[HN Gopher] The Math of Hunting Lions
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       The Math of Hunting Lions
        
       Author : finite_jest
       Score  : 32 points
       Date   : 2021-11-04 12:05 UTC (2 days ago)
        
 (HTM) web link (www.gwern.net)
 (TXT) w3m dump (www.gwern.net)
        
       | topotorus123 wrote:
       | > 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.
        
         | finexplained wrote:
         | You can't; the sentence is an intentional simplification for
         | the purposes of a joke. A torus has two non-trivial elements in
         | its 1-dimensional homology group: there are two types of loops
         | that I can't contract to a point on a torus, around the handle
         | and orthogonal to the handle. A lion with 1 entrance and 2
         | exits has at least 3 such loops one around each entrance, and 3
         | more (I think) passing through each of the 3 choose 2
         | aforementioned holes.
        
           | topotorus123 wrote:
           | Extremely helpful, thank you!
        
         | ravi-delia wrote:
         | This vsauce video is about humans, but I imagine pretty much
         | every mammal will be just about topologically equivalent. As it
         | turns out we humans have quite a few more holes than fleshy
         | donuts would.
         | 
         | https://www.youtube.com/watch?v=egEraZP9yXQ
        
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