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?
In: 8
Once I get above 4 or 5 dimensions, I like to skip directly to thinking in terms of a large number of dimensions, like “Okay if this was like 10,000 dimensions how would it work?”
Since 10,000 dimensions is so far beyond your ability to track individually, it actually helps to clarify your thinking, because the sheer size of the number 10,000 forces you to think of the dimensions “in bulk”… “Okay this is the thing that happens for each extra dimension and it happens 10,000 times”.
Think about the jump from 1 dimensions to 2 dimensions. What did you add? What new possibilities open up?
Now think again about the jump from 2 dimensions to 3 dimensions. What did you add? What new possibilities open up?
Now, instead of trying to picture it, instead think about a dimension as “adding” a new direction which “opens up” the possibility of traveling in a way that’s “perpendicular” to all the existing directions.
Now imagine “adding” a new direction 10,000 times, so you can travel in 10,000 ways that are all “perpendicular” to each other.
Of course the number 10,000 isn’t special, you could just as easily do the same sort of thinking for 6 dimensions or 10,000,000,000 dimensions.
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