Scale Relativity

Last year, Terence Blake tweeted about Mark Wilson and the concept of “scale relativity,” and I have had the related clippings sitting in my notes since then, unsure of how to proceed—mostly because the work exceeds me, as with much of my research and reading of late. So perhaps a summary will suffice for now.

Laurent Nottale defines the theory of scale relativity in his paper “Scale-Relativity and Quantization of the Universe. I. Theoretical Framework” (1996) as “extend[ing] Einstein’s principle of relativity to scale transformations of resolutions,” and writes that the theory is “based on the giving up of the axiom of differentiability of the space-time continuum.” He goes on to argue that, as a consequence of giving up this axiom, the “geometry of space-time must be fractal, i.e., explicitly resolution-dependent.” This fractal structure allows for the breaking of “time reversibility” at the “infinitesimal level,” and so for the transformation of “classical mechanics into a generalized, quantum-like mechanics.”

In his “Scale Relativity, Fractal Space-Time, and Morphogenesis of Structures” (2000), Nottale continues his argument, writing that solving the resultant “generalized Schrödinger equation … provides us with a theory of morphogenesis and self-organization,” because solving this equation “yield[s] probability densities, which are interpreted as a tendency for the system to make structures.”

In “On Optimism and Opportunism in Applied Mathematics: Mark Wilson Meets John Von Neumann on Mathematical Ontology” (2004), Michael Stöltzner writes about the relationship between mathematics and physics in Mark Wilson’s work. I also saved Valia Allori’s article “Primitive Ontology in a Nutshell” (2015) here, but the link with Wilson and scale relativity is unclear after all these months. Perhaps a related paper on ResearchGate where I found Nottale’s papers?

The works of Wilson’s that are of primary interest to Blake are his Wandering Significance: An Essay on Conceptual Behaviour (2006) and Physics Avoidance: Essays in Conceptual Strategy (2017). Blake links Thomas Ryckman’s review for Notre Dame Philosophical Reviews in which Wilson is characterized as “the moral compass of analytic philosophy,” as well as a video discussion of scale relativity in Mark Wilson’s work from the Subset of Theoretical Practice (their previous video is on Laurent Nottale). It looks like Wilson has a new book out this year, Imitation of Rigor: An Alternative History of Analytic Philosophy (2022), which “attempts to reconnect analytic philosophy with the evolving practicalities within science from which many of its grander concerns originally sprang.” Fascinating stuff.

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