A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).
- Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote comments/posts on LW/OB.
- No more than 5 quotes per person per monthly thread, please.
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!"
And so is skepticism of canonical Turing machines, as far as I can tell. Specifically, skepticism that there is always a fact of the matter as to whether a given TM halts.
I think you might be able to make the skeptical position precise by constructing nonstandard variants of TMs where the time steps and tape squares are numbered with nonstandard naturals, and the number of symbols and states are also nonstandard, and you would be able to relate these back to the nonstandard models that produced them by using a recursive description of N to regenerate the nonstandard model of the natural numbers you started with. This would show that there are nonstandard variants of computability that all believe in different 'standard', 'minimal' models of arithmetic, and are unaware of the existence of smaller models, and thus presumably of the 'weaker' (because they halt less often) notions of Turing Machines.
Now, I'm not yet sure if this construction goes through as I described it; for me, if it does it weighs against the existence of a 'true' Standard Model and if it doesn't it weighs in favor.
I'm not sure, but I think it's impossible to construct a computable nonstandard model of the integers (one where you can implement operations like +).