Scale Theory Insights
Dive deeper into the mathematical foundations, recent developments, and applications of Scale Theory across physics, cognitive science, and artificial intelligence.
May 20, 2025
Scale dynamics in context: Connecting our framework to recent literature
Scale Dynamics in Context: Connecting Our Framework to Recent Literature
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May 20, 2025
A scale Hamiltonian framework for multiscale systems: A Hamilton–Jacobi approach with application to glass-forming liquids
Abstract We develop a comprehensive scale Hamiltonian formalism for multiscale systems by recasting the renormalization group (RG) flow in a Hamiltonian framework and then reformulating it in terms of Hamilton–Jacobi...
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May 20, 2025
Irreversible scale dynamics: Contact geometry and the arrow of renormalization
In the post “From Time to Scale Dynamics” we treated scale evolution as perfectly conservative: a Hamiltonian $H_{\text{scale}}$ moved through symplectic phase‑space $(g_i,p_i)$ just like a planet through ordinary space....
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May 20, 2025
Canonical transformations and scheme independence
Recap. In the post “From Time to Scale Dynamics” we traded the ordinary notion of time for the log‑scale $\tau = \ln(\mu/\mu_0)$ and promoted the Hamiltonian itself to the role of...
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May 20, 2025
Beyond the linear β: Higher-order scale dynamics — Revised
This post builds on “From Time to Scale Dynamics”, “Canonical Transformations & Scheme Independence”, and “Irreversible Scale Dynamics”. There we treated the renormalisation‑group (RG) β‑functions as the sole engine of...
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May 15, 2025
From time to scale: A gentle introduction to scale dynamics
From time to scale: A gentle introduction to scale dynamics
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March 20, 2025
One more Copernican revolution: Reconsidering scale-centrism
One more Copernican revolution: reconsidering scale-centrism
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