Ok so I just read somebody else’s question on dimensions and that prompted me to ask this question. It is kind of hard to explain my thought process but I’ll do my best.
So we often think of 2 dimensional objects as being flat, but I feel like a truly flat object would be as un-perceivable as a 4d object to us. So if we imagine a cube made of paper we have a 3d object.
Now if we squish the cube down and flatten it we have a “2d” object, a square. But in reality that square isn’t flat because the thickness of the paper still exists. So how do we make the paper truly flat? We can cut it in half to make it thinner and flatten it out, but there is still depth. No matter how much we “flatten it” there will still be some depth. Even if it’s 0.00^ to the trillionth degree.
So my thought is for something to be truly flat it must be completely non-existent in our universe. So how can we know that it’s flat? Once we can perceive of a truly 2d object wouldn’t you also perceive an entirely new plane of existence that we can’t even fathom?
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You’re right. Physical objects are made of atoms, so the thinnest possible object would be one layer of atoms. It would definitely have a height as well as a length and width. Only a theoretical or imaginary object can have exactly zero height.
You’re right, 2D objects don’t actually exist in the physics of our world. They’re just as hypothetical as 4D objects. We can do stuff with it in math and simulations, but they aren’t tangible objects.
You’re right, a truly 2D object is impossible in our universe.
> how can we know that it’s flat
The object does not physically exist, so it has all the properties _we_ decide, so it is flat _by definition_. Same reason as a 1D line is straight _by definition_ and a 0D point is infinitely small and dimensionless _by definition_.
You could use the same reasoning for numbers; the number “5” does not exist in nature. How do we know that “5” matches the number of fingers in a hand? We know, because _we_ decided it is so.
Well you see u/dayton44 circles and triangles and squares don’t actually exist. Yep, they just don’t. In fact, everything in mathematics is made up and imaginary, none of it is a **real**, existing, tangible **thing**. Have fun sleeping tonight.
The other answers are good, and yes – generally things have to be a certain size to be real.
But then we get to fundamental particles.
In theory fundamental particles – things like electrons, neutrinos, quarks – are dimensionless; they have no height, width or depth! They cannot for them to be fundamental (if they had length you could cut them in half lengthwise, and you’d get something smaller that makes up them – meaning they’re not fundamental any more).
So in theory everything is made up of things that are not just flat, but infinitely small points, with no length in any direction.
Except then we get into quantum mechanics, and uncertainties. We find that things don’t have absolute values, but average values and uncertainties. Including where something is. An electron is supposed to be in a particular spot, but when we look for it it might be there, or a bit to the left, or a bit to the right… there is an uncertainty to where it is. And so even though it has no dimension in theory, we can treat it as taking up space in practice because of the fuzziness of where it is.
Physics can get fun and weird.
You are correct that no physical object is truly 2D. But that obviously doesn’t mean we can’t conceive of the idea.
You might find this video interesting where the guy measures the thickness of sharpie marks.
In a three-dimensional world, there can be no truly two-dimensional material objects, because everything is necessarily made of three-dimensional objects.
So a geometric plane is *flat* only conceptually, just as a line is not infinitely thin but with a length, and a point is not infinitely small with a definite position. But in spite of that, the mathematics of planar geometry is quite useful in a three dimensional universe.
Two dimensional objects do not exist in practice, just like 4 dimensional objects. They are concepts. We know for certain that two dimensional objects are flat because we defined two dimensional objects as flat objects.
>Ok so I just read somebody else’s question on dimensions and that prompted me to ask this question. It is kind of hard to explain my thought process but I’ll do my best.
>
>So we often think of 2 dimensional objects as being flat, but I feel like a truly flat object would be as un-perceivable as a 4d object to us. So if we imagine a cube made of paper we have a 3d object.
>
>Now if we squish the cube down and flatten it we have a “2d” object, a square. But in reality that square isn’t flat because the thickness of the paper still exists. So how do we make the paper truly flat? We can cut it in half to make it thinner and flatten it out, but there is still depth. No matter how much we “flatten it” there will still be some depth. Even if it’s 0.00^ to the trillionth degree.
>
>So my thought is for something to be truly flat it must be completely non-existent in our universe. So how can we know that it’s flat? Once we can perceive of a truly 2d object wouldn’t you also perceive an entirely new plane of existence that we can’t even fathom?
I may be misunderstanding your question, but I think you might be using the wrong definition of flat. In physics, particularly when discussing space and dimensions, the term flat pertains to the curvature (or lack there of) of space itself.
We believe our universe to be flat. What this means, is that if you were to take say two lasers, and shoot them perfectly parallel to each other in the same direction, that the beams would always be exactly the same distance apart. There is evidence that this is true through the local cluster of galaxies at least, and we have no reason to suspect the curvature of space would be different beyond that.
Physicists like to reduce the number of dimensions when working on a problem because it makes the math a little easier and makes visualizing the results possible. The human brain isn’t designed to process information beyond the 3 physical dimensions you can see. Two dimension space is even easier to mentally process.
You mentioned thinking of a piece of paper as two dimensional. It might be better to think of the paper as the fabric of a two dimensional space. The actual ‘space’ is the square you draw on it. If you draw two parallel lines on your paper, they will stay parallel all the way to the edge. You can even wrap your paper around a cylinder, and continue to draw those lines around the cylinder for ever and they will stay parallel. The two dimensional space on the paper is flat.
Take that same paper and put it in a dish or on a ball. Now try to draw two parallel lines. In this curved space, the lines will converge or diverge. Or even do other weird things.
We can use these models of flat, convex, and concave 2D ‘space’ to get our minds wrapped around how light or on object traveling through our 3D space might behave if our space was curved in a similar manner in a 4th or higher dimension than we can perceive.
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