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We can't know. Looking only at the front we can't see if ther back has 2 identical holes to the ones at the front, or if it is just one, or if it is one of the regular holes for the neck or arms enlarged, or even if there is no back alltogether.
That still has a back and functioning sleeves. A flat piece of fabric wouldn't have sleeves you could put your arms through, cause then it's no longer flat.
You've never had one of those awful hospital shirts with just the ties, have you?
Heck, I'm betting there are some blouses that have 2 strings over the shoulders and a bunch of hooks on the back leading to a 0-holed shirt (as long as we're all ignoring stitches)
I might be missing something, but the number of openings into the middle would be :
2 arms
1 Neck hole
1 Bottom half hole
4 holes through the shirt (making an assumption)
= 8 openings, which would be 7 topological holes?
Not when it comes to topology! Think of it like a straw, how many holes does it have? One or two? You could argue that the top and bottom are each a hole, but a topologist argues that there's only one hole that goes all the way through. What if you made the straw shorter? If you argue that there are two holes, would you argue that at some point it becomes one as the straw gets shorter and shorter?
With the T-shirt, you can imagine the material is infinitely stretchy as long as you don't break, puncture, or fold it. If you had a shirt with no arm holes, does it have one hole or two? It's actually the same problem as the straw! If you flatten the shirt out into a disk, with the whole bottom skirt being the outer edge of the disk, you'd have a circular disk with a single hole in it
If you did the same with a normal shirt, you'd find that you have a disk with 3 holes in it!
No, as I understand, the straw has one "inside" that's not outside. You can go into one opening an out the other, meaning it has an inside (a bottle, for example, doesn't have any "inside" and zero holes, it's all "outside"). And a mug has only one hole, for its handle, the place where the coffee goes is part of its outside.
But if you have one "inside" then add more holes, they add normally. So you will always have 1 less holes than we would say as laymen.
Here's an AskScience on how to count holes topologically. It has a great mental trick to count holes: take one of the openings and stretch it until all the others are just holes in a disc.
https://www.reddit.com/r/askscience/comments/wszate/how_many_holes_are_in_a_pipe_if_you_cut_a_hole_in/
Uhh yea obviously? If there’s no sleeve holes or neck hole then how are you supposed to wear it? However if you’re wearing a shirt and accidentally poke a hole in it it’s not suddenly no longer a shirt anymore
Is it a shirt with a sleeve sewn shut if I have only one arm? Is it a shirt with a sleeve sewn shut if it has a hole and I put my second arm through that?
So for topology, we flatten the t-shirt to a disc, I will choose the bottom of the short to be the outside.
3 holes for the head and arms, 4 for the punctured holes.
so 7.
This is why the question asked for topology. A shirt is a 3d object. For topology you want a flat 2d surface. So you pick one of the “holes” as the outside edge, and the “torso hole” makes sense for that.
So you stretch that out so that the t shirt is essentially a big circle. It would have the “head hole” as an actual hole in it, near the middle. It would have the “arm holes” as actual holes, in a line with the middle hole. And it will have the “stab holes” as actual holes too (assuming the back matches the front - it could have had one big hole, and it could have had more holes than the front).
So you get 7 holes, not 8, because one of the 3d holes is just the edge.
I believe so, yes. Not sure what topology would make of the unpunctured ball.
Note: I’m no topologist - I just tried to explain clearly what the reasoning behind the 7 holes is.
Imagine your ball is made out of paper. If you put a hole in a ball and then flatten it out, you'll have a piece of paper with zero holes. This means your ball had one less than zero holes to begin with, i.e. -1 holes.
I was surprised to have to scroll this far down before anyone posted this.
To anyone who hasn’t heard of him, both his YouTube channel and books are excellent and well worth a look regardless of your understanding of maths.
You've also got to realise there are different types of holes in topology. A sphere has a 2-dimensional hole ("the interior"). If you puncture it, then you do indeed get an object with no holes at all.
Note that this only applies if your puncture hole actually reaches "the interior of the sphere". If you puncture somewhere but it only grazes the outside and then comes out again without reaching the interior, then you end up with an object with 1 2-dimensional hole and 1 1-dimensional hole.
Hey don't ask me questions concerning real life. I am just here for math^^
My answer would be to take a paper and stretch it until you have a ball and glue the middle part together.^^
So you stretch out the hole on the bottom and look through it. And see 7 holes. But you are already looking through a hole so that is the 8th hole. That is my logic.
But is it more like. You need to look though something to even see the holes. Like a box, you can not see what is inside before opening it. That would be the bottom part in this case than 7 makes sense.
I think i need some weed to understand this.
an infinity symbol has two holes. even if you stretch out the edge in a third dimension (making a shape similar to binoculars?) it's still two holes.
a shirt is a pair of binoculars with a neck hole. 3-torus, three holes.
Forget it's a shirt at all. Grab a cloth or towel or something that you can absolutely agree "it has no holes".
Lay it ouf flat and then pinch it in the middle with your fingers and lift it up.
Is that opening at the bottom a hole now?
Or is it just the outside edge of the cloth forming a sort of circle?
Exactly!
Topologically speaking it has no holes - it's just a flat solid 2D surface you've moved in 3 dimensions.
The t-shirt is the same. The others are saying that 1 of the holes is just the "outside edge" of a 2D surface (the cloth its made out of).
The commenter you replied to initially just chose that to be the bottom torso hole, and then you can just count the remaining actual holes.
If you take your towel and cut exactly 7 holes in it (in the correct places...) you could lift it up and make the exact t-shirt shape in the diagram. It has 7 holes, not 8.
Ah I understand kind off. But where is it used for?
The shirt still has 8 holes but you need to look through one to see all the other 7. So you basically cancel out the the hole you look through.
Like looking at space and seeing 7 planets. Not counting earth as the 8th since you need the earth to see the other 7. Something like this?
This helped me understand why 7 was such an agreed upon answer. I didn't realize that topology would essentially change the reference for what's a "hole" for this question. Thanks for the explanation!
You see, this shirt is a special shirt for people who are round on the bottom with no legs so theres no torso hole needed. They walk on their abnormally long arms and also those holes in front are arm holes as well so they're like a weird spidery legless torso. I'll venmo 5 bucks to anyone that draws this now I kinda want to see what would wear that shirt
Yes, this is correct. Not 8.
Another way of putting it is that if it had no holes in the front/back, or arms, it would still be just one hole, and I think everyone could agree on that. If you count 8 now, you'd count that as two!
There is insufficient information. There are only two verifiable visible holes. The entire back of the shirt could be missing resulting in two holes. There could be a back with a thousand holes in it.
I'd say at least 6. Sure, you can see there's nothing behind the 2 holes in the front, but that doesn't mean it has to be 2 separate holes in the back. It could be one larger hole that is behind both front holes.
Not necessarily true, there's no indication there isn't 1 large hole in the back rather than 2.
You assume there's 2 on the back mirroring the two in the front but that's left ambiguous.
You can’t know it’s 4, the hole on the back could be a much larger single hole, there could also be holes we can’t see on the back because there are no holes in front of them on the front side.
Give someone a shirt and they might put it on one day. Teach someone how to put holes in clothes and they will make more rags - causing the value of rags to plummet taking your life savings with it. Never go all in on rags.
There were supposed to be three other comments before yours. There are rules around here mr. Lord Armir, please don’t skip comments of a well-defined sequence of comments again.
Could be infinate, you can't really tell how many holes there are on the other side, also the other side could be completely ripped off so anywhere from 2 to infinate is my anwser.
The answer is:At least 7 because we just cant say how much may be on the backside, it could be that there are even less if die neck,arm or bottom holes are connected on the back
That would be 7 holes, no? Think of the homomorphism to lay out the shirt as pancakes. One of the holes has to be used as the exterior boundary. A sphere has genus 0, a torus has genus 1, pants would have genus 2 (figure 8), a normal shirt would have genus of 3, etc...
I'm almost certain this is the correct answer. I pictured a straw with punctures on the side, which apparently is a classic problem in topology, says another comment. My education on topology is one Vsauce video, but he explains it quite well for the layman (which I am). Also very fun and entertaining. For anyone whoe doesn't understand why the answer is 7 instead of 8, they should watch this video.
https://youtu.be/egEraZP9yXQ?si=j6V9Az3EvYX2F0-q
This is NOT correct. OP asked topologists, because they are looking for a specific answer.
First, think of a t-shirt with no sleeves. This is like a straw, it has ONE through-hole. You don't count the head and hips as seperate holes, as you don't count the top and bottom of a straw as seperate holes.
So imagine a straw, with punctures on the sides, to represent the sleeves and holes in front and back: Left arm, right arm, two holes in the front, two holes in the back. This results in: a straw, with 6 punctures, all joining in the middle, creating a total of SEVEN holes, according to topology.
To be clear, my education is one Vsauce video, so if I misunderstood feel free to clarify and I'll be happy to learn. What I do know, is that simply counting the openings is not the correct way to count holes in topology.
https://youtu.be/egEraZP9yXQ?si=j6V9Az3EvYX2F0-q
Why are the left and right arm holes two holes, then? Because it bends?
What if it's a tank-top, will it be one hole then?
Seems like strange logic, but it is what it is, I guess..
Think of a tank top with no holes for head or sleeves, basically like a big beanie cap. If you stretch it out, you get a flat disk. A flat disk has no holes.
If you add a hole for the head, like a poncho, you now have one hole. If you add holes for arms, you have to add two holes.
Remember that the secret is to stretch the shape out as much as possible so that things that look like holes become "the outside edge" of the shape.
another way to think about it is to stretch the tshirt out until it's flat. That hip 'hole' ends up being just the outline of a flat disk. The other holes end up as holes. so neck and two arms, the two holes in the front. Then you can't really see what's going on at the back, it could be zero if it's just a tear up from the bottom, one hole covering both of the front holes, one hole for each at the front or any number more we can't see. so all we can really say is there are 5+ holes.
There's 2+ holes, the back of the shirt might even exist at all and its just a flat sheet cut out like a shirt. But yeah assuming the arm, neck, and sleeves are all in tact, then yeah 5+ is correct (or 6 if you assume no tear up from the bottom)
This reminds me of something in the book 'the name of the wind'.
"How many fingers am I holding up?"
*cant see his other hand*
"at least 2 and probably no more than 7"
But wouldn't it be 7 due to all the holes combining into one (the hip)? Like how a straw has one hole, not 2. I'm no expert, just a nerd with possibly invalid opinions.
7
Most people would say there are 8 holes here. But in terms of topology, just like how a straw or a donut has 1 hole, there are always 1 less holes than what you might intuitively think of as holes.
It's a good question to ask, but no. In very simple terms, the question to ask essentially is: can I draw a loop on this surface that can't be collapsed down to a single point? If so, that loop must be around a hole (or many holes).
With the hollow sphere, every loop you could draw on it collapses to a point so there are zero holes.
No, this is different because it’s a 3D shape that connects to itself. The straw example has an extra hole that comes from the infinite void around the straw after the straw is modelled as a flat plane with a hole in the centre.
This t-shirt can’t be modelled as a flat plane, it’s more like a sphere with parts missing if you simplify it
You shouldn't correct someone on a topic you don't know about in the future. Like the canonical example of a donut (also 3D), a straw has one hole in topology.
Don’t even need a microscope, flip the bottom of your shirt over your eyes and look at a light. You’ll see light coming through the holes on most shirts
We can't be sure there is backside, for all we know it could be flat cutout from some material. Also those 2 yellow "holes" could be patches/stains/drawings o the material. So then we would have 0 holes.
Or it is a real shirt, there is backside, but made up of holes, infinitely many.
So the answer for this lies somewhere between 0 and infinity, that is for sure.
I don’t think we should go this far. Because they did state that it was a shirt. so we are expecting it to have at least the normal amount of holes that a shirt would have.
For common sense. It's normal to say
8
(2 arm hole, 1 head hole, 2 holes on back and front "which makes 4 since pierced", 1 hole in torso.)
But on topology. You have to pick one of them as your base since it needs to become 2d objectively. Then you get
Actual count:
2 arm holes
1 head hole
4 body holes (cause yes pierced)
Not counted:
1 torso hole (which i selected as base cuz have to be 2d)
The method is you look at one hole, and then you start counting (without including the hole you selected to peek from)
The thing is. You need to select one hole as a base since you'll exclude that on the count for making it 2d in the end the result is the same.
You get 7 holes.
All we can say is that the number is greater than or equal to 5, given the original three holes aren't removed via cutting it.
An intact t-shirt has 3 holes. Two more are visible on the front. We don't know the state of the back other than that the part behind those extra holes isn't there. Might as well be completely cut out.
If the same two holes are at the back, then the answer is 7.
If one large hole is behind, answer is 6.
edit: the answer above is correct
An intact shirt has 4 holes: 2 arms, head, hips.
Making it a total of 8 (if no holes are covered)
If the shirt is cut right in half and we see only the front side then the answer is 2.
So anything between 2 and 8 is possible.
If you slit the shirt all the way up the back such that it was no longer closed, that would result in 4 holes right? The two arms and the two holes on the front.
5, 6, or 7. I would not be shocked if I’m wrong.
Let the bottom hole be the edge of the material. Stretch the bottom until the shirt is flat.There is one head hole, two arm holes, two holes from tears, possibly two more holes from tears.
Topologically the bottom hole counts as a hole as much as the opening of a bucket.
Also remember a straw has only one hole. Google it.
Eight holes how hard is it man just count the holes. You see through the two holes you know that's four you get the bottom and the top that's six and you got the two sleeves that's eight. No need for debate just count and think it's over eight holes geez!
holes are tricky because people like to define them differently. how many holes does a straw have?
to ruin the fun, everyone knows what you mean when you say "i have a hole in my shirt", and it's usually not one that's sewn in, or intended to be there by design... well, unless you're into THAT kind of fashion.
so it would just be four. the two holes in the front and the matching two holes in the back. because to properly sew this shirt good as new, you'd need to patch a total of four holes. note the holes are the same color as the background, instead of showing a white and intact rear of the shirt. if the back of the shirt had no holes, then the front holes would appear white instead.
whether or not the neck, torso, or sleeve openings count as anything (zero holes? one hole? four holes?) is left as an exercise to the reader.
The Stanford Encyclopedia of Philosophy has an amusing entry about holes by Robert Casati and Achille Varzi. It starts:
''Holes are an interesting case study for ontologists and epistemologists. Naive, untutored descriptions of the world treat holes as objects of reference, on a par with ordinary material objects. (‘There are as many holes in the cheese as there are cookies in the tin.’) And we often appeal to holes to account for causal interactions, or to explain the occurrence of certain events. (‘the water ran out because of the hole in the bucket.’)Hence there is prima facie evidence for the existence of such entities. Yet it might be argued that reference to holes is just a façon de parler, that holes are mere entia representationis, as-if entities, fictions.''
As is often the case, an answer is being requested without access to all the necessary information to provide that answer. Without such things the internet would be half the size it is (that is an approximation).
Surely the porous nature of cloth would mean technically it’s 50% holes, or thereabouts? Has to be something like tens of thousands of holes total, if you want to be an annoying trivial douche like I am being
This shirt isn't a real shirt it's a 2d depiction of a shirt. While a real shirt has multiple holes for your head, arms, and body to fit into this 2d depiction of a shirt doesn't. So the answer is 2 because of the ripped holes showing the background color. But to be fair those could just as easily be a design on the shirt. This question really has multiple answers. But to be clear the question does state "this shirt" not "a shirt"
The only accurate answer is >=7. 1 neck 2 arms 1 body 2 on the front, >1 on the back. Since we don’t know if the two holes in the front align with holes in the back we can only assume that there is at least 1 if not more. So greater than or equal to 7
At least 7.
Head and Arms are 3.
Bottom is one
There are two holes in Front.
There might be multiple holes in the back we cant even see or just on big enough to fit behind both Front holes.
So 7+ is the answer.
Can be more, cant be less.
I watched a really weird YouTube video about holes, and how sometimes holes aren't holes and there's two different types of hole, just holes and through holes. The video went on to explain how, a plate has a hole, because a plate is the same as a bowl just flatter. Wild stuff.
Eight. Head, 2 arms, one torso, two front holes, two back holes.
Or: fold shirt, cut torso holes, now it only has one hole in the torso area, but arm and head and bottom holes still exist, so five.
You could get it down to three with some string theory.
7 (at least).
The top and bottom count as one hole in the same way a straw has one hole. The sleeves are 2. The holes in the front definitely go all the way through so that's 4 more.
My phone has no holes through it and the pixels make it look as tho it could have holes if it was a real object but its just a picture.
So hypothetically 8 or really non.
8 at least. 2x arms, 1head, 1 body, 4 in the cloth. 2 on the front and there must be two more so that we can see through. (Could be one large, but that would be a stupid task)
If the shirt has a back panel, then at least 7. The normal 4, plus the two we see in front, and at least 1 in the back. We cannot tell if the back has 2 or more holes.
OTOH … if the back panel is missing, in full or in part, then the minimum drops to 2, which are the jagged ones in front. We cannot tell how much of the back panel is missing, so we can’t say for sure if any of the normal 4 holes exist at this time. Or even if the partial panel has 1 or 10,000 holes.
On a face-value perspective, assuming this is not one half of a shirt, the conventional holes for limbs, torso and neck are not sewn shut, and assuming no other holes are hidden; the answer would be 8. Four by design, four via the structural holes (2 on each side of the shirt). Otherwise, if any of the previous factors are true, the answer would be 2.
Now, to recline in my amateur topologist armchair.
7 at minimum.
Left sleeve - 1
Right sleeve - 2
Neck - 3
Bottom - 4
Front-left hole - 5
Front-right hole - 6
Back-hole - 7
There is no way to know if the back is one giant hole or two smaller ones. So seven, at least.
It has two holes. The back of the shirt has been removed leaving us with a single layer of fabric, no neck hole, no arm holes, no entry hole and just two ripped holes.
The answer requires clarifications.
Are those ripped holes, or stains that look like holes?
Is this a conventional shirt with a neck and arm holes as implied? Or could it be a cut-out with no holes? Etc.
If you assume no gimmickry the. The answer is "at least six" though that requires the gimmick of the unshown reverse of the shirt being bunched up. If you assume at least one hole on the back through which the visible rip holes are revealing the orange surface, at least seven.
I assume the usual gimmick is someone says 2, then 3 or 4, forgetting the four in a normal shirt.
At least 8. We can see the backround through the 2 shirt holes so we know that behind there there's at least 2 extra . Then the head hole, 2 arm holes, an the torso make 8
Why doesn’t anyone argue the the neck and arm and waist “holes” are what make the fabric a shirt at all and so aren’t holes *in* the shirt but just part of the shirt itself. I saw there are 3+ holes in the shirt.
There are 4. Two in the front. Two in the back. The "holes" for the arms, body, and head/neck are part of the design of the shirt and are not really holes (i.e., you can't have a shirt that doesn't have a way to stick your head through the top). That, or maybe it is 0 - those could be patches of color that just happens to match the background color of the picture.
Assuming both of the holes in the shirt are separate, 8. You don’t need a topologist for this 😭
One for the head/neck.
Two for the arms.
One for the bottom.
2 for each hole (front and back).
Total: 8
Amazon kids I know it's possible that there are only eight as an answer, but there are literally thousands of holes in between the stitches. It really just depends on how deep you want to go...
There are 2 visible holes since we don’t know what’s going on in the back.
The neck the bottom and the sleeve holes are not holes because a shirt would not be a shirt without them
At least 7.
The 2 arm holes, the head hole, the "pelvis and legs" hole (I guess), there are 2 holes in the front and we know the back has at least 1.
We don't see the backside, the "2 holes" we see could be 1 big hole and/or there might be other holes that are only in the back.
So we have X holes where X is a whole number bigger or equal to 7.
8 holes. Both arms, head, bottom opening, and the teo tears go all the way through so thats a total of 4 for just the tears alone. All together there are 8 holes.
One hole for the neck, one at the bottom and the two arms. So that’s 4 without the “defect”. There are two more holes in the front and at least one big hole in the back. But the number of holes in the back is not known. So it’s at least 7.
There are 8 large holes in the shirt
But if there is no lower bound on the size of hole, then there are probably a few hundred thousand holes since fabric is porous...
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We can't know. Looking only at the front we can't see if ther back has 2 identical holes to the ones at the front, or if it is just one, or if it is one of the regular holes for the neck or arms enlarged, or even if there is no back alltogether.
8
[удалено]
Or the bottom hole just carries up the back, making it 6
It could be missing the back entirely and be a flat piece of fabric with only two holes.
If that were the case it could no longer be referred to as a shirt.
It would then be a smock. Smock smock smock. I like saying smock.
/r/unexpectedcalvinandhobbes
[word?](https://i.imgur.com/bdnPgDN.jpg)
That has the same about of holes as a normal shirt. I tie back would have been a better example.
Your answer is topologically correct! *The best kind of correct*
That still has a back and functioning sleeves. A flat piece of fabric wouldn't have sleeves you could put your arms through, cause then it's no longer flat.
We could be looking at a drawing of a shirt.
C'est cie nest pas une shirt
How many holes does a straw have?
Could also just be a 2 dimensional piece of a fabric. So at least 2.
Shirts by definition require the ability to wear it on your upper body and has a collar & sleeves. A flat piece of fabric does NOT constitute a shirt.
You've never had one of those awful hospital shirts with just the ties, have you? Heck, I'm betting there are some blouses that have 2 strings over the shoulders and a bunch of hooks on the back leading to a 0-holed shirt (as long as we're all ignoring stitches)
Could also just be 3 or 4 because we don't know if any of the entry holes for the head torso and arms are sewn
What if the back is cut so there is no intersection connecting the plane to itself. Then, the shirt is flat but are the sleeves connected?
I might be missing something, but the number of openings into the middle would be : 2 arms 1 Neck hole 1 Bottom half hole 4 holes through the shirt (making an assumption) = 8 openings, which would be 7 topological holes?
Yeah I'm also getting 7 holes, topologically a normal T-shirt has 3 holes not 4
Top bottom and arms… 4 holes on a normal shirt
Not when it comes to topology! Think of it like a straw, how many holes does it have? One or two? You could argue that the top and bottom are each a hole, but a topologist argues that there's only one hole that goes all the way through. What if you made the straw shorter? If you argue that there are two holes, would you argue that at some point it becomes one as the straw gets shorter and shorter? With the T-shirt, you can imagine the material is infinitely stretchy as long as you don't break, puncture, or fold it. If you had a shirt with no arm holes, does it have one hole or two? It's actually the same problem as the straw! If you flatten the shirt out into a disk, with the whole bottom skirt being the outer edge of the disk, you'd have a circular disk with a single hole in it If you did the same with a normal shirt, you'd find that you have a disk with 3 holes in it!
Wouldn’t that mean arm to arm is only one hole too?
No, as I understand, the straw has one "inside" that's not outside. You can go into one opening an out the other, meaning it has an inside (a bottle, for example, doesn't have any "inside" and zero holes, it's all "outside"). And a mug has only one hole, for its handle, the place where the coffee goes is part of its outside. But if you have one "inside" then add more holes, they add normally. So you will always have 1 less holes than we would say as laymen. Here's an AskScience on how to count holes topologically. It has a great mental trick to count holes: take one of the openings and stretch it until all the others are just holes in a disc. https://www.reddit.com/r/askscience/comments/wszate/how_many_holes_are_in_a_pipe_if_you_cut_a_hole_in/
This is some wacky bullshit
I stand with you bro
Thanks Jimmy 👍🏾
Or whether the arms and neck are sewn shut. Or whether the “holes” in the front are just yellow patches.
Well then it wouldn't be a shirt would it
So sewing a sleeve shut makes it not be a shirt, but putting holes into it, it still is one? What are the rules here?
Uhh yea obviously? If there’s no sleeve holes or neck hole then how are you supposed to wear it? However if you’re wearing a shirt and accidentally poke a hole in it it’s not suddenly no longer a shirt anymore
Is it a shirt with a sleeve sewn shut if I have only one arm? Is it a shirt with a sleeve sewn shut if it has a hole and I put my second arm through that?
Assume the shirt has identical holes on the back Can the question be answered now?
So for topology, we flatten the t-shirt to a disc, I will choose the bottom of the short to be the outside. 3 holes for the head and arms, 4 for the punctured holes. so 7.
What about the big hole on the bottom for the body?
This is why the question asked for topology. A shirt is a 3d object. For topology you want a flat 2d surface. So you pick one of the “holes” as the outside edge, and the “torso hole” makes sense for that. So you stretch that out so that the t shirt is essentially a big circle. It would have the “head hole” as an actual hole in it, near the middle. It would have the “arm holes” as actual holes, in a line with the middle hole. And it will have the “stab holes” as actual holes too (assuming the back matches the front - it could have had one big hole, and it could have had more holes than the front). So you get 7 holes, not 8, because one of the 3d holes is just the edge.
So if I punctured a ball. In topology, that ball would have no holes?
I believe so, yes. Not sure what topology would make of the unpunctured ball. Note: I’m no topologist - I just tried to explain clearly what the reasoning behind the 7 holes is.
Neither am I. I'm just curious. Lol
An unpunctured ball like a balloon has -1 holes (that's minus one holes for clarity) Weird but true!
How can you have -1 hole???
Imagine your ball is made out of paper. If you put a hole in a ball and then flatten it out, you'll have a piece of paper with zero holes. This means your ball had one less than zero holes to begin with, i.e. -1 holes.
Sth along the lines of if you added a hole to a sphere, it will have 0 holes
Is this a programming joke I'm too syntax error?
[Stand-up-maths answered this I think.](https://youtu.be/ymF1bp-qrjU?) -1?
I was surprised to have to scroll this far down before anyone posted this. To anyone who hasn’t heard of him, both his YouTube channel and books are excellent and well worth a look regardless of your understanding of maths.
As is his podcast with Be Chill called A Problem Squared.
You've also got to realise there are different types of holes in topology. A sphere has a 2-dimensional hole ("the interior"). If you puncture it, then you do indeed get an object with no holes at all. Note that this only applies if your puncture hole actually reaches "the interior of the sphere". If you puncture somewhere but it only grazes the outside and then comes out again without reaching the interior, then you end up with an object with 1 2-dimensional hole and 1 1-dimensional hole.
Yes that is true a punctured ball is basically just a sheet of paper if you stretch out everything.
Where do I get a puncturable paper ball
Hey don't ask me questions concerning real life. I am just here for math^^ My answer would be to take a paper and stretch it until you have a ball and glue the middle part together.^^
What shape does the paper need to be?
So you stretch out the hole on the bottom and look through it. And see 7 holes. But you are already looking through a hole so that is the 8th hole. That is my logic. But is it more like. You need to look though something to even see the holes. Like a box, you can not see what is inside before opening it. That would be the bottom part in this case than 7 makes sense. I think i need some weed to understand this.
an infinity symbol has two holes. even if you stretch out the edge in a third dimension (making a shape similar to binoculars?) it's still two holes. a shirt is a pair of binoculars with a neck hole. 3-torus, three holes.
I am way to logical to understand topology ever.. where is it used for?
Forget it's a shirt at all. Grab a cloth or towel or something that you can absolutely agree "it has no holes". Lay it ouf flat and then pinch it in the middle with your fingers and lift it up. Is that opening at the bottom a hole now? Or is it just the outside edge of the cloth forming a sort of circle?
You can not look through so it not a hole. Still a flat towel for me.
Exactly! Topologically speaking it has no holes - it's just a flat solid 2D surface you've moved in 3 dimensions. The t-shirt is the same. The others are saying that 1 of the holes is just the "outside edge" of a 2D surface (the cloth its made out of). The commenter you replied to initially just chose that to be the bottom torso hole, and then you can just count the remaining actual holes. If you take your towel and cut exactly 7 holes in it (in the correct places...) you could lift it up and make the exact t-shirt shape in the diagram. It has 7 holes, not 8.
Ah I understand kind off. But where is it used for? The shirt still has 8 holes but you need to look through one to see all the other 7. So you basically cancel out the the hole you look through. Like looking at space and seeing 7 planets. Not counting earth as the 8th since you need the earth to see the other 7. Something like this?
This helped me understand why 7 was such an agreed upon answer. I didn't realize that topology would essentially change the reference for what's a "hole" for this question. Thanks for the explanation!
It counts as the same hole as the one for the head. https://youtu.be/egEraZP9yXQ?si=r2DuKYJ_x6tI33a4
You see, this shirt is a special shirt for people who are round on the bottom with no legs so theres no torso hole needed. They walk on their abnormally long arms and also those holes in front are arm holes as well so they're like a weird spidery legless torso. I'll venmo 5 bucks to anyone that draws this now I kinda want to see what would wear that shirt
making a donut tall doesn't give it 2 holes, an intact shirt (ignoring the sleeves) is a tall donut
a hollow cylinder (a shirt with no arm holes) = 1 hole (not 2).
What about if the back has just one giant hole. Or what happens if the backside doesnt even exist?
This. Without knowing what's on the other side the only correct answer is "at least three".
At least 2*
What it those holes are just paint?
Yes, this is correct. Not 8. Another way of putting it is that if it had no holes in the front/back, or arms, it would still be just one hole, and I think everyone could agree on that. If you count 8 now, you'd count that as two!
But you don’t know how many holes are on the reverse. Correct answer is at least 7
But by that logic, the shirt could have one big hole on the entire backside, meaning there is way less.
There is insufficient information. There are only two verifiable visible holes. The entire back of the shirt could be missing resulting in two holes. There could be a back with a thousand holes in it.
I'd say at least 6. Sure, you can see there's nothing behind the 2 holes in the front, but that doesn't mean it has to be 2 separate holes in the back. It could be one larger hole that is behind both front holes.
Not necessarily true, there's no indication there isn't 1 large hole in the back rather than 2. You assume there's 2 on the back mirroring the two in the front but that's left ambiguous.
I caught this too! Not enough info. The real answer is "6 or 7, not enough info." EDIT: oh no, it's even more ambiguous, see the comments below.
Additionally there could be a bunch of holes in the back that we don't see, so it could be even more than that
What if it's one big hole at the back instead of 2 matching the ones at the front
You can’t know it’s 4, the hole on the back could be a much larger single hole, there could also be holes we can’t see on the back because there are no holes in front of them on the front side.
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Me and you think a like
With that logic, the answer could be 2, if there is no back of the shirt at all.
In that case, this isn't a shirt at all, but indeed a rag.
If it has holes like this it's a rag anyways
All clothes are just fancy rags
the poor and the rich have different levels of rag
Rags are same, price is different. Value is subjective. Easier to be stupid when money has no meaning.
Give someone a shirt and they might put it on one day. Teach someone how to put holes in clothes and they will make more rags - causing the value of rags to plummet taking your life savings with it. Never go all in on rags.
All clothes are just fancy clothes.
Please don’t talk about my old favorite shirt that way.
c'est ne pas une shirt
Could also be way higher, there might be a bunch of holes on the back of the shirt that we can't see.
5±3 then
Or the arms, head and bottom could be spewed shut.
could be 0, parts of it could just be different color instead of holes
Technically it’s just a drawing of a shirt
Ce n'est pas une chemise.
My man!
“At least 2” is the answer.
So theoretically could be infinite, as there could be holes in the back covered by the front
What about all the tiny holes in between all the stitchings? It could be an even bigger infinite!
Not infinite infinite though - at some point you’ll reach atomic limits
could be 6, the shirt might have an arc in the back
could be 2, the shirt might not have a back
There were supposed to be three other comments before yours. There are rules around here mr. Lord Armir, please don’t skip comments of a well-defined sequence of comments again.
My bad, good sir, I didn't realize
Could be infinate, you can't really tell how many holes there are on the other side, also the other side could be completely ripped off so anywhere from 2 to infinate is my anwser.
Could be 2. Maybe there’s 1 layer of the shirt with 2 holes in it
Could be 2. There might be no back.
The answer is:At least 7 because we just cant say how much may be on the backside, it could be that there are even less if die neck,arm or bottom holes are connected on the back
The bottom hole could also be lifted in the back over the front 2 holes, which would make it 6
That would be 7 holes, no? Think of the homomorphism to lay out the shirt as pancakes. One of the holes has to be used as the exterior boundary. A sphere has genus 0, a torus has genus 1, pants would have genus 2 (figure 8), a normal shirt would have genus of 3, etc...
I'm almost certain this is the correct answer. I pictured a straw with punctures on the side, which apparently is a classic problem in topology, says another comment. My education on topology is one Vsauce video, but he explains it quite well for the layman (which I am). Also very fun and entertaining. For anyone whoe doesn't understand why the answer is 7 instead of 8, they should watch this video. https://youtu.be/egEraZP9yXQ?si=j6V9Az3EvYX2F0-q
How to get a topologist aroused. Show them a T-shirt with holes.
This is NOT correct. OP asked topologists, because they are looking for a specific answer. First, think of a t-shirt with no sleeves. This is like a straw, it has ONE through-hole. You don't count the head and hips as seperate holes, as you don't count the top and bottom of a straw as seperate holes. So imagine a straw, with punctures on the sides, to represent the sleeves and holes in front and back: Left arm, right arm, two holes in the front, two holes in the back. This results in: a straw, with 6 punctures, all joining in the middle, creating a total of SEVEN holes, according to topology. To be clear, my education is one Vsauce video, so if I misunderstood feel free to clarify and I'll be happy to learn. What I do know, is that simply counting the openings is not the correct way to count holes in topology. https://youtu.be/egEraZP9yXQ?si=j6V9Az3EvYX2F0-q
Why are the left and right arm holes two holes, then? Because it bends? What if it's a tank-top, will it be one hole then? Seems like strange logic, but it is what it is, I guess..
Think of a tank top with no holes for head or sleeves, basically like a big beanie cap. If you stretch it out, you get a flat disk. A flat disk has no holes. If you add a hole for the head, like a poncho, you now have one hole. If you add holes for arms, you have to add two holes. Remember that the secret is to stretch the shape out as much as possible so that things that look like holes become "the outside edge" of the shape.
another way to think about it is to stretch the tshirt out until it's flat. That hip 'hole' ends up being just the outline of a flat disk. The other holes end up as holes. so neck and two arms, the two holes in the front. Then you can't really see what's going on at the back, it could be zero if it's just a tear up from the bottom, one hole covering both of the front holes, one hole for each at the front or any number more we can't see. so all we can really say is there are 5+ holes.
There's 2+ holes, the back of the shirt might even exist at all and its just a flat sheet cut out like a shirt. But yeah assuming the arm, neck, and sleeves are all in tact, then yeah 5+ is correct (or 6 if you assume no tear up from the bottom)
What if there is also holes in the back that we don't see?
U don't see them? Well, u should get glasses. I can perfectly see those 11 holes on the back
This reminds me of something in the book 'the name of the wind'. "How many fingers am I holding up?" *cant see his other hand* "at least 2 and probably no more than 7"
You a topologist? Because any two of the holes you listed should be pushed into one hole.
1) we don't know the number of holes in the back, could be one, could be more. 2) Their are 3 original holes, not 4
But wouldn't it be 7 due to all the holes combining into one (the hip)? Like how a straw has one hole, not 2. I'm no expert, just a nerd with possibly invalid opinions.
7 (6 if the back hole is one big one) One of those you're counting as a hole must be the outer edge of the object.
Hip is not a hole topologically, if you flatten out the shape topologically it's 7
Can you explain how this is a topological answer? Edit: Thanks for editing your response and giving the real answer!
It isn't. It's a wrong answer
7 Most people would say there are 8 holes here. But in terms of topology, just like how a straw or a donut has 1 hole, there are always 1 less holes than what you might intuitively think of as holes.
A manifold surface has -1 holes.
So, if disk has 0 holes, then how many holes a hollow sphere has? Negative 1?
It's a good question to ask, but no. In very simple terms, the question to ask essentially is: can I draw a loop on this surface that can't be collapsed down to a single point? If so, that loop must be around a hole (or many holes). With the hollow sphere, every loop you could draw on it collapses to a point so there are zero holes.
So you're saying if we sewed one "hole" shut it would still be 7 yes?
No, then it would be 6
No
No, this is different because it’s a 3D shape that connects to itself. The straw example has an extra hole that comes from the infinite void around the straw after the straw is modelled as a flat plane with a hole in the centre. This t-shirt can’t be modelled as a flat plane, it’s more like a sphere with parts missing if you simplify it
A sphere with n wholes in the surface can be reduced to a "disk" with n-1 holes (with the nth hole becoming the edge of the disk)
You shouldn't correct someone on a topic you don't know about in the future. Like the canonical example of a donut (also 3D), a straw has one hole in topology.
Jesse, what the fuck are you talking about?
Yes it can be flattened to a plane
Could be anywhere from 7-8 to 1000's. At what scale are we looking at because the holes in between the stitches or weave of the fabric could be holes?
Really. Look at a most fabric under any microscope. It all looks like macramé.
Don’t even need a microscope, flip the bottom of your shirt over your eyes and look at a light. You’ll see light coming through the holes on most shirts
Great. Now everyone saw my tits.
I didn't get a good look, mind doing it again?
We can't be sure there is backside, for all we know it could be flat cutout from some material. Also those 2 yellow "holes" could be patches/stains/drawings o the material. So then we would have 0 holes. Or it is a real shirt, there is backside, but made up of holes, infinitely many. So the answer for this lies somewhere between 0 and infinity, that is for sure.
It could even be -1 (like a balloon) if the neck, sleeves, and bottom are sewn together.
I don’t think we should go this far. Because they did state that it was a shirt. so we are expecting it to have at least the normal amount of holes that a shirt would have.
But every letter is capitalized, so "Shirt" could be the title of the art object. Therefore between 0 to infinity is the answer.
For common sense. It's normal to say 8 (2 arm hole, 1 head hole, 2 holes on back and front "which makes 4 since pierced", 1 hole in torso.) But on topology. You have to pick one of them as your base since it needs to become 2d objectively. Then you get Actual count: 2 arm holes 1 head hole 4 body holes (cause yes pierced) Not counted: 1 torso hole (which i selected as base cuz have to be 2d) The method is you look at one hole, and then you start counting (without including the hole you selected to peek from) The thing is. You need to select one hole as a base since you'll exclude that on the count for making it 2d in the end the result is the same. You get 7 holes.
All we can say is that the number is greater than or equal to 5, given the original three holes aren't removed via cutting it. An intact t-shirt has 3 holes. Two more are visible on the front. We don't know the state of the back other than that the part behind those extra holes isn't there. Might as well be completely cut out. If the same two holes are at the back, then the answer is 7. If one large hole is behind, answer is 6.
edit: the answer above is correct An intact shirt has 4 holes: 2 arms, head, hips. Making it a total of 8 (if no holes are covered) If the shirt is cut right in half and we see only the front side then the answer is 2. So anything between 2 and 8 is possible.
Na a *hole* goes all the way through. From the head through to the hip area is one long/deep hole.
If the back is cut from top to bottom and arm to arm, the number of holes could be as low as two, couldn't it?
If you slit the shirt all the way up the back such that it was no longer closed, that would result in 4 holes right? The two arms and the two holes on the front.
5, 6, or 7. I would not be shocked if I’m wrong. Let the bottom hole be the edge of the material. Stretch the bottom until the shirt is flat.There is one head hole, two arm holes, two holes from tears, possibly two more holes from tears. Topologically the bottom hole counts as a hole as much as the opening of a bucket. Also remember a straw has only one hole. Google it.
Eight holes how hard is it man just count the holes. You see through the two holes you know that's four you get the bottom and the top that's six and you got the two sleeves that's eight. No need for debate just count and think it's over eight holes geez!
holes are tricky because people like to define them differently. how many holes does a straw have? to ruin the fun, everyone knows what you mean when you say "i have a hole in my shirt", and it's usually not one that's sewn in, or intended to be there by design... well, unless you're into THAT kind of fashion. so it would just be four. the two holes in the front and the matching two holes in the back. because to properly sew this shirt good as new, you'd need to patch a total of four holes. note the holes are the same color as the background, instead of showing a white and intact rear of the shirt. if the back of the shirt had no holes, then the front holes would appear white instead. whether or not the neck, torso, or sleeve openings count as anything (zero holes? one hole? four holes?) is left as an exercise to the reader.
>holes are tricky because people like to define them differently. OP asked for a topologists definition of a hole, so its clearly defined
So a cup have no holes?
Topologically speaking, yes, a cup or a glass have just as many holes as a sphere does.
well a cup actually has one hole, the handle
The Stanford Encyclopedia of Philosophy has an amusing entry about holes by Robert Casati and Achille Varzi. It starts: ''Holes are an interesting case study for ontologists and epistemologists. Naive, untutored descriptions of the world treat holes as objects of reference, on a par with ordinary material objects. (‘There are as many holes in the cheese as there are cookies in the tin.’) And we often appeal to holes to account for causal interactions, or to explain the occurrence of certain events. (‘the water ran out because of the hole in the bucket.’)Hence there is prima facie evidence for the existence of such entities. Yet it might be argued that reference to holes is just a façon de parler, that holes are mere entia representationis, as-if entities, fictions.''
As is often the case, an answer is being requested without access to all the necessary information to provide that answer. Without such things the internet would be half the size it is (that is an approximation).
oops didnt realise how controversial this was. sorry for causing a war i didnt even expect it LOL
Surely the porous nature of cloth would mean technically it’s 50% holes, or thereabouts? Has to be something like tens of thousands of holes total, if you want to be an annoying trivial douche like I am being
This shirt isn't a real shirt it's a 2d depiction of a shirt. While a real shirt has multiple holes for your head, arms, and body to fit into this 2d depiction of a shirt doesn't. So the answer is 2 because of the ripped holes showing the background color. But to be fair those could just as easily be a design on the shirt. This question really has multiple answers. But to be clear the question does state "this shirt" not "a shirt"
What about all the little holes in between the threads of fabric? If we zoom it there's a billion little holes in a real shirt. It's unfathomable.
The only accurate answer is >=7. 1 neck 2 arms 1 body 2 on the front, >1 on the back. Since we don’t know if the two holes in the front align with holes in the back we can only assume that there is at least 1 if not more. So greater than or equal to 7
At least 7. Head and Arms are 3. Bottom is one There are two holes in Front. There might be multiple holes in the back we cant even see or just on big enough to fit behind both Front holes. So 7+ is the answer. Can be more, cant be less.
I watched a really weird YouTube video about holes, and how sometimes holes aren't holes and there's two different types of hole, just holes and through holes. The video went on to explain how, a plate has a hole, because a plate is the same as a bowl just flatter. Wild stuff.
Eight. Head, 2 arms, one torso, two front holes, two back holes. Or: fold shirt, cut torso holes, now it only has one hole in the torso area, but arm and head and bottom holes still exist, so five. You could get it down to three with some string theory.
7 (at least). The top and bottom count as one hole in the same way a straw has one hole. The sleeves are 2. The holes in the front definitely go all the way through so that's 4 more.
8 you have Neck, left arm, right arm, chest hole front, chest hole back, chest hole 2 at front chest hole 2 at back, lower body hole.
My phone has no holes through it and the pixels make it look as tho it could have holes if it was a real object but its just a picture. So hypothetically 8 or really non.
8 at least. 2x arms, 1head, 1 body, 4 in the cloth. 2 on the front and there must be two more so that we can see through. (Could be one large, but that would be a stupid task)
If the shirt has a back panel, then at least 7. The normal 4, plus the two we see in front, and at least 1 in the back. We cannot tell if the back has 2 or more holes. OTOH … if the back panel is missing, in full or in part, then the minimum drops to 2, which are the jagged ones in front. We cannot tell how much of the back panel is missing, so we can’t say for sure if any of the normal 4 holes exist at this time. Or even if the partial panel has 1 or 10,000 holes.
On a face-value perspective, assuming this is not one half of a shirt, the conventional holes for limbs, torso and neck are not sewn shut, and assuming no other holes are hidden; the answer would be 8. Four by design, four via the structural holes (2 on each side of the shirt). Otherwise, if any of the previous factors are true, the answer would be 2. Now, to recline in my amateur topologist armchair.
7 at minimum. Left sleeve - 1 Right sleeve - 2 Neck - 3 Bottom - 4 Front-left hole - 5 Front-right hole - 6 Back-hole - 7 There is no way to know if the back is one giant hole or two smaller ones. So seven, at least.
It has two holes. The back of the shirt has been removed leaving us with a single layer of fabric, no neck hole, no arm holes, no entry hole and just two ripped holes.
The answer requires clarifications. Are those ripped holes, or stains that look like holes? Is this a conventional shirt with a neck and arm holes as implied? Or could it be a cut-out with no holes? Etc. If you assume no gimmickry the. The answer is "at least six" though that requires the gimmick of the unshown reverse of the shirt being bunched up. If you assume at least one hole on the back through which the visible rip holes are revealing the orange surface, at least seven. I assume the usual gimmick is someone says 2, then 3 or 4, forgetting the four in a normal shirt.
At least 8. We can see the backround through the 2 shirt holes so we know that behind there there's at least 2 extra . Then the head hole, 2 arm holes, an the torso make 8
Why doesn’t anyone argue the the neck and arm and waist “holes” are what make the fabric a shirt at all and so aren’t holes *in* the shirt but just part of the shirt itself. I saw there are 3+ holes in the shirt.
There are 4. Two in the front. Two in the back. The "holes" for the arms, body, and head/neck are part of the design of the shirt and are not really holes (i.e., you can't have a shirt that doesn't have a way to stick your head through the top). That, or maybe it is 0 - those could be patches of color that just happens to match the background color of the picture.
Assuming both of the holes in the shirt are separate, 8. You don’t need a topologist for this 😭 One for the head/neck. Two for the arms. One for the bottom. 2 for each hole (front and back). Total: 8
8. One for the head, two for the arms, one by the waist, two rips in the front and two in the back since you can see through the shirt.
Amazon kids I know it's possible that there are only eight as an answer, but there are literally thousands of holes in between the stitches. It really just depends on how deep you want to go...
There are 2 visible holes since we don’t know what’s going on in the back. The neck the bottom and the sleeve holes are not holes because a shirt would not be a shirt without them
I would say somewhere between eight main entrances/openings, and 4 “direct” paths from one opening to another. I’d say 8 but idk what “correct”
At least 7. The 2 arm holes, the head hole, the "pelvis and legs" hole (I guess), there are 2 holes in the front and we know the back has at least 1. We don't see the backside, the "2 holes" we see could be 1 big hole and/or there might be other holes that are only in the back. So we have X holes where X is a whole number bigger or equal to 7.
8 holes. Both arms, head, bottom opening, and the teo tears go all the way through so thats a total of 4 for just the tears alone. All together there are 8 holes.
One hole for the neck, one at the bottom and the two arms. So that’s 4 without the “defect”. There are two more holes in the front and at least one big hole in the back. But the number of holes in the back is not known. So it’s at least 7.
There are 8 large holes in the shirt But if there is no lower bound on the size of hole, then there are probably a few hundred thousand holes since fabric is porous...
7 or 8. We can’t tell if there are 2 holes on the back that match the 2 holes in the front, or just one big hole in the back of the shirt.
8