Replying to my last post on Chaitin, Noah Horwitz (who is working very closely with Badiou and Wolfram as am I) comments on the potential similarities and differences of our position. It’s an important conversation, so its worth elevating to its own post as it were. His original comment is here, but I’ve directly copied what Horwitz thinks regarding OOO and computation.
We are also different in that I think OOO is essentially a dead-end and misguided approach. Objects cannot be sets of irreducible complex bit strings in the OOO sense. I do not think OOO can even admit the notion of the bit. OOO is transposing Husserlian intentional objects onto being itself in act of reification (with the caveat that they ‘withdraw’–which just means their unity is not perceivable and only intended ultimately– and perceive each other–although there is no phenomenological analysis of the analogy from human perception that could flesh out such a claim in the way Husserl gives such an analysis in Cartesian Meditations relative to subjectivity). If an OOO object were a set of non-compressible bits, then the object itself would be the computation of those bits. That means one has a formula that captures the object itself as such. The conception of the thing and the thing would be the same. It’s then just a matter a la’ Woflram to see how that computation plays out. The bit I argue involves the existence of the void, numbers, pure differentiality, etc. Admitting that things are bit strings means admitting that at bottom there is an ‘atom’ and that atom is relationality in itself. It’s not surprising that OOO has nothing to my knowledge to say about numbers as objects or the nothing/void as non-object.
It’s a fairly decent criticism I think, especially in light of the subject he’s talking about (Computation and theology) But from this statement alone (I’ve not read the book). There are (at the very least) three things going on here; let’s list them.
1.) Defining information
I do not think OOO can even admit the notion of the bit.
I think OOO can admit the notion of the bit, but it lies in a different ontology from the recursive formalism upon which the bit is normally derived – ‘objects’ in OOO are just indifferent discrete finite units in my mind, so there is a clear link there. It depends on which OOO-theorist you wish to refute, but I’d imagine the same reply would surface: there is no co-determination between mind and bit, where the two are basic equivalencies of thought and Being. This is something OOO strictly denies, whilst Horwitz whom Iknow is also committed to Badiou, would probably follow (I’m presuming, not stating directly). I would personally uphold the notion that information can only be related to by input and output; my own position (which I’m tentatively calling Actor Recursion Theory) suggests that the recursive procedures, built on symbolic logic and physical computational infrastructure (of all actual kinds, past, present and future) are themselves real, not the bits they calculate or spit out.
The only possible link refuting this are the uncomputable real numbers which perhaps favour a different mode of withdrawal.
2.) Defining computational equivalence in an object oriented ontology.
If an OOO object were a set of non-compressible bits, then the object itself would be the computation of those bits. That means one has a formula that captures the object itself as such. The conception of the thing and the thing would be the same. It’s then just a matter a la’ Woflram to see how that computation plays out.
I disagree. This isn’t about the ontological execution of non-compressible bits. Because seeing how a given program plays out or executes is the OOO unknowable – epistemological act par excellence. One may have the formula, the rules, the axioms, symbolic language, the number of N bits – but the actual work executed by the thing is not the thing in the mind, but the computation executing it ontologically in it’s own specific actual execution. One cannot have any direct knowledge of what these determinate rules will offer, (a la’ Hume) other than repeating the rules again and again under the same initial conditions, but even then the information produced is still structurally random – and the key insight here is the discovery that no algorithm has the capability or computational sophistication to always-already reduce the output to its formula whether it is another algorithm or a human mind.
This is where Chaitin’s Algorithmic Information Theory and Wolfram’s mining of the computational universe meet – although there is one key difference between Chaitin and Wolfram in this regard, Chaitin’s level of complexity is vastly different from Wolfram’s. Chaitin’s theorems start out from Universal Turing Machines and get more complex from there, while Wolfram believes that no entity can reach a higher complexity than a Universal Turing Machine. This is where Wolfram’s ‘Principle of Computational Equivalence’ draws it power by setting a maximum limit of function available to an entity and thus making it equal by default of computational sophistication. Again, I’d argue that this chimes with the OOO statement that every computational-executant entity is on an equal footing and apprehends it in a similar manner, albeit my own take on Wolfram is different from Harman’s Husserl influence.
3. Badiou’s Anti-contrucivsism
The bit I argue involves the existence of the void, numbers, pure differentiality, etc. Admitting that things are bit strings means admitting that at bottom there is an ‘atom’ and that atom is relationality in itself. It’s not surprising that OOO has nothing to my knowledge to say about numbers as objects or the nothing/void as non-object.
This I feel is where the crucial difference lies and it has to do with a particular viewpoint (which Badiou has unfortunately started) that conflates any philosophical discussion involving pure mathematics (and hence computation) with anti-constructivism. Stating that OOO has nothing to say about numbers or the void in set theory depends on which side of mathematical analysis you reside: constructible or immanent. I don’t think OOO has anything to say on numbers and the void as non-object mainly as it resides in a mereology which submits to a constructive ontology. This is the Leibniz relation.
Before you actually start to take Badiou seriously in his endeavour which submits an argument that ZF set theory discourse explains what is expressible ontologically, you have to realise what Badiou’s philosophical intention is. And bluntly put, his intention is to privilege an efflorescent, immanent conception of number and set theory which is always-already unbounded in presentation. In so doing, Badiou despises and ridicules any discussion involving the construction of numbers outside of presentation, in the form of rules and general syntax. Why? There are a ton of reasons, but suffice to say two will do for this post.
The first reason is to do away with the importance of language and grammar in mathematical construction, because (understandably) he despises the Wittgenstein idea that numbers are constructed in a post-structural or analytic sense – for this destroys the potential for generic truth. The second reason is that constructible numbers don’t fit into his anti-Heideggerian schema in setting up an eventual politics for deciding upon the undecidable, because it submits a line of praxis whereby;
‘it is precisely around the exclusion of the indiscernible, the indeterminate, the un-predicable, that the orientation of constructivist thought is built. If all difference is attributed on the basis of language and not on the basis of being, presented in-difference is impossible.’ (Being and Event p.319: Mediation 30 on Leibniz)
But Badiou doesn’t hold a monopoly on the undecidable just for subjective truth procedures. Just because constructible thought has different goals concerning the political mode of thinking ( in particular the ‘state’ succeding the situation, and the basis of artificial symbolic language), it doesn’t mean it can be surpassed by ridiculing Leibniz and/or ignoring the vast historical work of mathematicians working with the concept of computers, where surprises do occur in recursive rules. Turing repeatedly stated this (for reasons derived from Hilbert’s Formal axiomatic systems no less!) Badiou seems to think that submitting to a constructible universe posits a static, decidable, discernible mode of thinking which fails to measure up to the novelty of militancy. Ask any computer scientist, or programmer worth his/her salt if this is the case, I’m sure you won’t get a positive answer back. Constructible recursive rules do produce invention and novelty, and they do so without being reducible to thought or counting.
In my opinion, I’ve seen no evidence (apart from his very early essays) of any attempt from Badiou to actually take computation seriously – and this is probably why; because Badiou does not like the idea that a computer can actually execute logical statements equivalent to human thought. But this can’t be ignored, because formalism and ZF theory relies on recursion. Axioms often don’t work out the way mathematicians want them to.