Incomputable Aesthetics: Open Axioms of Contingency is a big read. I’ve looked up the definitions of ontology and epistemology more times in the last week that I care to admit. It’s fair to say I don’t yet feel comfortable using them in a sentence. This write up is (like most) an attempt to organise my thoughts as I dig through this pile of long words. It seems worth it though!
Fazi opens his argument with a summary of the work carried out by Alan Turing in developing the thought experiment of the Universal Turing Machine (UTM). Turning, inspired by the research of David Hilbert and Kurt Gödel, later proved that there are certain incumputable functions which the UTM could never solve, thus putting limits to what can be computed, and giving rise to the notion of computable numbers. Fazi uses this work, from 1936, as a basis for his argument that in fact the inherent indeterminancy in computation with is concern for the ‘intelligable and sensible alike’:
For the aesthetics of computation, I wish to argue, this proposition involves a reassessment of the potential of its formal structures. This is because the proposed ontology of the contingent computational structure allows us to think computational forms beyond the limits of formulae, and to engage with formalism beyond the idealisation of beautiful and truthful determinisms.
Fazi then goes on to talk about how current and traditional computational systems (Turing-like) are largely axiomatic, in that ‘they involve a starting point that is self-evident, and which defines the inferential steps that can be taken from it towards a result via the manipulation of a list of finite instructions’.
…computationalism has had something of a bad press, most significantly due to its implicit assumption that the rationalising calculations of formal axiomatic systems might be able to account for the entirety of the thinkable and the doable.
New conceptualisations of the computing machine have been proposed … non-Turing or post-Turing explorations of computability, which attempt to open axiomatics to the biological and the physical realm, preferring the inductions of empirical sciences to the deductions of logic.
I presume here there is a conflict between the empirical and the rational (which I now know are two modes of thought from the world of epistemology). Where the rational is in fact showing it’s limits. But Fazi is arguing that these moments where the rational “fails” in it’s presuppositions show a future in an alternative way of thinking about computation as an indeterminate but rational system.
Gottfried Wilhelm Leibniz envisioned a complete discipline which he called mathesis universalis through which one would have ‘been able to design a compendium of all human knowledge’:
by specifying the rules of the game, expect that we can also know what we can achieve by playing it.
Fazi applies this ideal to computation and names it Universal Computation.
In the metaphysics of Universal Computation, computational abstraction is above the empirical: software rises above hardware.
Drawing parallels from Keats’ poetry and Jaromil’s ASCII Fork Bomb (which I can’t re-produce here because it messes with the Markdown to CSS formatter), Fazi says:
It is my contention that Universal Computation justifies and grounds, both ontologically and epistemologically, this classicist equivalence between beauty and truth … metacomputational abstraction thus enters computational culture and its aesthetics in terms of a commitment to a non-sensuous conception of the aesthetically worthy, and translates into classicist concerns such as beauty, elegance, harmony and simplicity. Logical necessity, on this view, becomes an aesthetic value, pertaining to closed, self-referential rules that are deductively true under all circumstances.
I like Fazi’s interpretation of Jaromil’s Fork Bomb. By admiring the beauty in the nature of the program, which does exactly as it intends to do in as consice a way as is thought to be possible. And in it’s exectution it finds the physical limits of the machine on which it operates. The aesthetics of such a program does have quite important implications, as it suggests there is a elegant aesthetics to behold with computation, to create somethings which explores it own potential, whilst providing us (as hoomans) with a beautifully-complex system to pick apart and understand.
When Fazi says that with ‘Universal Computation and mathesis universalis on the one hand, and the aesthetics of computational idealism that is grounded on them on the other’ I understand it to mean that
In Ordering the Real: Forms become Formulae, Fazi explains that axiomatisation, within which symbolisation is a part, is a central part of computer programming where ‘complex statements are reverted into higher principles and into an alphabet of symbols’. Through further abstraction in mathematics:
Deductive abstraction becomes, then, formulisation: partly a tool to uncover the a priori principles of valid thought, and partly an instrument to enumerate these intelligible principles via the mechanisation of reasoning through symbols and formal languages.
I think Fazi takes this notion of abstraction to see beyond the ‘proofs’ of logical and deductive reasoning and to suggest that there is a layer of onto-epistemology which exists through these layers of indeterminancy.
This demonstration, I believe, does not amount to saying that beauty and truth do not exist. Rather, it shows that there cannot be a ‘golden ratio’ that will provide us with the exact proportion of their relation.
Gödel’s proofs of incompleteness and Turing’s computational limits can be understood to have rephrased the impossibility for man-made formal encodings to exactly mirror the empirical world.
[A slightly premature summary] What I think Fazi is getting at, is that there exists a higher plane of (I’m going for it) ontology and epistemology within computation which is based on a formal, axiomatic system, which we (hoomans) can understand and design. But within that there is a certain aesthetics which must allow for the furthur abstraction of these axioms and forms, to something which is not inherently designable. To use another phrase I don’t fully understand: it’s like the entropic nature of the system, which when a certain complexity and abstraction is reached, it cannot be reverse-engineered.
The pre-programmed axiomatic rule itself contains an internal level of undecidability that cannot be systematised by rationing, measuring and counting, despite the fact that it is exactly these actual procedures of systematisation that engendered the very possibility of such undecidability.
From the standpoint of an incomputable aesthetics, however, the relation is already immanently established with every computation, because the formal structure has its own way of being eventual, and therefore of ‘experiencing’ insofar as it determines itself vis-à-vis indeterminacy. Via the notions of incompleteness and incomputability one discovers that the inherent indetermination of computation pertains to its intelligible dimension, and that this indetermination is encountered by way of abstraction: this is a formal indeterminacy, not an empirical one.
It is worth noting here that Fazi sees the ‘incomplete and incomputable’ as lenses through which to see the abstractions beyond, which are partly made acheivable by ideas of infinity, which computation can provide.