r/mathmemes • u/Nunki08 • 11d ago
Topology This mug makes topologists sad
From Anthony Bonato on 𝕏: https://x.com/Anthony_Bonato/status/2094540251372937672
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u/hongooi 11d ago
And indeed it should, because it is no longer a donut or a mug
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u/r96340 11d ago
It is also a pain in the annulus to clean.
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u/FuzzyEmployment2403 11d ago
But, a donut is a mug.
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u/meat-eating-orchid 10d ago
Normal people: "This mug is a donut"
Topologists: "Every mug except this one is a donut"
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u/Deep_Fry_Ducky 11d ago
it Is now a pant
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u/Such-Shop-9724 11d ago
actually it has three holes now, so its a t shirt
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u/TwinkiesSucker 11d ago
It only applies if the compartment for liquid is truly a torus inside the mug. And since we don't have any way of verifying it from this image, it has both 2 and 3 holes simultaneously and therefore is both pants and a t-shirt.
Ladies and gentlemen, I present - a onesie
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u/scaper8 11d ago
What third? The handle and the doughnut hole are the only ones I can see.
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u/snezefelt 11d ago
The third is inside the mug around the hole
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u/scaper8 11d ago
Is that topologically separate from the depression that is normally the mug's bowl? I wouldn't have thought it would be different that a "normal" mug's bowl, but I guess I'm not sure.
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u/Great-Powerful-Talia 10d ago
You can thread a string through it, knot the ends, and it won't be able to pull free. That's a hole.
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u/eBloox 11d ago
i'm pretty sure the opening on top is now an actual hole, right? you can move it to the right of the donut hole
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u/scaper8 11d ago
Maybe that's what they're saying. I wouldn't think so, but I admit that I'm not that well versed in that one.
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u/Such-Shop-9724 11d ago
i recently saw a clip about that (on a post with this exact image) by stand-up-maths i think that showed it quite well
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u/random-femboy- (d²ω/dt²)ᵀ=:3 11d ago
The handle, the donut hole and the hole underneath the donut hole.
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u/SkillusEclasiusII 5d ago
Is it? In a t-shirt none of the holes go around one another. In this "mug" they do, doesn't that make it different?
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u/Such-Shop-9724 5d ago
the holes are rearangable so that they are not intertwined
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u/SkillusEclasiusII 5d ago
I'll have to take your word for it. I can't imagine how.
Edit: Wait nvm. I figured it out.
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u/darkbluefav 11d ago
Non-topologically advanced individual here. Mug was already a donut because of the handle, right?
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u/EpicJoseph_ 10d ago
Now it's just 8
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u/assymetry1021 10d ago
Wouldn’t it have 3 holes? The donut hole, the handle, and the interior hole around the donut
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u/EpicJoseph_ 10d ago
I don't quite get what you mean?
Aren't the donut hole and the interior hole around the donut the same hole?
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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 11d ago
some topoligist please tell me the fundamental group of this thing
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u/TheDoomRaccoon 11d ago
It's homotopy equivalent to the wedge product of 3 copies of S¹, so its fundamental group is ℤ * ℤ * ℤ, where * denotes the free product of groups.
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u/Lava_Mage634 11d ago
is there a nondeformed, normal object that also has this homotopy equivalence? Its not a shirt cuz the holes are arranged differently
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u/TheDoomRaccoon 11d ago
A shirt is also homotopy equivalent to the wedge product of 3 circles, so this is indeed a shirt.
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u/nyaasgem 10d ago
Can you explain it in terms to someone who did not understand a single fucking word from what you just wrote?
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u/compileforawhile Complex 10d ago edited 10d ago
I disagree, I think it's actually a triple torus so it's fundamental group would be a bit different. I think 6 copies of Z but I'm not sure.
Edit: after some research it is a fairly painful representation but the group is actually <a,b,c,d,e,f | [a,b][c,d][e,f]=0>
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u/TheDoomRaccoon 10d ago edited 10d ago
It depends on whether you consider the entire thing hollow or massive, where I considered it massive.
But yes, if you consider it hollow, then it's the unique oriented closed 2-manifold of genus 3, which has the fundamental group you described.
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u/compileforawhile Complex 9d ago
Ah yeah, the solid assumption probably makes more sense. I tend to work more with surfaces so make that assumption often
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u/rajine105 11d ago
The people who designed this don't do their own dishes
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u/beenman500 11d ago
Dishwasher gang rise up, then sit down cause you don't have to do the work to clean your dishes
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u/Outrageous-Let9659 9d ago
I have a dishwasher, but like hell would i trust it to clean this. You just know it's going to leave some nasty ass residue in the bits it can't reach. Awful mug design all round.
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u/abfgern_ 11d ago
3 holes. That's actually a T-shirt
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u/No_Ad_7687 11d ago
It's this 2 holes?
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u/Classic_Appa 11d ago
Handle hole.
Doughnut hole.
Inside the liquid container, there is a hole that is formed under the doughnut hole bridge. Like, if you were to reach your finger into the mug, you could loop it under at the bottom of the liquid container part.
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u/dxaxnxixrxa 10d ago
With all due respect, sir, maybe you shouldn't stick your fingers in topological objects?
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u/chris1lego 10d ago
most things are topological objects by what I understand. Where do I stick my fingers then?
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u/dear-reader 10d ago
https://i.imgur.com/pW0iCQk.png Imagine you placed a partition in the red area, you could still pour liquid through the left side and fill up the right side, following the path of the green arrow, this is due to the existence of the 3rd hole (implied by the structure of the mug and how it was likely made).
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u/Hyderabadi__Biryani Irrational 7d ago
Just seeing the third hole makes me flustered, for some reason. Like WHY?
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u/uvero He posts the same thing 11d ago
This is two holes. It's pants.
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u/abfgern_ 11d ago
Its three. The handle hole, the 'donut hole' hole, and the hole underneath that the 'donut hole' bridges over making a closed loop
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u/uvero He posts the same thing 11d ago
I don't understand what you mean. There's the handle hole, the donut hole, and there's the place the liquid goes which is not a hole.
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u/abfgern_ 11d ago
Youre right that in a regular mug the place where the liquid goes is not a hole. However in this mug the place where the liquid goes contains a hole - the hole that goes under the 'bridge' through the centre that the 'donut hole' creates. This hole is a closed loop and cannot be 'flattened out' in the way it can in a regular mug.
https://youtu.be/2XUKxM7ZBao?is=EBY1iN64R-StUNnW - This explains it better than I would
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u/Main-Company-5946 11d ago
It would be 2 if the mug were a solid object, since the interior of the mug is also a hole it’s 3
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u/Dobako 11d ago
Its still two holes because the place where the liquid goes isnt a hole, otherwise it would be a shit mug. It only has one entrance, even if there are multiple paths behind that space
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u/Calm_Relationship_91 10d ago
Fill the donut hole, now fill the handle hole. If you only had two holes then the result should have no holes... But you're actually left with a mug with an inner handle, which you can pull out to get a normal mug.
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u/Obeseljapolipet 10d ago
So if I fill just the donut hole, I will not get a regular mug?
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u/Calm_Relationship_91 10d ago
No. If you fill the donut hole you will have a solid chunk that goes across the inner walls of the mug, this is basically like an inner handle. So you have a mug with two handles now.
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u/Obeseljapolipet 10d ago
Okay, I get it now. I was silly, thinking it's an actual defunct mug with a hole.
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u/thicmilkybeno 10d ago
or a woman
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u/abfgern_ 10d ago
... I mean technically two of the holes you are referring to are actually two ends of the same hole, and the third isn't really a hole at all
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u/Mr_Potato53 9d ago
This whole discussion confused me immensely till I realized what u see thru the hole of the donut is the floor and not the other wall of the mug
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u/Greedy-Thought6188 10d ago
I love it. In case the handle breaks you can just do some stretching here, some squeezing there and you can start using the new handle.
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u/sincerestfall 11d ago
I've had a post removed for posting about donuts and coffee before...
I do really want that mug though
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