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#312 to #118
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Ruspanic (11/23/2012) [-]
Probably a bit late to reply here (I haven't had Internet for a day or so), but here's a 2-dimensional representation of what you're saying.
Would you believe me if I told you that the shape outlined in red was a perfect square?
This is actually a 2D model of a cube, viewed from the front. All sides of the cube are perfect squares, and there are 6 sides (even though you can only see 5 of them from this angle, and only one of those appears to be a square).
Same thing with the tesseract. What you have is a 2D picture of a 3D model of a 4D object.
Just as a 1D line segment has two 0D "sides" that are points, a 2D square has 4 1D sides that are line segments, a 3D cube has 6 2D sides that are squares, and a 4D tesseract has 8 3D sides that are cubes. And so on.
Of course the 4th spatial dimension is a hypothetical mathematical concept. It could exist in theory, but if it does we cannot observe it.
Would you believe me if I told you that the shape outlined in red was a perfect square?
This is actually a 2D model of a cube, viewed from the front. All sides of the cube are perfect squares, and there are 6 sides (even though you can only see 5 of them from this angle, and only one of those appears to be a square).
Same thing with the tesseract. What you have is a 2D picture of a 3D model of a 4D object.
Just as a 1D line segment has two 0D "sides" that are points, a 2D square has 4 1D sides that are line segments, a 3D cube has 6 2D sides that are squares, and a 4D tesseract has 8 3D sides that are cubes. And so on.
Of course the 4th spatial dimension is a hypothetical mathematical concept. It could exist in theory, but if it does we cannot observe it.
After this entire conversation I did more research that I'd like to admit about the subject, mainly because I found it very interesting. I found out what a tesseract actually even is beyond my previous comprehension and basically found a textbook length explanation of what you condensed into a comment. I'll admit I did not know what I was talking about at the time and now am better educated for circumstances involving the subject in the future.
it's called a linear transformation.
If you transform an object consisting of 8 cubes from a 4 dimensional vector space onto a 3 dimensional vector space, and then onto a 2 dimensional vector space, you get this.
The 4th dimension in physics might be time, but its not in mathematics
If you transform an object consisting of 8 cubes from a 4 dimensional vector space onto a 3 dimensional vector space, and then onto a 2 dimensional vector space, you get this.
The 4th dimension in physics might be time, but its not in mathematics
#122 to #121
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Xepheros (11/21/2012) [-]
You obviously don't, since it's not a cube. Let me repeat that, the tesseract is the 2D representation of the 3D shadow of a 4D cube. The actual 3D shadow looks different, because humans cannot percieve 3D - and the 4D cube looks very different, because humans can't even imagine 4D since we live in 3D and our eyes watch in 2D.