eli5: what is 4D space?

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I just dont know what Is 4D space and i can’t imagine it…

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Anonymous 0 Comments

Imagine that one day you picked up a piece of paper, and you found these 2-dimensional, living, intelligent (and English-speaking!) people on that paper. How would you describe our 3-dimensional world to them?

Well, they still have these basic 2-D shapes such as circles, squares, etc. They lack understanding of the 3-D version of these shapes (spheres, cubes). But, there is a relationship between the 3-D shapes and the 2-D shapes – a circle is just the cross-section of a sphere.

A more visual example: if you are somehow able to physically enter into these 2-D people’s space, then from their point of view, what they are seeing is a cross section of you. Let’s say that you happen to be “waist-deep”, then they’d see a roughly oval shape, with a layer of skin on the outside, cross-section of the spine off to one side, jumbled cross-section of your intestines in the middle, wrapped around half digested dinner from last night, like a CT scan.

Now, back to your question. The above thought experiment applies if you just change the 2-D/3-D to 3-D/4-D. The 3-D world that we live in is just a cross section of the 4-D space. That is another dimension out there that we literally can’t fathom, but if we were to ever meet a 4-dimensional being, we may very well be talking to a blob that happens to be a cross section of their pinky toe.

Mathematically, the 2-D world has the x and y axis, and they are perpendicular to each other. Here in 3-D world, we add a z axis which is perpendicular to both x and y. In the 4-D world, we then add a 4th dimension that is perpendicular to all 3 of x, y and z!

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