topotorus123

Great vid! (Was rather cringe though when he eats the toilet dunked donut. Some years ago I recall the Exploratorium science museum in SF had a psychology exhibit consisting of a toilet drinking fountain made from a toilet that had never been used. The question posed was, if you aren't willing to drink from the toilet fountain, why not? It's hard to articulate why so many of us find it gross even if we are logically perfectly aware there isn't a sanitary risk.)

Extremely helpful, thank you!

> We observe that a lion has the connectivity of the torus

Dear topologists of HN, how do I visualize the deformation of a lion made of clay into a donut, if we model that a biologically accurate lion has one entrance orifice for solids and liquids and not one, but two, exit orifices which form a connected cave system inside the lion? (We may ignore nostrils, lungs, skin pores, and all other orifice systems.)

I was looking at the Wikipedia genus article:

https://en.wikipedia.org/wiki/Genus_%28mathematics%29

If my layman's understanding is correct, this means if we start with a clay sphere of genus 0 and bore a hole through the center of it we get genus 1, a torus. If we continue to bore additional holes through the center of the sphere that connect to our existing cave system we never get to genus 2, because with genus 2 you have two separate cave systems, a lump with two holes A and B such that entering hole A to explore it means that you can't explore hole B until you first exit hole A, so I conclude we must remain at genus 1.

But I don't see how you do a continuous deformation of a clay lump with three or more entrances into tunnels that meet in the middle into a donut with only one hole.