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!"
Well, if you need to simulate a squirrel for just a little while, and not for unbounded lengths of time, a substructure of N (without closure under the operations) or a structure with a considerable amount of sharing with N (like 64-bit integers on a computer) could suffice for your simulation.
The problem you encounter here is that these substructures and near-substructures, once they reach a certain size, actually require more information to specify than N itself. (How large this size is depends on which abstract computer you used to define your instance of K-complexity, but the asymptotic trend is unavoidable.)
If this seems paradoxical, consider that after a while the shortest computer program for generating an open initial segment of N is a computer program for generating all of N plus instructions indicating when to stop.
Either way, it so happens that the biological information you'd need to simulate the squirrel dwarfs N in complexity, so even if you can find a sufficient substitute for N that's "lightweight" you can't possibly save enough to make your squirrel simulation less complex than N.
Splat:
1)
This depends on what you mean by "specify". To distinguish N from other mathematical structures requires either an infinite (indeed non-recursive) amount of information or a second order specification including some phrase like "all predicates". Are you referring to the latter? Or to something else I don't know about?
2) I do not know Chaitin's de... (read more)