platonism and randomness

My favorite part of How We Became Posthuman so far is Hayles' description of the Platonic backhand and forehand. The first process, the Platonic backhand, describes the way in which the world is transformed in the human mind from dirty special cases to beautiful abstractions. She claims that humans see the world's inconsistencies as exceptions to rules because they create descriptive systems and treat them as prescriptive ones. The second process, the Platonic forehand, describes the recent tendency among such theorists as Stephen Wolfram to claim that simple rules generate the complexity of the world through sufficiently gnarly cellular automata or other similar formal systems.

Over the summer I read a book by Gregory Chaitin called The Quest for Omega. In it, he discusses the mathematics of randomness and undecidability and does a wonderfully accessible job of proving that all formal systems must be incomplete. He also reveals the philosophical implications of of such proofs. In his mathematical description he shows that finite axiomatic systems, which are an abstraction of all systems which start with axioms and rules and then derive 'truths' from them, are necessarily incomplete. That is to say, there will be facts which are true in the real world which will be unprovable in such systems. The systems he treats in his proof are analogous to the systems which the Platonic forehand generates.

According to Hayles, applications of the Platonic forehand have worked to separate information and materiality. I wonder if it would be possible to demonstrate that all rigorous abstractions generate fallacies like these. The universe has been shown to include randomness as a constituent by quantum mechanics, and mathematics has been shown to include randomness by Chaitin. Any extraction of abstraction from a system which includes randomness must fail with nonzero probability.

I believe that applications of both the Platonic forehand and backhand lead to inconsistent theories of the world. In the search for truth it is best to keep truth in your sights. To ignore the randomness, the "noise", or the "fuzz" (as Hayles calls it) is to ignore truth. With no amount of effort will humans be able to compress the universe into a series of axioms and theorems.