Deflating Hyperspace

[Richard Fiero]

Daniel Harper wrote:
>. . .
>As near as I can tell, quaternions and vectors are essentially just 
>different ways of expressing the same mathematical truths, and each 
>can be useful in different contexts. It's something like Newton vs. 
>Leibniz's alternate notations for calculus that caused so much 
>ruckus a few hundred years ago...

I don't have it quite right if at all but I offer that the duality of 
quaternions and vectors stands in for energetics and mechanics or 
conservation of energy and conservation of mass.  It's not really the 
science that's interesting, it is the metaphors that are adopted by 
popular culture and disciplines like economics.