This is one of those “if you cut a hole in a net, it then has less holes than before” type arguments and I’m all here for it.
I think it would still techically be more hole since a larger total area would be hole.
I would be fewer holes, though.
A circle is a plane folded on itself so the answer is technically 0 holes. But first what is a hole?
A goal?
a sphere is a plane folded in on itself, and spheres have no (one-dimensional) holes. but spheres do have a two-dimensional hole, which is basically a way of saying they’re hollow.
a circle is a line folded in on itself, and circles have one (one-dimensional) hole.
The average person is a straw.
This is a strawman argument.
Not really, they’re some sort of tube, but they don’t classify as straws
I’m a series of tubes!
You’re the Internet?
Yes! You can call me… The lawnmower man!
(I’m seriously dating myself with that reference)
I remember thinking this was top notch graphics in 1992.
How about a pair of jeans?
If anyone wants to see an entertaining mathematician talk about this exact topic for 30 minutes, here you go:
And here’s Michael from VSauce talking about the topic:
I knew this was going to be Stand-up Maths before I clicked the linked.
One of my friends is a Taurus as well. He’s a car.
How many holes does he have?
At least 5. I’m unwilling to do a more thorough count, tho.
what an interesting looking Tesla
S¹ × [0, L]
I don’t understand why a circle has one/a hole though.I don’t even know what a hole is.Edit: Ok, circles might not have holes, they have interiors?
Make sure you’re distinguishing between a circle and a disc.
What specifically constitutes a hole is somewhat ambiguous, but if you pull on the thread a bit, you’ll probably agree that it’s a topological quality and that homotopy groups and homology are good candidates. The most grounded way to approach the topic is with simplicial homology.
🕳
a torus is not homotopic to a straw though unless you take the straw and glue it at its ends. a straw is homotopic to a circle, a torus is homotopic to product of two circles, Baldur’s gate is homotopic to a disk unless we are talking about the game storage medium which used to be a CD which is also homotopic to a circle
Wouldn’t a straw be the product of a circle and a line?
I think people don’t know a torus is hollow.
You are talking about a straw of zero wall thickness right? A real straw should be homo-whatever to a torus
Even if it has thickness still homotopic to a circle. For instance a band with thickness is homotopic to a circle, you can retract along the radius to arrive at a circle that is inside the band. Similarly a plane, or a slab with thickness are all homotopic to a point.
Note that all of these are proved by using collections of transformations from the space to itself (not necessarily from the space to all of itself though, if it maps the space to a subset of it that is fine). So if you want to say something like “but you can also shrink a circle to eventually reach a point but it is not homotopic to a point” that won’t work because you are imagining transformation that maps a circle not into itself but to a smaller one.
ps: the actual definition of homotopy equivalence between “objects” is slightly more involved but intuitively it boils down to this when you imagine one space as a subset of the other and try to see if they are homotopy equivalent.
A CD is clearly homotopic to a torus, though…
And the walls of a straw do have thickness…
A straw goes:Gas - solid - gas - solid - gas
If solid torus yes, if just the regular torus (surface of the solid torus) no. CD is homotopic to a circle and so is a solid torus.
OK, that’s my ignorance. I didn’t realise toruses were usually hollow.
Thank you for letting me know, you’re right and I’ve learnt something.
Reminds me of the old “Are there more doors or wheels in the world?” question
Definitely wheels. All that machinery with wheels for the belts, all transportation, toys, … I can’t fathom there being as many doors.
Unless I’m wooshed :D
The answer is “yes”.
The real issue is “Hole” is not desctiptive enough for a clear answer. A straw has one “Through Hole”. If you dig a hole in the ground you have one “Blind Hole”.
What size does a hole need to be to be a hole
In theory, the smallest hole possible would be a ring of atoms combined into a molecule with an empty center
benzene got that nanopussy
That is one way of putting it, a bit crude though…
Twice as big as half a hole, obviously.
Thinking about it, humans have one less hole than I would’ve guessed, since the tube from our mouth to our anus sort of makes us a complicated straw.
The human body is just a series of tubes.
The internet and I have that in common, I guess.
Think of a box with an arrangement of holes that allows us to look through it if we are correctly positioned.
Would anyone dare to say that such a thing is possible to achieve with only one hole? (I’m not allowing holes in corners and edges to make my point)
A straw has 2 holes.
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Zero
