Richard,

A model is no more than a way of seeing the information (or displaying the information). In this case I am merely looking at information (reality) as a set of numbers. My model of this information is nothing more than a plot of these numbers in a coordinate system. That model is as capable of displaying any asymmetry in the data as any other model.

Consider a coordinate system which is symmetric around the origin. Does that prevent you from plotting asymmetric data?

Given the fact that all possible information is in your data set (as it is "the universe"), moving the origin in the example above cannot influence any display of that data. Only two possibilities exist. Either the data itself defines a unique origin (in which case you can pick out that "preferred position" from your data and the actual origin in your display is immaterial) or it does not and there is no "preferred position". Neither case prevents you from moving the origin in your display!

This is a fact of the method of display and says nothing about the "rules" to be deduced from the data! Your concern with the symmetry of my model (my picture of the data) is completely spurious. The fact that moving the origin can have no influence on the problem (which is to decipher the rules of the universe) is the source of the translation symmetry in my model of the data. It is not an assumption or an axiom; it is impossible for it to be false!

The central reason the symmetry appears is because the "data" referred to is the entire "universe". The entire collection of all data available to be analyzed. There exists no information outside the "data".

Think about it -- Dick