The Civilizational Equation: V=N/D as a Predictive Model for Human Civilization's Future

Every civilization in history has eventually collapsed or transformed. This paper proposes that all theories of civilizational collapse — resource depletion, political corruption, military overextension, climate change — describe the same underlying phenomenon: D (friction) growth exceeding N (productive output) growth, driving V (value) toward zero. Using the formula V=N/D, this paper examines three historical collapses (Rome, Ming Dynasty, Soviet Union), diagnoses contemporary civilization as currently in a D-acceleration phase, and identifies a bifurcation between two mathematically possible futures: a D collapse scenario and a D=0 phase transition scenario. The paper argues that the difference between these futures is not destiny but design — a choice being made in this decade.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-10
DOI
https://doi.org/10.5281/zenodo.19491156
Primary Topic
World Systems and Global Transformations
Type
article
Field-Weighted Citation Impact
0.00
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article

The Civilizational Equation: V=N/D as a Predictive Model for Human Civilization's Future

Yoshihikaru Katayama
Zenodo (CERN European Organization for Nuclear Research)
World Systems and Global Transformations
article

The Civilizational Equation: V=N/D as a Predictive Model for Human Civilization's Future

Yoshihikaru Katayama
article en

Abstract

Every civilization in history has eventually collapsed or transformed. This paper proposes that all theories of civilizational collapse — resource depletion, political corruption, military overextension, climate change — describe the same underlying phenomenon: D (friction) growth exceeding N (productive output) growth, driving V (value) toward zero. Using the formula V=N/D, this paper examines three historical collapses (Rome, Ming Dynasty, Soviet Union), diagnoses contemporary civilization as currently in a D-acceleration phase, and identifies a bifurcation between two mathematically possible futures: a D collapse scenario and a D=0 phase transition scenario. The paper argues that the difference between these futures is not destiny but design — a choice being made in this decade.

Zenodo (CERN European Organization for Nuclear Research)
Genesis Research Institute (JP)
Peace, Justice and strong institutions
Openalex Percentile: Top 2%
World Systems and Global Transformations
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