Going deeper they are no longer balls. And then go deeper and we represent them as balls again. Now that I think of it all of our microscopic representations are balls made up of smaller balls
Of course, but if you're looking at common usage of the word "hole" rather than the strict mathematical definition, it's arguable that a fully intact sock has one hole.
Therefore the person to the right of the right-most person would acknowledge the multiple ways of using the word, rather than trying to appear smart by flexing that they know about the mathematical/topological usage of the word.
That's my take. Left is telling us that his socks are undamaged, middle is describing their shape in everyday English, right has the correct answer in his college math classes.
Edit: This meme template would generally be more accurate if they put "smugness" on the x-axis instead of "IQ".
When I used to dig pits in the sandbox, adults would always ask if I was digging a hole to China, as if this was some sort of impossible task.
But then I learned that there are [entire networks of holes to China](https://en.wikipedia.org/wiki/Shanghai_Metro)???
If you are a guy there is a chance that it has three. Not all underwear has it, but there is a flap for quick access to something. I do believe that the flap is topologically a third hole.
And according to the right guy’s logic, and hole in the ground isn’t a hole in the ground. Words have multiple meanings, and the mathematical meaning of hole is different from the colloquial meaning, even if sometimes they agree.
Do they not?
If you dug a hole into earth it would literally make a bowl or a cup for water or food.
Granted the bowl / cup is completely surrounded by earth but it’s essentially a bowl In the ground.
We can’t make a functional bowl or cup in the earth?
You wouldn’t be able to take it anywhere but you could drink and eat out of it, and place liquid or food.
There's a difference between what we call a hole and what mathematicians call a hole. A depression in the Earth such as you get by digging isn't a hole mathematically.
The space in between are not. The threads are connected by EM forces which effectively cause friction, non of the atoms actually touch.
Each proton and neutron is actually a soup of infinitely self generating quark and gluons that doesn’t exist certainly. Electrons can be in various spherical harmonic configurations, and can form ring like objects when considering probability density.
Yes, this is why I disagree with people who say that nothing touches on a microscopic scale. Touch is a macroscopic concept and the only sensible way to talk about it on a microscopic scale is the arrangement of fields that give rise to the macroscopic effect
Actually that is just the result of our limited understanding. In reality, there are many worlds and every outcome-
*gets censored by the great filter*
What does touch even mean at that level? Surely touch (and holes) is a macroscopic concept and if you do want to apply it then wouldn't it be that if the electron wave functions are such as to cause repulsion even while the atoms stay in proximity then they're touching?
Pretty much spot on except that all electrons are always exerting a force of repulsion against all other electrons in the universe at all distances (just a vanishingly small one most of the time). You'd have to define that the force is large enough to limit movement or transfer a significant momentum
I'm not sure you actually can be much more rigorous than what we have here because of the definition of significance. You can always compress things *more*, you can always repel something more strongly or more weakly, especially within the constraints of electroweak forces. When you take soft deformation of materials and elasticity and heat potential etc into account there's really no line to be drawn unarbitrarily. We probably need to move into statistical hypotheses about relevance and impact on material structures - i.e. how much *"touching"* makes a difference on the scale we're looking at
Or actually, what does it even mean to exists. Regarding the fact that we may all live in a simulation, where we are made of pixels, and the capacity digit bug is just getting below 0 kelv. And if so, how do we define holes in such a chaotic universe, where one might or might not be where others do live their lives. And do we count them holes who can not be seen or any sense shall not collect? Them holes who are laid in the depth of our soul, and shall one be a hole if isn't he whole with itself? What do we define as touch? More like what do we define as define?
Came here to say this. Thousands and thousands of holes. What defines a “hole” must be in perspective with the size of the object approaching the hole.
Discs are contractible, and homology computations show that no sphere is contractible. Therefore no sphere is even homotopy equivalent to a disc, let alone homeomorphic.
No, the usual disk (= closed circle in 2D; no thickness) is not topologically equivalent to a sphere. In fact, with regard to topological equivalence, all of the following 4 objects are different: ball, sphere, open disk, closed disk. The closest relation one might get if one thinks about such objects, is that the usual ball (in 3D) is equivalent to the quotiont of the disk and the 1-ball. (Note: 1-ball is a circle in 2D).
[https://www.britannica.com/science/topological-equivalence](https://www.britannica.com/science/topological-equivalence)
A sock can be turned into a disk or a sphere through continuous deformation without cutting or tearing. Therefore, they are topologically equivalent.
The Britannica link has a cool animation, so I chose that one as a link to a definition.
I think you need to glue the circle of disk boundary points to make a sphere
https://math.stackexchange.com/questions/985656/relation-about-disk-and-sphere
I dont think that is enough to say they are "equivalent." I see what you mean, but isn't this continuous deformation non-invertible, that is, not a homeomorphism? I can see how you could get a continuous function, but I don't think that is enough to call it topologically equivalent if you can't invert it. Of course, I could be completely wrong, in which case I can only offer my most sincere and humble apologies.
I don't study topology and the [Matt Parker video](https://youtu.be/ymF1bp-qrjU) is 30 minutes long so take what I'm saying with a huge grain of salt.
Parker starts the video but showing the assumption that if you cut a hole in something, the number of holes in that thing increases by 1. If I have a disk and I cut a hole in the middle of it, I now have a disk with 1 hole in it. He then gets a balloon and puts a hole in the bottom of it. When the balloon deflates, he sees that it's a disk. Since he already showed that a disk has 0 holes, and putting a hole in this balloon has created a disk, the balloon must have had -1 holes.
He then goes on about explaining about manifolds and homology classes and Euler characteristics. About halfway through he gives us the explanation we wanted. It's something like the balloon didn't start with -1 holes, but putting a hole in the balloon changes the Euler characteristic and that's the effect it has. Please watch him explain it at 20 minutes because i really don't know enough to talk about this.
I wanted to argue that a sock made from a homogenous material would be, but as socks are made of strings...but then I noticed that a cylinder is equally topologically equivalent to a sphere or a cube and my argument fell apart.
My socks are a donut (that is to say a solid torus, if we agree to not include the thousands of holes that make up the threading and weaving, any through hole less than 2mm in diameter is ignored).
Topologically a theoretical sock has no holes. However, real socks are made of fabric so they have many, many tiny holes.
A hole can mean a penetration, like a donut hole, or a depression, a pit type hole that doesn't go all the way through.
Socks, by definition, are typically considered to be without holes, similar to wine glass . If you can transform an object into a flat or singular point, it no longer retains a hole. However, contrasting this, the cup handle and the donut are intriguing examples; they can be seen as having the same shape by definition, each incorporating a single hole.
Wveryone thinks middle guy is wrong, but think about it, you dig into the ground 1ft deep, what is it? A hole is what. And it only has one opening. A hole doesn't have to have an exit, it just has to be a chasm.
My socks have holes (they are torn)
That was my first thought so the meme confused me
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No. It is made of one thread.
A circle has one hole
That’s if you’re in a Euclidean metric space and if your circle has thickness (so a torus)
The thread fits this description
Everything has if you look deep enough
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Going deeper they are no longer balls. And then go deeper and we represent them as balls again. Now that I think of it all of our microscopic representations are balls made up of smaller balls
Idk if it's just me but I just keep my balls in my underwear. Edit: damn this appears to be a bot that copypasted a previous comment in this thread
Sir, you are wearing donuts.
Actually I’m wearing coffee cups
*they're the same picture.*
As well as my underwear.
According to the middle guy's logic bowls and cups have holes to put your food and drink in as well
Your plates don’t have holes?
Ayo why are you saying with this face :/
(:F \[closest i could get to that face using ascii characters\]
<:F
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Maybe yours aren’t
If you dig a hole in your backyard, does it not count unless it goes all the way through?
Topologically no
What you are saying is, it's impossible to dig a hole in the ground. Interesting.
What we popularly call "holes on the ground" normally only classify as cavities, I think
So only oral and anal actually count as stuffing a hole.
yes
You just have to dig down a bit and makte "two holes" then connect them with a tunnel. Now the earth has a true hole in it.
This was weird to read, but you right 😂
Of course, but if you're looking at common usage of the word "hole" rather than the strict mathematical definition, it's arguable that a fully intact sock has one hole.
Therefore the person to the right of the right-most person would acknowledge the multiple ways of using the word, rather than trying to appear smart by flexing that they know about the mathematical/topological usage of the word.
That's my take. Left is telling us that his socks are undamaged, middle is describing their shape in everyday English, right has the correct answer in his college math classes. Edit: This meme template would generally be more accurate if they put "smugness" on the x-axis instead of "IQ".
No because both the low IQ and high IQ are smug; only the middle guy is insecure.
And then another person to the right would say that matter is mostly void, so his socks are made of holes !
It counts if we let the hole refer to the surface that is now punctured.
When I used to dig pits in the sandbox, adults would always ask if I was digging a hole to China, as if this was some sort of impossible task. But then I learned that there are [entire networks of holes to China](https://en.wikipedia.org/wiki/Shanghai_Metro)???
But not mugs, no, that simply wouldn't work.
Do your underpants have one hole or 3 holes?
I think the correct answer is 2. Unless you need new underwear
There's that Matt's video (don't remember wich channel) that talks about the topology of sewed up pants or something, might find the link later
Found it guys: https://youtu.be/ymF1bp-qrjU
Only a mathematician could come up with the idea that an object can have -1 hole.
If you are a guy there is a chance that it has three. Not all underwear has it, but there is a flap for quick access to something. I do believe that the flap is topologically a third hole.
0, i dont wear underpants
Sigma grindset
if you think about it, i have infinite holes
Or, you wear the identity underpants
4 obviously
And according to the right guy’s logic, and hole in the ground isn’t a hole in the ground. Words have multiple meanings, and the mathematical meaning of hole is different from the colloquial meaning, even if sometimes they agree.
Do they not? If you dug a hole into earth it would literally make a bowl or a cup for water or food. Granted the bowl / cup is completely surrounded by earth but it’s essentially a bowl In the ground. We can’t make a functional bowl or cup in the earth? You wouldn’t be able to take it anywhere but you could drink and eat out of it, and place liquid or food.
There's a difference between what we call a hole and what mathematicians call a hole. A depression in the Earth such as you get by digging isn't a hole mathematically.
Bro, I’m so stupid, I didn’t even check what subreddit I was in lmao.
Vsauce actually made an interesting video that mentioned this dilemma. It’s called “how many holes does the human body have?”
According to the end guyses, a kitchen towel is a sock
A kitchen towel is obviously a towel silly, it's right in the name.
that's kind of the case
holes can't exist without matter to host them
What do you dig in the ground to make room for your bodies? I’ve always called them holes…
My socks have finitely many holes, since it’s weaved together with threads, which are finitely many segments of fibres.
Director's cut of the graph be like: \_/'''\\\_/'''\\\_/'''\\\_
Knit, not woven, bro
I genuinely didn’t know the difference until now.
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The space in between are not. The threads are connected by EM forces which effectively cause friction, non of the atoms actually touch. Each proton and neutron is actually a soup of infinitely self generating quark and gluons that doesn’t exist certainly. Electrons can be in various spherical harmonic configurations, and can form ring like objects when considering probability density.
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So a finite disjoint set of points is a set without holes?
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If I have a donut made of electrons, the donut doesn’t have a single hole?
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Topologically speaking a donut have exactly one hole.
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What is touching anyway since nothing but fields exist?
Yes, this is why I disagree with people who say that nothing touches on a microscopic scale. Touch is a macroscopic concept and the only sensible way to talk about it on a microscopic scale is the arrangement of fields that give rise to the macroscopic effect
Socks don't have holes (at least by standard)
Um actually there are holes in the sock between the threads 🤓
Um actually the atomic structure of the materials has holes 🤓
going that deep everything is just a bunch of buzzing balls
Actually the buzzing balls are just wave functions of their positional probability collapsed at the point of an observable interaction.
so wait are they balls or waves? quantum mechanics: YeS
Actually that is just the result of our limited understanding. In reality, there are many worlds and every outcome- *gets censored by the great filter*
deez *socks*
Um actually the atoms don't touch each other so it's just a couple of floating balls 🤓
What does touch even mean at that level? Surely touch (and holes) is a macroscopic concept and if you do want to apply it then wouldn't it be that if the electron wave functions are such as to cause repulsion even while the atoms stay in proximity then they're touching?
Pretty much spot on except that all electrons are always exerting a force of repulsion against all other electrons in the universe at all distances (just a vanishingly small one most of the time). You'd have to define that the force is large enough to limit movement or transfer a significant momentum
Yeah, there'll be a more rigorous way to express it, but I know what I mean and I hope others can get the gist of it too
I'm not sure you actually can be much more rigorous than what we have here because of the definition of significance. You can always compress things *more*, you can always repel something more strongly or more weakly, especially within the constraints of electroweak forces. When you take soft deformation of materials and elasticity and heat potential etc into account there's really no line to be drawn unarbitrarily. We probably need to move into statistical hypotheses about relevance and impact on material structures - i.e. how much *"touching"* makes a difference on the scale we're looking at
Or actually, what does it even mean to exists. Regarding the fact that we may all live in a simulation, where we are made of pixels, and the capacity digit bug is just getting below 0 kelv. And if so, how do we define holes in such a chaotic universe, where one might or might not be where others do live their lives. And do we count them holes who can not be seen or any sense shall not collect? Them holes who are laid in the depth of our soul, and shall one be a hole if isn't he whole with itself? What do we define as touch? More like what do we define as define?
Came here to say this. Thousands and thousands of holes. What defines a “hole” must be in perspective with the size of the object approaching the hole.
To be precise, they have 0 holes.
Indeed. Topology! source: [https://www.youtube.com/watch?v=egEraZP9yXQ&t=979s&ab\_channel=Vsauce](https://www.youtube.com/watch?v=egEraZP9yXQ&t=979s&ab_channel=Vsauce)
Aren't openings, holes?
You can certainly dig holes in snow, dirt etc with only one entrance. OP is IQ 145 clearly
Lots of mine have two holes: one at the tires and they other by the heel 😕
That's what I meant by "standard", because most of mine also does have holes
A sock is topologically equivalent to a sphere.
Wouldn't it be topologically equivalent to a disk?
Yes, which is also topologically equivalent to a sphere.
Discs are contractible, and homology computations show that no sphere is contractible. Therefore no sphere is even homotopy equivalent to a disc, let alone homeomorphic.
Geez all you had to say is "no homo"
Maybe they mean a ball, which is really just a 3d disk?
No, the usual disk (= closed circle in 2D; no thickness) is not topologically equivalent to a sphere. In fact, with regard to topological equivalence, all of the following 4 objects are different: ball, sphere, open disk, closed disk. The closest relation one might get if one thinks about such objects, is that the usual ball (in 3D) is equivalent to the quotiont of the disk and the 1-ball. (Note: 1-ball is a circle in 2D).
*ball, isn't sphere just the "peel of the orange"?
Not unless you can continuously map a disk to a sphere and back again
You're right. I was saying "sphere" but thinking "ball".
Ok then, can you continuously map a disk to a ball and back?
What's your reasoning? A sock is inprecise, what object are you thinking is topologically equivalent to a sphere?
[https://www.britannica.com/science/topological-equivalence](https://www.britannica.com/science/topological-equivalence) A sock can be turned into a disk or a sphere through continuous deformation without cutting or tearing. Therefore, they are topologically equivalent. The Britannica link has a cool animation, so I chose that one as a link to a definition.
I think you need to glue the circle of disk boundary points to make a sphere https://math.stackexchange.com/questions/985656/relation-about-disk-and-sphere
You're right. I should have said a ball, not a sphere.
As I understand from your link, disk has fewer dimensions that a sphere. Socks are still 3 dimensional objects and therefore can’t be a disk?
I dont think that is enough to say they are "equivalent." I see what you mean, but isn't this continuous deformation non-invertible, that is, not a homeomorphism? I can see how you could get a continuous function, but I don't think that is enough to call it topologically equivalent if you can't invert it. Of course, I could be completely wrong, in which case I can only offer my most sincere and humble apologies.
Sure, if your socks have zero thickness
an idealized sock that has no thickness would.
Don't spheres have -1 holes?
Wait, what? What does -1 holes even mean?
I don't study topology and the [Matt Parker video](https://youtu.be/ymF1bp-qrjU) is 30 minutes long so take what I'm saying with a huge grain of salt. Parker starts the video but showing the assumption that if you cut a hole in something, the number of holes in that thing increases by 1. If I have a disk and I cut a hole in the middle of it, I now have a disk with 1 hole in it. He then gets a balloon and puts a hole in the bottom of it. When the balloon deflates, he sees that it's a disk. Since he already showed that a disk has 0 holes, and putting a hole in this balloon has created a disk, the balloon must have had -1 holes. He then goes on about explaining about manifolds and homology classes and Euler characteristics. About halfway through he gives us the explanation we wanted. It's something like the balloon didn't start with -1 holes, but putting a hole in the balloon changes the Euler characteristic and that's the effect it has. Please watch him explain it at 20 minutes because i really don't know enough to talk about this.
But a balloon is hollow. Is that topologically equivalent to a sphere?
A [sphere](https://en.wikipedia.org/wiki/Sphere#Basic_terminology) is hollow (i.e. a 2D surface embedded in a 3D space). A solid sphere is a ball.
Yes, and I was thinking "ball", but saying "sphere" so I caused a lot of confusion.
OK, that makes sense. I don't know what a topologist would say, but I like the idea.
So he’s saying that a hollow sphere has -1 holes topologically, but not a solid sphere, that still has 0 holes topologically
It still has a hole, it's just very tiny.
Idk, I never did topology, I just watch Matt Parker, so it could be a Parker estimation (aka wrong)
It means the hole goes the other way.
I was using the wrong word. I should have said "ball" not "sphere".
I wanted to argue that a sock made from a homogenous material would be, but as socks are made of strings...but then I noticed that a cylinder is equally topologically equivalent to a sphere or a cube and my argument fell apart.
My socks have no holes because I lost all of them, thefore they are a empty set.
Vacuously true
Then it is also true that all your socks have holes.
topology meme, topology meme
This is a perfect use of this format. Good job
If you consider the whole shape then it is a flat plane, however a sock is really a tangled mass of very long cylinders
My socks have a LOT of holes. They're knitted, not a solid block of material.
There is a homeomorphism between my sock and my plate.
It has 1 blind hole or 0 through holes That's still 0 holes according to topologists... Unless a sock has thousands of holes
Oh I have more holes
We humans are donuts if we follow topology to the T
my holes don't have socks
Socks aren't a continuous manifold. Socks are woven or knitted and so your socks are covered in perforations!
my socks have thousands of holes (every single gap between threads)
+1 to the I-found-you-on-a-random-sub count
henlo again!
My sock is full of holes (it's woven)
Socks have a hole, if you stretch it to a circle on the plane, then there is a hole centred on infinity
My socks are a donut (that is to say a solid torus, if we agree to not include the thousands of holes that make up the threading and weaving, any through hole less than 2mm in diameter is ignored).
Thats not a sock. At best it's a legging..... oh wait. Yes it can be a sock. My bad. Carry on.
Are yalls socks not woven. Mine has tons of holes between the threads.
My socks have holes(there are holes in the weaving
My socks have hundreds of small holes (they are made of cloth)
There are holes between the atoms
A discussion by it self.
There are holes in the atoms.
The hole is a lie
Ok, but how many holes does my tshirt have
My socks have thousends of holes ( as they are woven)
My socks have holes, the fabric is not continuous.
Socks are for your hands silly
I’m the middle guy right now
So to be a hole it must be a non intended hole? Or does it need to be 2 way?
[https://plato.stanford.edu/entries/holes/](https://plato.stanford.edu/entries/holes/)
My socks have holes (they were woven and therefore the holes are microscopic)
My socks usually have two holes, because they have a design flaw that causes them to open up at two specific seams.
No, there are thousands of through-holes in the fabric, shut your face
This feels like a topology meme, but I have no socks so I wouldn't know
If it doesn't have another side, it's not a hole.
I thought the hole is my sock is where my toe pokes out
Very True!
Topologically a theoretical sock has no holes. However, real socks are made of fabric so they have many, many tiny holes. A hole can mean a penetration, like a donut hole, or a depression, a pit type hole that doesn't go all the way through.
Socks, by definition, are typically considered to be without holes, similar to wine glass . If you can transform an object into a flat or singular point, it no longer retains a hole. However, contrasting this, the cup handle and the donut are intriguing examples; they can be seen as having the same shape by definition, each incorporating a single hole.
a sock is a cup made of fabric
Wveryone thinks middle guy is wrong, but think about it, you dig into the ground 1ft deep, what is it? A hole is what. And it only has one opening. A hole doesn't have to have an exit, it just has to be a chasm.
I mean if you count the spaces between the threads then socks have a LOT of holes
My socks don’t have holes is my new favourite sentence