Greta, once more you have set us on a promising trail by bringing the sphere into our discussion - it being, as you say, “the most compacted possible shape, symmetrical in all directions.” If I am not mistaken, Steve3007 is thinking along similar lines here:
Steve308 wrote:Physical symmetry is a particular example of a kind of pattern; a repetition.
Correct me if I am stepping awry, but I think we might state this perspective as follows: symmetry is
simpler than asymmetry, insofar as it involves less variation.
It may be useful to pause a moment on this point. I say this because the issuance of complexity from simplicity is, to my mind, one of the great mysteries of things, and one of the principle stumbling blocks to the final comprehensiveness of scientific investigations. (Though it may well be that I am simply ignorant of the relative scientific theories.) For our present inquiry, then, I propose the following questions as worthy of consideration: can symmetry be regarded as a principle of economy on the part of the world? Or is symmetry, as a species of order, actually
more complex than chaos?
John Bruce Leonard