I get 1, 2, and 3 dimensions and their visual representations. For instance, 3-dimensional space has width, length, and depth but how about a 6-dimensional space, how can we grasp it in n intuitive manner free of mathematical analysis?
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I found it best to imagine it in terms of grids. 2d is normal, 3d is a cube of cells, and I started to imagine 4d as a line of these cubes, but not connected, 5d is a grid of the cubes, and 6d is a cube of cubes. The important part to remember is you can move between the cells in the original cube, but also along a line in the larger dimensional cube just as easily. In a 3d world this higher dimensional movement looks like teleportation but that is just what higher dimensions look like to a lower dimension.
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