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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> how can we grasp it in n intuitive manner free of mathematical analysis?
Like others have said, the short answer is that you can’t, but I want to point out that this is what makes math so awesome. The things you find to be intuitive feel that way because you have learned them through experience with your senses. If you have seen it or felt it many times in your life, it becomes “obvious” and “intuitive” just because your brain recognizes the patterns. However, do you believe that there is more to the universe than what you can directly see and touch? If so, you are right! There is _a lot_ more. Infinitely more, even. The amazing thing about math is that we can use it to explore those things that we cannot directly experience. We can do that because math is just symbolic logic. It’s a system for making statements that _must_ be true, no matter how complicated or far removed from what we can directly experience they are. It lets us understand things that are not intuitive, or even more incredibly, things that are _counter_-intuitive, meaning that what happens is the opposite of what you would normally expect to happen. That gives us incredible powers of prediction and lets us solve problems that would be unsolvable otherwise.
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