##### 1. eBook Edition

978-1-03-915189-5

- PDF format

##### 2. Paperback Edition

978-1-03-915187-1

- Black & White
- 896 pages
- 8.5 x 11.0 inches

##### 3. Hardcover Edition

978-1-03-915188-8

- Black & White
- 896 pages
- 8.5 x 11.0 inches

##### Categories:

- Mathematics, Probability & Statistics, Bayesian Analysis
- Science, System Theory
- Business & Economics, Forecasting

##### Keywords:

Maximum entropy principle, Pareto distributions, Edwin Jaynes, Diminishing returns, Historical cycles, George Spencer-Brown, Mathematical dialectic

## The Decline Effect

The Hidden Probability Law Controlling Markets, Politics, Culture, Religion, Epidemics and War

by
Dean Brooks

A crisis is coming for everyone who uses math and science. For decades now, the classical model of probability (the indifference principle and the Gaussian distribution) has been breaking down and revealing its limitations in fields from economics to epidemiology. Now a new approach has revealed the underlying non-classical principle behind all these 'anomalous' laws:

— Pareto’s law of elite incomes

— Zipf’s law of word frequencies

— Lotka’s law of scientific publications

— Kleiber’s law of metabolic rates

— the Clausewitz-Dupuy law of combat friction

— Moore’s law of computing costs

— the Wright-Henderson cost law

— Weibull’s law of electronics failures

— the Flynn Effect in IQ scores

— Benford’s law of digit frequencies

— Farr’s law of epidemics

— Hubbell’s neutral theory of biodiversity

— Rogers’ law of innovation classes

— Wilson’s law of island biogeography

— Smeed’s law of traffic fatalities

The general law behind all these particular laws (and countless others) is the "decline effect". As a system ages or grows in size, the rules of probability subtly change. Entropy increases, rare items become rarer, and average performance measures decline. The human meaning of a decline may be positive (decreasing costs, falling epidemic mortality) or negative (lower customer loyalty, decreasing efficiency), but the mathematical pattern is always the same. The implications are enormous, as these examples show:

All epidemic diseases decline in infectiousness and in lethality. HIV-AIDS went from a highly infectious, 95-percent fatal disease, to a survivable condition with a latency of decades. COVID-19 went from a death rate of 7 percent in early 2020, to under 2 percent in 2022.

Hereditary dynasties around the world declined smoothly in lifespan, from hundreds of years to tens of years. When democracies replaced monarchies, the decline (in spans of party control) continued.

Dean Brooks is Canadian. He holds a B.A.Sc. in Engineering Physics, and has worked as a technical writer explaining complex subjects to busy people for three decades.

In the late 1990s he first came upon a remarkably simple set of curves that can model how long a political dynasty (or a comic book series) will last, how fast a religion (or an epidemic) will spread, how many new stores WalMart or Burger King will open in the next decade, the growth of the human fetus, the distribution of competing species in an ecosystem, and countless other phenomena.

It turned out that these curves had already been observed and given dozens of names in different fields. But how could such simple patterns apply to such a fantastic diversity of phenomena? And why had no one else written about the similarities until now? The search for a unifying explanation led the author to a new view of basic probability, using multiple overlapping Bayesian reference frames and the maximum entropy principle.

Based on concepts from physicist Edwin Jaynes, and the mathematician George Spencer-Brown, Dean Brooks has produced a scientific and philosophical manifesto -- a radically new way of looking at the world.

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