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Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
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Entropy After the Point: Why Shannon Was Wrong and What the Infinitum Has to Say About It

Authors: Petrov, Alexey (KAMAZ);

Entropy After the Point: Why Shannon Was Wrong and What the Infinitum Has to Say About It

Abstract

In 1948, Claude Shannon proposed a formula that became the cornerstone of information theory: entropy as a measure of uncertainty. This formula works brilliantly in engineering applications, but as a fundamental concept it is deeply flawed. Shannon entropy ignores the internal structure of states and the connections between them — it is the entropy of a point‑based world, where the foundation is a structureless atom. In the present work we show that replacing the structureless point with a structural geometric quantum — the Infinitum △₁ₓ₁ (a right isosceles triangle) — leads to a radical rethinking of entropy. In △‑ontology, entropy becomes a measure of deviation from balance, a measure of fractal depth, and, ultimately, a measure of non‑understanding that diminishes as the complex becomes simple and clear. We introduce the concept of intropy — the striving of a system towards an energy minimum, which at the cognitive level is experienced as harmony, joy, and happiness. The fundamental conclusion: everything tends towards happiness — because thermodynamics dictates it.

Keywords

entropy, intropy, Shannon, Infinitum, △‑ontology, information theory, energy economy, Landauer's principle, point, structureless primitive, heat death, singularity, fractal self‑similarity, balance, harmony, clarity, happiness, arrow of time, thermodynamics, cognitive science, predictive coding, free energy principle, Friston, Synthetic Differential Geometry, Kock, structuralism, foundations of mathematics, topos, forcing, measure, smoothness, metric, prime numbers, Millennium Prize problems, P vs NP, Riemann hypothesis, Goldbach conjecture, Collatz conjecture, neurophysiology, grid cells, hexagonal lattice, √2, √3, golden ratio, fine‑structure constant, SU(3). Mathematics, Foundations of Mathematics, Information Theory, Thermodynamics, Cognitive Science, Neuroscience, Philosophy of Science, Physics, Category Theory, Number Theory, Complexity Theory, Artificial Intelligence, Theoretical Biology.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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