SteveLandsburg

If you're going to write a book hundreds of pages long in which you crucially rely on the concept of complexity, you need to explicitly to define it. That's just how it works. If you know what concept of complexity is "the" right one here, you need to spell it out yourself.

Well, Silas, what I actually did was write a book 255 pages long of which this whole Dawkins/complexity thing occupies about five pages (29-34) and where complexity is touched on exactly once more, in a brief passage on pages 7-8. From the discrepancy between your description and reality, I infer that you haven't read the book, which would help to explain why your comments are so bizarrely misdirected.

Oh, and I see that you're still going on about axiomatic descriptions of squirrels, as if that were relevant to something I'd said. (Hint: A simulation is not an axiomatic system. That's 48 bajillion and one.)

Splat: Thanks for this; it's enlightening and useful.

The part I'm not convinced of this:

to simulate any biological creature, you need N plus a bunch of biological information

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.

Bo102010: Thanks for the kind words. I'm not sure what the community standards are here, but I hope its not inappopriate to mention that I post to my own blog almost every weekday, and of course I'll be glad to have you visit.

The only error is to refuse to "cash out" the meaning of "arithmetic" into well-defined >predictions, but instead keep it boxed up into one ambiguous term,

Silas: This is really quite frustrating. I keep telling you exactly what I mean by arithmetic (the standard model of the natural numbers); I keep using the word to mean this and only this, and you keep claiming that my use of the word is either ambiguous or inconsistent. It makes it hard to imagine that you're actually reading before you're responding, and it makes it very difficult to carry on a dialogue. So for that reason, I think I'll stop here.

Eliezer: There are an infinite number of truths of euclidean geometry. How could our finite brains know them all?

This was not meant to be a profound observation; it was meant to correct Silas, who seemed to think that I was reading some deep significance into our inability to know all the truths of arithmetic. My point was that there are lots of things we can't know all the truths about, and this was therefore not the feature of arithmetic I was pointing to.

Silas: I agree that if arithmetic is a human invention, then my counterexample goes away.

If I've read you correctly, you believe that arithmetic is a human invention, and therefore reject the counterexample.

On that reading, a key locus of our disagreement is whether arithmetic is a human invention. I think the answer is clearly no, for reasons I've written about so extensively that I'd rather not rehash them here.

I'm not sure, though, that I've read you correctly, because you occasionally say things like "The Map Is Not The Territory" which seems to presuppose some sort of platonic Territory. But maybe I just don't understand what you meant by this phrase.

[Incidentally, it occurs to me that perhaps you are misreading my use of the word "model". I am using this word in the technical sense that it's used by logicians, not in any of its everyday senses.]

mattnewport: This would seem to put you in the opposite corner from Silas, who thinks (if I read him correctly) that all of physical reality is computably describable, and hence far simpler than arithmetic (in the sense of being describable using only a small and relatively simple fragment of arithmetic).

Be that as it may, I've blogged quite a bit about the nature of the complexity of arithmetic (see an old post called "Non-Simple Arithmetic" on my blog). In brief: a) no set of axioms suffices to specify the standard model of arithmetic (i.e. to distinguish it from other models). And b) we have the subjective reports of mathematicians about the complexity of their subject matter, which I think should be given at least as much weight as the subjective reports of ecologists. (There are a c), d) and e) as well, but in this short comment, I'll rest my case here.)