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How many holes does a donut have?
Now make the donut higher. A lot higher. Now you have a donut-tunnel. Now make the walls thinner. Now shrink it. Now you have a straw.
One hole.
Now take that straw and tie a knot in the middle of it.
That doesn't change the topology though. Or at least you can't without it no longer being a straw.
A straw is the product of a circle and an interval. Either the knot doesn't fully seal the interval, meaning it's topology is maintained, or you completely seal the straw, changing it from 1 long interval to 2 separate intervals, changing the object entirely.
In this situation, the straw would not be completely sealed. It is clearly inefficient, but technically there exists a path for which there is a level of force that could applied that would make the straw function.
Take a sealed tin can. Punch a hole in it. Punch another hole in it. You now have one hole.
No, but that's two holes. And it's because the holes are not connect by a single, unbroken cylinder. It's the material at the edge of those holes and the 90° turn at the corners that makes the holes disconnected.
The edges and corners mean nothing for the purposes of counting holes. Counting holes is a concept of topology that relies on continuous deformation. All non-opening features of the object just get squished and stretched away in the process of identifying holes.
For the purpose of counting holes a can with two openings punched into it is equivalent to a donut which we know has only one hole.
This seems overly reductionist to the point where I could just as easily describe my mouth and my anus as the same hole.
Yeah, that's a concept that gets covered extensively in anatomy, immunology, and microbiology. It's called "the donut model". This is not a joke. It clearly shows how your digestive system is exposed to the outside world, similar to skin. You can obviously see why this is important immunologically, since germs can just get into the mouth/butthole in a way that they can't penetrate skin.
It's one long hole.
that is actually the case. there is an unimpeded path from your mouth to your anus
Because they are the same hole. Welcome to topology
It's perfectly reductionist. You have defined our biology in exactly the same way medical texts do.
Now you're getting it!
Yes. It's called the gastrointestinal tract.
They did the math!
I understand geometrically they have the same number of holes but in my head straws still have two holes because they have an "inside" so both entrances to the inside have to be a hole.
That's because a straw has two more holes than a sphere.