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#312 to #118

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 2dimensional 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.
#313 to #312

pandation (11/24/2012) []
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.
#128 to #118

ruinsage (11/21/2012) []
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

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.