Quote:
Originally Posted by jwaltos
Thanks for responding Nick. Unfortunately it didn't really help me out...

Well you have a very individual perspective so any suggestions are bound to be a bit hitandmiss!
Mathematically, quartic polynomials tend to arise from 4dimensional spaces,
for example as the determinant of a 4x4 matrix. And a key difference between those and
3dimensional spaces is that 4 is even  yes, it sounds trivial, but it has deeper consequences.
Calculate the volume of the unit ball in n dimensions, for example, and you will see one pattern
for the odd dimensions and another pattern for the even ones.