Table of contents

  1. Introduction to the decline effect
  2. The distribution of history — The skewness of human events, such as for example many short and small wars, versus a few long and terrible ones. Also, the tendency (noted by historian Arthur Schlesinger Jr. and many others) for great social movements to exhaust themselves even as they gain in numbers and authority.
  3. A world far from normal — Examples of the common misuse of classical statistics, especially the Gaussian or normal curve. Includes failures of the normal curve in IQ studies, political polling, financial models, achievement in sports in science, and other fields.
  4. Pareto, Zipf, and Juran — A brief look at how each of these pioneers grappled with the extreme nonlinearity of wealth, achievement, productivity, and other human phenomena. The need for a more comprehensive framework of ideas about power laws.
  5. Benford and Jaynes on scale — A clue to forward progress with power laws turns up in a 1961 paper on Benford’s first-digits law: Nature prefers distributions that are scale-invariant. But is Benford’s log-frequency law truly scale-invariant? What the maximum entropy principle has to say about applying multiple measurement yardsticks to the same physical system.
  6. An ‘ontic’ distribution — A truly scale-invariant law that works for integer quantities as well as for real numbers, based on the golden ratio phi = 1.618034. Numerous practical examples from the masses of extrasolar planets to the lengths of railroad bridges.
  7. 61.8 percent — One of the more common and tangible consequences of the ‘ontic’ distribution: In countless situations where we might expect a 50 – 50 split between two alternatives, we get a split close to 61.8 – 38.2 instead.
  8. A universal decline curve — The big payoff from the ontic distribution is that it gives us a forecasting tool: A standard model for how later items in a long series will tend to be smaller in magnitude, and rare items in a long series will tend to get rarer.
  9. When costs go down forever — Contrasting the pessimistic Malthusian view of diminishing returns with the optimistic view of the ‘Singularitarians’ that technological progress will bring practical immortality. Why neither view is complete or correct without the other.
  10. Learning and manpower curves — The revolution in productivity brought on by Henry Ford, and demonstrated by the victorious Allied powers in WW II. The less well-known corollary that while manufacturing yields increasing returns, mobilization of large amounts of manpower yields diminishing returns.
  11. The experience revolution — Bruce Henderson’s post-WW II popularization of the learning curve as an ‘experience curve,’ something as universal and basic as gravity. The continuing mystery of what causes the experience curve to work, and its limitations.
  12. Nonlinearity in economic law — Reconciling two solitudes in economic thought, diminishing and increasing returns. The case for treating the Cobb-Douglas elasticity function and cost-reduction experience curves as fundamentally the same.
  13. The game as economy — Increasing personal productivity of PGA Tour golf pros, fighter pilots, and other skilled professionals follow essentially the same form as diminishing costs in a factory. How these curves are implemented in games like Dungeons and Dragons or World of Warcraft in which players earn ‘experience points’.
  14. Traffic accidents and entropy — Smeed’s Law of traffic accidents shows that accident rates per capita diminish in eerily consistent fashion from small countries to large. A maximum entropy approach suggests this really is the same underlying law as Henderson’s experience curve, or the Dungeons and Dragons experience curve, or Cobb-Douglas elasticity.
  15. Industrial declines — Electronics failures diminish dramatically with increasing total usage of the unit they are in, yielding yet another case where rare events become rarer in familiar fashion. Six-Sigma process control shows evidence of long-run ‘drift’ that has the same mysterious quality.
  16. The universal loyalty curve — Discovery of customer loyalty curves, and the consequent ‘customer relationship management’ revolution. Loyalty fatigue and the fundamentally different behavior of ‘early adopters’ versus ‘late adopters’ in a product life cycle.
  17. Cultural entropy — Case studies in the continual fragmentation of markets and cultural categories as they grow. Examples include the forty-year history of Star Trek fan activity, and exponential growth but declining audience participation for YouTube and other Internet media.  The curves for cultural output are the same ‘ontic’ shape as the curves for economic output.
  18. Revolution and freedom — Statistical questions about the recent rise of the Iranian Green movement and the usefulness of the ontic curve in forecasting social change are considered in detail.
  19. 52 Supermen — The relentless decline of the comic book industry and the fragmentation of markets, titles, and characters is contrasted with the dramatic rise in comics-based movies and games. Why both trends reflect increasing cultural entropy.
  20. Religious entropy — Church recruitment attendance, tithing, adherence to doctrine, and other variables are all shown to follow relatively simple ontic curves. As a church grows in membership, it declines in per capita commitment and effort. The same is true for Christianity taken as a whole.
  21. The Mandate of Heaven — The ancient ‘dynastic cycle’ is considered in terms of a standardized decline in citizen loyalty and regime effectiveness. Modern voter turnout data and variations in the average size of majorities with size of voting population show that the ‘dynastic cycle’ continues to operate in present times.
  22. A mathematical dialectic — Reconsidering the claim by Hegel, and more recently by Francis Fukuyama, that history unfolds according to an inner logic or dialectic. The decline effect takes the place of Hegel’s World Spirit, causing a similar sort of evolution but for very different reasons.
  23. Crime, achievement, and age — Applying the maximum entropy principle to the variation of crime and achievement with age.
  24. Declining rates of growth — An omnibus chapter comparing examples of smoothly declining growth in social movements such as the ‘velvet revolutions’ of 1989, the Internet, Wikipedia, Second Life, the Nazi and Communist parties, sales of the Model T Ford, and so on. The most popular existing tool for tracking social changes of this type, the logistic S-curve, is contrasted with the ontic curve.
  25. The politics of decline — Reviewing the pioneering work of 19th century historian Henry Adams on entropy in human affairs. How entropy imposes limits on information and constrains policymakers. Possibilities for an ‘evolutionary libertarian’ perspective based on Friedrich Hayek and the Austrian school of economics.
  26. The fate of civilization — Review of a variety of ‘declinists’ including the 19th century racial-degeneration theorist Count Gobineau, and 20th century arguments about ‘peak oil’. Why growth curves tend to end in crashes; why the timing of the crash cannot be predicted by the structure of the curve itself.
  27. Efficiency laws in warfare — A history of paradoxes and counter-intuitive outcomes in battle: The smaller side wins most battles, increasing the number of targets decreases the number of hits. A review of the work by the leading expert in this area, Trevor Dupuy. Explaining Dupuy’s findings using maximum entropy methods.
  28. Abundance of species — It has recently been proposed that maximum entropy might be a kind of ‘Rosetta Stone’ for explaining the very orderly distribution of different species within an area. What the evidence shows and why maximum entropy works so well to explain it.
  29. A cause for Kleiber’s Law — We have known for more than a century that the metabolisms of animals vary inversely with body mass. More recently it has become clear that insects and even single-celled organisms fit on that same curve. The case is made that this is the standard ‘ontic’ curve at work once again.
  30. A universal law of epidemics — The recent H1N1 ‘pandemic’ has underlined a longstanding problem in epidemiological theory. Our models assume that mortality and transmission rates remain constant. In fact, both of these measures decline as an epidemic grows, a fact that was known to pioneers like Farr in the 19th century but that is overlooked today. Once again the ontic curve proves a better fit than existing methods.
  31. The rise of decline — Concluding thoughts on the significance of the decline effect to science, as well as on the integrative, cross-disciplinary approach taken in this book.