Scale Invariance and Fractal Theories

Appreciation of mathematics means understanding the various interpretations of lemmas and postulates of logic such that there is an expansion of knowledge in the basis of the scientific enterprise. What this means is that the knowledge base must expand. The laws that govern the large scale scientific world are ontologically and epi-phenomenally connected to the small scale observer in the enterprise. Basically, the interactions and operator picture that develops in the philosophy of local interactions governs the behavior of larger global interactions. This theory was proposed in its modern form by Serge Lang, a Berkeley mathematician, who suggested that local and global stability are related, or, that local stability generates global stability. Applying this idea to the scientific enterprise seems simple. Operators at the experimental and theoretical scale of individuals sum to create emergent properties of projects at larger scales. Additionally, in politics and economics, uncertainty and stability are modeled in micro and macro settings. Grassroots politics is critical for American electoral predictions. What is interesting in the scale invariant approach is understanding the fundamental nature of things that are representative of timeless and permanent constants of nature. Rather than thinking of the fundamental forces, reimagine the universe as a topological affine connected Weyl space. Thus, one can generate isomorphic fractal laws of self-similar curves and relations of points, to real world physical events and geodesics in the string landscape. Of course, string theory is contentious and it goes without saying that there is a battle between quantum loop theory and string theory. Motivating a philology of science is a Judeo-Christian approach to western physics which, although powerful, must also learn to make peace with Middle Eastern and Hindu philosophies of eternal states and geometric representations of objects. The beauty of the world is in the diversity, which Gell-Mann found in the complexity of the jaguar in the jungle and the condor in the California mountains. Extrapolating this to the quark in the ensemble made distinguishability a critical feature of particle entropy. Thus, it seems fractals are powerful in their self-similar approach to eternal forms or invariant curves that contain the asymmetry needed for spontaneous symmetry breaking.

In any case, to make this simple, there has to be a focus on how to find self-similar curves in scientific fields such that we find relations that are invariant and elucidate patterns. Predictions will then come. Of course, one has to rethink the traditional physical space of the universe and tack of Riemann zeta function turbulence to the primes of space filling curves in the connection to mathematical space too. It means that the affine topology of space has to supplant the idea of traditional space.