These Shapes Are Topologically Equivalent
twitter.com
These Shapes Are Topologically Equivalent
1–10 of 32 posts
Re: These Shapes Are Topologically Equivalent
#2I feel like this is a trick in many wood & string puzzles.
Re: These Shapes Are Topologically Equivalent
#3I feel like this is a trick in many wood & string puzzles.
I had the same initial impulse, but I think the transformation 1 -> 2 can't work irl. especially if those are compact solids.
Edit:
2->3 also seems impossible. you basically move the hole around.
Re: These Shapes Are Topologically Equivalent
#4The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!
Re: These Shapes Are Topologically Equivalent
#5I feel like this is a trick in many wood & string puzzles.
No, you can't do this trick with wood and string. Try tracking what would happen to the "string" joining the two loops.
Re: These Shapes Are Topologically Equivalent
#6The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!
Thanks for clarifying. It was unclear to me what they meant by "topologically equivalent". In other words, I didn't see what the problem was...
Re: These Shapes Are Topologically Equivalent
#7I feel like this is a trick in many wood & string puzzles.
I had the same initial impulse, but I think the transformation 1 -> 2 can't work irl. especially if those are compact solids. Edit: 2->3 also seems impossible. you basically move the hole around.
You can do it IRL with something like plasticine.
Re: These Shapes Are Topologically Equivalent
#8Topology seems like a field AI could help isnt? Cant AI generate topology equivalent shapes for example?
Re: These Shapes Are Topologically Equivalent
#9Topology seems like a field AI could help isnt? Cant AI generate topology equivalent shapes for example?
[deleted]
Re: These Shapes Are Topologically Equivalent
#10Topology seems like a field AI could help isnt? Cant AI generate topology equivalent shapes for example?
I do research mostly in general topology and topological dynamics, but I don't really see how AI would help, producing homeomorphic (topologically equivalent) spaces is not really the point.
In general even presenting a topological space to a computer is not easy. This can be done for very good spaces, for example those admitting (finite) triangulations, and there are some algorithms there, but my understanding is that you run into undecidability issues very quickly. But for the kind of spaces I work with (which are usually compact metrizable connected, so way better than arbitrary topological spaces) there seems to be no hope to get a computer to work with them.