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
You remember what a 2 dimensional graph is? Like coordinates X,Y. That’s how you describe where a point is on a 2d plane. A point 7,2 is “7 to the right and two up” (all in inches).
You can do the same thing with 3 dimensions. Imagine a cardboard box and there’s a fly in it. To describe the point where it is, you could say it’s at 7,2,5 “7 to the right, 2 up, then 5 deep (from center origin)”.
Now imagine a whole bunch of cardboard boxes, neatly stacked up, filling an entire room. Again, we want to describe where the fly is, so we can say it’s position is 7,2,5 but it’s **in box 14**. Or we can say its position is 7,2,5,14.
But here’s the thing — the boxes aren’t *actually* stacked up as you’re probably imagining. All of the boxes are taking up the same space. The fly is in box 14. The fly isn’t in box 13, even though 13 and 14 take up the same space.
Now imagine a whole bunch of rooms, neatly stacked up, where each room is full of those cardboard boxes….
Now, you might be wondering how a bunch of cardboard boxes can take up the same space while there being a fly in one box but not another. They aren’t *actually* taking up the same space, but we can’t really imagine it otherwise. Here’s a way to kind of extrapolate it:
Go back to looking at the 2d graph that’s just X,Y. Pretend like you don’t know what 3d is, everything just looks flat. You may see the fly at position (3,8) and a caterpillar at the same position. How? Because the caterpillar is crawling around on the ground while the fly is up in the air. Yes, they’re both at (3,8), but that’s because you’re only able to see in 2d, not 3d. The fly and caterpillar are both in the same spot from a 2d viewer but not a 3d viewer.
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