Rowan Brad Quni-GudzinasThe same ultrametric tree—where every triangle is isosceles—appears in spin glasses, QCD jets, phylogenetics, p-adic numbers, and cognition. New synthesis traces one pattern from physics to perception: "More become one; one becomes more; repeat." https://doi.org/10.5281/zenodo.20329583
#Physics #Mathematics #Consilience #Ultrametric #Hierarchy #Cognition
The Tree at the Bottom of Thought: A Synthesis of Ultrametric Branching
The strong triangle condition — that for any three points the two largest distances are equal — is not merely a mathematical curiosity. It is the signature of hierarchical branching, and it appears wherever things nest inside things: in spin-glass valleys, in QCD parton showers, in phylogenetic trees, in the Bruhat–Tits geometry of p-adic numbers, in the structure of language itself, and in the deepest pre-linguistic acts of perception. This synthesis traces the full arc: from the formal definition of ultrametricity, through its physical and mathematical manifestations, to the distinction calculus of Laws of Form, to the cognitive primitives of subitizing and chunking, and finally to a cross-linguistic essence that survives translation into any human language — and beyond language entirely.
Doug Bostrom
mindsets
troytop
Skeptical Science
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Marcel Waldvogel
sceeba