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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Think of a line on a piece of paper. The line represents one dimension while the piece of paper represents 2 dimensions.
For every spot on the line, there is an infinite number of spaces above and below it in the 2 dimensional space.
Now think about the 2 dimensional paper in 3 dimensions. For every spot own that 2 dimensional paper, there are infinite number of spaces above and below the piece of paper.
So the leap you have to make in order to understand extra spatial dimensions is that you have to realize there are different types of above and below than just the kind represented by the 3rd dimension. So traveling through a 4th spatial dimension would be sort of like moving either up-and-down through different three dimensional spaces, each one of which is just a cross-section of the larger 4 dimensional space you cannot fully see at any time.
For instance, a small rock might be a large 4D boulder just barely protruding into our 3 dimensional space. So going upwards in 4 dimensions might make it seem to grow bigger in front of you, while going downwards might make it seem to get smaller. This is because you are moving through different 3 dimensional cross-sections of 4 dimensional space.
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