Re: Where is it? In 3D or 4D?

Clifford Nelson wrote:

Is gimbal lock a hint that the definition of physical space as three dimensional instead of four dimensional is just a case of too much brevity by mathematicians?

No. Orientation space is quite definitely three-dimensional. The "shape" of this space (technically: its topology) is just not as simple as a 3D rectangular brick; just like the surface of a sphere is not quite as simple to navigate as a rectangular map.

Gimbal lock is no stranger than the fact that there's no way to go west while standing exactly at the north pole

and a method to overcome gimbal lock uses four dimensional unit quaternions.

Which means it's still three-dimensional in effect --- the "unit-length" restriction eats one of the four degrees of freedom in a quaternion.

But that's only *one* alternative method. The other one uses rotation matrices.
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