Rationality Quotes: February 2010

wedrifid

Rationality Quotes: February 2010 — LessWrong

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It seems to me that the definition of complexity is the root of any disagreement here. It seems obvious to me that the natural numbers are not complex in the sense that a human being is complex. I don't understand what kind of complexity you could be talking about that places natural numbers on an equivalent footing with, say, the entire ecosystem of the planet Earth.

SilasBarta16y00

Contrary to what SteveLandsburg says in his reply, I think you are exactly right. And this is how our disagreement originally started, by me explaining why he's wrong about complexity.

Scientists use math to compress our description of the universe. It wouldn't make much sense to use something infinitely complex for data compression!

So, to the extent he's talking about math or arithmetic in a way that does have such complexity, he's talking about something that isn't particularly relevant to our universe.

0Jack16y

I think the system of natural numbers is pretty damn complex. But the system of natural numbers is an abstract object and Dawkins likely never meant for his argument to apply to abstract objects, thinks all abstract objects are constructed by intelligences or denies the existence of abstract objects. I think there is a good chance all abstract objects are constructed and a better chance that the system of natural numbers was constructed (or at least the system, when construed as an object and not a structural analog, is constructed and not discovered. That is numbers are more like adjectives then nouns, adjectives aren't objects.)

-1SteveLandsburg16y

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.)

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