How Poetry will Supersede Mathematics in Science

These days in the parlance of mathematical physics the concept of "symmetry breaking" is ubiquitous. This would be the description of a phase of a process that through a singularity emerged into a sort of new domain of functioning.   However, it were more productive perhaps to start from a thorough grounding in what is invariant across the organization of reality in all its relevant incarnations.

Self similarity as a principle of organization and development is invariant within what Vladimir Vernadsky termed the domains of lithosphere, biosphere and noösphere. In order to grasp this fact, broaden your viewpoint of the first category lithosphere to include the Riemannian hypothesis that there is a characteristic stasis for a curvature tensor that adheres within the bounds between the very small and the very large but that may break down outside those bounds.

Next, shift your focus to an aesthetic standpoint versus a merely analytic one. View this photo of a starburst cluster:

  

...And this photo of a polished opal:

And finally this Leonardo Da Vinci's Salavator Mundi 

The human mind is naturally entranced with wonderment at the beauty of seemingly inorganic and lifeless remnants of a universal process: galactic star creation at one boundary of the very large and mineral creation at the very small. It is Leonardo's artistic depiction of this very connectedness that evinces the extraordinary and unique power of the human mind to encapsulate this ironic invariance that is the true substance and motivation for scientific progress. 

The Soap Bubble Nebula: Credit & Copyright: T. Rector (U. Alaska Anchorage)