0

I apologize if this is a bit simplistic, but how can there be rotational degrees, or in simpler terms more than one "direction," even if we are speaking about a single plane? Is this just a supposition which is required in order for geometry to correspond to the world insofar as it is (for normal people) practically a Euclidean space, or instead is its soundness derived from a prior proposition? Similarly, how can there be multiple planes -- which, as I understand, are at right angles to each other? And to this questions about planes, I also have the same question regarding its logical soundness.

I am not trained in mathematics, so if the answer is complicated, it may need to be simplified for me. I cannot explain it, perhaps because I lack the terms to be more precise, but I find it very strange. That there is more than one direction and dimension is obvious enough. But as to how... I am very much left speechless.

(As a side note, this question reaches for me even to the level of the distinction between points on a line. Unless, I suppose, there is somehow an absolute and fixed point [which, on second thought, would seem to push the question back a step further], how can there be any distinction between one point and another without recourse to brute factuality?)

Anthony V
  • 1
  • 1
    This is fairly confusing read, and you've asked multiple questions within the same paragraph. I would refine this and ask something more concrete. Essentially however, mathematics is made up of definitions and from these definitions we make deductions. So if you have a $2$ dimensional plane, you can define some direction however you like with respect to some reference point. The question of "how" is irrelevant. It has this direction because we have defined it as such. – J P Feb 01 '19 at 06:09
  • I think your question is related to the concept of dimension. – with-forest Feb 01 '19 at 06:12

1 Answers1

2

Rotation as such takes place within a 2D subspace. Everything what is orthogonal to that subspace serves as "axis" to rotate around. So in a 2D space you just can rotate around a point. Within 3D you can rotate around a linear axis. Within 4D you can rotate around an orthogonal 2D subspace. And therefore you can have there 2 independend rotations at the same time, one within the one suspace and one within the orthogonal subspace. This then is what is called a Clifford rotation. Within 5D you even can rotate around a 3D subspace. Etc.

--- rk

Dr. Richard Klitzing
  • 4,241