|Simian Pride |
why would you want to turn a sphere inside out?
the sexual tension between Infomercial Joe and GLaDOS is staggering
|Robert DeNegro |
Why can't you crease the surface? Is it an arbitrary complication for chronic mathturbators or will it break the universe?
The "no creases" (or corners) constraint is there because the result isn't counter intuitive without it.
The constraint has to do with "immersions", that is a maps between spaces that are bi continuous and whose derivatives are injective (don't map two points to the same corner/crease).
It makes sense to me but I'm not sure how well I can explain it... that little pinchy loop would just be getting infinitely smaller and smaller but never actually "snapping" around to the other side.
Because a system that uses creases isn't useful for modeling the curvature of space time. So I guess that means maybe the Universe would break?
What are you guys talking about?
It is simple to create function that introduces creases into a volume; that's the problem, it is simple. If we don't care abou the constraint, the solution to "everting" the sphere would just be to pull it through itself and no one would care.
When we do introduce the "no creases" constraint, most of us end up being very surprised that it is possible (as this video shows it is); and that's why this is interesting.
Why does anyone care? It is interesting in the same way other neat little mathematical facts are interesting e.g. there are more irrational numbers than there are natural numbers.
In my limited research experience, the answer for "why is that constraint there" has always been "so I'd have a problem to solve."
HOW ABOUT A HYPERSPHERE HUH? HOW ABOUT THAT SMART GUY?
I can't believe this video managed to get me to understand this.
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