A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).
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ETA: It would seem that rationality quotes are no longer desired. After several days this thread stands voted into the negatives. Wolud whoever chose to to downvote this below 0 would care to express their disapproval of the regular quotes tradition more explicitly? Or perhaps they may like to browse around for some alternative posts that they could downvote instead of this one? Or, since we're in the business of quotation, they could "come on if they think they're hard enough!"
Your biggest problem here, and in your blog posts, is that you equivocate between the structure of the standard natural numbers (N) and the theory of that structure (T(N), also known as True Arithmetic). The former is recursive and (a reasonable encoding of) it has pretty low Kolmogorov complexity. The latter is wildly nonrecursive and has infinite K-complexity. (See almost any of Chaitin's work on algorithmic information theory, especially the Omega papers, for definitions of the K-complexity of a formal system.)
The difference between these two structures comes from the process of translating between them. Once explained properly, it's almost intuitive to a recursion theorist, or a computer scientist versed in logic, that there's a computable reduction from any language in the Arithmetic Hierarchy to the language of true statements of True Arithmetic. This implies that going from a description of N to a truth-enumerator or decision procedure for T(N) requires a hypercomputer with an infinite tower of halting, meta-halting, ... meta^n-halting ... oracles.
However, it so happens that simulating the physical world (or rather, our best physical 'theories', which in a mathematical sense are structures, not theories) on a Turing machine does not actually require T(N), only N. We only use theories, as opposed to models, of arithmetic, when we go to actually reason from our description of physics to consequences. And any such reasoning we actually do, just like any pure mathematical reasoning we do, depends only on a finite-complexity fragment of T(N).
Now, how does this make biology more complex than arithmetic? Well, to simulate any biological creature, you need N plus a bunch of biological information, which together has more K-complexity than just N. To REASON about the biological creature, at any particular level of enlightenment, requires some finite fragment of T(N), plus that extra biological information. To enumerate all true statements about the creature (including deeply-alternating quantified statements about its counterfactual behaviour in every possible circumstance), you require the infinite information in T(N), plus, again, that extra biological information. (In the last case it's of course rather problematic to say there's more complexity there, but there's certainly at least as much.)
Note that I didn't know all this this morning until I read your blog argument with Silas and Snorri; I thank all three of you for a discussion that greatly clarified my grasp on the levels of abstraction in play here.
(This morning I would have argued strongly against your Platonism as well; tonight I'm not so sure...)
Splat: Thanks for this; it's enlightening and useful.
The part I'm not convinced of this:
A squirrel is a finite structure; it can be specified by a sequence of A's, C's, G's and T's, plus some rules for protein synthesis and a finite number of other facts about chemistry. (Or if you think that leaves something out, it can be described by the interactions among a large but finite collection of atoms.) So I don't see where we need all of N to simulate a squirrel.