, which, as Gödel proved it, is irreducible to the purely syntactic, to the purely logical.

To digitize the mathematical continuum in the mathematical discrete means to abolish, from the thought, a universe of thinkable forms, to impose the limit of the digital, useful to an effort of computative mechanocracy in which the instrument of the number abolishes the analogical and, thus, the interval itself and the continuum. Without interval, without continuum, without shades, without infinitesimal differences, without empty spaces, thought as empty spaces because continua of nothing. End of the différance towards the end of the différence.

Even if different, digitized, we come to occupy the same houses in the bar codes in which we become, clones in our condition of slaves to the digit.

Badly interpreted Gödel’s theorem, to justify that the notion itself of mathematical truth is reducible to a logical validity, in a first step towards the algorithmization of truth, of geometry, of the continuum, of the interval, of the grey, of the individual as individual, separated from the rest, and non-slaved to the number… and non-slaved to a machine incapable of imagining, incapable of innovating, incapable of jumping outside the tyranny of the formal system, itself limited in itself and right from the point in which it deals with the numbers themselves and with simple arithmetic.

The end of the mathematician (second target), as well as the end of the philosopher (first target) are the two first steps to abdicate from our thought and from those natural systems of systemic homeostasis, thinkable as antibodies that protect us from the dictatorships of the formal and of the machines as ends in themselves.

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