The theory of groups is a branch of mathematics in which one does something to something and then compares the results with the result obtained from doing the same thing to something else, or something else to the same thing. This is a broad definition but it is not trivial. The theory is a supreme example of the art of mathematical abstraction. It is concerned only with the fine filigree of underlying relationships; it is the most powerful instrument yet invented for illuminating structure.
—  James Roy Newman, The World of Mathematics

The Golden Mean was used in the design of sacred buildings in ancient architecture to produce spiritual energy that facilitated connectivity with spiritual realms through prayer. Our reality is very structured, and indeed Life is even more structured. This is reflected though Nature in the form of geometry. Geometry is the very basis of our reality, and hence we live in a coherent world governed by unseen laws.  These are always manifested in our world.  The Golden Mean governs the proportion of our world and it can be found even in the most seemingly proportion-less (active) living forms.