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All is Number = All is Geometric Structure: Returning to Pythagoras through △‑Ontology

Authors: Petrov, Alexey (KAMAZ);

All is Number = All is Geometric Structure: Returning to Pythagoras through △‑Ontology

Abstract

The ancient Pythagorean thesis "all is number" is traditionally understood as the assertion that the world consists of numbers or that numbers are the first cause of things. The discovery of the irrationality of √2 is considered its refutation. In the present work we propose a new interpretation of this thesis based on △‑ontology. If we recognise that a number is not an abstract symbol and not a cardinality of a set, but a geometric structure, then the Pythagorean thesis acquires a new meaning. Since the entire objective world has a geometric structure and is expressed through numbers, the statement "all is number" turns out to be identical to the statement "all is geometric structure". In △‑ontology this structure is concrete: it is the Infinitum △₁ₓ₁ — a right isosceles triangle with legs of length 1 and hypotenuse √2. All numbers, all spaces, and all manifolds are generated from it. Pythagoras was right — but not in the sense that is usually attributed to him.

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