A tesseract can be represented in normal 3D space, but it’s labelled a 4D object – why is this?
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A tesseract is the 4D version of a cube, which in turn is the 3D version of a square, which is the 2D version of a line, which is the 1D version of a dot.
The thing in common with all these shapes, is that each corner connects lines in a L shape, that’s a right angle. The number of lines it connects depends on its dimension. A square connects 2 lines, a cube 3 and a tesseract 4.
You can draw a cube (3D) onto a square of paper (2D) if you’re good at drawing, but you’d only see the cube from one point of view. This is called projection because it’s like you’ve drawn the shadow of the cube on the paper. Imagine the cube was floating between a bright light and the paper.
You don’t really appreciate this when you’re drawing because your brain is amazing, it takes shortcuts and just draws what seems natural in our 3D world.
A tesseract is definitely a 4D object, but you can project it onto a 3D space like drawing the cube. It’s a bit more involved and requires using mathematical rules rather than visualisation but if you think about what information you need to draw a cube (3D) on a square of paper (2D) and how that changes with dimension, then you’re on the right track.
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