4 ms·

Is there a reason why the bagel/donut shape seems to appear so much in math/physics? Just yesterday I was watching a kurzgesagt video that explored the idea of

Is there a reason why the bagel/donut shape seems to appear so much in math/physics? Just yesterday I was watching a kurzgesagt video that explored the idea of the universe being a "hyperdonut", or something. There probably isn't a simple answer but I'd appreciate any attempt to explain it in laymen's terms.

thegabez 3y ago
The bagel looks like a black hole
hnhg 3y ago
I think it’s because they can be modelled “easily” as a 2D plane with no edge in any direction but i am not an expert
groby_b 3y ago
It's the simplest two-dimensional surface[1] with at least one hole in it. In topology - the math branch that deals with properties of geometric objects and how they can be deformed - it's one of the two simplest objects, the other being a sphere. (There's a lot of those, too). Donuts ("tori") have the advantage that they're a bit more complex, so they're more interesting, and have interesting properties. Nobody gets much excited by spheres anymore ;) That also means they get a bit more attention. That means you'd expect it to be very common. Not having a lot of donuts would be weird. (Now there's a maxim to live by!) Yes, it's extremely handwavy, and there are probably explanations that are much better and more detailed. Sorry. Best I have. [1] I lie. It's a compact orientable 2-manifold, not a 2D surface. For laymen's terms, I hope the math folks will let me get away with "surface" though.
- davkan 3y ago
  Vsauce has an interesting video regarding topology[0]. Probably a bit rudimentary for anyone already familiar with the math, but still entertaining in the typical vsauce way. [0] https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D
deleted 3y ago
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nyrikki 3y ago
Not exhaustive but a lens , but the 3D rotation groups SO(3) is not simply connected. The antipodal points Pac-Man and so while a 360 degree rotation is considered 'invariant' that only holds for rigid objects with no connections. Rolling up a hose, twirling a baton, or the belt trick shows that 720 is the real invariant rotation. Merge and Delete those two points at infinity and you get a donut.
zmgsabst 3y ago
Addition looks like a donut with a twist, in both finite and infinite, one-point compactified cases. (A reason we recognize them as “the same” operation.) Imagine a clock laying on a table, and then placing clocks at each number which are rotated that number of steps. (Equivalently, so the number on the new clock matches the original clock at that spot.) If you trace where the numbers are on these clocks, you get bands that twist around the torus. This shape [0]. So we have: 1. Product of two circles. 2. A simple 2D shape with a hole. 3. Addition. …all mixed up in one shape. So it shows up a lot of places. [0] - https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Knot-Soliton_2880x1620_Lede.jpg https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Knot-S...
- alanbernstein 3y ago
  Can you elaborate on how addition fits into this? You don't mean vector addition of the "clocks" do you?

thegabez 3y ago

The bagel looks like a black hole

hnhg 3y ago

I think it’s because they can be modelled “easily” as a 2D plane with no edge in any direction but i am not an expert

groby_b 3y ago

It's the simplest two-dimensional surface[1] with at least one hole in it. In topology - the math branch that deals with properties of geometric objects and how they can be deformed - it's one of the two simplest objects, the other being a sphere. (There's a lot of those, too). Donuts ("tori") have the advantage that they're a bit more complex, so they're more interesting, and have interesting properties. Nobody gets much excited by spheres anymore ;) That also means they get a bit more attention. That means you'd expect it to be very common. Not having a lot of donuts would be weird. (Now there's a maxim to live by!) Yes, it's extremely handwavy, and there are probably explanations that are much better and more detailed. Sorry. Best I have. [1] I lie. It's a compact orientable 2-manifold, not a 2D surface. For laymen's terms, I hope the math folks will let me get away with "surface" though.

davkan 3y ago
Vsauce has an interesting video regarding topology[0]. Probably a bit rudimentary for anyone already familiar with the math, but still entertaining in the typical vsauce way. [0] https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D

deleted 3y ago

[deleted]

nyrikki 3y ago

Not exhaustive but a lens , but the 3D rotation groups SO(3) is not simply connected. The antipodal points Pac-Man and so while a 360 degree rotation is considered 'invariant' that only holds for rigid objects with no connections. Rolling up a hose, twirling a baton, or the belt trick shows that 720 is the real invariant rotation. Merge and Delete those two points at infinity and you get a donut.

zmgsabst 3y ago

Addition looks like a donut with a twist, in both finite and infinite, one-point compactified cases. (A reason we recognize them as “the same” operation.) Imagine a clock laying on a table, and then placing clocks at each number which are rotated that number of steps. (Equivalently, so the number on the new clock matches the original clock at that spot.) If you trace where the numbers are on these clocks, you get bands that twist around the torus. This shape [0]. So we have: 1. Product of two circles. 2. A simple 2D shape with a hole. 3. Addition. …all mixed up in one shape. So it shows up a lot of places. [0] - https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Knot-Soliton_2880x1620_Lede.jpg https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Knot-S...

alanbernstein 3y ago
Can you elaborate on how addition fits into this? You don't mean vector addition of the "clocks" do you?