Science Memes

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this one goes out to the arts & humanities (mander.xyz)

submitted 8 months ago by [email protected] to c/[email protected]

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[–] CowsLookLikeMaps 4 points 8 months ago* (last edited 8 months ago) (1 children)

In fact, there's infinite problems that cannot be solved by Turing machnes!

(There are countably many Turing-computable problems and uncountably many non-Turing-computable problems)

[–] [email protected] -1 points 8 months ago (2 children)

Infinite seems like it's low-balling it, then. 0% of problems can be solved by Turing machines (same way 0% of real numbers are integers)

[–] CowsLookLikeMaps 2 points 8 months ago (1 children)

Infinite seems like it's low-balling it

Infinite by definition cannot be "low-balling".

0% of problems can be solved by Turing machines (same way 0% of real numbers are integers)

This is incorrect. Any computable problem can be solved by a Turing machine. You can look at the Church-Turing thesis if you want to learn more.

[–] [email protected] 1 points 8 months ago (1 children)

Infinite by definition cannot be “low-balling”.

I was being cheeky! It could've been that the set of non-Turing-computible problems had measure zero but still infinite cardinality. However there's the much stronger result that the set of Turing-computible problems actually has measure zero (for which I used 0% and the integer:reals thing as shorthands because I didn't want to talk measure theory on Lemmy). This is so weird, I never got downvoted for this stuff on Reddit.

[–] CowsLookLikeMaps 3 points 8 months ago

Oh, sorry about that! Your cheekiness went right over my head. 😋

[–] [email protected] 1 points 8 months ago (1 children)

The subset of integers in the set of reals is non-zero. Sure, I guess you could represent it as arbitrarily small small as a ratio, but it has zero as an asymptote, not as an equivalent value.

[–] [email protected] 1 points 8 months ago

The cardinality is obviously non-zero but it has measure zero. Probability is about measures.