Monday, 4 August 2014

Dark thinking with Quaternions

When I hear about the fourth, (or more) spacial dimensions it reminds me of
Quaternion multiplication.

I am impressed the indignation for the square-root of -1 seemed to be an impediment to an equation, and the gall of using i as a solution. I'm amused that in many cases that provides the solution to an actual equation resulting in a solution back in the plain of the number line.

Just as we can avoid the physical limits of three gimbals and the associated problems with Euler angles by converting our calculation to using quaternions I would argue that i,j and k do not exist, but that we need to imagine that they do in order for our minds to accept the logic that teleports us from problem to solution.

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