At work we somehow landed on the topic of how many holes a human has, which then evolved into a heated discussion on the classic question of how many holes does a straw have.
I think it’s two, but some people are convinced that it’s one, which I just don’t understand. What are your thoughts?
1 ‘hole’ if you can call it that. Imagine if the straw started life as a solid cylinder and you had to bore out the inside to turn it into a straw: if that were the case, you would drill 1 hole all the way through it.
Another analogy is a donut. Would you agree that a donut has just 1 hole? I would say yes. Now stretch that donut vertically untill you have a giant cylinder with a hole in the middle. That’s basically now just a straw. The fact you stretched it doesn’t increase the number of holes it has.
Imagine if the straw started life as a solid cylinder and you had to bore out the inside to turn it into a straw
This would mean a straw has a hole, yes. It would be like a donut indeed - donuts are first whole, then have the hole punched out of them. This meets a dictionary definition of a hole (a perforation). A subtractive process has removed an area, leaving a hole.
But straws aren’t manufactured this way, their solid bits are additively formed around the empty area. I personally don’t think this meets the definition.
Your topological argument is strong though - both a donut and straw share the same topological feature, but when we use these math abstractions, things can be a bit weird. For instance, a hollow torus (imagine a creme-filled donut that has not yet had its shell penetrated to fill it) has two holes. One might not expect this since it looks like it still only obviously has one, but the “inner torus” consisting of negative space (that represents the hollow) is itself a valid topological hole as well.
“This meets a dictionary definition of a hole.
But straws aren’t manufactured this way, their solid bits are additively formed around the empty area. I personally don’t think this meets the definition.”
By this logic, how I make a doughnut changes whether it has a hole.
If I make a long string of dough and then connect the ends together and cook it (a forming process) it doesn’t have a hole.
If I cut a hole in a dough disc and then cook (a perforation) it has a hole. Even though the final result is identical?
On the matter of the doughnut: If you make them at home, you’re almost always just rolling a cylinder and then making it a circle. I have never actually punched a hole out of a doughnut. That would mess up the toroidal shape.
But also: So you’re saying a straw has 0 holes?
But here’s the thing. Take that doughnut and stretch it until it’s a cube with two square cutouts in it. Stretch in some of the inner walls. Now you have a house, with a door and a window. Now: does the house have two holes - a door and a window - or does it have one hole?
Locally has two extrinsic holes, that is holes relative to things outside and inside the house, globally has one intrinsic hole. We say that the door is a hole respect to the wall no to the house itself. So both the door and the window are holes locally. But we never say the house has holes, we talk about walls and ceilings so globally that house has 1 hole. Another way of thinking it is that if the house can be deformed into a filled doughnut then it can be compressed to a circle and that’s the definition of a 1-hole.
So as you begin to bore, that is one hole. But when you go through the other side, you have in fact made two holes. I think a donut can actually be thought of either as one hole or two holes, or more correctly; two holes that are the same hole.
Back to the straw; if you make another hole in the side of the straw half way up, would it still have one hole? Or two holes? Or three holes?
A bit like thinking of the human digestive tract, most of us would agree that your mouth is a different hole to your anus, but we agree that they are in two ends of the same system
What if you bored from both ends of the cylinder until they meet in the middle?
There would be two holes until, at the moment of contact, it becomes one?
Does the method with which the straw shaft is created influence the number of holes it has?
No, topologically there would be no holes until the moment of contact. This is the same as there being no hole when drilling through from only one side until the surface on the opposing side is broken.
So how does one “dig a hole?” Straight to China? Or whatever is opposite of you?
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.
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.
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.
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.
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.
How many holes does a rubber band have? A donut?
Topologically a rubber band, a donut, and a straw have the same number of holes. The hole at either end of the straw is just a continuation of the same one hole.
By that argument your mouth is a continuation of your asshole… No offense.
Some people haven’t realized almost all animals are just tubes with various fancy shit glued on.
Edit: including humans
Indeed, and when you kiss someone you are making one big hole connected by two assholes.
Stick your finger through a donut, does it go in one side and out the other?
A straw’s “in” and “out” are completely arbitrary. You can flip a straw either way and it’d still work.
Anything with a hole through it that isn’t perfectly 2D could have a “in” and “out” side. Your rubber band your doughnut only don’t have one because nobody ever thought to define one.
Mathematically It’s one. Think of a disk, like a CD, does it have one hole or two? One, right? Now imagine you can make it thicker, I.e. increase the height, and then reduce the outer radius… Making it progressively more straw-like. At what point does it stop having 1 hole and begin to have 2?
Topologically they’re the same shape.
I’m sure Matt Parker has a video on this topic in YouTube. Here
Classic topology question. Absolutely one hole; it goes all the way through.
Of course, connotatively, two is a fine assessment, but not in topology.
How many holes does a donut have? Now just try to image the real difference between a straw and a donut. Is there one, aside from deliciousness?
That’s nice but topology is quite removed from everyday language. A hole in the ground is a hole.
I completely agree. That’s what I’m saying. Topologically if you dig into the earth with a shovel, it hasn’t changed at all; there is no hole, but connotatively there clearly is.
And what I’m saying is that answering this with topology is quite misplaced because topology explicitly doesn’t deal with physical objects, ever. It uses very specific abstract definitions which cannot apply to everyday life.
That is not to say it isn’t useful. It’s an amazing discipline with wide applications, but answering questions about the properties of physical objects is not its intended use.
