# Physical History

#### By Mark Ciotola

First published on May 17, 2019. Last updated on February 13, 2020.

# Physical History

### By Mark Ciotola

First published on May 17, 2019. Last updated on February 13, 2020.

This book strives to demonstrate how humanity has developed and progressed as a result of cosmological processes, as well as to explore the development of a science of historical processes. This book goes on to discuss the implications and uses for analyzing societies.

This book strives to demonstrate how humanity has developed and progressed as a result of cosmological processes, as well as to explore the development of a science of historical processes. This book goes on to discuss the implications and uses for analyzing societies.

1. ## 1 Introduction

First published on May 16, 2019. Last updated on January 20, 2021.

## Mission

This section introduces the subject of Physical History and Economics (PHE). Physical History and Economics is a small treatise on the development of a unified science of history. It is chiefly a physical model, in that it deals with physical principles, quantities, tendencies and constraints. At attempts to do so quantitatively where possible. It also delves into other areas such as psychology, and traditional history. However, the author has great respect for researchers and their work in those areas, and does not assert expertise in those areas.

## Work In Progress

This entire publication is a work-in-progress. Substantive research is being conducted behind the scenes and presented in academic settings. Trying to weave everything together is a challenge, and one never knows how much time may be left to improve the content. The author engages in this work in the hope that it may be of great benefit to both the positive advancement and sustainability of humanity, and the seeking of knowledge.

So changes will be made in a hard-to-predict manner to the various sections. Therefore, if you do cite this work, please include the date last viewed.

## Imagine…

Imagine the hot sun shining brightly upon the Earth situated in cold space. Much light is reflected back from the Earth into space. The remainder of the light is absorbed by the Earth and heats its surface. Nature abhors temperature differences, and tries to rectify the situation as quickly as possible by having the Earth emit heat back into space. Yet the Earth’s atmosphere a good insulator. To bypass that insulation, great blobs of hot air at the surface rise wholesale into the upper atmospheric cooler regions, so the escape of heat is greatly increased, and Nature is pleased.

Yet the light that gets reflected from the Earth is not heat nor does much to warm the coldness of space. Nature does not gladly tolerate such rogue light. So living organisms develop upon the Earth that can capture and photosynthesize some of the rogue light. Those organisms release heat or are consumed by other organisms that produce heat. Nature is still not satisfied and demands greater haste. Intelligent organisms form that can release heat faster, and civilizations form that can release heat yet faster, further pleasing Nature.

Nature is greedy and demands all that it can seize. Just as great blobs of air form and rise through the atmosphere, dynasties and empires form in succession one after another, releasing heat that is otherwise inaccessible. History is literally a pot of water boiling on a hot stove in a cold kitchen, with dynasties and empires forming and bubbling up to the surface. Is there more that Nature can yet demand? New technologies and untapped sources of energy? New forms of civilization? Or the yet totally unknown?

This book is intended to serve as an introduction and handbook. Rich descriptions as well as much technical detail have been omitted to improve readability and avoid confusion. Additional sources of information are cited for the reader who wishes to know more. In this book, you will envision how humans are linked to the entire universe and how we share its drive and destiny. Unfortunately, PHE does not provide quick, easy answers to society’s challenges. Nevertheless, you will discover analytical tools as powerful as the astronomer’s telescope and the biologist’s microscope to investigate human affairs. This is a tall order to fill. It is best to remember that this book is more of a framework of perspectives and tools to help you get started, rather than an encyclopedia of answers. This is still a pioneering field. There are considerable opportunities for further contributions of the greatest significance.

PHE derives social science primarily from physics, but also from other areas such as cosmology, ecology and psychology. PHE is more fundamental than social science derived merely from the observation of humans, because it views the existence of humans as the result of cosmological trends and physical processes. Likewise, PHE strives to be generic, so that it can be used to describe and analyze any society anywhere and anytime, be it the Carolingian dynasty in medieval France or an extraterrestrial society across the galaxy. Observation strongly suggests that the laws of physics remain invariant across time and space, allowing for the possibility of a truly generic, non-geocentric social science derived from physical principles.

Although PHE is based upon the physical sciences, no claim is made for its ability to “produce” a perfectly deterministic science. In fact the approaches of PHE are only practical because people act as individuals and have a wide freedom of action. This seems paradoxical, but that is the way things work out.

## Inner Versus Outer Philosophy

In ancient times, natural (outer) and social (inner) philosophy were closely linked. Then, a philosopher’s view of the composition of matter might be closely linked to their view of the best type of government for society. This unity of inner and outer philosophy continued in Europe until the Renaissance.[1] However, the heliocentric universe proposed by Copernicus and the findings of imperfect heavens by Galileo were deemed inconsistent with the inner, social philosophy of that time. The resulting severance of inner and outer philosophy began in earnest and has continued to this day.

PHE approaches social science from the perspective of outer philosophy. Both approaches are necessary for the development of a complete and meaningful social science. We are humans who attempt to develop social science. We try to be impartial, but must admit that our ability to do so is inherently limited. Motivation and incentives are always a factor in what gets studied. Why should we develop social science if it does not benefit those of us who endeavor to do so? Even physical scientists are human and have the same sort of needs that other people have. The subject of psychology and how it colors people’s reaction to PHE is discussed in a later section.

## A Unified Model

The social sciences already utilize some quantitative methods. Economists utilize them perhaps exhaustively and several historians practice cliometrics. Nevertheless, the social sciences have lacked the type of unified model that Newton provided for the physical sciences. Ever since Newton created his three laws to describe the mechanical universe, numerous philosophers and social scientists have tried to create a mechanical model of society without success. Meanwhile, in the early 1900s, Newton’s laws of mechanics were shown to be idealizations of a much less deterministic, statistical universe. Ironically, it is the fall of Newtonian mechanics that allows for the achievement of a true “science of society.” PHE is not the purely deterministic dream of early “Newtonian” sociologists. Rather PHE uses concepts from modern statistical mechanics to provide a firm foundation for a fundamental understanding of history and economics.

This book provides the skeleton of such a unified model. The Principle of Fast Entropy, an extension of the Second Law of Thermodynamics[1], is suggested as a unifying, driving principle. Just as gravity is the key force in Newton’s unified model of the physical universe, Fast Entropy is the key tendency for a unified model of the social universe. Fast Entropy is literally the “gravity” of social science. Fast Entropy applies to both the social and physical sciences. Fast Entropy can be used to analyze, understand and validate other economic and historical methodologies. It is a constraint that can be used to identify other constraints. In science, a known constraint is a valuable piece of knowledge.

The author hopes you will find this text useful. The philosophical implications are glossed over in favor of presenting pragmatic approaches and tools. It is hoped that this work will stimulate you to develop your own ideas and approaches, for one of the fundamental characteristics of science is that it is always unfinished.

## Notes & References

[1] H. Scott had previously proposed deriving economic policy from thermodynamics, in particular the works of W. Gibbs, in the 1920s.  Source: www.technocracy.org.

2. ## 2 Big Bang and the Formation of Our World

First published on . Last updated on January 19, 2021.

Here, we describe the cosmological context of Physical History and Economics. Without the contrasts provided by this context, the rest of this book would be moot.

## The Big Bang and the Expansion of the Universe

13.772 billion years ago, the known universe began from a single point in time and space in a tremendous explosion known as the Big Bang. For a brief moment, the universe was filled with pure light containing all of the energy in the universe, a literal swarm of light. The universe was so hot that no matter could exist.

Cosmology from Big Bang to present (credit: NASA)

## Growing Darkness and Clumpiness

In the Universe, total  energy has essentially remained constant (but see below). As the universe began to expand, that constant amount of energy spread over a larger area, first rapidly during its inflationary area, then more slowly until relatively recently. Therefore, as the energy density of the universe decreased, the universe cooled down and became darker. At the same time, the universe began to exhibit clumsiness in terms of temperature and density variation.

Cosmic microwave background radiation (photo credit: NASA)

## The Contrasted Universe

As the universe progressed in time, contrasting trends have occurred.  Overall, the universe expands, cools and dims. Yet, in local areas, the universe heats up and grows brighter. In certain very important ways, the universe has become less homogeneous in some regions over particular periods of time.

## The Formation of Matter, Stars and Planets

As the universe continued to further expand, it eventually became sufficiently cool for matter to form.[1]The first matter comprised sub-atomic particles, since the universe was still too hot for more atoms and molecules to form.

The, eventually, as the universe continued to further expand and cool, atoms[2]and then molecules formed. Matter gravitationally attracts itself[3], so it pulled itself together into gigantic clouds and structures.

Within those clouds, some matter condensed into spheres of gas. When gravitational contraction caused many of those spheres to  heat up sufficiently so that nuclear fusion[4]occurred in their centers, those spheres became stars[5]. Fusion caused those stars to become much hotter and begin to emit large amounts of light. Disks of dust and gas formed around many of those stars.

Dust disk around protostar (photo credit: NASA)

Some of those dust particles stuck together due to gravity and heat, forming larger and larger clumps. Gravitational attraction between these clumps and gasses resulted in the consolidation of increasingly larger rocky and gaseous spheres. Some of those spheres further violently collided together to form planets.

Collision of planetessimals form Earth’s Moon (photo credit: NASA)

Some of those planets were dominated by rocket components. Eventually, some of them cooled down sufficiently to allow liquid water on their surfaces, but remained close enough to their stars to prevent all of that water from freezing. Planets such as the Earth formed.

Earth as seen from Apollo 17 (credit: NASA)

## Summary

As the Universe progressed in time, tremendous differentiation of temperature, density and structure have developed. Overall, the Universe has expanded, resulting in a decreasing energy and matter density as manifested by a decreasing mean temperature. Yet, in local regions, density and temperature have increased to the point that complex structures, such as stars, have formed and have triggered energy release mechanisms such as nuclear fusion. In between the coldness of the voids of space and the hot stars are planets, which receive sunlight then expel that energy back into space.

## Notes & References

[1]As Einstein’s relationship between mass and energy shows, it takes a great deal of energy to form even a small amount of matter, since the speed of light is a large quantity. However, the universe contains a great deal of energy. Energy = mass x (speed of light)2, or more familiarly E = mc2.

[2]Most of the initial atoms that formed were of the element hydrogen, with a lesser amount of the element helium.

[3]Hydrogen and helium are the least massive of all the elements. Yet they still have mass, and so are gravitationally attracted towards other matter.

[4]When hydrogen gas becomes hot enough, individual hydrogen atoms combine to form helium atoms. This nuclear reaction releases a tremendous amount of energy.

[5]Stars themselves are part of larger structures called star clusters such as the Pleiades, which in term are part of galaxies. Galaxies themselves are part of clusters and super-clusters of Galaxies that weave the fabric of the universe.

3. ## 2.1 Energy Balance of the Earth

First published on May 17, 2019. Last updated on May 16, 2022.

## Sources of Energy

Sunlight is the chief source of energy for the Earth. Gravitational contraction provides a tiny amount. Tidal interactions with the Moon provide a small but significant amount at the surface. Radioactive decay provides an important source of energy below the Earth’s surface. The burning of fossil fuels can release considerable heat locally (enough to upset ecosystems), but the total amount of heat released is small compared to that from solar and radioactive heating.

Sun photographed in various wavelengths. (Credit: NASA)

## Energy in the Atmosphere

The Earth is bathed in sunlight. Some of that sunlight is reflected back into space by the Earth’s surface and atmosphere. The reflectivity of the Earth is called its albedo. Some of the remaining sunlight directly heats up the atmosphere. A small amount is absorbed by processes such as photosynthesis.

Much of the remaining sunlight heats up the Earth’s surface. As surface temperature becomes raised, the Earth emits increasing amounts of infrared energy. This radiation in turn further heats the atmosphere.  Much atmospheric radiation is re-emited to the Earth’s surface. Some of it eventually makes it to the upper atmosphere and is radiated back into space.

The amount of energy entering and leaving the Earth’s atmosphere is called its energy balance. If more energy enters the Earth’s atmosphere than is emitted, the temperature of the Earth’s atmosphere increases. This is the current situation and is called global warming. Climate change results from global warming.

Energy flows to and from the Earth’s surface and atmosphere (credit: U.S. Govt.)

4. ## 2.2 Energy of Life

First published on . Last updated on January 19, 2021.

## Development of Energy Processes In Life

Energy is essential to the functioning of life. A chief characteristic of life is that it moves, does things and changes. Such activities require energy. As early forms of life on Earth metabolized hydrocarbons in their environment, which were initially abundant. These initial hydrocarbons were limited in quantity and nonrenewable, and as they became consumed, they became scarce. Life required a more sustainable energy source to endure.

Sunlight arrived at the Earth in bountiful supply. Plankton and plants formed that could photosynthesize sunlight into sugars, an energy-rich fuel. Animals formed that ate plants or each other for energy. Living organisms can be viewed as a form of engine. An engine requires a potential to operate across. The relative coolness of the environment (ocean, atmosphere) in contrast to the higher energy of sunlight provides such a potential.

Jungle plants (credit: NASA)

## Chemical Processs

Energy from photons in sunlight gets photosynthesized into carbohydrates by plants and phytoplankton. Such molecules are composed of carbon, hydrogen and oxygen. Mitochondria are specialized organelles in both plant and animal cells that can metabolize carbohydrates to produce ATP in a process called aerobic respiration. The cell can than use ATP to power its own processes. Waste energy is given off as heat.

Ball and stick model of organic molecule (credit: US NIH)

## Reference:

• Aydin Tözeren, Stephen W. Byers, New Biology for Engineers and Computer Scientists. Pearson Prentice Hall, 2004.

5. ## 2.3 Energy Flows in Ecology

First published on . Last updated on February 6, 2021.

Energy flows through ecological networks such as food webs. Generally, sunlight flows into plants that create sugars. Animals eat sugars. Both plants and animals expel heat into their environment.

Marine food web in Alaska (Source: US Govt.)

Food webs are generally energy webs. Energy in the form of high order photons flows to plants and phytoplankton that produce sugars and starches. Other organisms and animal eat plants and phytoplankton to gain energy. Predators eat those animals to gain energy. All plants, animals and organisms give off some heat into the atmosphere.

The Jouleis the standard unit of energy, but for food, the calorie and Calorie are often used. A calorie is sufficient energy to raise one gram of water one degree Celsius (1 K). A Calorie (with a capital C) is equal to 1000 calories, and also known is a kilocalorie.

If the energy leaving the food web is the same as that entering it, then the temperature will generally stay the same (after being adjusted for season and weather). However, a food web will typically store some of the energy into biomass, which contains varying amounts of energy. Organism bodies contain some energy, such as the cellulose that makes up much plant structure, such as cell walls. Proteins also contain energy. Fruits contain considerable energy in the form of sugar, typically 4 Calories per gram. Seeds contain tremendous amounts of energy in the form of oils (typically 9 Calories per gram) and starches.

Food webs can also release more energy than is imputed for relatively short amounts of time, such as during forest fires.

Energy typically enters and leaves an ecological system in the form of higher energy photons (visible light) and leaves in the form of lower energy photons (but possibly more of them). Yet, there are alternatives. Some of the energy may leave in the form of “waste” biomass. Such as dead plant structures, dead animal bodies and dead bacteria that get stored in the soil or ocean sediments, and eventually become nutrients, minerals or fossil fuels. Alternatively, some energy may enter an ecosystem in the form of high energy molecules, such as near ocean thermal vents.

Energy typically travels through an ecosystem in the form of chemical energy, such as sugars, carbohydrates, fats and proteins.

Note: only part of physical energy can be utilized by living organisms and in industrial processes. The useful part is called exergy. A related quantity, emergy, is the amount of energy consumed in these processes.

## Reference:

• Aydin Tözeren, Stephen W. Byers, New Biology for Engineers and Computer Scientists. Pearson Prentice Hall, 2004.

6. ## 2.4 Formation and Endurance of Life

First published on . Last updated on January 19, 2021.

## Recall the Contrasted Universe

Recall that due to expansion, the universe has become much cooler and darker over time. In fact, the typical temperature of the space between stars is nearly absolute zero. We have learned that heat energy tends to flow from warmer places to cooler places, as systems attempt to move towards thermal equilibrium (that is, until their temperatures are the same). Space is much cooler than stars, so energy tends to flow from within stars out into space. This is why we see stars shine.[1]

Planets are typically much cooler than stars. In fact, the temperature of a geologically dead, barren rocky planet would be about the same as space, that is nearly absolute zero. Shaded areas of moons and planets that lack atmospheres quickly drop to near zero. The side of the planet Mercury that faces away from the sun is such an example.

Solar System showing sun and planets (credit: NASA)

Yet planets orbiting around a star receive a significant continuing dose of energy in the form of light emitted from that star that then warms up the planet. The planet then becomes warmer than space, and so then the planet must start shedding energy into space. For example, the Earth receives significant amounts of sunlight that warms the earth. The Earth must then shed some of the energy into to attempt to move towards thermal equilibrium with space.[2]

Sun-Earth-Space Potential

## Heat Engine Analogy to Life

Recall the heat engine example. A heat engine bridges a temperature difference. Heat flows across that difference through the heat engine. Some of that heat energy is converted to work while the rest is exhausted as waste heat. Entropy is produced while the engine continues to function.

Part of the work done by a heat engine can be used to maintain that heat engine. More significantly, part of the work can go to build additional heat engines. These additional heat engines can produce yet more work to produce even more heat engines. The growth of heat engines is then exponential, at least until limiting factors come into play. This is a key point. Because heat engines can beget heat engines, an exponential increase in entropy production can take place.

Here, entropy production is proportional to the quantity of heat engines. Fast entropy favors exponential growth in entropy production, so fast entropy favors the “spontaneous” appearance and endurance of heat engines. Under the Second Law along, the spontaneous appearance of a heat engine is improbable but possible.[3]Fast entropy then utilizes those improbable appearances to create probable, self-sustaining, exponentially growing systems. Some of those systems have developed into what we call life.

## Formation of Life

### Steps

The motion of atoms and small molecules in a liquid or gas is nearly random. The statistics of these particles is known as statistical mechanics, or more traditionally, thermodynamics. The formation of life from this random motion involves several steps.

1. Microscopic structures frequently appear by random chance. For example, atoms can combine to form molecules, and some molecules combine form to larger molecules.
2. Even more complex microscopic structures occasionally appear by random chance.
3. Some very complex microscopic structures form. Some of those forms will be durable.
4. Some of those durable structures will be self-replicating. (Or they will be replicated by environment such as by catalysts). Such structures can be defined as the simplest form of life.
5. Durable, self-replicating structures that degrade energy more quickly than their environment will be more probable (they will be favored under the principle fast entropy). Free energy will tend to be degraded through these structures.
6. Where frequent chemical reactions can take place, where they can be durable and where there is an available source of free energy (such as from a thermodynamic potential), then the existence of the most basic life forms (as defined above) will approach being a certainty, given the passage of sufficient time.

### Life Appears!

Jungle plants (credit: NASA)

Once these steps have occurred, life has developed. One can view life as the residue of random action subjected to the principle of fast entropy.

## Summary

The Earth’s surface reflects some sunlight into space. Reflected light results in little entropy.
However, plants absorb much of that sunlight that would otherwise maintain its high level energy by being reflected into space.
Plants store some of that energy in the form of biomass. Animals have evolved to consume biomass.

## Life As A Faster Path

Life itself can be viewed as the process of heat engines begetting heat engines. Bacteria are an easy example.
Hence, life represents a mechanism to maximize the rate of entropy production. Therefore, life is not due to pure luck; rather, the formation and evolution of life is favored under the e th Law.
Intelligence allows life to produce entropy even faster; thus the formation of increasingly powerful brains and intelligence are favored.

## Notes and References

[1]That humans should have developed eyes that are particularly sensitive to the peak wavelengths emitted from the star our planet orbits should not be surprising.

[2]As long as the sun shines upon the Earth, the Earth will not reach thermal equilibrium with space. This continuing energy flow between the sun and the Earth maintains a continuing potential.

[3]I. Prigogine has proposed that dissipative structures can appear that increase entropy production. In his terminology, living organisms can be viewed as dissipative structures. Astrobiologist J. Lunine has paraphrased Prigogine’ s finding as follows: “complicated systems that are held away from equilibrium and have access to sufficiently large amounts of free energy exhibit self-organizing, self-complexifying properties.” (J. Lunine, Astrobiology, A Multidisciplinary Approach. Peason Addision Wesley, 2005).

7. ## 2.5 Statistical and Evolutionary Intelligence

First published on . Last updated on February 15, 2020.

## Introduction

Reproducing molecules are a far cry from the complex genetic machinery of the living cell. this section will explain how Fast Entropy results in the development of a form of random intelligence known as evolution.

## Random Action Recalled

Random action involves a statistically significant amount of actors that are free to behave independently of each other in at least one way.

One example of random action would involve the roll of a dice. The results of a large number of rolls should be random. Another example of random action is the movement of molecules in a gas. Even though the gas may have an overall motion, such as in a gust of wind, the individual molecules may be moving in absolutely any direction. Molecules moving about in a liquid may be a reasonable representation of random movement.

## Steps in the Development of Random Intelligence

1. Random action can “figure out and solve” some problems. Recall the parallel conductor example, where the correct proportion of heat flow through each conductor was channeled through each conductor to maximize free energy degradation. The combination of the random actions of many tiny particles[1]within the conductors effectively figures out how to solve this problem and maximize entropy production.

The term “random action intelligence” may seem an oxymoron. Perhaps a more appropriate sounding term would be “dumb luck” or to refer to the proverbial monkey at a typewriter who eventually pounds out Shakespeare. Yet, the term “dumb luck” here is not accurate. In reality, random action is not quite random. There are slight asymmetries in the distribution of behavior. It is the combination of these asymmetries along with large numbers of nearly random acting actors (such as particles) that produces the intelligent result.

1. Some of the durable complex structures (see Chapter 5) developed into RNA[2]and (most likely later) DNA[3]and represent the genetic code and operating instructions for all known living organisms.
2. RNA and DNA mutations may themselves involve a significant component of random chance in forming mutations. (Naturally occurring radiation, itself a random phenomena, may have played a role in this).
3. Most RNA and DNA mutations are of no known consequence, and most others will be detrimental and even fatal.

Neutral changes will be passed on but not favored.

Detrimental changes will be disfavored and less likely to be passed on.

Positive changes will be favored and be more likely to be passed on.

1. Therefore, the mutations of RNA and DNA can be viewed as a form of random intelligence. Essentially, nature throws the dice again and again until it gets to solve problems (such as maximizing entropy production), if given enough time. This process is commonly known as evolution. Typically considerable time is required.

Fast entropy represents an asymmetry that tilts the random mutations of RNA and DNA in favor of maximizing entropy production. Therefore, the desire to maximize entropy production is essentially the driving desire of each one of our cells. Yet remember, what matters is the maximization of entropy by an entire system. Cells within multi-cellular organisms have specialized. So each such specialized individual cell will act in a manner to maximize entropy production by the organism (or some larger system), and not necessarily in a manner to maximize entropy production as an individual cell.

[1]Typically electrons, if the conductors are metals.

[2]More fully known as ribonucleic acid. RNA is involved in the synthesis of proteins, that in turn form much of the structure and processes of cells.

[3]More fully known as deoxyribonucleic acid. DNA encodes genetic information that is vital for cell and organism reproduction.

8. ## 2.6 Smarter Intelligence

First published on . Last updated on February 15, 2020.

## Introduction

Recall how the random action of microscopic particles and energy reactions acts as a “brain” to “figure out and solve” problems such as degrading free energy more quickly. Evolution (the random mutation of RNA and DNA) acts to figure out problems related to the endurance of more complicated life, typically requires considerable time. If faster energy degradation is favored, then it is conceivable that faster means of problem-solving and intelligence will have developed. This section will discuss how Fast Entropy encourages the formation of more powerful, efficient forms of intelligence.

## Random Action Considerations

Random action intelligence uses considerable amounts of time and is relatively inefficient. Evolution is a form of random action intelligence. Nature literally keeps throwing the dice, producing random genetic mutations. Most are unsuitable and can even be fatal. However, all it takes is one successful mutation to solve a problem, as long as the bearer of that gene reproduces.

Evolution can take many millions of years to solve problems and can result in incomprehensibly large amounts of wasted mutations.

## Chemical Signaling

Even simple living organisms have developed chemical signaling that can respond to internal and environmental changes, such as the need for a cell to absorb more oxygen within seconds as compared to millions of years for evolution. Chemical signaling may be sufficiently quick to help an organism decide to move out of the sunlight into shade to keep from overheating. However, chemical signaling may itself be dependent upon evolution to adapt the way it functions, so its short-term abilities apply to only a range of situations, and cannot easily keep pace with unprecedented environmental changes.

## Nervous Systems

Nervous systems are electric networks in more complex, multi-cellular organisms. They can perceive and relay information nearly instantaneously across many cells, and so they can make decisions quickly. Yet, their reactions are in the form of reflexes, so that their problem-solving is quite limited and inflexible.

## The Development of Brains and Bigger Brains

Nervous systems can further develop so that they can be partially controlled and operated by a computing organism known as a brain. Nervous system brains have formed that can make decisions quickly. Such brains can change the way in which decisions are made and make more complicated decisions. Further, brains can learn, and so are more quickly adaptable. The formation of such brains is favored to the extent that they improve endurance of their entropy-producing species. Species with bigger brains displace other groups of less brainy organisms who degrade free energy less quickly, so there is a thermodynamic push for brain size and capability to grow.

## Characteristics of Brains

The simplest brains, such as of a worm or insect, follow regular patterns of decision making that vary relatively little among members of a species (although there is some variation). However, even for the simplest of organisms that possess a brain, changes in environment and physical characteristics will provide a large range of actions. Imagine a fly deciding which direction to fly. Wind direction and the presence of predators can be from any direction, and so the fly may decide to fly in any direction. Yet, an individual brain does not appear to make decisions randomly, but rather it tends to act in particular ways with patterns of reaction These traits are often called habit and stubbornness.

The more complex a brain, the greater flexibility it has to vary its decisions from those of other members of its species. Memory becomes more consciously accessible. Processing becomes more sophisticated. For example, a simple nervous system may respond to one-dimensional changes of light intensity. A sudden change in light might cause a jerking reaction, which may be sufficient to escape from a predator. However, a brain may be able to organize sensations of light and recognize images. Predator versus prey can be distinguished visually. Plans for hunting or escape can be devised and improvised. Certain types of problems can be solved more quickly or with greater sophistication.

Further, organisms with brains have more complicated social interactions, particularly with members of its own species. Brains allow organisms to differentiate between other members of its species, so that organisms become individual, rather than just another member of their species. Preferences, grudges and hierarchy can be formed, organized and remembered.

So the development of nervous systems allow living organisms (and by inference nature) to solve numerous problems of entropy maximization much more quickly than they could have been solved by mere random intelligence. Therefore the formation of such “smarter” intelligence is favored under the principle of fast entropy. For example, the human brain learned how to make and master fire, which more quickly produces entropy from materials such as wood than mere rotting. The human brain’s next type of solution, civilization, would really put entropy maximization into the fast lane.

9. ## 2.7 Development of Agriculture and Civilization

First published on . Last updated on January 19, 2021.

## Introduction

Important events in the progression of humanity is the development of agriculture and civilizations. Societies involve collective action between individual organisms such as individual humans that tends to increase entropy production by increasing efficiency or accessing otherwise inaccessible useful energy. Civilization tends to further involve centralization and coordination that  increases efficiency even further.

Green field (Credit: US govt.)

## From Brains to Civilization

1. Although brains do not make random decisions, a collection of brains can exhibit nearly random behavior. Recall that even the simplest brains provide a large range of actions in response to environmental factors. Further, the more complex a brain, the greater flexibility it has to vary its decisions from those of other members of its species.

Admittedly, diverse action is not necessarily purely random. Certainly, brains of a particular species will tend to exhibit similar responses to certain types of events, to the extent that brains are an artifact of evolution. This can be thought of as evolutionary “inertia”. Further, an individual brain does not appear to make decisions randomly, but rather it tends to act in particular ways with patterns of reaction. These traits are often called habit and stubbornness.

Nevertheless, despite the particular habits and stubbornness of individual brains, a collection of brains, especially the highly developed brains of humans, act in many different ways. For some purposes, a large of collections of brains produces a roughly random set of reactions.  (Although for other purposes, brains make very similar decisions, such as where “swarm logic” applies). Random types of decisions can be modeled statistically, in some ways even thermodynamically. In fact, the random aspects of brain decision-making can be used to give predictability to social models.

1. Fast entropy still favors the more rapid degradation for free energy. Although an individual brain can make decisions that are highly unencumbered by the considerations of fast entropy, there will still be the subtle pressure of fast entropy on each deciding brain. Therefore a collection of brains will, everything else being equal, tend to make decisions that are consist with more rapidly degrading energy. Otherwise, the collection of brains may lack endurance, especially when there are other competing collections of brains.
2. Civilization tends to act to more rapidly degrade free energy. It forms organization and develops technology. In fact, civilization often replicates biological structures that themselves increase entropy production. Roads and railroad lines are analogous to blood vessels. Telephone and internet lines are analogous to nerves.
3. Civilized, more organized groups of people (who degrade free energy more quickly) tend to displace other groups of less civilized, less organized groups of people who degrade free energy less quickly. This there is thermodynamic pressure to become more and more civilized. The term civilization refers to developing a complex, organized, technologically capable society rather than polite “civilized” behavior. For example, having the complex social structure required to build a nuclear weapon would be considered being civilized here, while merely wiping ones mouth with a napkin after dinner would not, although those traits often do go hand in hand.

## Summary

• Civilizations form that consume energy even more quickly.
• Irrigation allows more areas to be covered by plants. Mining allows depletion of energy trapped in fossil fuel biomass. Cities are a complex structure that allows greater concentrations of energy use.

### Civilization As An Even Faster Path

• Civilization allows for coordinated behavior that allows a society to produce entropy even more quickly.
• The e th Law can be used as the foundation for a unified social science that can be used to describe any society, whether on Earth or elsewhere.

Agriculture patterns (credit: NASA)

10. ## 3 Fast Entropy and the eth law

First published on . Last updated on January 19, 2021.

“The question is not whether nature abhors a vacuum, but how much nature abhors it.”

## Introduction

Here we introduce the ethLaw of Thermodynamics, or more descriptively as Fast Entropy. (Here, “e” represents the transcendental number e, which is about 2.718.  The number efits nicely between Laws 2 and 3 of Thermodynamics and expresses the importance of the eth Law in numerous cases of exponential growth.)

Physics is a relatively “pure” subject. Physics is not as pure as mathematics. However, the motions and behaviors of subatomic particles exhibit a beauty and perfection reminiscent of the celestial spheres of the ancient Greeks. Newton’s Three Laws likewise brook no ambiguity, and describe a precise ballet of mechanical motion in the vacuum of the planetary heavens.

With this purity in mind, physicists tend to consider thermodynamic systems in terms of before and after a change. Thermodynamic processes themselves tend to me “messy”. The state of a system in terms of entropy, temperature and other quantities is compared before and after a change, such as heat flow or the performance of work. By doing so, it is possible to neglect the amount of time required for thermodynamic changes to take place. This works well in physics, and the First and Second Laws of Thermodynamics typically suffice.

However, much of the world is a mess (involving tremendous complexity and uncertainty) and frequently must be studied in less than ideal conditions. Further, in the fields of Physical History and Economics, time is of the essence. Utopian idealism aside, how long changes take can make all of the difference in societies. For example, people can’t wait forever to be fed and late armies will often lose wars.

The element of time mustbe introduced in order to apply thermodynamics to social science, which is the thrust of this entire book. This chapter will do so.

## Fast Entropy As A Unifying Principle

Fast entropy can be used as a unifying principle among both the physical and social sciences. Fast entropy has application to applied and professional fields as well. A better name for fast entropy could be the “e” th Law of Thermodynamics.

The ethLaw of Thermodynamics states that an isolated  system will tend to configure itself to maximize the rate of entropy production.[1]

### Heat flow through a thermal conductor example

Most introductory physics textbooks do have an example concerning thermodynamics that involves time.[2]Picture a simple thermal conductor through which energy flows from a hot reservoir to a cold one. For this example, we will consider the term reservoirhere refers to a body whose temperature remains constant regardless of how much heat energy flows in or out of it. [3]

Heat flow through a thermal conductor. The magnitude of that flow is proportional to both the area of the conductor and as its thermal conductivity. More heat will flow through a broad conductor than a narrow one. Also, more heat will flow through a material with a high thermal conductivity such as aluminum than through one with low thermal conductivity such as wood. Heat flow is inverselyproportional to the conductor’s length. Thus, more heat will flow through a short conductor than a long one.

Heat flow is also proportional to the difference in the two temperatures that the thermal conductor bridges. This difference in temperatures has nothing to do with the conductor itself. A greater temperature difference will provide a greater heat flow across a given conductor, regardless of the characteristics of that conductor.

Equation for thermal energy flow through a conductor:

$$\frac{\Delta Q}{\Delta t} = k A \frac{\Delta T}{L}$$.

where, Qis the flow of thermal energy, tis time, kis a constant dependent upon conductor material, Lis conductor length, and A is conductor area, and $$\Delta T$$ is the temperature difference.  This equation states how much heat will flow through a conductor, assuming the temperature difference remains constant. So once again, we face an example that is constant with respect to time, but it provides a reasonable starting point.

Electrical engineers will find this equation similar to a rearrangement of Ohms Law, where electric current is proportional to voltage divided by resistance:

$$I = \frac{V}{R}.$$

## Recalling The Second Law of Thermodynamics

The Second Law of Thermodynamics states that the universe is moving towards greater entropy. Stated another way, the entropy of an isolated system shall tend to increase.[4]A corollary is that a system will approach a state of maximum entropy if given enough time. A system in a state of maximum entropy is analogous to a system in equilibrium.

However, neither law nor corollary describe the rate at which entropy shall be produced, nor how long it would take a system to produce maximum entropy.

## The ethLaw—Fast Entropy

The author has proposed[5]that the Second Law can be extended by stating that not only will entropy tend to increase, but also it will tend to do so as quickly as possible.[6] (Others have made the same observation. e.g. A. Annila, R. Swenson). In other words, entropy increase will not happen in a lazy, casual way. Rather, entropy will increase in a relentless, vigorous manner.  The author calls this extension the ethof Thermodynamics[7], or more descriptively, Fast Entropy. A more precise statement of the ethLaw is that “entropy increase shall tend to be subject to the principle of least time.” The ethLaw gives teeth to the Second Law. It will need those teeth in order to be useful for the social sciences.

Really, though, the ethLaw is already widely practiced astrophysicists and atmospheric scientists. Whether a stellar or planetary atmosphere tends to convect or radiate depends on which results in the greatest heat flow. The maximization of heat flow results in the maximization of entropy increase, so this scenario represents the ethLaw in action.

Fast Entropy can be used as a unifying principle among both the physical and social sciences. Fast entropy has applications to applied and professional fields as well.

## More Precise Statement of ethLaw

The ethLaw needs to be stated more precisely to be of much use. A more precise statement is that “entropy increase shall tend to be subject to the Principle of Least Time.” The Principle of Least Time is a general principle in physics that applies to diverse areas such as mechanics and optics. Snell’s Law of Refraction is an example.

## Physical Examples

Neither the ethLaw nor Fast Entropy will be found in a typical physics textbook, although it could said to fall under non-equilibrium thermodynamics or transport theory discussed in some texts. Fast Entropy involves an element of change over time that can involve challenging mathematics and measurements. Nevertheless, a few simple examples can be offered to support the validity of Fast Entropy.

One example is heat flow through two parallel conductors each bridging the same two thermal reservoirs (see figure). No matter what area, materials or other characteristic comprise each of the conductors, the percentage of heat that flows through each conductor is always that which maximizes total heat flow. In this case, when total heat flow is maximized, so to is entropy production maximized.

Thermal conductors in parallel

Another example is heat flow through conductors in series between a warmer and cooler heat reservoir (see figures). This example replicates the classic demonstration the applicability of the Principle of Least Time in optics (Snell’s Law), but using thermal conductors in place of refractive material, and replacing the entrance point of light with a contact point with a warmer reservoir and the exit point of light with a contact point with a cooler reservoir.[9]

Thermal conductors in series

While heat flow tends be a nebulous affair, the path of maximum heat flow can nevertheless be ascertained. This can be accomplished by noting perpendicular paths to isotherms indicated by placing temperature sensitive color indicator film upon the conductors (below). The greatest color change gradient represents the path of maximum heat flow. Observations show that the path of maximum heat flow is consistent mathematically with Snell’s Law (which is based upon the principle of least time but usually reserved for light rays). This example is reasonably easy to replicate.

Idealized path of maximum heat flow through conductors in series

A third example is well known to atmospheric scientists. Here, in an atmosphere where heat is flowing from a warm planetary or stellar surface, whether thermal radiation or convection will occur tends to be dependent upon whichever produces the greatest heat flow. Whichever produces the greatest heat flow tends to produce the entropy most quickly.

## A Heat Engine Begetting Heat Engines

The work done by heat engines can be used for human activities.  Part of it can be used to maintain the heat engine. More significantly, part of the work can go to build additional heat engines. These additional heat engines can produce more work to produce even more heat engines. This idea is pictured here (see figure). The growth of heat engines is then exponential, at least until limiting factors come into play. This is a key point.  Because heat engines can beget heat engines, an exponential increase in entropy can take place.

Heat engines begetting heat engines

Here, entropy production is proportional to the quantity of heat engines.  Fast entropy favors exponential growth in entropy production, so fast entropy favors the “spontaneous” appearance and endurance of heat engines. Under the Second Law alone, the spontaneous appearance of a heat engine is possible, but improbable. Fast entropy then utilizes those improbable appearances to create self-sustaining, exponentially growing systems.

## Emergence of Complex Dissipation Structure

When systems are far out of equilibrium, there is a tendency for complex structures to form to dissipate potential (Progogine, ___). Such a process is an example of fast entropy. The emergence of atmospheric convection structures are examples of complex dissipative structures. Convective structures tend to form where convection results in greater thermal energy transport  from the surface of the Earth to its upper atmosphere than does simple radiation. Storm systems, tornadoes and hurricanes are further examples. The spiral arms of galaxies are similar in appearance to those of hurricanes. this is no coincidence, since the spiral structure of galaxies also result in greater production of entropy (see paper from Naval Observatory astrophysicist ____).

Rising cloud column (credit: NOAA)

## Applicability of Fast Entropy to Life and Social Sciences

If Fast Entropy is a fundamental tendency in physics that especially applies to living organisms, life would have evolved to produce entropy in a manner consistent with the Principle of Least Time. Evolution is quite similar to statistical mechanics.  It finds the answer it is seeking by rolling the dice an unimaginable amount of times. Statistical mechanics, including thermodynamics, operates most reliably upon systems of many components. Evolution likewise requires a sufficiently high population to operate upon. Endangered species are especially at risk, because their populations often become to small to support the evolution of that species, making it especially vulnerable to change. Evolution is whatever survives the “dice throwing” in response to environmental change. Successful mutations out survive non-mutants and other mutations to multiply and dominate their environment.

In thermodynamics, the Second Law statistically allows small regions of lower entropy. Most of these regions will quickly disappear due to the random motion of molecules.  However, a rare few of these regions, by pure statistical chance, will be able to act as heat engines and will increase overall entropy (despite their own lower entropy). If these rare, entropy-creating regions can reproduce, then they will be favored by fast entropy, and will come to dominate their region. Certain chemical reactions are examples, and from chemistry comes life.

So then, life can be viewed as a literal express lane from lower to higher entropy. Although living organisms comprise regions of reduced entropy, they can only maintain themselves by producing entropy. Life has produced a diversity of organisms in order to maximize entropy production with respect to time. For example, if one drops a sandwich in a San Francisco park, a dog will rush by to bite off a big piece of the sandwich, then the large seagulls will tear away medium sized pieces to eat. Smaller birds will eat smaller pieces, and injects and bacteria will consume smaller pieces yet. If only one or two of those organisms existed, some of the pieces or certain sizes could not easily be consumed. If they couldn’t be consumed, they could not be used to increase entropy.

Humans are living organisms and do their part to contribute to maximizing entropy production with respect to time. In fact, the more complex, structured and technologically advanced human civilization becomes, the faster it creates entropy. It is true that cities and technology themselves represent regions of lower entropy, but only at the cost of increased overall entropy.

## Further Applications

There are both physical and social applications for Fast Entropy.[8]Physically, Fast Entropy might be used to improve heat distribution and removal. Socially, Fast Entropy drives Hubbert Curves. Further, Fast Entropy might be used to determine key parameters of Hubbert curves and constraints upon them.

Fast Entropy analysis requires that some indication of entropy production with respect to time be determined. An exact determination might prove to be difficult, but comparisons of entropy production are easier. For example, if people consume a known mean number of calories, then the more people a regime has, the more entropy it produces. Most historic regimes have a sufficiently low level of technology that this type of analysis is quite practicable.

## Conclusions and Future Research

Fast Entropy can be used in history as a criterion of success for a regime. Was a regime overtaken by another regime that was able to produce more entropy more quickly? In economics, Fast Entropy can be used to study the progress of a regime along its Hubbert curve, and infer factors such as efficiency, economic centralization and wealth distribution. Fast Entropy can be a power tool for the analysis of proposed social policy. However, an important issue to be investigated is whether and how the value of entropy production needs to be weighted with regards to its distance in time.

## Notes & References

[1]However, the behavior of systems the atomic level can vary from that discussed in this chapter.

[2]One can infer the passage of time by multiplying the calculated heat flow by time. However, this is example is not really time dependent. The heat flow remains constant regardless of how much time passes in this idealized example. It is nevertheless a good approximation for many real situations.

[3]Heat flow is also proportional to the difference in two temperatures that the thermal conductor bridges. This difference has nothing to do with the conductors themselves. Heat flows through a thermal conductor in proportion to the area of the conductor as well as its thermal conductivity. More heat will flow through a broad conductor than a narrow one. Also, more heat will flow through a material with a high thermal conductivity such as aluminum than through a material with low thermal conductivity such as wood. Heat flow is inverselyproportional to the conductor’s length. More heat will flow through a shorter conductor than a long one. This is known as Fourier’s heat conduction law

[4]A more precise definition is that “any large system in equilibrium will be found in the macrostate with the greatest multiplicity (aside from fluctuations that are normally too small to measure).” D. Schroeder, An Introduction to Thermal Physics.  San Francisco: Addison-Wesley, 2002.

[5]This proposed extension was anticipated in a talk given by the author to a COSETI conference (San Jose, CA, Jan. 2001, SPIE Vol. 4273), was presented at a talk entitled Hurting Towards Heat Death (Sept. 2002) and appeared in the Fall 2003 issue of the North American Technocrat. Subsequent to this proposal, the author has observed that a form of this extension is already in use by astrophysicists and meteorologists. When modeling atmospheres, their models will tend to choose the form of energy transfer that maximizes heat flow, such as convection versus conduction or radiation. See B. Carroll and D. Ostlie, An Introduction to Modern Astrophysics, 2ndEd., Pearson Addison-Wesley, 2007, p. 315.

[6]The Second and A Half Law is not well known and therefore is neither generally accepted nor rejected by most physicists. Although the Second and A Half Law is fairly consistent with standard physics, it is primarily intended for use in the applied physical sciences and the social sciences.  There is some possibility that this proposed law is flawed. However, it has somemerit and is somewhat better than what we have without it.

[7]As stated above, e in ethlaw referring to the transcendental number e, that is 2.718.

[8]Psychologist and musician Rod Swenson had proposed some elements of this, perhaps as early as 1989. He suggested that a law of maximum entropy production could apply to economic phenomena.

[9] Mark Ciotola, Olivia Mah, A Colorful Demonstration of Thermal RefractionarXiv, submitted on 21 May 2014.

11. ## 4 Flows and Bubbles

First published on . Last updated on February 6, 2021.

Many phenomena in both nature and society can be examined in terms of bubbles and flows. Many can be modeled as a combination of potential, flows, barriers and bubbles.

## Flows

In the most general sense, a flow is the continuous transport of something from one place to another. In a more abstract sense, it is the continuous change of a quantity. For a short amount of time, a flow can be caused by inertia. For longer periods, something must drive the flow.

The consumption of potential can drive a flow. Then the flow can be said to contribute to the achievement of the potential. The flow can continue indefinitely as long as both the potential and that which flows are both steadily replenished. For many purposes, a flow can be viewed as a the result of a continuous supply of potential.

The shining of the Sun on the Earth in cold space is a continuous flow of energy that has lasted billions of years. The current of water down the Nile River is another flow that has lasted thousands of years.

## Physical Flows

The current of water down the Nile River is another flow generated by a gravitational force. Let us examine this. Water flows from higher elevations to lower ones, such as via the Nile. Water in highlands represent a higher gravitational potential than water at sea level. Water flowing downhill consumes (achieves) this potential.

Yet the Nile has been flowing for many thousands of years. How does the water at the high elevations get replenished? Atmospheric storm systems represent complex structures to dissipate potential. Sunlight places powerful amounts of energy at the surface of the oceans and wet land. Storms form to pump this energy more quickly away from the surface into the cold upper atmosphere. The transport of water into the atmosphere and its rain on the Earth’s surface increases the rate of energy transport. (Condensing water vapor in the upper atmosphere releases prodigious amounts of energy into outer space).

## Resource and Economic Flows

There are also many physical flows in our economy. The transport of food from farm to city and of mineral from mine to factory represent flows.

## Generalizing the Emergence of Structures

We discussed how regimes can emerge from civilizations as dissipative structures to increase entropy production. Here, we generalize the concept of a regime.

## Formation of Bubbles

Bubbles emerge when a flow gets blocked. As potential builds up, the force against the blockage increases. Eventually the accumulation and force become so large that the blockage can no longer impede the flow. At this point, the blockage might be partially overcome, or it might become catastrophically destroyed. This is analogous to the formation and popping of a bubble. Another term for blockage is “Logjam”.

## Emergence of Exponential Structures

### Limits

In the case of a flow, heat engines will exponentially grow until they reach a limiting efficiency. Heat engine population and entropy production will reach a limit called a carrying capacity.

### Thermodynamic Interpretation

Heat engines begetting heat engines results in exponential growth in both quantity of heat engines and entropy production. Where the magnitude of potential is fixed, as entropy is produced, the potential decreases. As potential decreases the efficiency of the heat engines decreases. This decrease in efficiency comprises a limiting factor.

This decreased efficiency decreases the ability of heat engines to do work. Eventually, the total amount of both work and entropy production will decrease. Less work will be available to beget heat engines. If the heat engines require work to be maintained, the number of functioning heat engines will decline. Irreplaceable potential entropy continues to decrease as it gets consumed. Eventually, the potential entropy will be completely consumed, and both work and entropy production will cease.

As this scenario begins, proceeds and ends, a dissipative structure (a literal thermodynamic “bubble”) forms, grows, possibly shrinks and eventually disappears. Entropy production versus time can often be graphed as a roughly bell-shaped curve, giving a graphic illusion of a rising bubble.

## Bubbles Involving Life

Populations of living organisms can experience thermodynamics bubbles. A bacteria colony placed in a media dish full of nutrients faces a potential of fixed magnitude. Each bacterium fills the role of a heat engine, producing both work and entropy. The bacteria reproduce exponentially, increasing the consumption of potential entropy exponentially. Eventually, it becomes increasingly difficult for the bacteria to locate nutrients[1], decreasing their efficiency. As efficiency decreases, the bacteria will reproduce at a slower rate and eventually stop functioning.

### Ultimate Bubbles

Ultimately, all potentials are fixed in magnitude. Possibly, the entire Big Bang and its progression could be viewed as a bubble. In practice, many potentials are renewable to a limited extent. For example, as long as the Sun shines upon the Earth in cold space, a potential will exist there.

### Series of Bubbles

As long as a system maintains the ability to produce new heat engines, then instead of a single bubble, there will be a series of bubbles over time. There are several reasons that systems form bubbles instead of maintaining a single flow. Chaos (in the mathematical sense) provides one reason. Another reason is that a series of bubbles may provide for an overall higher entropy production rate than a more steady, consistent rate of production. Heat engines in a bubble may be able to obtain much higher efficiency during a bubble than during steady state, so that the average production in a series of bubbles may be much higher than during a steady flow, despite the below average production between bubbles.

### Overshoot and the Predator-Prey Cycle

Yet even in the case of a flow, the rate of replenishment will be limited. Yet the rate of engine reproduction may have continued beyond carrying capacity. This can be called overshoot, a systematic “momentum” in a sense. In this case, even the flow can be treated as a substantially fixed (or “conserved” in the physics sense) quantity. A thermodynamic bubble will form.

Another case such as predator-prey cycles can also form where overshoot occurs, where the population of a predator overshoots the available prey, reducing both the population of the predators and the prey, so that there are cycles where the population of the predator is always “reacting “ to the population of the prey. Predator-prey cycles can also be expressed in terms of flows, bubbles and efficiencies.

## Notes and References

[1]Or escape toxins produced by the colony.

12. ## 4.1 Resource Bubbles

First published on . Last updated on February 6, 2021.

## Introduction

Rise-fall nonrenewable resource consumption functions (“curves”) are examples of resource “bubbles”. M. King Hubbert’s modeling of Peak Oil is the most famous example of a resource bubble. However, that case was inspired by the earlier  work of Donnel Foster Hewett regarding regional metal mining.

The essence of a bubble is a build up of potential that then gets relieved. The key is that there is a critical resource that is not renewable. Any amount that gets consumed cannot get replaced. Once that resource is consumed, it is gone forever. So production must eventually end.

Deposits of gold are an example that represent built-up potential. Usually achievement (consumption) of the potential begins slowly, but then grows exponentially. Hence production will grow quickly, but intrinsic efficiency begins to drop, impacting production. Eventually efficiency will drop below the level at which achievement can be obtained, or the entire potential will be consumed, and the bubble ends.

## Regional Example—San Juan Mining Region

To apply bubble analysis, the region considered must be sufficiently large enough to initially support many mines. The San Juans region in Colorado is such a region, and is a suitable example of a single historical regime is the mining society that developed in the San Juan mining region. Since precious metals tend to be a nonrenewable resource, they can be said to be conserved (that only a fixed amount of the resource ever will exist) for a given region. In other words:

Potential consumption + cumulative production = constant

at any point of time. Potential consumption equals that constant before exploitation begins.

The San Juan mining region of Colorado produced gold and silver from dozens of mines, around which towns and communities eventually developed. Mining began as early as 1765. Its heydays were between about 1889 and 1900. There is again mining in miscellaneous minerals, but the not much in gold, which was the primary economic driver for the “great days”. The region is now used primarily for recreation and some agriculture. (Smith, 1982)

Spanish gold mining of placer deposits took place between about 1765-1776 (native pieces of nearly pure gold found on the surface). Some mining took place in 1860, but it was interrupted by U.S. Civil War. At this point, “only the smaller deposits of high-grade ore could be mined profitably.”  Mining slowly started again in 1869. There were 200 miners by 1870. An Indian Treaty was negotiated in 1873, which removed a major obstacle to an increase of mining. (Smith, 1982)

By 1880 there was nationally a “surplus of silver; pressures to lower wages; labor troubles.” In 1881 a railroad service was established, resulting in a “decline in ore shipping rates.” By 1889, $1 million[1] in gold and silver were being produced each year (for one particular sub-region). Around 1889, English investors had come to control the major mines by this time. The 1890 production total for San Juans was$1,120,000 in gold; $5,176,000 in silver. The region produced saw$4,325,000 in gold and \$5,377,000 in silver in 1899. (Smith, 1982)

By 1900, the region began to take on more of the characteristics of a settled community. There was a movement for more “God” and less “red lights.” By 1909, “the gilt had eroded” (dilapidation set in; decreasing population). In 1914, production greatly fell, due to decreased demand from Europe (because of World War I) and the region lost workers. Farming becomes more important to local economy than mining. Recreation and tourism revenues become the only bright spot for many mining towns. Silver and gold mining all but ceased by about 1921. (Smith, 1982)

Here, the end of mining has a fairly clear cut-off date. However, the beginning of mining seems to have stretched out over a longer period of time, during which mining levels were quite small. [The curve was previously modeled using a Maxwell-Boltzmann distribution, but this was a more empirical approach. Originally, only a few data points were readily available (Smith, 1982), but digitization of sources, even if just scans, has made much more data available.]

Deviations will be shown in the curve occurred to both random events, social, economic and logistic “turbulence”, business cycles and major external events such as the U.S. Civil War.

Colorado San Juans gold production versus model

A EDEG model was created (in 2010) for U.S. domestic petroleum extraction (see below). Actual data exceeds model prior and after peak. Parameters were set to match peak, but could have beed adjusted to for less error elsewhere at the expense of greater peak error. This model used a older version of EDEG than the most recent San Juans model, so the overall plot is not as well matched.

EDEG model for US petroleum production up to 2008.

Another example, on a multi-continental basis was gold and silver production in areas of the Americas controlled by Spain, primarily during the Habsburg dynasty. An EDEG model was produced for that period. This model used a cruder version of EDEG than the most recent San Juans model, so the peak is not as well matched.

Silver and gold exports from New World versus model (data from Gibson, 1996)

### References

Ciotola, M. 1997. San Juan Mining Region Case Study: Application of Maxwell-Boltzmann Distribution Function. Journal of Physical History and Economics 1.
Ciotola, M. 2001. Factors Affecting Calculation of L, edited by S. Kingsley and R. Bhathal. Conference Proceedings, International Society for Optical Engineering (SPIE) Vol. 4273.
Ciotola, M. 2003. Physical History and Economics. San Francisco: Pavilion Press.
Ciotola, M. 2009. Physical History and Economics, 2nd Edition. San Francisco: Pavilion of Research & Commerce.
Ciotola, M. 2010. Modeling US Petroleum Production Using Standard and Discounted Exponential Growth Approaches.
Gibson, C., Spain in America. Harper and Row, 1966.
Hewett, D. F. 1929. Cycles in Metal Production, Technical Publication 183. New York: The American Institute of Mining and Metallurgical Engineers.
M. King Hubbert. 1956. Nuclear Energy And The Fossil Fuels. Houston, TX: Shell Development Company, Publication 95.
Hubbert, M. K. 1980. “Techniques of Prediction as Applied to the Production of Oil and Gas.” Presented to a symposium of the U.S. Department of Commerce, Washington, D.C., June 18-20.
Mazour, A. G., and J. M. Peoples. 1975. Men and Nations, A World History, 3rd Ed. New York: Harcourt, Brace, Jovanovich.
Smith, D. A. 1982. Song of the Drill and Hammer: The Colorado San Juans, 1860–1914. Colorado School of Mines Press.

13. ## 4.2 Economic Bubbles

First published on . Last updated on January 19, 2021.

Here we discuss economic regimes, more commonly known as “bubbles”.

## Economic Flows

Food and mineral flows also represent economic flows. So do transfers from one group to another, such as from parent to children, workers to retirees, exporter to importer. Flows often work at least two ways. For example, goods and services flow from an exporter while money flows from an importer. Many trade partners engage in both importing and exporting with each other.

## Financial Flows

Economic flows can be abstracted into financial flows, such as an annual market demand or income. An example of a steady income flow is called an annuity.

Direct Logistic or Gaussian Approach

It is traditional to model growth by one of two types of curves, the pure exponential growth curve or the logistic growth curve. Since most new business plan for three to five years, this is a reasonable approach.

All things end sooner or later, so it might make more sense to model growth with a Gaussian or Maxwell-Boltzmann distribution. However, most businesses don’t like to plan for a downturn. Yet for particular products or businesses in industries where the typical lifetime may only be a few year or a single season, either of these curves may be superior to the pure exponential or logistic approaches.

### Beginning Point

None of these approaches has a clear beginning point, mathematically speaking. The pure exponential, logistic and Maxwell-Boltzmann curves can arbitrarily be assigned a beginning point without too much thought.

The Gaussian curve can prove more challenging to assign a beginning point. A fair approach is to initially establish a pure exponential growth curve, then later fit a Gaussian to that curve.

### Pure Exponential Growth Phase

Sometimes it is hard to determine the parameters soon enough to make useful forecasts. Yet there are ways to handle this, although they are imperfect. However, if a business has a great product, and there is strong demand for it, the question is how quickly can the business expand to meet that demand? If the expansion cost and resultant speed can be calculated, then a model exponential growth curve can be generated, assuming that the business will expand as quickly as possible. Also assumed is that the growth of the business at a particular time will be proportional to its size at that time. If the business can only expand linearly, then a linear model must be generated.

### Leveling or Decline Phases

Eventually, limiting factors will level off growth and even cause a decline in business. A logistics curve is appropriate for a product or business that will have relatively long-term, stable sales, such as a popular soft drink. For products that will have a known or likely decrease, a Gaussian or Maxwell-Boltzmann curve can model both the growth and decline.

## Efficiency Approach

A more fundamental approach is to use efficiency data for modeling. This approach can work better if there are similar cases available for comparison so that reasonable parameters for reproduction costs and efficiency can be proposed at an early phase so that reasonable forecasts might be possible. This approach is similar to modeling a single historical regime.

### Two Places to Begin—Relation to Supply and Demand

There are two placed to begin using the efficiency approach. One way is to determine the total lifetime sales for the product or business. (Take the raw value, not the Net Present Value-discounted value). If you can then determine what the peak sales amount will be, and the beginning and end dates of the business, you can treat efficiency as a linearly decreasing quantity (this is not entirely accurate, particularly for the beginning and end of the lifecycle, but can be a reasonable approximation).

A perhaps better, but more complicated way is to first model demand for the product (in terms of a series of classical economic demand curves over time). Then determine a series of classic supply curves over time. This will tell you the sales revenue and volume over time. The trick is to use fast entropy and thermodynamic efficiency to model how the supply and demand curves will change over time. Fast entropy will cause the quantity supply curve to fall: as the business develops, the business will likely increase production capacity, so that it can afford to sell more at a lower per unit price.

However, as time goes on, the demand curve will also fall due to growth leveling off or falling as the market becomes saturated. It is also possible, that there will be limits to how much production can grow is a required resource becomes scarcer (and thus expensive), so that the supply curve can only fall so far. These events represent decreasing thermodynamic efficiency. Thermodynamic efficiency should be differentiated from empirical efficiency, which may be due to such factors as economies of scale. In fact, it is often falling thermodynamic efficiency that required increased economies of scale to meet demand at sufficiently low prices. This is one reason why there is often consolidation in maturing industries.

It is possible to use this approach to model entire macro economic business cycles. (Despite their name, these cycles are really thermodynamic bubbles).

Figure below shows US adjusted GNP for 1993-2013 (the scale is nominal), a litter “sizzle” plot of the U.S. economy during that period. Long-term trends have been stripped out of the data. The figure shows the dot com bubble peaking around 2001 and the housing bubble peaking around 2006. These bubbles are not just random occurrences, for they share a similar structure. There is an underlying thermodynamic potential. . An engine of GNP growth forms to bridge that potential, such as firms that can create or take advantage of new computing technology or a relaxation of banking standards. At the beginning of the bubble, the potential is high, so that exploitation can take place at a high thermodynamic efficiency. However, as potential is consumed, the amount potential decreases, so efficiency necessarily drops. At the same time, old firms are expanding and new firms are being formed, resulting an increasing amount of heat engines” to consume potential.

US Economy Sizzle Index 1993-2013

Once formed, these firm heat engines remain “hungry”. They need to consume potential to survive and they very badly want to survive and grow. So they keep growing, even though potential is decreasing. Eventually, the potential (and therefore thermodynamic efficiency) drops so low and there are so many heat engines, that most of the heat engines can no longer support themselves. Chances are, industry overshoot has occurred (i.e. formation of too many hungry heat engines), and a crash occurs. This cycle usually repeats itself for each macroeconomic business cycle bubble, although the chief industries involved may vary among bubbles. The bubble itself apparently increases overall entropy production of a society, which is consistent with the principle of fast entropy.

First published on . Last updated on May 17, 2019.

Businesses are interesting cases to study. There are many businesses, both large and small. Some are long-lived, many are short-lived. They utilize many different types of opportunities. They all involve people. Many involve money, which is quantifiable and often the figures are recorded.

Many businesses can also represented as bubbles, using the approach of a heat engines (or collections of heat engines). A business faces a new market opportunity of fixed magnitude. Businesses exploit the market opportunity, producing both work and entropy. The business or its industry reproduces exponentially, increasing the consumption of potential entropy exponentially. Eventually, it becomes increasingly difficult for the business or industry to locate new customers or orders, resulting in increased competition and decreased margins, hence lower efficiency. As efficiency decreases, the business will expand at a slower rate and eventually stop functioning.

Some businesses can endure for longer than many dynasties. Yet most businesses go through common sorts of life cycles. They usually start small and are founded by an innovative entrepreneur. They get bigger and become efficient but start getting institutionalized. Eventually the overhead of their bureaucracy becomes more of a drag than help on overall efficiency. At the same time, the company has a harder time adapting to change. Eventually the opportunity the company originally exploited is gone, management can’t adapt and the company ends.

Companies don’t exist in a vacuum. They are dependent upon their government for law and security, the the population for revenues. So a business can find new opportunities, be bought by another business, be regulated out of business, etc. The business does not progress on the same precise lifecycle as an animal, but there are frequent patterns.

## Phases

### The Opportunity and Conception

The business opportunity (potential) is identified. The opportunity could be one-time in nature, such as the discovery of a deposit of gold. It could be ongoing, such as a new technology that will be adopted for a long period, such as the commercialization of electricity in the 1800s or the internet.

A means (engine) to exploit it is identified. The means could be a new mechanical invention, the building of a factory or construction of a mine. The development of the engine will require some initial “seed” resources, and literally has a “start-up” cost, called an initial investment (fixed cost).

### Growth

The company embarks upon exponential growth, which often starts slowly and then becomes rapid. Either the engine gets bigger or more engines are built. Often profits are reinvested in growing capacity.

### Peak

The growth slows as it approaches its peak then levels off. Also, both the engines and developing bureaucracy involve maintenance (overhead) costs.

### Decline, Acquisition or Transformation

Eventually the business may decline as the original business opportunity declines or ends. The business might be able to take advantage of new opportunities, or may be bought by another company. It might buy other companies who are better at developing new opportunities.

### Businesses as consumers of limited resources

Businesses can be modeled as of consumers of limited resources and therefore as Hubbert curves. A business based upon an oil well or a gold mine is an obvious example. The limited resource can be intangible. Nearly all businesses are ultimately dependent upon a particular business opportunity that is often in turn dependent upon a limited resource. That limited resource might be satiable customer demand for a highly durable product. It might be a technology niche that has a limited lifetime or marketing window in a rapidly transforming marketplace. Other examples include resources can include intangibles such as goodwill and patents.

Businesses tend to develop through fairly well-defined stages: start-up, growth, stalling, acquisition of or by other businesses (or decline and then termination).

Businesses tend to operate in one of two modes, depending upon their current development stage. Growing start-ups are in an exponential growth (EG) mode, while established businesses move to an exponential decay (ED) mode. Operation in the EG mode is characterized by emphasis on revenue growth. Sources of revenue growth include new products, increased sales or acquisition of other businesses. Operation in the ED mode is characterized by emphasis on cost cutting. Forms of cost-cutting include consolidating product lines, reduced R&D spending, and layoffs. (The former case of stable major airline striving to raise profits by removing an olive per salad served is such an example). A firm that is experiencing the plateau of a logistic growth curve will rend to oscillate between the EG and ED modes, depending on short-term events.

The transition from the EG mode to the ED mode can be a dangerous time for a business. Sometimes businesses grow too quickly and cannot make a successful transition. Cash shortages and the inability to fulfill customer orders are symptoms. Frequently the founder and the original management will be replaced at this point.

Some business managers desire growth, so much that they don’t especially mind the ensuing disorder. Other people prefer order and harmony, even at the expense of growth.

Managers who emphasize getting sales, launching truly new products, and even mergers and acquisition tend to be operating in an exponential growth mode. Managers who attempt to increase profits by focusing on reducing product costs and decreasing workforce size tend to be operating in a plateau of exponential decline mode.

## Precautionary Considerations

General statements about a society or a category of people within a society should certainly not be taken to apply to individuals. Individuals tend to have a wide range of freedom to act and don’t fit into most generalizations.

15. ## 4.4 Exponential functions

First published on . Last updated on February 6, 2021.

## Introduction

### Functions

Functions relate at least one variable to at least one other number or variable. is a variable. Its value could be anything. Yet, consider the equation:

$$x = 1$$

Here, x is constrained to equal to a single particular number, which is 1. Such a number is known as a constant. It’s value in the equation cannot change. Things get more interesting when a variable is related to another variable. For example, let’s say that

$$y = 2x$$.

Both x and y are variables. However, the value of either variable can change, depending on the value of the other variable. Below are some sample pairs of values allowed by this equation:

x y
-2 -4
-1 -2
0 0
1 2
2 4
10 20

Such a function acts as a constraint of the values. If x is 1, then y must be 2.

Functions can take many forms, such as y = x^3, z = 2x + 5y, or y = sin x, where sin is shorthand for the trigonometric function sine, what can be expressed quantitatively as a series of numbers.

### What Exponential Functions Are

Exponential functions are functions where a constant is raised to a power. For example,

$$y = 7^x$$.

Here, the values of x and y are:

x y
-2 1/49
-1 1/7
0 1
1 7
2 49
3 343

You can see that exponential functions can increase very quickly. There is a very special constant called equal to 2.71828. e is a very special number in mathematics for many reasons. However, it is also a very useful base for exponential functions. e is typically used as the base for exponential functions.

## Pure exponential growth

Pure exponential growth is that which is proportional to its current quantity. In principle, a system that is capable of self-replication can experience pure exponential growth.

It can apply to populations of bacteria, fish and even humans. It can apply to chain reactions in nuclear physics as well.

Bacteria (photo credit: CDC US government)

Humans can self-replicate, so human societies can also experience pure exponential growth, in the form of y = et, where the value of e is approximately 2.72.

Pure exponential growth begins slowly, then literally explodes over time. Sometimes the plot of exponential growth is described as a “hockey stick” because it starts nearly horizontally, then “turns the corner” and grows nearly vertically.

It typically concerts population differential equations such as

$$\frac{dP}{dt} = kP$$.

where P is population, t is time and k is a proportionality constant. The solution for this equation is the classic exponential growth function

$$P = P_0 e^{kt}$$.

where is the initial population.

Pure exponential growth

Different growth rates result in different levels of growth at a particular point of time, but growth is still ultimately explosive (see below).

Pure exponential growth for different growth rates

Human social movements can also experience exponential growth.  Many philosophies have been subject to exponential growth, because the founder could teach others to teach yet others. Investment pyramid schemes can also experience exponential growth.

Certain types of growth not only grow, but cause changes in their environment to enable further growth.

Some futurists make dire projections of explosive population growth and resource consumption by extending a pure exponential function into the future.[2]In reality, exponential growth is never seen for long periods of time, due to limiting factors.

It is noticed that systems in both nature and human society often grow exponentially at times (Ciotola 2001; Annila 2010). Exponential growth essentially means that a system’s present growth is proportional to its present magnitude. For example, if a doubling of population (say of mice) is involved, then 10 mice will become 20 mice, while 20 mice will become 40 mice. A formula for exponential growth is:

$$y = ek^t$$

where $$y$$ is the output, $$k$$ is the growth rate, and $$t$$ represents time.

### Logistic Growth

A resource that is renewable, but limited in the short-run, can be modeled with a logistics curve. Examples of such resources are new-growth forests and wild Pacific salmon. They can be nearly totally consumed in the short run, but these resources can restore themselves if they have not been exploited too completely. A logistics curve is not shown here, but is in the shape of an elongated “S” and can be found in many differential equations textbooks. The beginning (and bottom) of the “S” represents the initial exploitation. The forward-sloping “back” of the “S” represents nearly pure exponential growth. The end and top of the “S” represents a leveling off of growth, as consumption of the resource matches its ability to restore itself.

In logistic growth, population tends to move towards a particular population level that reflects the carrying capacity of the system or environment. Such functions are also called S-curves.

Logistics functions are in the form of:

$$\frac{dP}{dt}=k (1-\frac{P}{N})P$$,

where P is population, t is time, k is a growth rate coefficient and N is the carrying capacity. N can also be viewed as the periodic replenishment of potential.

Logistic growth

Achieving a logistics curve is the holy grail of sustainability enthusiasts. Applying concepts of sustainability to an entire dynasty or regime is called Big Sustainability, and involves social and economic sustainability, as well as physical resource sustainability (e.g. sufficient desired resources and ability to avoid toxins).

## Decay

Exponential decay of efficiency is produced by a Carnot engine operating across an exhaustible thermodynamic potential. It is a fundamental form of decay. The following is an equation for an exponential decay function:

$$y = e^{-k^t}$$ ,

where $$k$$ is the decay factor. This appears nearly identical to the exponential growth function, except that the exponent is negative.

## Efficiency-Discounted Exponential Growth

Efficiency-Discounted Exponential Growth (EDEG) involves the consumption of a non-replenished resource over time by a system of reproducing agents. It can be useful for modeling mineral production of a mining region.

The efficiency-discounted exponential growth (EDEG) approach is relatively new, although functions similar in output have existed for over 100 years. A few rough simulations were conducted earlier (Ciotola 2009, 2010), but this approach is being further refined and structured. EDEG produces a model based on two mathematically simple components, but allows the addition of other, more sophisticated components.

This author’s original efforts at developing the EDEG approach were heavily influenced by M. King Hubbert, a geologist who used such curves to model domestic petroleum production (including peak oil) as well as labor model.[7] Hubbert in turn was influenced by D. F. Hewett.

It is possible to create differential equations that produce EDEG. It is also possible to empirically synthesize functions that closely replicate EDEG. An analytical solution to EDEG differential equations from fundamental principles has not yet been created. However, the  differential equations can be iteratively calculated via a spreadsheet or computer program to produce useful results.

The author originally used the normal distribution approach (Ciotola, 2001) discussed by Hubbert, but this approach was not sufficiently broad for the authors need to model history, since few historical dynasties utilized petroleum in major quantities, nor did Hubbert’s attempts involve a driving tendency for history. The author began some related models for French and Spanish dynasties (2009) and more fully developed EDEG for petroleum modeling (Ciotola 2010).

It is not yet possible to analytically create a EDEG function from fundamental principles. However, EDEG can be expressed as a differential equation, which can then be iteratively calculated via a spreadsheet or computer program.

When developing an EDEG model, an effort should be made to express parameters in terms of a potential and changing efficiency. If the quantity of the most critical conserved resource is known, then the model for total consumption over time should match that quantity.

An EDEG function can be approximated by multiplying a pure exponential growth function by an efficiency function:

$$P = k_1 e^{k_2 t} (1 – \frac{Q}{Q_h})$$,

where P is power (or production), is a constant of proportionality, typically the initial prediction (or power), is a growth factor, is the amount of a nonrenewable critical resource thus far consumed, and is the initial quantity of the nonrenewable critical resource.

represents the exponential growth component.”

$$(1 – \frac{Q}{Q_0})$$

represents the efficiency component.

Colorado San Juans gold production versus model

## HS Curves

It may also be possible to create a function that transforms an H-Curve (EDEG) to an S curve. There is an initial amount of a non-renewable critical resource, and then periodic replenishment of that resource.”

## Efficiency Discounted-Exponential Growth (EDEG) Approach

The efficiency-discounted exponential growth (EDEG) approach is relatively new, although functions similar in output have existed for over 100 years. A few rough simulations were conducted earlier (Ciotola 2009, 2010), but this approach is being further refined and structured. EDEG produces a model based on two mathematically simple components, but allows the addition of other, more sophisticated components.

## Origins of This Approach

This author’s original efforts at developing the EDEG approach were heavily influenced by M. King Hubbert, a geologist who used such curves to model domestic petroleum production (including peak oil) as well as labor model.[7] Hubbert in turn was influenced by D. F. Hewett.

The author originally used the normal distribution approach (Ciotola, 2001) discussed by Hubbert, but this approach was not sufficiently broad for the authors need to model history, since few historical dynasties utilized petroleum in major quantities, nor did Hubbert’s attempts involve a driving tendency for history. The author began some related models for French and Spanish dynasties (2009) and more fully developed EDEG for petroleum modeling (Ciotola 2010).

## Exponential Growth

In principle, a system that is capable of self-replication can experience pure exponential growth. Examples include bacteria, fire and certain nuclear reactions. Humans can self-replicate, so human societies can also experience pure exponential growth, in the form of y = et, where the value of e is approximately 2.72. An example of pure exponential growth is graphed below.

Human social movements can also experience exponential growth.  Many philosophies have been subject to exponential growth, because the founder could teach others to teach yet others. Investment pyramid schemes can also experience exponential growth.

Certain types of growth not only grow, but cause changes in their environment to enable further growth.

Some futurists make dire projections of explosive population growth and resource consumption by extending a pure exponential function into the future.[2]In reality, exponential growth is never seen for long periods of time, due to limiting factors.

It is noticed that systems in both nature and human society often grow exponentially at times (Ciotola 2001; Annila 2010). Exponential growth essentially means that a system’s present growth is proportional to its present magnitude. For example, if a doubling of population (say of mice) is involved, then 10 mice will become 20 mice, while 20 mice will become 40 mice. A formula for exponential growth is:

$$y = ek^t$$

where $$y$$ is the output, $$k$$ is the growth rate, and $$t$$ represents time.

## Efficiency-Discounted Exponential Growth

Efficiency-Discounted Exponential Growth (EDEG) involves the consumption of a non-replenished resource over time by a system of reproducing agents. It can be useful for modeling many phenomena, including the mineral production of a mining region.

It is possible to create differential equations that produce EDEG. It is also possible to empirically synthesize functions that closely replicate EDEG. An analytical solution to EDEG differential equations from fundamental principles has not yet been created. However, the  differential equations can be iteratively calculated via a spreadsheet or computer program to produce useful results.

When developing an EDEG model, an effort should be made to express parameters in terms of a potential and changing efficiency. If the quantity of the most critical conserved resource is known, then the model for total consumption over time should match that quantity.

An EDEG function can be approximated by multiplying a pure exponential growth function by an efficiency function.

$$P = k_1 e^{k_2 t} (1 – \frac{Q}{Q_0})$$,

where P is power (or production), $$k_1$$ is a constant of proportionality, typically the initial prediction (or power), $$k_2$$ is a growth factor, $$Q$$ is the amount of a nonrenewable critical resource thus far consumed, and $$Q_0$$ is the initial quantity of the nonrenewable critical resource.

$$k_1 e^{k_2 t}$$

represents the exponential growth component.

$$(1 – \frac{Q}{Q_0})$$

represents the efficiency component.

Colorado San Juans gold production versus model

## Notes and References

[1] Meadows, et al. makes this point in Limits to Growth.

[2] For an opposing, but still dire view, see D. H. Meadows et al, Limits to Growth, Universe Books, New York (1972).

[3] The work of Forrester on system dynamics and the Club of Rome project Limits to Growthby Meadows et al involve attempts to better understand these limiting factors. The work of M. K. Hubbert and Howard Scott on peak oil and technocratic governance are other examples.

[4] M. Butler, Animal Cell Culture and Technology.  Oxford: IRL Press at Oxford University Press, 1996.

[5] Ciotola, M. 1997. San Juan Mining Region Case Study: Application of Maxwell-Boltzmann Distribution Function. Journal of Physical History and Economics 1. Also see M. K. Hubbert.

[6] Heilbroner, R. L., The Worldly Philosophers 5thEd.  (Touchstone (Simon and Schuster), 1980.

[7] Such curves were proposed by W. Hewitt as early as 1926 (source unavailable).

[8] See Gibson, C., Spain in America. Harper and Row, 1966.

Annila, A. and S. Salthe. 2010. Physical foundations of evolutionary theory. J. Non-Equilib. Thermodyn. 35:301–321.

Ciotola, M. 2001. Factors Affecting Calculation of L, edited by S. Kingsley and R. Bhathal. Conference Proceedings, International Society for Optical Engineering (SPIE) Vol. 4273.

Ciotola, M. 2003. Physical History and Economics. San Francisco: Pavilion Press.

Ciotola, M. 2009. Physical History and Economics, 2nd Edition. San Francisco: Pavilion of Research & Commerce.

Ciotola, M. 2010. Modeling US Petroleum Production Using Standard and Discounted Exponential Growth Approaches.

Hewett, D. F. 1929. Cycles in Metal Production, Technical Publication 183. New York: The American Institute of Mining and Metallurgical Engineers.

M. King Hubbert. 1956. Nuclear Energy And The Fossil Fuels. Houston, TX: Shell Development Company, Publication 95.

Hubbert, M. K. 1980. “Techniques of Prediction as Applied to the Production of Oil and Gas.” Presented to a symposium of the U.S. Department of Commerce, Washington, D.C., June 18-20.

Mazour, A. G., and J. M. Peoples. 1975. Men and Nations, A World History, 3rd Ed. New York: Harcourt, Brace, Jovanovich.

Schroeder, D. V. 2000. Introduction to Thermal Physics. San Francisco: Addison Wesley Longman.

Smith, D. A. 1982. Song of the Drill and Hammer: The Colorado San Juans, 1860–1914. Colorado School of Mines Press.

16. ## 5 Psychological Reactions

First published on . Last updated on February 6, 2021.

Human psychology is connected with resource availability and trends. Maslow’s hierarchy indicates that when people have one thing in sufficient quantity, they then desire something “higher up” on their needs pyramid.

Maslow’s Hierarchy Of Needs

17. ## 5.1 Psychology Versus Fast Entropy Paradox

First published on . Last updated on May 17, 2019.

Here, we discuss the inherent conflict between fast entropy and psychology. It is ironic, but fast entropy has shaped human psychology to reject the very idea of fast entropy.

## People View Science Through the Filter of Feelings

### People are emotional beings

People have emotions. They naturally form impulsive judgments based upon their feelings or physiological reaction. Thinking takes time. Emotion can be instantaneous. People evolved from times when there was little time to think. Organisms who thought first were eaten by something bigger. Organisms who emotionally reacted (were immediately scared and ran way) lived to have offspring. Our ancestors evolved to be emotional reactors and we inherit this trait.

### New Ideas Are Psychologically Costly

New ideas typically require changing ideas about what is already known. This can make a person feel ignorant, uncertain, out-of-control and even unsafe.

### New Ideas Can Be Deadly

To some extent, the social status of all people is at least partially dependent upon their knowledge and wisdom. New discoveries and theories therefore automatically decrease the social status of existing people, for there are by definition unknown. Status has been demonstrated the most important determinant of longevity (how long the worker lives).[1]Therefore the decrease in status caused by new discoveries can shorten the longevity of people, especially older people.

Since new discoveries are actually life-threatening, it is natural that people will resist new discoveries, as if their life depends on their resistance, which it indeed does. Of course, new discoveries are often in fact incorrect in one or more aspects, so it is reasonable for people to initially reject new ideas.

However, the duty to winnow and sift is often not enough to explain the visceral negative reactions that academic workers sometimes have towards new ideas. Therefore, emotions often color judgment. Incidentally, this subject has been studied, such as by Kuhn in the Structure of Scientific Revolutions. Such impulsive judgments cannot be stopped. However, many decisions and final judgments can be accepted after time passes and reason has a chance to examine new discoveries.

## People Don’t Like the Second Law of Thermodynamics

### People life freedom of choice

People have the need to feel that they have freedom of choice. Although the Second Law of Thermodynamics is statistical in nature, it tends to be deterministic in effect. People prefer having choices and feel that they do have choices. Therefore anything that is deterministic is unacceptable.

### People don’t like limits

People don’t like limits. They don’t like to feel that the choices they do have are limited. Unfortunately, the laws of physics suggest all sorts of limits. The limits on efficiency under the Second Law, or the limited amount of petroleum under the surface of the Earth don’t seem very pleasant to people.

### People like immortality

People like immortality. Therefore the illusion of immortality, infinity and perfection are extremely desirable images. People like circles, for they are perfect and have no end. People also like pure sine waves, for they have no end, either. If you can view one cycle of the wave, you will know how it is forever and from one end of the universe to the other, so to speak; by grasping a piece of a pure sine wave, you grasp the whole. Also, pure sine waves exhibit the same sort of perfection as circles.

### Motivation Is Inherently Irrational

People need to maintain their motivation. Indeed, the more they maintain their motivation, the more entropy they can each produce. Yet, the laws of physics feel constraining; it is hard to feel motivated when one is aware one is trapped by the laws of physics. So the principle of fast entropy has dictated through the evolution of the brain that people tend to deny the existence of fast entropy or other laws of physics.

Instead, people live by impossible maxims. Have you not heard the saying “You can achieve anything you put your mind to.” You could solve world hunger, cure cancer and finish reading this book by dinnertime. Yet you haven’t done those things yet. Don’t you care about the starving children of the world? Perhaps not. Mother Theresa didn’t solve the problems of poverty or world under either. According to the above maxim, she could have, but chose not to, so she apparently didn’t care either, or was all in favor of starving children. Another maxim is to give something 110% effort. That is physically impossible.

The point is that such impossible maxims help us to achieve more in life. We may not achieve everything we wish to, but we’ll achieve more than the scientifically cynic.

## The Complete Picture

Inner and Outer Philosophy

You may recall that it was asserted that both inner and outer philosophies are needed for a complete social science. The emotions and motivational necessities of inner philosophy need to be considered along with the cold, hard scientific facts of outer philosophy, and vice versa. If you can appreciate and practice this, then you have learned the most important lesson in this book.

## Great Escapes

The author periodically presents on fast entropy to conferences of sociologists and other social scientists. A frequent audience reaction is to devote the rest of their lives to disproving the principle of fast entropy, or at least its application to the social sciences. How can we escape from the jaws of its limits?

The best way to escape is to remember that as individuals, our rate of entropy consumption is not the primary determinant of our happiness. The quality of our personal relationships and sense of community may be far more important to our happiness, self-esteem and status.

A second point is that, as individuals, we have a great scope of freedom. Specific consideration of the laws of thermodynamics rarely constrain the day-to-day actions or decisions of individuals, even of physicists. You only need to worry about them if you are deciding whether to invest in an exotic energy technology, designing a mechanical device or promulgating a macro social policy.

Third, time is often your friend as much as your enemy. The world is not going to run out of oil today, tomorrow or even next year. To paraphrase French King Louis XV, it may very well last your time. Just as thermodynamic processes are nearly inevitable, they are rarely instantaneous.

Finally, if you are able to use fast entropy as a crystal ball (albeit an often foggy one), you can arrange your life so to use fast entropy to your advantage.

[1]BBC News article.

18. ## 5.2 Psychological Reactions to Change

First published on . Last updated on May 17, 2019.

People who might be accepting of something in general, may react differently when it is accompanied by change. Rates of change matter as well. People’s immediate “gut” reaction to rapid change may differ from a slow, reasoned, adjusted reaction.

People prefer to feel in control of their lives, and to feel secure in their environment. Rapid change involves uncertainly and a loss of control.

Also, change can require a mental adjustment. Just the process of adjusting itself can be mentally painful or challenging to people, especially as they age. Older people have a lot of knowledge in their brains. Having to learn new stuff and reconcile inconsistencies between the old and new can be a greater challenge than merely learning the materials with an emptier brain when one is young. Older people must unleard andlearn.

Finally, change can require physical adjustment. A person may have to move, change jobs, or learn new skills or languages.

19. ## 6 Modeling History

First published on . Last updated on February 6, 2021.

Here, we discuss how to use fast entropy and other methods described in this text to model history.

### References

[1] Note that dollar amounts are unadjusted for inflation — they reflect actual historical figures.

[2] See M. Ciotola, Journal of Physical History and Economics, Vol. 1, Is. 1 (1996).

Gibson, C. (1966) Spain In America. Harper and Row.

Smith, D. (1982) Song of the Drill and Hammer.

20. ## 6.1 Creating And Using Models

First published on . Last updated on February 6, 2021.

A model is a hypothesis about how something exists or works. A model could be a small version of something large, such as a table top copy of the Notre Dame cathedral in Paris. Such a model would represent the large, most important features of the cathedral such as the towers and flying buttresses, and possibly representations of some of the more distinctive smaller features such as the stained glass windows.

A model can also be one or a set of mathematical equations that relate one quantity to another. For example, an equation could relate dynasty power to time. Such a model could be refines, such as to represent central versus regional power. We will primarily be concerned with creating quantitative models.

Creating a quantitative model is really easy. Just relate two quantities to one other. For example, write the following equation:

.

According that his model, the number of soldiers in the Roman empire is equal to the year in current era years. So in 100 CE (AD), the number of Roman imperial soldiers would be 100. This certainly is a model, because it produces results that can be compared with actual data. Historians evaluate the validity of such data, which may come from literary or archeological sources, and then can compare it with the model. A range of uncertainly is estimated. If the model produces a result that not within the range of uncertainty for the data, the model is rejected or revised. If the model fits within the range, then it is valid, although not necessarily absolutely correct (no model ever gets proved) or representative of ultimate truth. Generally, models that fit the data the best and are consistent with other valid models tend to be more accepted.

It often requires several attempts to get a valid model, and many attempts to obtain better ones. The above example concerning Roman soldiers can be quickly rejected using commonly available data.

Models can be improved by including additional terms. and changing parameters. For example, adding a baseline number of soldiers, and then a term that might take into account the growth of mercenaries might improve the accuracy of the model.

In history, often the available or accepted data is limited, and uncertainties may be high. So initially, a more pragmatic approach may be to propose models and explore to what extent they might be valid.

21. ## 6.2 Fitting, Uncertainty, Significance and Error

First published on . Last updated on February 16, 2020.

## Fitting

For the moment, let assume that we have a validated, precisely known data set. However, we don’t know the relationship between the data, its trends or driving tendencies. So we decide to develop a model to gin a deeper understanding. Generating a model is easy. Personal income = (5 * personal height) + 6. There. Done! Yet to what extent is it a valid model? There are tools for that. In fact, modeling is often a process of adjusting the model function and parameters until the model fits the data well.

One technique is minimizing the sum of the squares. For each term of data, calculate the value the model would produce (e.g. for each point of time). Take the square of difference between calculated and actual value. Add up all of those squares. Adjust your unknown parameters to produce the smallest value for the sum of the squares. This will be your best fit model.

## Significance

There is a limit in the significance of quantities. Here, we are only referring to mathematical significance. For example, a quality is only significant up to half of the smallest unit being measured. For example, if you measure a distance with a meter stick, and the stick is only ruled in 1 centimeter units, then you can express the distance in terms of the smallest subdivision of the rulings: in this case, that would be 1/2 of a centimeter. So the significance would be 0.5 cm, which is three digits, e.g. 91.5 cm.

## Uncertainty

Measurements involve a degree of uncertainly. Once again, here, we are only referring to mathematical uncertainly. Using the previous example, the distance is likely not exactly at any specific centimeter ruling. It is somewhere between centimeter marks, and it can sometimes be a bit of a judgment call to determine which is the closest mark. So the uncertainly here would be plus or minus 0.5 cm. So if the distance was measured as 91.5 cm, then the measurement would be expressed as 91.5 cm +/- 0.5 cm. This sort of error cannot typically be eliminated.

## Error

Measurements can be subject to systematic error. This type of error occurs due to a consistent flaw in the measurement system.

For example, suppose the end of the meter stick was once cut off at the 1 cm mark, so that it always understates the distance by 1 cm. Such sources can sometimes be identified through examination of the measuring apparatus, and eliminated if identified.

## Statistical Approaches to Improving Quality of Data

Large regimes are comprised of vast numbers of individuals. Even a small city might contain tens of thousands of people. Most large urban areas contain millions of people. Most powerful countries contain at least 50 million people to over one billion people in modern times.

Even if a regime is governed by a single individual such as a monarch or dictator, the regime is nevertheless comprised of all of the individuals governed, each with their now needs, perspectives, influence and power (even if individually small).

22. ## 6.3 To What Extent Can History Be Quantitatively Modeled?

First published on . Last updated on February 16, 2020.

We are concerned with developing a unified history of science, which means that we must be able to propose testable hypotheses. It is a lot easier to reject hypothesis that can be quantified. Yet given how complicated individuals are, and how much complex entire societies of many individuals must be, how could it every be possible to quantify societies? There are ways, but there are some phenomena that first require discussion.

## Regimes As Vast Numbers of People

Large regimes are comprised of vast numbers of individuals. Even a small city might contain tens of thousands of people. Most large urban areas contain millions of people. Most powerful countries contain at least 50 million people to over one billion people in modern times.

Even if a regime is governed by a single individual such as a monarch or dictator, the regime is nevertheless comprised of all of the individuals governed, each with their now needs, perspectives, influence and power (even if individually small).

### Individual Freedom of Action

These thousands and millions of people each possess their own interests and scope of action. Individuals appear to have a significant scope of freedom of action, even when they have limited civil rights.

### Does the Time Make The Hero?

Does individual freedom translate into freedom of action for the entire regime? This brings to mind an age-old question. Does the time make the hero or does the hero make the time? Consider the following two cases.

In football, the San Francisco 49ers were a legendary football team in the 1980s. For much of that time, they were lead by a legendary quarterback, Joe Montana. In one game, the 49ers were behind with 15 seconds left in that game. Then Joe Montana threw a winning touchdown pass and the rest was history. Joe Montana was certainly a great quarterback. Yet, while acknowledging Montana’s skill, coach Bill Walsh pointed out that this last minute play had been rehearsed time and again in a comprehensive system of team training. Montana was part of that system.[1]Without that system, Montana could have thrown a great pass, but there would have been no one there to catch it.

A second case applies to factory assembly lines.[2]  In an assembly line a conveyer belt moves an uncompleted product past a series of workers. Each worker completes a task, which is often dependent upon the already-expended efforts of workers “up-line.” What if one worker works exceptionally diligently and quickly? What will happen? If the worker processes products too fast, there will be a pile of “work-in-process” waiting in front of the next worker who is working more slowly. Unless that next worker speeds up, all that will happen is that the factory’s inventory of unfinished goods will increase, which is a waste of money and resources.  The factory will be harmed. Or the hard-working worker, dependent upon an “up-line” worker for work-in-process, will simply run out of product to work on and have idle time. In neither case do the extra efforts of the diligent worker contribute to the productivity of the factory and in one case even reduces productivity.[3]

In a large, interdependent system, such as a large society, the conclusion here is that it is the time that makes the hero, even if the time is silent as to which individual will earn the title of hero.

### Regime As The Summation of Individual Behavior

A regime can be viewed as the sum of the individual contributions and actions of its individuals.  When one thousand carpenters strike one thousand nails with one thousand hammers, the regime is one thousand nails-hits richer. A city is a single legal entity, but is comprised of numerous houses, factories, shops and other structures.

This summation effect appears to tend to cancel out any effect of individual free will over material lengths of time.  Many individuals will behave in one way while many others will behave in the opposite way. Some carpenters will drive nails into boards, while others will remove nails. The larger the society, the greater this canceling effect will tend to be.

Is a regime then completely at the mercy of historical destiny? This is not necessarily so, but the ways a regime can escape its “destiny” are limited and fairly specific in nature.

### Regimes As Producers and Consumers of Resources

Regimes can be viewed as produces and consumers of resources. Just as an individual human requires air, water, food and other goods, so does a city albeit in larger amounts. Humans are to regimes as are cells to the human body. Great networks of blood vessels supply nutrients to individual cells and carry away waste. Networks of nerves convey information. In a contemporary society, water is carried in great aqueducts, rail lines and freeways channel in nutrients and remove garbage, and a myriad of telephone and internet lines transmit information. Such resources can be anything necessary to sustain the regime.

### Resource Exhaustion

Some resources are partially renewable, such as agriculture production.  Others are limited and can be totally exhausted. Such resources can include fossil fuels, ground water, and old growth forests for example. Social resources can also be exhausted. In business, social resources are accounted under the term “good will” and even have a quantitative financial value placed upon them.

### Societies Dependent Upon a Nonrenewable Resource

When a regime is substantially dependent upon a limited, nonrenewable resource, it can be modeled as a function of a normal distribution or other similar distribution. Regimes which are substantially dependent upon mining mineral reserves such as gold and silver are a prime example. Spanish governance over the New World and the mining communities of the San Juan region of Colorado were both highly dependent upon producing gold and silver. Even where a critical physical resource is not apparent, most regimes are dependent upon limited social resources and can therefore be modeled as a Hubbert curve.

### Transition Points

A new society grows exponentially. Its people expect that exponential growth will continue. They frequently do not recognize limits to growth soon enough. Production does not match expectations, leading to social disruption. Where growth slows and expectations diverge from actual production represents a transition point and may graphically appear as an inflection point.

[1]William Walsh et al, Finding the Winning Edge.

[2]This example is inspired from Elihu Goldratt, The Goal.  Great Barrington, MA: North River Press, 1992

[3] Goldratt, The Goal.

23. ## 6.4 Long-Term Trends and the Emergence of Societies

First published on . Last updated on February 16, 2020.

There are several long-term trends concerning humanity. Although these trends might not be observed every day, and there can even be periods and locations contrary to the trends, they still operate on long periods of time.

## Longterm Trends

### Precession

The inclination of the Earth with respect to the Sun changes in 26,000 year cycles (NASA). The Earth is slowly wobbling on its access. This affects regional climates, including wind, rainfall and temperature. This change can be significant when considering periods of more than a few centuries.

### Evolution and Selection

Modern humans have existed for at least 10,000 years. There may not have been much genetic mutation over the past few millennia, so the scope of human evolution during that period may be limited. However, there has likely been some effects due to selection, that is the ability of people to adapt to particular local and social changes ad well as due to mating preferences. For example, during the 1950s-1970s, there was apparently a tremendous mating preference for those who were able and willing to master the electric guitar, an example of a new technology.

## Human Population Growth

The human population has grown tremendously in the past 10,000 years (U.S. Census).

### Other Trends

• Environmental change
• Climate change
• Species changes (extinction, domestication, monoculture)
• Destruction of forests
• Salinization of soil in irrigated lands
• Total land area used by humans

## Emergence of Societies

Due to these trends, and arguably the driving force of the eth Law, human societies formed. Living organisms formed,then multi-cell creatures. Animals formed, then vertebrates, then mammals. Primates became smarter and able to use tools. Homo sapiens developed. Language and agriculture were discovered and adopted, allowing people to form complex societies.

24. ## 6.5 Emergence of Dynasties

First published on . Last updated on February 16, 2020.

## Introduction

The term dynastyis used broadly to refer to a continuous ruling group; it could be a related family but does not have to be. The term regime can also be used. The term societyrefers to a group of related people, typically of a single or similar group of ethnicities, such as the Han people in China or the Frankish people in France. Dynasties exist within a society, but can conquer other societies as well.

Fast Entropy can drive the formation of dynasties or regimes. Within the context of a civilization progressing over millennia, it is often possible to degrade built-up potential even more quickly even given current types of social structures for a particular society. Hence, dynasties form to more quickly achieve that potential  (just as a convection bubble forms in a boiling pot of water to release heat more quickly). Dynasties result in more rapid degradation of energy than does a more static society.

Each dynasty has a lifecycle. A dynasty is similar to an individual biological organism than a swinging pendulum. A dynasty is born, matures, endures for awhile, then dies. A new dynasty will not necessarily follow an old one, or might not immediately appear. Yet dynasty will continue to form as long as there exists a potential that cannot be more quickly achieved by other means.

Does a dynasty have to have a life cycle. Could it not last forever, or at least indefinitely? Societies and some institutions can last much longer than dynasties. It is conceivable that a dynasty could be managed in a sustainable manner, but this is not what we typically observe in history.

Why has the 300-year pattern appeared so frequently in history from France to China to West Africa? It could be that humans who organize in large, durable regimes traditionally chose monarchies. It could be that the values that lead to success and failure go through a roughly fifteen generation progression. It could be that these regimes have utilized the same sort of resources such as agriculture, and perhaps land becomes excessively exhausted after about 300 years. Conserved social resources could include good will or social flexibility. Property rights, concentration of wealth and gentrification could eventually petrify a regime. Or, this could be viewed in terms of a standard 300 year predator-prey prey scenario.

Movements towards stabilization can be described as a march towards thermodynamic or statistical equilibrium. There is a short term type of equilibrium related to on-going flows and a longer-term equilibrium that relates to the “life-cycle” of the regime itself.

### Considering Dynasties As Bubbles

A human society can experience bubbles. A new dynasty within a civilization encounters a potential of good will and other physical and social resources, albeit of fixed magnitude. The society governed by the dynasty fills the role of a collection of heat engines, producing both work and entropy. Prosperity expands exponentially, increasing the consumption of potential entropy exponentially. Eventually, it becomes increasingly difficult for the dynasty to rely upon its store of goodwill and physical and social resources, decreasing its efficiency. As efficiency decreases, the dynasty will experience social crises and will eventually stop functioning.

## Summary

So far, the discussion has been largely speculation. The correct application of factual evidence will demonstrate to what degree the above is valid. The underlying mathematical formulae will be proposed in other sections. This approach is different than mere philosophy or opinion, because it is capable of being numerically disproved or restricted to limiting cases.

25. ## 6.6 Modeling A Dynasty Using EDEG

First published on . Last updated on January 19, 2021.

## Introduction

This section concerns generating models of the rise and fall of power of dynasties versus time and how a single dynasty can be modeled using the efficiency-discounted exponential growth (EDEG) approach.

This sort of model can be called a power progression. Various approaches to modeling dynasties will be explored, then a new physical approach will be proposed. All of the approaches presented are simplifications that assume a gradual rise and fall. Of course history is rarely so cooperative. Hence, the models shown should be considered mere first approximations. Mathematical treatment of dynasties will be novel to most historians, so simple approaches will be discussed first, and more complex ones later.

It is simpler to model a sufficiently large, robust, independent dynasty than one that existed merely at the whim of its neighbors, for there are less significant dependencies, and thus can be approximated as a substantially isolated system. So we will utilize Russia’s Romonov dynasty as an example. Widely accepted start and end dates are 1613 and 1917 (Mazour and Peoples 1975). Peter the Great and Catherine the Great were the two important rulers of the Romanov dynasty, and the Russian Empire gained much of its most valuable territory by the end of Catherine’s reign. The Romanov dynasty was big, robust and essentially independent. It fought wars, but it generally was not under serious threat of extinction. Even Napoleon could not conquer Russia, but rather Russia nearly conquered Napoleon. This dynasty was reasonably long-lived, rather than just a quick, “flash-in-the-pan” empire.

By developing a fundamental approach to modeling the rise and fall of dynasties, it is possible to accept or reject models based upon both qualitative historical evidence and quantitative historical data.

A regime can be a dynasty or corpus of government. A society here is defined to be a particular people or culture over time. The people occupying the area of modern day France from the time of the Frankish invasions to the present could be viewed as French society. A dynasty, such as the Capets in France, would be viewed as a regime.  The nominal term “government” does not always describe a regime, however. A regime can be recognized by having a clear rise and fall connected with production or consumption of a critical resource.

Historical dynasties are consumers of energy and producers of power, so models in terms of such quantities are inherently fundamental in that they can be derived directly from the laws of physics and expressed in physical quantities. Such models are not theories of everything, but rather describe certain types of broad macro-historical phenomena rather than the intricate workings of the interactions of individual people.

The term energy is meant in the physical sense here. There are several possible measures of the physical energy of a dynasty, such as population governed or grain production. Each of these is translatable into physical units of energy. For example, the quantity of people multiplied by the mean Calorie diet per person will result in an amount in units of energy. These figures can be estimated for most dynasties over their lifespans, albeit with differing degrees on uncertainty. The proportion of this energy that rulers of the dynasty actually have at their disposal is beyond the scope of this paper, but should be considered for improved accuracy.

Power is a physical term. It refers to energy expended per unit of time. Yet it also has meaning within social and political contexts, and will be discussed in both senses. Absolute power would generally be presented in physical units of power such as Watts. However, it is possible to express any type of power in terms of proportions, such as the ratio of power at a dynasty’s peak to its start date. Such a ratio can apply to physical, political or even military power. So the EDEG approach can be utilized to model any type of power. In fact, the EDEG approach provides a framework to explore the question of how political and physical power are related.

## Exponential Growth Component

A new regime will tend to experience exponential growth. A chief characteristic of exponential growth is that growth feeds even more growth, resulting in an increasing rate of growth. Increases in population and consumption can become explosive. Nevertheless, the growth rate in early stages tends to be relatively flat, while the growth rate later on tends to be relatively steep. In reality, the change between “flat” and “steep” can be surprisingly sudden despite warning signs.[1] Incidentally, the transition from flat to steep may be more painful than graceful for many people. Regimes that are unprepared can suffer greatly.

### Example of Mechanism of Exponential Growth

Recall our example of heat engines begetting heat engines. That is an example of exponential growth, because the rate of growth of heat engines was proportional to the existing population of heat engines at a particular instant.

Heat engines begetting heat engines

### Theory—Pure, Unlimited Growth

Sources of growth can include geographic expansion, infrastructure improvements and trade expansion. It will be assumed that dynasties will strive to grow exponentially. (This paper does not attempt to prove this assertion, but rather it is a rebuttable presumption). If so, this certainly explains the rise of a dynasty. There is a minor distinction between exponential growth and compounded growth. Exponential growth essentially involves continuous compounding which produces a larger effective growth rate than discrete compounding. It is similar to the difference of quarterly versus daily compounding of a bank savings account. This effect is less significant at small growth rates but more so at very large rates. For the growth rates that we will consider, the effect is negligible compared to the other sources of uncertainty that exist.

The Romanov dynasty with various growth rates is shown in Figure 5. The plot shapes appear similar, except that a greater rate produces a “sharper” corner. Also, notice the range of power values: a greater growth rate produces a disproportionately greater power value at later points of time.

Exponential growth for various growth rates

## Efficiency Component

Efficiency is the proportion of consumption that is transformed into production, or its equivalent in power.

### Limiting Factors

In reality, there will always be factors that limit the growth even of a self-replicating system. A regime that experiences pure exponential growth will eventually begin to experience such limiting factors.[3]The magnitude of these limiting factors will increase during growth (more than proportionately). These limiting factors restrain growth and sometimes stop it altogether.

Limiting factors usually exist due to a shortage of some essential resource or an excess of some “negative” resource.  In a simple case of exponential bacteria growth, limiting factors can include insufficient nutrients and production of excessive toxin. A toxin can reduce or prohibits growth even in a resource-rich environment.

Turning to the biotechnology, an examination of the case of growing cells shows that the chief limiting factors are typically a nutrient limitation or an accumulation of a toxic metabolite.[4]Even in an environment that is overall rich in resources, scaling issues result in the decrease of surface area to volume ratio of the organism colony. In other cases, some cells require a growth surface to anchor to. A lack of oxygen can be a limiting factor for large cell cultures. The organisms often cannot get access to abundant resources because they are crowded out by their neighboring organisms. Multi-cell organisms attempt to overcome the surface area limitation with structures such as veins and folding. However, an elephant still faces many challenges as compared with an ant, such as expelling sufficient body heat.

Human civilization meets a similar surface area challenge with similar structures. The great freeways and road networks in cities and even across the countryside in many ways resemble the blood circulation system in out own bodies.

Another source of limiting factors is the growing cost per unit to extract limited resources such as minerals. Societies attempt to use large-scale social and technical structures to overcome this challenge, but these structures create additional challenges.[5] There are other examples. In the U.S., the “closing” of the western frontier marked a limit of growth to homesteading. In petroleum production, the increasing cost of drilling for oil is a limit to growth. P. Malthus[6]pointed out limiting factors in the growth of agricultural production.

### Efficiency Decay

Dynasties inevitably end, which is typically preceded by a decline in power. Exponential growth alone is insufficient. Another physical principle comes to our aid. A dynasty can be viewed as a heat engine (or collection of such). Engines consume a potential to produce work or exert power. As an engine consumes a nonrenewable potential, the efficiency of that engine may decrease. (For physics-savvy readers, picture a Carnot engine operating across exhaustible thermal reservoirs. As heat is transferred, the temperature difference will decrease, and so to will efficiency. (Ciotola, 2003)). Therefore the engine’s net production will decrease and eventually fall to zero.

Likewise, as the dynasty progresses, non-renewable resources will be consumed, and efficiency will decrease. There will still be production until the end, but there will be a lower return on investment, so to speak. Causes of decay can include overuse of agricultural land leading to nutrient depletion, the build-up of toxins in the environment, depletion of old growth forests, and even running low on social goodwill.

There are two types of decay, linear and exponential, compared in the plot below. Figure 6 contains plots of linear and exponential decay. Note that efficiency is shown as a multiplier rather than a percentage.

Linear vs decay efficiency

A regime, past its prime and dependent upon a limited resource, may experience exponential decline. Exponential decline in an EDEG situation can happen more quickly than exponential growth. However, there are two disadvantages of exponential decay within the context of modeling dynasties. First, it is slightly difficult to set up. For example, exponential decay has an infinitely long tail. While this allows for mathematical immortality, most of the tail is superfluous in the context of a dynasty of limited lifetime. Second, it may not provide the most consistent models with observations.

A linear approach as simpler to set up. Importantly, it also provides some reflection of efficiencies achieved through centralization and economies of scale as the dynasty progresses. It has unambiguous beginning and end points. Efficiency cannot be greater than one, and is typically no lower than zero. Therefore, as a first approximation, one can set the efficiency to 100% at the start date of the dynasty and 0% at the end year (except that the math is simpler if the value 1 is used for 100%). Using a value of 0 for ending efficiency ensures that the dynasty actually does end by its historical end date. Although physical efficiency is typically lower than 100% for real life heat engines, 1 provides an easy starting point that also produces the correct shape of curve. The following is an example of linear decay function:

efficiency = 1 – ((year – start year)/(end year – start year)).

As the year increases, efficiency will decrease. Using a lower initial efficiency reduces the magnitude of production increase for the dynasty compared to its initial production. It also flattens out the curve. Using a value of zero for ending efficiency ensures that the dynasty actually does end by its historical end date. It is possible to use a value other than zero for the ending efficiency, but then some other factor must be used to end the dynasty.

### Double Injury—Declining Efficiency Can Occur Even As Resources Become Very Scarce

The key impact of limiting factors, whether insufficient positive resources or excessive negative resources, is a decrease in the efficiency of whatever is acting as the “heat engine” to do work.

Even where the EDEG function appears symmetric, the intrinsic efficiency function can be extremely asymmetric: high in the beginning and low towards the end.

Centralization can produce economies of scale that can boost net efficiency, but when a centralized system goes bad, it can go really bad. It can be difficult to go gradually to a less centralized system, and failed central institutions can bring a regime crashing down quickly. This is an example of an irreversible process.

## Exponential Growth Where A Nonrenewable Resource Exists

We still need to go a step further.

The effect of limiting factors, even upon exponential growth, is that growth will either reach a plateau or will become negative. In all cases, given sufficient time, growth will become negative, and that negative growth shall substantially cancel out past positive growth. Here, growth refers to that derived from consumption of a critical limited resource.

Production in a society is ultimately dependent upon a scarce, conserved resource. The term conserved means that the resource is non-renewable. The total amount everrecoverable cannot exceed a fixed quantity. In the case of a gold mine, certainly no more gold than is already present in the mine can be captured. A regime will typically consume both conserved andrenewable resources. It is the consumption of the critical conserved resource that shall determine the growth characteristics of the regime.

So now we bring exponential growth and declining efficiency together. We need to use the decay to discount exponential growth, just a little in the beginning, then completely at the end.

Linear vs decay efficiency

Growth will not only slow down but often will actually start to reverse.  Such growth and decline can be represented by a EDEG function, where the area under the curve represents either the total production or consumption of a conserved resource over time.

Note that the critical resource becomes more expensive as each successive unit of it is utilized. In the case of petroleum or a precious ore, the least expensive deposits are extracted first. Then the next least expensive deposits are extracted and so on.

The following is an example of an EDEG equation:

y = exponential growth function * efficiency function,

where * is a multiplication symbol.

Here is a simple way to generate a quantitative model for a dynasty. It is simplistic, but it produces generally qualitatively correct results. Assume exponential growth:

$$P_t = P_0 e^{kt}$$,

where $$P$$ is power, $$P_0$$ is initial power, $$t$$ is time and $$k$$ is a constant of proportionality.

Assume that a nonrenewable resource is being consumed that cannot be replaced within the lifetime of the dynasty. Then assume the efficiency of each subsequent unit of resource consumed produces power as a decreasing efficiency. A simple linear efficiency decay function could be:

$$\epsilon = 1 -\Big ( \frac{current~year – start~year~of~dynasty}{end~year~of~dynasty – start~year}\Big )$$,

where $$\epsilon$$ if efficiency. Then the efficency-discounted power is:

$$P = \epsilon * P_0 e^{kt}$$.

Substituting in our functions (utilizing linear decay):

$$Y = e^{kt} *(1 – (\frac{t}{(end year – start year)}))$$.

Or,

Y = ek(year – start year)*(1 – ((year – start year)/(end year – start year))).

This produces a steady rise, a level period and a slightly faster decay. So by discounting exponential growth by decreasing efficiency, we then have a rise and fall pattern that is consistent with the rise and fall of a dynasty.

That negative growth occurs often indicates resource exhaustion. External competition can result in negative growth, but the success of external competition can often be described as a function of internal resource exhaustion.

For example, by the early 13th century, the Byzantine empire had consumed much of its timber reserves, so essential for the maintenance of its navy. The Byzantine capital fell for the first time in 1205 A.D.

## Sample Description of the Progression of a Traditional Single Regime

A major dynasty (e.g. China, France, West Africa) would typically begin with a daring, competent, often unpolished leader, but with effective power loosely distributed. The future generations of rulers will become increasingly desirous of luxurious living and will also demand expensive “trophies” such as palaces, major public works or optional conquests. This will stress the natural resources of that society, and the dynasty will experience financial difficulty. Taxes will be raised. Bureaucracy will need to be greatly expanded in order too collect the increased and taxes and to administer increasingly complex tax codes. Internal dissatisfaction will increase, so greater internal military effort will be required to suppress rebellions The dynasty rulers will become increasingly dependent upon their military to maintain internal order and to enforce tax collection. At the same time, the rulers will tend to become increasingly occupied with court etiquette and pursuit of such civilized activities as art and scholarship; but they will become less competent at governance and further removed from the realities of the population they govern. Eventually competing figures from within the society, backed by military figures, will challenge the rulers. These initial challenges will be put down brutally, further increasing discontent, and destroying much of the social structure and institutions required for the effective maintenance and defense of the society and its economy.

Due to the decreasing magnitude of economic activity, the population and strain on natural resources will decline, allowing for some recovery of productive capabilities. Then, eventually, further challenges from either within or without the society will replace the dynasty, and a new dynasty will form.

## Thermodynamic Interpretation of Sample Description of the Progression of a Traditional Single Regime

A thermodynamic potential has built up. A new major dynasty in effect represents a new collection of heat engines that is capable of consuming such built-up potential. The magnitude of built-up potential is relatively high, so heat engine efficiencies are relatively high. Such heat engines utilize some of their work to produce additional heat engines. The population will rise, and economic activity will increase. As future generations of rulers become increasingly desirous of luxurious living and will also demand expensive “trophies” such as palaces, the thermodynamic costs of maintaining such heat engines will increase. Initially, due to high efficiencies and growth of production, such maintenance costs will not be problematic. Yet while demands for maintenance increase, built-up potential is being depleted resulting in decreasing thermodynamic efficiency. (Although a continuing flow of potential exists from such sources as agriculture, it cannot keep up with consumption).

Centralization temporarily successfully regains high efficiencies by increasing economies of scale and allowing access to difficult-to-extract potential (that has a high “activation energy”). Yet thermodynamic maintenance costs continue to escalate while efficiency decreases due to continued consumption of built-up potential. Overshoot results. The dynasty will no longer be able to maintain its structure, and total production (thermodynamic work) declines. This decline continues, but additional attempts at overshoot cause the decline to be chaotic.

The population of heat engines continues to decrease. Chaotic decline place the population of heat engines below what can be supported by “renewable” flows of potential. Hence a thermodynamic potential will build up again. Then, eventually, a new dynasty (thermodynamic “bubble”) will form.

An exception is where the original built-up potential is from a source that can never be replenished, or that can be replenished over periods of time much longer than a typical dynasty lifetime. Rainforests, agricultural lands vulnerable to erosion, and mineral deposits may fall into this latter category. New dynasties can form in these areas, but their absolute magnitudes may be different from the original regime, since they are consuming a different source of potential.

Another exception is where a truly breakthrough technology becomes utilized, such as dynamite versus manual labor for accessing mineral deposits. Very few technologies are sufficiency significant to fit in this category, though, and are usually incremental in nature and are already anticipated by the thermodynamic approach.

## Example: Romanov Dynasty

Let us apply the EDEG approach to the Romanov dynasty. Let us assume a conservative 1% growth rate. Let us further assume linear decay from 100% to 0% efficiency. A simulation has been written in the Ruby programming language. This language is mathematically robust, yet involves code that is relatively easy to read and understand. The dynasty is run through the Ruby simulator, using the above parameters. A data table was produced to generate in the plot shown in below.

Efficiency-discounted exponential growth (EDEG)

Here the peak is close to 1820. Napoleon had been conquered, and the dynasty had achieved much of its geographic expansion by them. Yet by this time, social unrest began to shake the Romanov dynasty. Also, note how the dynasty power begins at a level of 1 and ends at a level of 0. This is appropriate, since the dynasty had to begin from something, but typically ends in nothing. For example, the ancestors of the Romanovs existed before 1613, but the entire immediate family was killed during the Russian revolution. The peak occurs at a relative power value of height of 2.6, which indicates that the dynasty was over twice as powerful at its peak as it its beginning. Remember, this model is merely a hypothesis that is either valid or invalid for a particular level of uncertainty.

The simulation was run again with higher growth rates. We again assume linear decay from 100% to 0% efficiency (see Figure 8). Note several in the response of power to a changing growth rate parameter. First, a higher growth rate results in a later peak. Second, the total peak to initial power ratio skyrockets as the growth rate is increased.

Additional factors can be imposed as adjustment functions. One-time events (such as a rare but large natural disaster) can be superimposed as an event “mask”.

It may be of further interest to tie the rise and fall to patterns concerning the production and consumption of resources, to determine what correspondence, if any, there is between physical and political power. This can be explored by utilizing actual physical energy data to produce a model of physical power, and then comparing that model with evidence of political power over time. With the wealth of historical data being gathered in anthropological data warehouses, and other “big data” facilities, this may be accomplished with increasing validity.

## Discussion and Future Directions

This discussion of the EDEG approach is more of a barebones beginning than a complete end. It raises more questions than it answers, but it enables a broad framework to answer these questions. This framework acts as a unifying skeleton to link the humanistic elements of history with the quantitative constraints of the physical universe.

The power of such a framework should not be underestimated. It is possible to gather quantitative data (or quantify qualitative evidence), perform statistical analysis and accept or disprove hypotheses. Yet such results, while often important, are merely empirical. They are often hard to use to constrain or illustrate each other. In a unified framework, all results act to constrain all other results. When we learn about one thing, we necessarily learn something about everything else. This is where the physical sciences have derived much of their strength.

There are many immediately apparent improvements to improve the value of the EDEG approach. One improvement would be to better understand efficiency decay. Another improvement would be to start using actual data of physical energy, to the extent such data is available. Another improvement will be to separate the power level of the underlying society from that of the dynasty. For example, Russia did not disappear upon the death of the Romanov dynasty. On the contrary, it is still one of the most powerful societies on Earth. The brings up the need to be able to model the emergence of a series of dynasties in a way that connects and constrains each dynasty, such as concerning relative strength and timing of emergence. Further, there needs to be a way to compare co-existing dynasties and model their interaction within this framework. While the EDEG approach suggests possible means, the devil will be in the details.

[1]Meadows, et al. makes this point in Limits to Growth.

[2]For an opposing, but still dire view, see D. H. Meadows et al, Limits to Growth, Universe Books, New York (1972).

[3]The work of Forrester on system dynamics and the Club of Rome project Limits to Growthby Meadows et al involve attempts to better understand these limiting factors. The work of M. K. Hubbert and Howard Scott on peak oil and technocratic governance are other examples.

[4]M. Butler, Animal Cell Culture and Technology.  Oxford: IRL Press at Oxford University Press, 1996.

[5]M. Ciotola, San Juan case study.  Also see M. K. Hubbert.

[6]Heilbroner, R. L., The Worldly Philosophers 5thEd.  (Touchstone (Simon and Schuster), 1980.

[7]Such curves were proposed by W. Hewitt as early as 1926 (source unavailable).

## References

Annila, A. and S. Salthe. 2010. Physical foundations of evolutionary theory. J. Non-Equilib. Thermodyn. 35:301–321.

Ciotola, M. 1997. San Juan Mining Region Case Study: Application of Maxwell-Boltzmann Distribution Function. Journal of Physical History and Economics 1.

Ciotola, M. 2001. Factors Affecting Calculation of L, edited by S. Kingsley and R. Bhathal. Conference Proceedings, International Society for Optical Engineering (SPIE) Vol. 4273.

Ciotola, M. 2003. Physical History and Economics. San Francisco: Pavilion Press.

Ciotola, M. 2009. Physical History and Economics, 2nd Edition. San Francisco: Pavilion of Research & Commerce.

Ciotola, M. 2010. Modeling US Petroleum Production Using Standard and Discounted Exponential Growth Approaches.

Gibson, C. 1966. Spain in America. New York: Harper and Row.

Hewett, D. F. 1929. Cycles in Metal Production, Technical Publication 183. New York: The American Institute of Mining and Metallurgical Engineers.

M. King Hubbert.1956. Nuclear Energy And The Fossil Fuels. Houston, TX: Shell Development Company, Publication 95.

Hubbert, M. K. 1980. “Techniques of Prediction as Applied to the Production of Oil and Gas.” Presented to a symposium of the U.S. Department of Commerce, Washington, D.C., June 18-20.

Mazour, A. G., and J. M. Peoples. 1975. Men and Nations, A World History, 3rd Ed. New York: Harcourt, Brace, Jovanovich.

Schroeder, D. V. 2000. Introduction to Thermal Physics. San Francisco: Addison Wesley Longman.

Smith, D. A. 1982. Song of the Drill and Hammer: The Colorado San Juans, 1860–1914. Colorado School of Mines Press.

Mark P. A. Ciotola, ArXiv, Efficiency Discounted Exponential Growth (EDEG) Approach to Modeling the Power Progression of a Historical Dynasty, submitted on 18 Nov 2014

26. ## 6.7 Comparing Historical Data to Dynastic Models

First published on . Last updated on February 16, 2020.

Creating a simulation and generating results is relatively straightforward, mathematically speaking. Yet an important part of validating the principles behind a simulation are a favorable fit with actual historical data. Sometimes data is sparse. Sometimes it is plentiful, but not in a form that facilitates an easy comparison. Authorities the validity, relevance or accuracy of the data itself is in doubt and must be carefully evaluated.

## Quantitative Challenges

What can be more difficult than identifying a regime is to identify its beginning and endpoints as well as quantifying the regime. For example, the Bourbon dynasty was disrupted by the French revolution in 1791, yet there were three more Bourbon kings up to the year 1848. Further, the movements behind many regimes begin well before the official birth date of the regime. For example, the family that become rulers of the Carolingian had ruled France in all but name since 700, which would have given it a duration of 287 years (see Table).

### General Approach

For modeling, one can adjust the constants involved to produce the best fit for the data. The ways to do so could fill whole volumes in themselves, and are better covered in mathematical texts devoted to that subject. For purposes of this text, adjusting the parameters of the proposed function to provide the best visual fit provides a method that anyone who knows how to use a graphing program can utilize. Although this method is easy to implement, make sure to use the proper units for the constants!

If you do not have any data, this method cannot be used. Also, if you only a small amount of data, or data for only a short time period, be warned that the model could be less accurate.

If you have data that appears to contain a great deal of noise (random variations), is quite inconsistent from period to period or contains a cyclic variation (such as an annual cycle or a regular seven year weather pattern), you may need to smooth out the data. To reduce noise, you can use a moving average smoothing technique. For purposes of this text, you could average the each value with the value immediately before and after it. For cyclical data, you can average over half a cycle before and afterwards. There are much more sophisticated smoothing techniques that can be found in textbooks on various types of forecasting.

### Derivative Approach

Full quantitative data for a historical regime is often unavailable, or is only available at great expense of time or money. Yet, historians frequently come across information that is anecdotal or qualitative rather than quantitative. Fortunately it is often possible to convert qualitative data into quantitative data using a trick from calculus. It is nearly always possible to attach somedate to anecdotal information. Often the date assigned can be quite precise.

Major trends can often be identified anecdotally, and numerical dates can be matched to anecdotal data. Therefore, a series of date-trend pairs can be created for whether the regime is growing, reaching a plateau or declining. A table such as that below can be created.

Anecdotal information indicating an increase or a decrease represents a positive or negative slope of an underlying function. Such a slope can be seen as the derivative of that underlying function.  Such slopes can typically be crudely plotted on a meta-velocity versus time graph. Then an underlying function can be proposed that is consistent with the meta-velocity graph. A change in slope indicates meta-acceleration that further indicates the presence of a net meta-force. Hence, even anecdotal or qualitative data can frequently be used to generate a meta-mechanical function.

TABLE: Date-Anecdote Data Pairs for a Hypothetical Regime

Date Regime Growth
603 CE (e.g. or AD) Official birth of regime
612 CE +
650 CE +
692 CE +
724 CE +
780 CE Level
807 CE Level
876 CE -
892 CE -
906 CE -
917 CE No longer exists

An exponential function can be created, whose first derivative function matches the anecdotal date-trend data. This is certainly rough approach, but it can give a first approximation of the quantitative rise and fall of the regime. If the potential and other characteristics can be identified, then a better quantitative characterization can be achieved.

Of course, there may be shorter term upward and downward trends. These can be modeled with a secondary function. Minor victories and setbacks should not be included in trend data for the major regime characterization.

27. ## 6.8 Secondary Dynastic Events

First published on . Last updated on February 16, 2020.

## Introduction

Although there may be a primary power source, such as agriculture, for a dynasty, there may be secondary sources of power and costs, as well as short-term events that will impact the primary power progression of s dynasty, and should be taken into account where possible.

## Superposition of Noise and Other Functions Upon Hewett-Hubbert Curves

Actual data regarding production or consumption of a critical resource will not be a smooth function, but rather lots of jagged peaks and dips. These peaks and dips often represent independent functions that are not functions of the critical resource. Sometimes the independent functions are harmonic in nature.  Often they are chaotic in nature. Sometimes the peaks and dips are due to random events or “noise”. Usually the magnitude of the random events will not seriously disrupt the regime. Sufficiently complex regimes are “self-healing.” They will react in a manner to compensate for these random events. (See discussion regarding conservation of shock under meta-mechanics).

There may literally be small, shorter duration Hewett-Hubbert functions, reflecting business cycles, short-term opportunities and setbacks superimposed upon the dynastic function.

Further, although a regime can be expressed as a function of a conserved critical resource, in some cases other resources may be good substitutes.  Such resources will entail their own infrastructure and merit a Hubbert curve in their own right. Consider the example of oil versus coal. The U.S. is heavily dependent upon petroleum. There are large oil companies as well as drilling operations and a significant oil processing and distribution network. Petroleum acquisition is supported by powerful lobbyists and the deployment of the U.S. military where required.

Coal can be an important substitute for petroleum. Gasoline can be made from coal. It’s more expensive, but not prohibitively so. Coal has its own companies, its own processing facilities and its own distribution network and customer base. Coal has its own lobbyists as well. Sometimes coal interests are at odds with petroleum interests.

Consumption of petroleum and coal can each be expressed as separate Hubbert curves. When describing the U.S. regime, the more significant of the two resources may considered as the critical resource. However, a better representation would be to superimpose both the oil and coal curves. This involves adding them up, period-by-period. Doing so for the past where data exists is relatively simple. Extending those curves into the future is possible, but more challenging. Standard economic analysis can provide some indication of relative demand for each resource.

## Secondary Functions from Hewett-Hubbert Curve

Other functions may themselves be secondary functions that are driven by the main Hewett-Hubbert curve function. The social values and moods of a society are to some extent a function of position along the Hewett-Hubbert curve. Such social values and moods can be considered secondary Hubbert functions. Examples include the distribution of wealth, economic centralization, development of infrastructure, aspects of philosophy, tolerance for “immoral” behavior and even number and size of libraries.

28. ## 6.9 Modeling History as A Series of Dynasties

First published on . Last updated on January 19, 2021.

## Describing A Society As A Series of Regimes

A society can be modeled as a series of regimes or Hubbert curves. Each curve would typically represent a dynasty for a traditional historic monarchy. Traditional, monarchical, agricultural-based regimes have historically tended to endure for about 300 or so years. This is a rough rule of thumb. Other types of societies will tend to have a governance change in that period of time but may maintain better legal continuity of government.

Not all regimes last for about 300 years. Where a potential has not restored itself, of those who attempt to rule the regime are not competent (i.e. a defective or inherently inefficient “heat engine”), a regime will be short lived. The other extreme is where the potential is too great. This can happen when neighboring regimes have become weak. In this case, a regime can expand too quickly and become a great, but brief empire. Such appears to have been the case of the first French Empire lead by Napoleon. There are plenty of exception to this 300 Year Rule. Yet, focusing attention on regimes that fit in this pattern can be useful to identify more general principles and constraints that govern humans. This is similar to the case of the development of astronomy, where first the easily observed bodies such as the Moon, Sun and visible planets were modeled first and lead to Newtonian mechanics. Later, smaller, further and more exotic objects were studied and modeled.

Further, the 300 Year Rule is much less likely to be applicable to most of the regimes in existence when this book is written. Few regimes today are traditional agricultural monarchies. Further, regimes have become much more interdependent with each other, so it can be expected that Hubbert Curves will become more distorted and even more merged than any time in the past, even for the largest regimes in existence today. Also, most of the current regimes are dependent upon non-renewable resources such as petroleum that have never driven regimes before the 19th century. Yet, as mentioned above, a study of historical traditional 300 Year regimes can help to develop generic principles that can be applied to a much broader range of regimes.

A common error would be to assume that the series of EDEG curves represents a periodic function. It’s not. However, many functions can be expressed as a Fourier series (a combination of sinusoidal functions) so perhaps a series of EDEG curves can be as well.

Regimes might not follow immediately one after another. Or there could be some overlap between older and newer regimes.

## Historical Dynasties

Dynasties in major historical civilizations are typically easy to identify. In a sense, dynasties are what fill the pages of historical textbooks. The flowing is a chronological list of French dynasties, along with duration data.

TABLE: Dynasty Series for France

Dates (CE) Regime Duration
481–751 CE Merovingian dynasty 270 years
754–987 CE Carolingian dynasty 233 years
987–1328 CE Capetian dynasty 341 years
1429–1588 CE Period of relative discontinuity
1589–1791*/1848 CE Bourbon dynasty 202/259 years

*1791 represents the French Revolution that interrupted the regime that was restored for awhile after the fall of Napoleon until 1848.

It is clear that the dynasties are not exactly periodic (exactly the same length in years as each other).

French dynasties 500-1850 CE

Below is a plot of the power progressions of several major West African dynasties, from 750 CE to 1591 CE. The lack of periodicity is more obvious. Although the geographic locations were all in West Africa, the exact locations varied. There was less territorial overlap than in the French dynasties plotted above.

Selected major West African dynasties, 750-1591 CE

## Thermodynamic Approaches to Model a Series of Dynasties

An exciting next step it to attempt to model a series of past dynasties. You could simply do this by superimposing a best fit set of distributions over time. This is fairly simple to do any might provide some utility and satisfaction.

However, the above series of French dynasties has been modeled.  In this case, each regime was modeled individually using the simple thermodynamic method described. An important point about applying fast entropy to real life situations is keeping the expression “it takes two to tango” in mind. Fast entropy only creates a potential. There must also be the equivalent of an engine (or conductor) to bridge the potential to observe fast entropy in action. In history, that engine may be produced by a new royal family replacing the prior family, or a group of organized invaders. Sometimes that engine comes along immediately after the end of the prior regime, or sometimes it may take a few hundred years before a new major regime takes root.

However, there is a more powerful approach. If you can determine past potential profiles for past regimes, and if they seem consistent or to follow some pattern, then you can create a “boiler” program to literally boil a series of regimes. In that sort of program, potential builds up until it reaches a trigger threshold, then a regime forms and goes through its lifecycle and exhausts the built-up potential and dies. Then the potential starts building up again and eventually another regime forms. If the pattern varies from actual history, it may be possible to identify catastrophes, unexpected events, and interference from more powerful regimes.

If you have appropriate software, you can literally reverse-simulate a past regime to determine a past potential at each point of the regime as well as the total quantity of the CCR. Such parameters can be sometimes useful for forecasts. The function that expresses the potential in terms of time (age of regime) is its potential profile.

Series of Russian dynasties

### Dynasty series Involving Nonrenewable Physical Resource

Below is a series of EDEG models for a series of Spanish dynasties where significant extraction of gold and solver occurs. The presence of tremendous metal extraction may have shortened the life of the Habsburg dynasty. Model for extraction with blasting is based on one data point, and is largely conjecture. Bourbon dynasty is considered to have ended with takeover by Francisco Franco, regardless of present monarchy.

Spanish dynasties 1531-1930s with some metal extraction data

For data, see Gibson, C., Spain in America. Harper and Row, 1966.

29. ## 6.10 Interrelations Between Concurrent Dynasties

First published on . Last updated on January 19, 2021.

## Simultaneously Existing Regimes

A Hewett-Hubbert Curve is a fairly robust creature, but it can still be affected by simultaneous or co-existing regimes or even overwhelmed. Potentials can exist between regimes, such as in the case where one regime has a persistent trade deficit with a co-existing regime.

Only something out of a science fiction movie could have eliminated either the Roman Empire or the Chinese Tang dynasty at their heights, for example. The Hewett-Hubbert curves for the very largest human regimes in history will be largely independent of each other. Many smaller regimes are still powerful enough to be fairly robust. However, regimes of small states that are highly affected by their neighbors. Likewise, new or dying regimes of larger states lie along portions of their Hubbert curves that are not as robust as middle portions.

Such vulnerable regimes may have Hubbert Curves that are abruptly terminated rather than gradually terminated. The remaining critical resource of the regime must either be considered to have been discarded, or must be consolidated into the Hubbert Curve of a conquering regime. Such consolidation can be handled by superposition.

### Dynasties as a Set of Co-Existing Regimes

Series of dynasties can be modeled, considered and plotted as a set of co-existing regimes without regard to interactions between them (see below figure).

Dynasties, England, France and Spain, 1400-1800 CE

### Modeling History As A Set of Interacting Regimes

Regimes often interact with each other. Therefore, one regime can impact another. This interaction can become quite complicated, especially for smaller regimes. However, the largest, most durable regimes can be studied, for there is often more data for them and they tend to be somewhat less affected by other regimes, so that the effects are more discernable.

Possible interdependence between Chinese and Russian dynasties

### The China Clock

Disclaimer: this example only applies to history preceding 1911. Since that time, China has had new forms of government and has also embraced fossil fuels. So regimes since 1911 will have fundamental characteristics that are different from those of traditional regimes. This same disclaimer could apply to most other contemporary societies as well.

To study a system of interacting regimes, it is best to study the greatest series of regimes. China has historically described itself as the central kingdom. Then have other historic regimes circles about china as do the planets circle around the Sun in a heliocentric system of astronomy? Does PHE propose a Sinocentric sociology? Yes, but to a limited degree. The mass of the sun is about thousand times greater than that of even the largest planet Jupiter. The social “mass” of China is generally historically larger than that of other societies, but not by far of such a high proportion, and at times other empires have eclipsed or absorbed China’s social “mass.” Yet to the extent that there has been anysolar equivalent in history, it would be China. Further, the Han people of China has exhibited a series of traditional regimes for a much longer period than any other single society, so it could be argued that it is the closest thing that exists to a historical “clock.” Yet perhaps and argument could be made for central Asia being such a clock, since its invasions have frequently affected societies in the continents of Asia, Europe and Africa. What drives the waves of invasions in history of central Asia? Is it a social cause or the build-up of a resource-driven potential? The answer to this question is not well known.

TABLE: Major Traditional Regime Series for China

Dates (CE) Regime Duration
-2000–1500 BCE Hsia 500 years
-1500–1028 BCE Shang 472 years
-1028–642* BCE Chou 1 386 years
-642*–256 BCE Chou 2 386 years
-202–220 CE Han 422 years
618–906 CE Tang 288 years
960–1279 CE Sung 319 years
1368–1644 CE Ming 276 years
1644–1912 CE Manchu 268 years

* Chou dynasty became essentially symbolic by about 700 BC, and China was chiefly ruled by small states during this symbolic “second” Chou dynasty.

So at times that China is ruled by a regime during the strong part of its lifecycle, does this block the Central Asiatic invaders so that their only outset is India, the Middle-East or Europe? The answer to this question depends upon several factors and changes depending on the state of those factors at a given time.

The following table shows several strong traditional regimes in China and corresponding waves of invasions in Europe. This list is not complete, but is suggestive for several regimes.

TABLE: Major Traditional Regime Series for China and Asiatic Invasions in European (CE)

Dates Regime Duration Invasion
618–906 Tang 288 years Lombards & Avars
960–1279 Sung 319 years Slavs & Magyars
1368–1644 Ming 276 years Ottoman Turks

Yet there are exceptions. The Huns, and later the Mongols, overwhelmed both China and much of the West. Conversely, a strong Roman empire might have pushed the Huns eastward before they went Westward, for the Huns attacked China in 317, while they did not invade western Europe until the mid 400s.It could be the coincidence of strong empires in both the East and the West built up potential in central Asia up to the point that the Huns became extremely potent. That both Russia and China were both relatively strong during the time of the Sung dynasty may have contributed to a build-up of potential in central Asia that helped the Mongols become so powerful. Such speculation should not detract from the achievements Mongols such as their innovative battle tactics. (The author is not as familiar with the history the Huns, so cannot comment further upon them).

30. ## 6.11 The Colossus Model of World History

First published on . Last updated on January 19, 2021.

Colossus is a computer-based simulator that generates models of world history. It utilizes a grid of dynasty-producing regions and interconnections between neighbors. This model focuses on the “old world” of Asia, Europe and Africa before World War I.

History grid (PHP/SVG)

A newer version coded in the D3 Javascript library, with a button for each century:

History grid (D3)

The Colossus simulator itself is written in the Ruby programming language, and results are exported as a CSV file. Sample output is below. Each row is a time period indicated by a year. The left bank of columns represent power. The right bank of columns represent power differenced between regions. This is an exploratory simulation. It has many deficiencies.

Colossus simulation output

An early example of graphical representation of output. It is not very meaningful.

Early graphical representation of Colossus results

31. ## 6.12 A GIS Approach to World History

First published on . Last updated on January 19, 2021.

Graphical Information Systems (GIS) can be used to analyze spatial aspects of societies, as well as their progression and interaction with concurrent societies over time.

The Colossus world history grid was superimposed on an image of the Europe, Africa and Asia. GIS was utilized to better understand the relations between societies. Spatial connections between adjacent or nearby societies were identified. Each connection was discounted for distance and terrain factors. It is possible to study correlations found in the Colossus model with such factors.

Satellite image of Asia showing political entities and possible connections (photo layer: credit Google)

32. ## 6.13 Modern Times and the Near Future

First published on . Last updated on February 16, 2020.

Modeling the near future cannot be done perfectly deterministically. It must be done using different approaches for different windows and levels of accuracy.

Weather provides a good example for understanding. Forecasters can predict the temperatures and precipitation over the next seven days reasonable well, but not beyond that. However, for the next year, forecasters can predict average temperatures and precipitation type and quantity reasonably well. Meteorologists have also identified patterns that repeat over several years (such as El Nino and La Nina), but they cannot predict the exact timing or strength. It is also possible to predict the general climate by location and for the entire Earth for the next hundred or so years, assuming there are no catastrophic changes such as a large meteor hitting the Earth.

There is often much short term “noise”. In weather, there might be a local tornado which deviates the local wind without changing the overall mean wind. One should use probabilistic methods when modeling the future to overcome noise effects.

## Current Trends

• Globalization
• Resistance to globalization
• Advancement in automation (robotics, AI)
• Consolidation of financial institutions
• Monetary shifts caused by trade imbalanced
• The 1800s colonia order continues to recede

33. ## 7 The Future: Beyond Our World And Time

First published on . Last updated on January 19, 2021.

We have looked backwards, in time and space. Let’s now look forwards. Looking forwards will use many of the ideas, but the techniques and subject matter will partially differ. Looking backwards involves uncertainty regarding the data, and using probability to estimate that uncertainty. Looking forwards involves applying probability to principles and trends to estimate the likelihood of future events.

34. ## 7.1 Longterm Trends – Future

First published on . Last updated on February 16, 2020.

Humanity has experience several long-term trends that have transcended multi-century dynastic structures. Will such be able to continue?

• Population growth
• Environmental change
• Climate change
• Species changes (extinction, domestication, monoculture)
• Destruction of forests
• Salinization of soil in irrigated lands
• Total land area used by humans

Humanity may be approaching limits to human population on Earth using only Earth resources, although serious technologies are expanding that limit. (See Club of Rome, Limits to Growth). Space resources might allow this limit to be increases, as well as to provide for additional people to live in space. Conversely, humanity is using up nonrenewable resources. If replacements are not found, the human population could decrease.

## Reference

• Meadows et al., Limits to Growth, 1972.  involve attempts to better understand these limiting factors.

35. ## 7.2 Modeling The Future

First published on . Last updated on February 16, 2020.

### Modeling The Near Future Of A Single of Regime

Modeling an existing regime may provide an indication of the magnitude of fast entropy tendencies upon that regime, especially if it is quite similar to a past regime, or is well advanced in age. Yet, the interdependent nature of today’s regimes and the possibility for nuclear or biochemical warfare or catastrophes create greater uncertainties than in the past, so that caveat must always be kept in mind. Further, the existence “unknown unknowns” must not be forgotten.

### General Approaches

There are two major approaches for modeling a future single regime. The first approach is to guess Gaussian or Maxwell-Boltzmann distributions and adjust the constants involved to produce the best fit for the data that you have so far. The ways to do so could fill whole volumes in themselves, and are better covered in mathematical texts devoted to that subject. For purposes of this text, adjusting the parameters of the proposed function to provide the best visual fit provides a method that anyone who knows how to use a graphing program can utilize. Although this method is easy to implement, make sure to use the proper units for the constants!

If you do not have any data, this method cannot be used. Also, if you only a small amount of data, or data for only a short time period, be warned that the forecasts could wildly vary from what will actually occur, evenif nothing unexpected happens.

If you have data that appears to contain a great deal of noise (random variations), is quite inconsistent from period to period or contains a cyclic variation (such as an annual cycle or a regular seven year weather pattern), you may need to smooth out the data. To reduce noise, you can use a moving average smoothing technique. For purposes of this text, you could average the each value with the value immediately before and after it. For cyclical data, you can average over half a cycle before and afterwards. There are much more sophisticated smoothing techniques that can be found in textbooks on various types of forecasting.

The second approach is to combine the initial characteristics of the data already obtained with the values of parameters of past regimes. This approach is more intelligent, but equally more complicated. A simple way to do this is described as follows. The first step is to try to create a pure exponential growth function that describes the growth seen in the initial data and identify the parameters in that function. Then plug these parameters into a distribution function, and use parameters from past regimes to fill in the remaining parameters. The past regime should be as similar to the present regime as possible, taking into account location, historical point of time, size of regime, type of resource use, and any other characteristics that seem applicable. If you need to alter anyof these parameters to improve the fit, only do so if you have a rational basis for doing so.  It is also possible that old values might give better long-term projections than parameters merely altered to improve the short-term fit.

### Thermodynamic Approach

The thermodynamic approach is similar to the second approach above. However, an effort should be made to express parameters in terms of a potential and changing efficiency. If the quantity of the most critical conserved resource is known, then the projected total consumption over time should match that quantity. If the present regime uses the same types of resources and does not utilize any major new technologies, then it may be possible to use the potential profile from that past regime

## Modeling The Future As A Series of Regimes

### Future Horizon Challenge

Modeling a single existing regime may be fairly reliable.  Modeling a series of regimes into the future may be much less reliable. First, all of the reasons that challenge modeling a single present regime apply even more so to modeling a series of regimes. Even worse, human society may face a fundamental change over the next hundred years, if not sooner. This could nearly completely throw off most forecasts. However, once society has made that transition, whatever it may be, then the nature of resource use and technologies of regimes may become more constant over time, so that it may be reasonably reliable to model a series of regimes after that point. If humans are involved and go back to traditional, agricultural technologies, and the same traditional population centers remain, then even the 300 Year Rule and the old potential profiles might be applicable. If robots replace humans in future regimes and they live off of nuclear fusion or some more exotic energy source, than some other potential profile may apply.

### Methodology

A similar methodology to that described in here may be useful in modeling a future series of regimes, especially if the probable potential and “heat engine” characteristics can be reasonably identified.

## Modeling The Future As A Set of Interacting Regimes

### Many Simultaneous Regimes

Numerous simultaneous regimes may co-exist. Such was the case of the ancient Greek city-states before the time of the wars between Athens and Sparta.  Each regime has some freedom of action. However, the collection of those states can often be considered aggregately to form a larger “super” regime.

### Interaction Between Two Simultaneous Regimes

A frequent tale in history is the interaction between two simultaneous regimes, often of apparent equal power. There will typically be oscillatory flow of wealth or military strength back and forth between the two powers as they compete with each other, or there will be the ongoing flow of wealth or military strength from one to the other. The second case represents a potential, and can be modeled by utilizing that potential as a conserved resource.

36. ## 7.3 Other Worlds and Societies

First published on . Last updated on May 1, 2021.

Physical history and economics is based on physics. Since the laws of physics are invariant across time and space, they should be equally applicable to societies across the universe, as well as to humans.

Out own galaxy may contain millions of planets. Some of those planets may be capable of hosting intelligent life and societies. The same thermodynamic tendencies as exist on Earth would drive the emergence of such life. Hence such life could be analyzed by the same approaches as used here.

Although the driving force may be fast entropy, and the laws of physics are the same, local conditions might be quite different for other planets. It would be interesting to see what different kinds of beings and societies have developed, given their local resources and constraints.

Habitable exoplanets (credit: PHL @ UPR Arecibo)

37. ## 8 Conclusions

First published on . Last updated on February 16, 2020.

Physical History and Economics represents a solid foundation for the future development of history and economics. PHE can provide new insight into some of the pressures and influences upon historical societies and the constraints that governed them. PHE can help to provide economists with another means to analyze regimes over their entire lifetime.

However, Physical History and Economics is not alone sufficient to develop practical solutions for society. Rather, think of Advanced Social Science as one of two filters. Physical History and Economics can be used to anticipate and also to filter out scientifically impractical solutions. Such solutions are impractical because they run counter to the tendencies of nature and probably will not work.

The other filter is human psychology. Even if a solution is scientifically valid, if it cannot be implemented due to the limitations and constraints of human psychology, then it is equally impractical and is doomed to probably failure. A good solution is one that can pass through both filters, that of Physical History and Economics and that of human psychology.

Thus, Physical History and Economics, used in conjunction with an understanding of human psychology, can save humanity the trouble and expense of attempting impractical solutions and can provide options that will probably work. That is the goal and dream of Physical History and Economics.