• they/she

wondering poet, codeweaver. systems have souls; souls have systems.

<3 @effinvicta


lea
@lea

So I was looking through my bookmarks and I came across a really good Quora post (a good Quora post, that's crazy) that explains how to solve this. It scares me.


ireneista
@ireneista

it doesn't say 5% can solve it. it just says (at least) 95% can't.


You must log in to comment.

in reply to @lea's post:

in reply to @ireneista's post:

it would be cool if we could have a nice algorithm that tells us if a given equation has integer solutions. but such an algorithm cannot¹ exist by a halting problem argument².

i.e., this sort of question (find integer solutions for some simple-looking equation) can't be solved by any kind of general method. this is because you can convert a Turing machine into one of these "find integer solutions to this equation" Diophantine equation problems. the computability theorists have figured out a lot of impossibility theorems about Turing machines, so we can transfer these theories over to the study of Diophantine equations

  1. see https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem for details
  2. a lot of "this algorithm does not exist" proofs are based on finding some equivalence to the halting problem. https://en.wikipedia.org/wiki/Halting_problem

a similar argument works for the field of Partial Differential Equations (PDEs). there is no general theory of how to solve them, because you can embed arbitrary computational problems into the language of PDEs. same idea.

It's the low-res janky-colored fruit, that's the part which makes you feel dumb for not getting it.

Also I am so terribly glad it's not something obvious I overlooked because of the shitty clip art variables, that would be embarrassing.