The Rubber band and the Ruler

TL;DR

This paper discusses the conceptual development of physical laws through successive approximations and explores how observed metrics can emerge from fractal structures and re-summations.

Contribution

It introduces a novel perspective on establishing physical laws via iterative approximations and reviews how fractal structures can influence metric emergence.

Findings

Successive approximations can effectively formulate physical laws.

Fractal structures at short distances can give rise to observed metrics.

Symmetrical situations can emerge from re-summation processes.

Abstract

In this short presentation, we address two somewhat separate issues. The first one deals with the establishment (vs discovery) of what we call "physical laws". The discussion runs on a "successive approximations" approach, suited to our own thinking process, and aiming at the "simplest \emph{possible} formulation ", as opposed to the idea of pre-existing laws to be discovered. In the second part, we review briefly an approach to the (observed) metric originating from a short distance fractal structure, and remind how a symmetrical situation can arise from mere re-summations.