this post was submitted on 11 Apr 2024
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Turing Incompleteness is a pathway to many powers the Computer Scientists would consider incalculable.
Is it possible to learn this power?
Not from an algorithm.
No, but it's extremely possible to copy someone else's work on it from stack overflow!
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)
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)
Infinite by definition cannot be "low-balling".
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.
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.
Oh, sorry about that! Your cheekiness went right over my head. 😋
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.
Except they have convinced themselves that if it can’t be calculated it’s worthless.