[HN Gopher] Topology 101: The Hole Truth
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       Topology 101: The Hole Truth
        
       Author : theafh
       Score  : 54 points
       Date   : 2021-01-26 17:24 UTC (5 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | Whitespace wrote:
       | > A hollow torus can be cut twice -- once around the tube and
       | then along the resulting cylinder -- so by this definition, it
       | has two holes.
       | 
       | Fascinating! This idea of an inner hole that is hidden and
       | connected is quite unintuitive to me. I majored in mathematics in
       | college but I wouldn't have reached this conclusion through
       | intuition.
        
         | vecter wrote:
         | > This idea of an inner hole that is hidden and connected is
         | quite unintuitive to me.
         | 
         | What do you mean by the hole in the torus being "hidden and
         | connected"?
        
           | thunderbong wrote:
           | This is how I understood the comment -
           | 
           | In a torus, there are effectively two holes -
           | 
           | 1. the center hole around which there is a cylindrical ring
           | 
           | 2. the whole _inside_ the cylindrical ring, which is hidden
           | and connected.
           | 
           | When we cut along the length of the cylindrical ring, we are
           | effectively creating two edges, just like if we were to cut a
           | circular ring of wire, we would end up with two points at the
           | end.
           | 
           | The two edges then open up, effectively forming another
           | cylinder, which has to be cut again.
           | 
           | Any other object which has only a single hole, would require
           | only a single cut to flatten out.
        
           | pontus wrote:
           | I suspect what was meant was that it's only apparent if you
           | can view the torus from "a bird's eye view". If you were an
           | ant walking on the surface at night, you would never run into
           | a hole in the usual sense. You would be hard pressed to find
           | a way to distinguish the surface from that of a sphere.
           | 
           | As an ant you could easily see that you were not on the
           | surface of an infinite plane simply because you keep coming
           | back to the same spot over and over again. In order to figure
           | out that there was a hole (or more appropriately named as
           | 'handle'), you'd need to leave some thread behind and notice
           | that there was no way to contract various loops to a point.
        
           | AnHonestComment wrote:
           | There's two holes: places you can draw a non-contractile
           | circle, which can't be turned into each other --
           | "circumference" and "around".
           | 
           | I think they mean the "around" holes have a center "inside"
           | the donut.
        
       | caminocorner wrote:
       | The author knows how to hook you right in the first paragraph:
       | 
       | >> If you're looking to pick a fight, simply ask your friends,
       | "Is Pluto a planet?" Or "Is a hotdog a sandwich?" Or "How many
       | holes does a straw have?" The first two questions will have them
       | arguing yay or nay, while the third yields claims of two, one and
       | even zero.
       | 
       | Two, one, or zero? Continues reading...
        
         | btilly wrote:
         | Actually if you want to start a fight, ask whether pineapple
         | belongs on pizza.
        
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