At the quantum level, metal is a liquid, if your a rock. Its all frame of reference.
What happens in the physical world and human's perception to define it (control it) are different things and perhaps will never conjoin. Exemplified by the example of fuzzy sets (and their role in AI and neural nets) vs. Bertrand Russells "hard" set theory. None the less, the usefulness of any model is the isolation (linerizations) of certain parts to illuminate and inquire into some of the other workings.
Good examples in the area of the manifolds of differential geometry and Topology (not the map kind). Moebis strips, Klein bottles, the infinite square shown earlier, folding a doughnut into a coffee cup. However these only give a "picture" and higher manifolds are very difficult (4 and up) to visualize. In any case they do not describe the process. At what point does chaos return to order or vice versa? Generally anything over 5 orders is considered (Thoms theory) catastrophe. The field of Bifurcation theory deals with this area. A new area that has grown out of this is fractional derivatives. Looking at the fractal levels hidden in between what was previous considered as modern thinking.
good example is the arguments seen here in the hunting sections. . Is kinetic energy the big deal or is it momentum? Momentum cannot exist without kinetic energy, it is the first derivative if kinetic energy.
what would the analysis look like if we looked at the the 1/2 or 7/8 first derivative using very small samples of time?
Faith--- hmm oh your talking about game theoretic modeling.
