| circular dysfunction
It can be shown by using the vertical line test that a circle in the Cartesian plane is not a function. So are all the ellipses, and hyperbolas. However, the parabolas are equivalent to all quadratic functions. Therefore, for the conic sections of degenerate lines, parabolas, circles, ellipses, and hyperbolas it is 3 to 2 in favor of dysfunctionality. This realization could then be used to assert that for a two dimensional universe, it is more dysfunctional than it is functional. Moreover, since the circle represents a two dimensional sphere of four degrees of freedom and by mathematical induction it is demonstrable that all multi-dimensional spheres are likewise dysfunctional. On the other hand, the functionality of circular trigonometric functions, namely sine and cosine, do implicitly assume piecewise functionality. For if one completes the circles as represented by standing waves, one finds that even the sines and cosines are all dysfunctional. Therefore, excluding all degenerate lines of conic sections, the 1/3 functionality and 2/3 dysfunctionality of physical reality is bounded by fractal edges between order and chaos, between sanity and insanity.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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Linear Mode
