Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

SilasBarta comments on The mathematical universe: the map that is the territory - Less Wrong

68 Post author: ata 26 March 2010 09:26AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (119)

You are viewing a single comment's thread. Show more comments above.

Comment author: SilasBarta 14 April 2010 04:14:33PM *  2 points [-]

It just happens, in our reality, that rocks satisfy Peano arithmetic (and don't resonate daughter rocks).

Well, it's complicated by the fact that rocks can break, which means that you need to go into a lot more detail to say the extent to which the standard axioms of math map to rocks. This is why simplistic proofs of 2+2=4 by reference to rock behavior are so misleading and unhelpful.

It's important to unpack exactly what is meant by "2+2=4". The most charitable unpacking I can give is that it means both:

a) There exists an axiom set under which (by implication, not definition), 2+2=4.
b) That axiom set has extremely frequent isomorphisms to (our observations of) physical phenomena.

But most people's brains, for reasons of simplicity, truncate this to "2+2=4". The problem arises when you try to take this representation and locate it somewhere in the territory, in which case ... well, you get royalties from The Big Questions, but you're still committing the mind-projection fallacy :-P