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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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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