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by epidemian 586 days ago
> For example, if I tell you that I can visualize more than 3 dimensions, then how could you verify or disprove that?

I don't really know. The first thing that came to my mind would be to ask to draw/model different cross-sections of a 4D object ("cross-volumes"?).

We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. Like, sections of a human body, or a house. So, maybe someone who can visualize 4D objects in their head could also model 3D "cross-sections" of that object at arbitrary "cuts". And we could check if those 3D radiographies are accurate, because we can model those 4D objects on a computer, and draw their 3D cuts.

Just a simple idea. I'm sure there could be other ways of probing this.
2 comments
JadeNB 586 days ago
> We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily.

Many people can draw cross-sections reasonably well, but I can't. Nonetheless, I believe that I can visualize 3D objects.

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wongogue 586 days ago
But you can still draw the concepts of a cross section, right?
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JadeNB 585 days ago
> But you can still draw the concepts of a cross section, right?

I'm not sure what that means, but my inability to draw is astounding.

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quuxplusone 586 days ago
> We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily.

I don't think that's true. For example, consider a regular octahedron: take a parallel pair of its faces and bisect the octahedron between those faces. What's the resulting figure? What happens to the figure as you tip the plane?

I mean, obviously the task I just set isn't impossible; and with a little reasoning anyone can give the answer in a few seconds; but it feels too me like the answer is not simply intuited merely by the virtue of our being 3D creatures.

Sure, part of the difficulty stems from that the octahedron (to most folks) is both less familiar and slightly more complicated than the cube. But the same applies to the hypercube!

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