Weirdest Thing In 4D

[PatrickPowers]

To me the weirdest thing is...

If you have two perpendicular planes then the two planes have no orientation with respect to one another. Every vector in every plane is perpendicular to every vector in the other plane. They are in two entirely different worlds. I just can't see this.

[PatrickPowers]

Suppose you have a 2D object floating in the wx plane in 4D space. Orbit that object in the yz plane. The object's appearance doesn't change at all.

Go to N dimensions. As long as your orbit has no wx element and the distance from it doesn't change, the object's appearance does not change. The foreshortening we are used to occurs only if there is an element in the wx plane. Moving in the N-2 other dimensions can change the distance from the object and hence its apparent size but nothing else. I still find it weird but at least I sort of get it. As said John von Neumann,

young man, in mathematics you don't understand things. You just get used to them.

The reason we are not used to this is because in 3D moving relative to a 2D object without changing its appearance isn't possible. But in 4D or above it is easily possible. All you have to do is have no element in the wx plane and keep the distance from the object constant.

[PatrickPowers]

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[PatrickPowers]

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