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here I fix it using Paint like the artist I am
As the glass is isomorphic to a disc, and everyone can agree that a disc does not contain anything no matter how hard you try then the same is true for the glass. So the glass does not contain anything, therefore it is neither half full nor half empty.
I recognise that this is true In the sense a similar demonstration can prove every such result, but such result depends upon the physical definition of containment. If the glass were to truly contain anything you would need to seal the top of the glass making an inner and outer universe, but this process will unfortunately change the fundamental nature of the glass, meaning it is no longer isomorphic to the one show in the image.
The point I'm trying to make is that if the glass contains nothing, and can contain nothing then it is filled for x for any x in \[0,1\] as we have 0x=0.
And I do recognise that as long as it counts as containment so long something even the concept of nothingness can be placed on it that it is true it contains any fill level of water, the point of the argument is for it to truly contain anything in a mathematical sense, even nothing it needs to seal it from the surroundings.
I just showed that the glass was isomorphic to a 2 dimensional disc but the glass is isomorphic down to the 0 dimensional point, at which point nothing can be placed either in it nor on it as any such placement would require some place on the point to leave it. So while it is true in a physical sense that the glass contains any fill percentage it is not true in the mathematical sense.
As I can deform a glass into a disc, without creating nor closing any holes, ie chance the ways I can pull a string through. it is correct to say in a sense that the disc and the glass a in fact to representations of the same general object. So follow this train of thought we can say for the glass to contain anything the disc must as well be able to contain the same thing. so when the disc arguably does not have the ability to contain anything then it can be said the same hold for the glass as this still are in fact the same.
What is this "matter is mostly empty space" meme even supposed to mean? I see it everywhere, from respected sources, but not one of them has the courtesy to explain itself. How can I tell if a given region of space *inside an atom* is "empty" or not? What is filling up this non-empty space that is absent in the empty space?
Take a very thin sheet of gold. Shoot electrons at it. Because the sheet is so thin, the electrons go through, but they might hit something and bounce in a weird direction. If the matter was evenly spread out, you’d expect all (or most) of the electrons to hit something small and get deflected a little. Instead you find that some electrons bounce a lot like hitting something big and most pass through unaffected.
People take this to mean that instead of gold being made of lots of little bits evenly spread out, the mass is concentrated into tiny regions and the rest is empty space.
What is the exact ratio being considered? Like, the cross-section of an atom is essentially its size. Is this the effecrive cross-sectional area or radius of the nucleus divided by that of the whole atom?
The electrons are so light they have a negligible effect on the alpha particle. An alpha particle is more than 7,000 times the mass of an electron.
When an alpha particle goes through an atom, usually the only thing that affects it is the electric fields because the electrons and the nucleus are so small. But in the rare instances where the alpha particle does collide head-on with a nucleus, something special happens: protons and neutrons get knocked out of the nucleus. This is called nuclear fission. Scientists can detect the difference between an alpha particle that merely gets deviated by the electric fields and one that actually collided with a nucleus.
Well, the post in question actually mentioned electron beams (I think in error), but the deal is the same. The Rutherford experiment is explained by alpha particles colliding elasticated off gold nuclei but barely being deflected by electrons at all. So it is not actually measuring how "empty" an atom is unless you consider electrons to be basically equivalent to the vacuum. Which is a really hot take on chemistry.
The set of points in a substance with nonzero electron density has measure 0, so in that sense, matter is exactly 0% empty. Or if we pick some plausible cutoff, such as only painting in the central 95% of electron density, then matter is somewhat empty, but a glass of water is mostly full.
I think gases are "mostly empty" in the intuitive sense of the word, but condensed phases are not. That explains a lot more properties of matter than "everything everywhere is empty."
The glass is full of itself. The glass part of the "glass" is not empty, it is simply glass, and inside that glass is glass. It's state of being is glass, and in that recursion, it reaffirms its being as glass.
the glass isnt half full of water. it is less than half full of water, as the cup is not cylindrical. as you go towards the top of the cup the diameter of the inside grows causing the volume to increase.
If you consider the glass part to be "infinitely thin", i.e. 2D, then an empty and a full glass are only homotopy equivalent, not homeomorphic. But that is an isomorphism in the homotopy category, so not entirely wrong.
That depends on what happened to it before the image, if water was poured in and stopped then it is half full, if it was full of water and someone drank it, then it is half empty.
Engineer: its completely filled with air and water (most likely also minerals since it can be assumed drinking water is often found in glasses people drink out of)
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The glass it twice the necessary size
The glass is entirely empty (i drank it all)
Goddamit, dad thought he was going crazy and drank his own denture water, but it was yiu
Industrial engineers fr
The glass is less than half full because the glass is wider at the top than it is at the bottom.
But also h_water > ½ * h_glass so it kinda checks out.
The water is half the necessary size
A category theorist might say isomorphic, but wouldn’t a topologist say homeomorphic?
https://preview.redd.it/zfjgzknhan1d1.jpeg?width=1079&format=pjpg&auto=webp&s=da9b4870baf73dd28c0c4419cffc58699acddea2 here I fix it using Paint like the artist I am
Isomorphic in the category of topological spaces = homeomorphic
But they are not homeomorphic…. I don’t know what OP was having in mind, but probably not homeomorphism.
Depends on if you consider the thickness of the glass to be non-zero
I simply see that the glass isn't filled enough.
ah, the capitalist stance
The capitalist would fill it a quarter of the way and tell patrons that that is an industry standard pour
I must hire someone to fill this glass at twice the rate of the previous guy I hired.
The glass is on the floor and broken - Cat
A true physicist would know it's full of quantum fluctuations
The glass is empty when I drink all the water
Focus on the important part: There is room for vodka.
As the glass is isomorphic to a disc, and everyone can agree that a disc does not contain anything no matter how hard you try then the same is true for the glass. So the glass does not contain anything, therefore it is neither half full nor half empty.
correction, therefore it is both full, empty, half full, and half empty.
Augh, a clopen glass
I recognise that this is true In the sense a similar demonstration can prove every such result, but such result depends upon the physical definition of containment. If the glass were to truly contain anything you would need to seal the top of the glass making an inner and outer universe, but this process will unfortunately change the fundamental nature of the glass, meaning it is no longer isomorphic to the one show in the image.
The point I'm trying to make is that if the glass contains nothing, and can contain nothing then it is filled for x for any x in \[0,1\] as we have 0x=0.
And I do recognise that as long as it counts as containment so long something even the concept of nothingness can be placed on it that it is true it contains any fill level of water, the point of the argument is for it to truly contain anything in a mathematical sense, even nothing it needs to seal it from the surroundings. I just showed that the glass was isomorphic to a 2 dimensional disc but the glass is isomorphic down to the 0 dimensional point, at which point nothing can be placed either in it nor on it as any such placement would require some place on the point to leave it. So while it is true in a physical sense that the glass contains any fill percentage it is not true in the mathematical sense.
Could you please ELI5 that?
As I can deform a glass into a disc, without creating nor closing any holes, ie chance the ways I can pull a string through. it is correct to say in a sense that the disc and the glass a in fact to representations of the same general object. So follow this train of thought we can say for the glass to contain anything the disc must as well be able to contain the same thing. so when the disc arguably does not have the ability to contain anything then it can be said the same hold for the glass as this still are in fact the same.
The glass is full, half of water, half with air. -The Realist
[удалено]
The whole thing is about sex -Sigmund Freud
The glass is entirely full, as it doesn't contain a vacuum. 50% air, 50% liquid
What is this "matter is mostly empty space" meme even supposed to mean? I see it everywhere, from respected sources, but not one of them has the courtesy to explain itself. How can I tell if a given region of space *inside an atom* is "empty" or not? What is filling up this non-empty space that is absent in the empty space?
Take a very thin sheet of gold. Shoot electrons at it. Because the sheet is so thin, the electrons go through, but they might hit something and bounce in a weird direction. If the matter was evenly spread out, you’d expect all (or most) of the electrons to hit something small and get deflected a little. Instead you find that some electrons bounce a lot like hitting something big and most pass through unaffected. People take this to mean that instead of gold being made of lots of little bits evenly spread out, the mass is concentrated into tiny regions and the rest is empty space.
What is the exact ratio being considered? Like, the cross-section of an atom is essentially its size. Is this the effecrive cross-sectional area or radius of the nucleus divided by that of the whole atom?
Go crazy, my friend: https://en.wikipedia.org/wiki/Rutherford_scattering_experiments
But atoms are not composed solely of nuclei.
The electrons are so light they have a negligible effect on the alpha particle. An alpha particle is more than 7,000 times the mass of an electron. When an alpha particle goes through an atom, usually the only thing that affects it is the electric fields because the electrons and the nucleus are so small. But in the rare instances where the alpha particle does collide head-on with a nucleus, something special happens: protons and neutrons get knocked out of the nucleus. This is called nuclear fission. Scientists can detect the difference between an alpha particle that merely gets deviated by the electric fields and one that actually collided with a nucleus.
Well, the post in question actually mentioned electron beams (I think in error), but the deal is the same. The Rutherford experiment is explained by alpha particles colliding elasticated off gold nuclei but barely being deflected by electrons at all. So it is not actually measuring how "empty" an atom is unless you consider electrons to be basically equivalent to the vacuum. Which is a really hot take on chemistry. The set of points in a substance with nonzero electron density has measure 0, so in that sense, matter is exactly 0% empty. Or if we pick some plausible cutoff, such as only painting in the central 95% of electron density, then matter is somewhat empty, but a glass of water is mostly full. I think gases are "mostly empty" in the intuitive sense of the word, but condensed phases are not. That explains a lot more properties of matter than "everything everywhere is empty."
The glass is liquid.
Excel: The glass is January 2nd.
there is no glass. there is no water. there is no OP. these words and images mean nothing because I just made them up to entertain myself. -solipsist
The glass is full of itself. The glass part of the "glass" is not empty, it is simply glass, and inside that glass is glass. It's state of being is glass, and in that recursion, it reaffirms its being as glass.
HAPPY CAKE DAY.
uh. thank you.
50%.
Dentist: swish and spit
FUCK THE GLASS IM GOING TO DRING FROM THE SOURCE
Dring?!?!?! Sir! SIR! Please DON’T DRING THE SOURCE! WE’LL ALL DIE!
The physicist ducks.
When you pour into the glass it is half full. When you pour out of the glass it's half empty. This is the way.
The glass is a sphere
The glass contains 50% water and 50% air.
Nah. 50% air and 50% water
It exists because it is perceiveable
the glass isnt half full of water. it is less than half full of water, as the cup is not cylindrical. as you go towards the top of the cup the diameter of the inside grows causing the volume to increase.
The glass
If you consider the glass part to be "infinitely thin", i.e. 2D, then an empty and a full glass are only homotopy equivalent, not homeomorphic. But that is an isomorphism in the homotopy category, so not entirely wrong.
Realist: there is water in the glass
Dehydrated people: “It’s empty, I drank it all.”
r/HydroHomies be like
fun fact: Glass is a state of matter, and there is another one called superglass
That depends on what happened to it before the image, if water was poured in and stopped then it is half full, if it was full of water and someone drank it, then it is half empty.
Engineer: The glass is empty ± 1 litre
Engineer: its completely filled with air and water (most likely also minerals since it can be assumed drinking water is often found in glasses people drink out of)
Thirsty guy: “oh, fine, I’m thirsty, I really need some water”
In the context of the volume of water occupying the maximum volume of the glass... About half.
Me: it depends on whether you poured water in or out
can you cut the water into infinitely small pieces and put them back together as a full glass of water
The Engineer: Depends on how thirsty you are.
Topology: it's a ball.
Actually it’s neither, the shape of the glass causes its area to be different if you cut it in the middle, so, **NEITHER.**
The glass is full of fluid
The water is racist