II- Review of the Nature Principles (cont.)

i) Symmetry

Symmetry is a major characteristic of Nature.

One speaks of symmetry when a quantity remain unchanged during a transformation.

A shape has line symmetry when one half of it is the mirror image of the other half.

Symmetry exists all around us and many people see it as being a thing of beauty.

Symmetry exists also in music. An example particularly clear is given by the composition, probably apocryphal, of a piece of music in two parts (Mozart ?), which starts by:

Such a piece should be numbered Kochel 609, but Alfred Einstein put it in the Anhang, or appendix, of the doubtful pieces: Anh 284dd (P. Atkins, 2003).

Central Limit Theorem (large numbers):

In probabilities, adding a large number of asymmetric distributions
gives a symmetrical normal distribution.

Individually the production curve of each field is asymmetric. However, when taken collectively the curve shows a quite sharp symmetry.

That's it.