Drank Holes

Drank Holes
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I write about mathematics and its applications
I came across this poll on Twitter:
https://twitter.com/gaileyfrey/status/952673380360101888
This question seems to be more controversial than I would have thought. I guess I understand the "two holes" camp; after all, a straw is a cylinder through which liquid flows from one end to the other and that seems like two holes.
But that's wrong. Let's describe a straw mathematically. A straw is the product of a circle and an interval; a topologist would denote this S ¹ × I , where S ¹ is usually thought of as the unit circle in the plane and I is the interval [0, L ] (here L = the length of the straw). Even the bendy straw in the photo above is of this form, as is one of those silly straws that kids like to use for their chocolate milk.
Some responders to the poll tried to argue that a straw is the same as a donut, by which I assume they mean a solid donut. Topologically, that would be the same as S ¹ × D , where D is a disc (imagine gluing a disc to each point around a circle). This is actually true since the disc can be deformed to an interval--just squash it to a diameter. The assertion is then that a donut "clearly" has one hole. This is actually the correct answer, but I want to explain it a bit more carefully.
First we need to decide what a "hole" is. Topologists have put a lot of thought into this, and the correct notion is measured by the homology groups of a space. We can all agree that a circle in the plane surrounds what we might think of as a hole. The hole itself in this case is a 2-dimensional object bounded by the 1-dimensional circle. This is what the first homology group of a space measures--the number of 1-dimensional simple closed curves that cannot be filled in inside the space . In the case of S ¹, there is just one such curve, namely the circle itself, and so the circle has one "hole." Now, you might argue that you can fill in a circle in the plane, and that's true, but filling it in requires leaving the space S ¹. This assertion shows that the first homology group of the plane is trivial--there aren't any simple closed curves that can't be filled in.
Thus, the circle has one hole. I hope it's clear that the interval I doesn't have any holes. But instead I will appeal to a fact about homology: given any space X , the homology groups of X and X × I are the same. In the case of the straw, we see that its homology groups are the same as those of the circle. It follows that the straw has one hole. The same is true of a solid donut since an interval and a disc are topologically equivalent and such spaces have the same homology. (Aside: if you hollow out the donut, you get a surface called a torus , which is the product of two copies of the circle. In this case, the first homology group is two-dimensional as there are two circles, one going around the center and one perpendicular to it going around the surface. The torus also has a second homology group because the surface itself cannot be filled in without leaving the space. The interior of the solid 3-dimensional donut fills in the surface and so it does not have a second homology group.)
So, that solves it. Straws have one hole. Topology wins the day.

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I'M NEVER DRINKING WATER OR MILK OR SODA OR ANYTHING EVER AGAIN.
A Reddit user allegedly let his OWN MOTHER accidentally drink his semen, and now he's writing about it on the internet.
Yup, put your drink down for this one. You're not gonna want to take another sip after reading this.
Today, I learned two very valuable lessons: One, never jack-off into a cup, and two, only drink beverages out of the bottle.
BRB, pouring my coffee out the window.
Citations: TIFU (Reddit) , Son Let Mother Drink Semen (Dude Comedy)
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