Is there a finite number of possible human ideas?

Well that would be something like a roulette but for 4D, right? We have equations for cycloids, trochoids and catenaries and these are linked into things like the Shortest Time  ^*

problem. We can consider that the essence of spheres is being equidistant from the origin in all dimensional or maybe it is symmetry under rotation so we need to find the essence of a cycloid or the essence of the shortest time problem. It's probably something to do with the relationship between derivatives in one dimension with measures in another.

I bet we could do it with Hamiltonian mechanics.

Brachistochrone?

[1] This facsimile operated in part by synAC.

You don't need any of that; The computer can do Newtonian mechanics in 4D just as easily as in 3D. (Though the results are harder to convey.)

edited 18th Jan '11 1:14:29 PM by Yej

Da Rules excuse all the inaccuracy in the world. Listen to them, not me.

@Zhe Toralf:
There is an old math joke that goes like:

A math student and a biology student visit a physics lecture in university about string theory. The biology student is confused - "How do you imagine a 9-dimensional space?" "That's easy." answers the math student "Just imagine an n-dimensional space and specify n equals 9."

Basically all of the examples you gave can be handled with practice - more difficult examples only require more practice. If you understand the essence of a dimension, applying it to more than three isn't that hard, and if you understand the essence of color (a collection of different frequencies that get interpreted in a certain way) it's not that hard to imagine another color with a different interpretation.

Pour y voir clair, il suffit souvent de changer la direction de son regard www.xkcd.com/386/