E-1 – About secular cycles

When I started the English side of this web site, I was planning to translate all my new posts from the French side. I now realize that it is too much work for me. Instead I have decided to post occasional summaries. Their number will start with an E (for English) like this one. Whenever they are true translations of the French side, their number will be the same on both sides.

In a book entitled «The Fourth Turning: An American Prophecy» (1), William Strauss and Neil Howe claim that history in America (and by extension, most other modern societies) unfolds in a recurring cycle of four generation-long eras, implying that America is now heading toward a «fourth turn» during which populism, nationalism and state-run authoritarianism might be on the rise. Today, the election of Donald Trump at the presidency of the United States is widely considered as a turning point in the political life of this country. It seems to confirm their prediction.

I already talked about economic cycles (2) and the evolution of political opinions (3) on the French side of this web site. Since I came to a conclusion similar to that of Strauss and Howe, it gave me an incentive to summarize here several posts from the French side.

Recurring cycles have long been reported in economy, first by Clément Juglar in 1862, later by Joseph Kitchin in 1920. These are business cycles with typical periods of less than 10 years. A Russian economist, Nicolaï Kondratiev, was the first to show evidence for economic cycles with a much longer period of, typically, 45 to 60 years. The Austrian American economist Joseph Schumpeter interpreted these cycles as due to recurrence in innovations, a process he dubbed «creative destruction», while Simon Kuznets, and more recently Thomas Picketty, have shown their relation with the unequal distribution of income.

In their 2009 publication (4), historians Peter Turchin and Sergei A. Nefedov have shown evidence for secular cycles in History. These demographic cycles are similar in length to those of Howe and Strauss, with successive turns, called «phases», described as a depression phase followed by an expansion phase and a stagflation phase. According to their description, the election of Trump would mark the beginning of a crisis phase.

In my own book (5), I have explained that human societies are «dissipative structure», a term first coined by Ilya Prigogine. Physicists now realize that all dissipative structures in the universe self-organise through the same universal process called «continuous phase transitions». Evidence for this process was found from both particle physics and cosmology. A Danish physicist named Per Bak (6) has shown how that this process applies as well to ecosystems, our own brain, or human economy. He named it «self-organized criticality».

Self-organized criticality consists of cycles of oscillations of the same nature as the Carnot cycles of a heat engine. These oscillations occur around a critical point where a slow continuous phase transition alternates with a fast abrupt transition. The slow continuous transition, also called macro-evolution, gives rise to large animals and plants, or large economic structures such as USSR and Europe. Biologist call this phase «K selection».
During the abrupt phase transition, also called microevolution, large structures break down or disappear and give rise to small animals, small plants or small economic structures such as transition towns. Biologist call this phase «r selection». Figure 1, inspired by Erich Jantsch, shows how this process has occurred since the beginning of the universe (7).

macro-micro evolution

Figure 1. Oscillations around a critical point between a macro-evolution (continuous phase transition) and a micro-evolution (abrupt phase transition), after Erich Jantsch.

According to this scheme, our current civilization will collapse through an abrupt phase transition during which the United States as well as the European community will, at least partly, split apart. Then will follow a slow continuous phase transition during which the whole mankind will progressively form a single planetary civilisation.

To further explore this process, I have proposed to describe the state of an economy in terms of Gibbs potentials where each product has two potential values: a use value and an exchange value (8). The use value expresses «demand» and plays the role of a social pressure P. The exchange value expresses «supply» and plays the role of an economic temperature T. Associated with these intensive quantities are two extensive quantities, a production volume V (number of items produced per year) and a revenue $ which plays the role of entropy. In a steady state, balance between demand and supply is given by the equation P.dV = T.d$.

For a given production, V can be expressed by a state equation V = f(P,T) which is the analog to the state equation of a fluid. When averaged over the production of a whole country, it describes the state of its economy. The state of a fluid near its critical point is well represented by the so-called van der Waals equation. I have suggested that the same equation could be used to describe an economy near its critical state. It represents a surface with a cusp fold as shown on fig. 2.

state of an economy

Figure 2. The state of an economy can be described by a point on the above surface. C is called a critical point, hence the name of self-organized criticality.

As the economy evolves, its representative point circles around the critical point C, moving from a depression phase to an expansion phase, then a stagflation phase, a process which reminds Schumpeter’s image of a gale. With the election of Trump as president, the American economy seems to be now entering a crisis phase.

Fig. 2 shows that during this phase two economies co-exist in the same country in the same way as two phases, such as liquid and gas, co-exist in the same fluid during an abrupt phase transition. At any time, production can drop from the upper level, where the old fuel-based economy collapses, down to the lower level where a new economy, hopefully based on renewable energy, starts over.
This scheme compares well with the «metamorphosis model» developed by the German economist Gerhard Mensch during the seventies (9). This model is shown on fig. 3 reprinted from his book. Today, Mensch’s metamorphosis model is widely used among Schumpeterian economists. It has even been used by historians such as Giovanni Arrighi (10).

Mensch’s metamorphosis model

Figure 3. Mensch’s metamorphosis model. Between arrows a and b, successive economies overlap as in fig. 2.

The French sociologist Emmanuel Todd has shown that political opinions can be classified along two criteria: authoritarism and egalitarianism (11). It gives rise to four types of political opinions as described below, with their radical form in parenthesis:

egalitarian inegalitarian
liberal Left (anarchy) Right (liberalism)
authoritarian Far-left (communism) Far-right (totalitarism)

Figure 4. A classification of political opinions

As the state of economy circles around its critical point, political ideology tends to do the same thing, varying from far left to far right, the two ends being only separated by an abrupt phase transition. Although it applies to an economy free for any external perturbation, it is likely to be true for an hegemonic country such as the United States. With the election of Trump, the U.S. are probably entering into their extreme right phase.

However, as shown by Emmanuel Todd, in most countries family structures impose a preferred ideology. For instance, in the United States of America, the prefered ideology is liberal-inegalitarian. Hence many people tend to stick to that ideology, while other people move toward a more right wing ideology. This brings dissent into the population and explains why the country is entering a crisis phase.

As crises occur, some of the States are likely to split apart. California seems to be already moving toward this direction. As already explained at the beginning of this paper, during an abrupt phase transition, large structures break down or disappear and are replaced by smaller structures. We already see the same phenomenon occuring in Europe with Great Britain’s attempt to leave the European Community.

In fig. 2, I have plotted an annual production V as a function of demand P and supply T. Instead of the annual production V, we could have as well plotted the annual revenue $. For a country, $ is called the gross national product or GNP. Whereas P is the economic analog of a pressure and T the economic analog of a temperature, $ is the economic analog of entropy. Hence, to understand money, one must understand entropy. This is however beyond the scope of this short post. It will be the subject of other posts.

(1) «The Fourth Turning: An American Prophecy», Broadway (1997).
(2) Post 72 of the French side of this Web site: «Les quatre saisons de l’économie» (Dec. 2014).
(3) Post 101 of the French side of this Web site: «Sur l’évolution des idées politiques» (Nov. 2016).
(4) «Secular cycles», Princeton (2009).
(5) «The Thermodynamics of Evolution», Free English version available on this web site.
(6) «How Nature Works», Springer (1996).
(7) «The Self-organizing Universe», Pergamon (1980).
(8) Res-Systemica (in French), Vol. 14, Oct. 2015.
(9) Stalemate in Technology, Ballinger, English ed. (1979).
(10) The Long Twentieth Century, Verso (1994, 2010).
(11) The Explanation of Ideology: Family Structure and Social Systems (1985).


100 – Gaïa or the awakening of a consciousness

It is the title of the talk I gave on october 7th, at the headquarters of ESA (European Space Agency) in Paris. I have been invited to give this talk for the launch of a book entitled: « SOS Treaty. The safe operating space treaty ». Written in cooperation by scientists and jurists, this book shows the urgency to develop international agreements for the protection of the environment.

The word « Gaia » refers here to the concept with which James Lovelock expresses the fact that all the structures that dissipate solar energy on Earth behave as a single living organism. As the brain of Gaïa, mankind is becoming conscious it is in charge of all the ecosystems as well as the Earth’s atmosphere, as an individual becomes conscious he is in charge of his own body to feed it and maintain it in good health.

The interested reader will find here attached the viewgraphs I used for this presentation. (format pdf ou diaporama).My talk at Salon de Provence on october 18 and my coming talk in Toulon are french versions of the same talk for a wider audience.

programme-for-the-launch-of-the-sos-treaty-at-esa-hq_7-oct-2016


92 – Entropy, money, investment and debt

This post is a follow-up to posts 89 and 90, in which I have shown that the state of an economy can be compared to the state of a fluid defined by its pressure P and temperature T. In post 49, I applied the concept of « temperature » to the economy. In my lecture of March 12, 2015 (post 75), I showed that the economic equivalent of the pressure P is a Gibbs potential that I called the « economic potential » of the production.

P and T are intensive variables. Each of them is associated with an extensive variable called the conjugate variable. The conjugate variable of pressure is the volume V while the conjugate variable of temperature is the entropy S. In economics, the volume V corresponds to the quantity of manufactured objects, while entropy S corresponds to their monetary value. The product P.dV represents the amount of mechanical work resulting from the manufacture a product, while T.dS represents the amount of energy dissipated by its consumption.

In my conference of March 12, 2015, I have identified the product P.dV to what economists call «demand», and the product T.dS to what they call «supply». The conservation of energy implies that supply must balance demand. In my two previous posts, I have directly assimilated P and T with demand and supply. I will continue to do so, bearing in mind that P now represents the intensity of the demand and T the intensity of the supply.

In physics, the variables P, V and T characterize the state of a fluid. They are linked by a relationship called the equation of state. For a so-called « perfect » gas, this relation is simply PV = RT, where R is the gas constant. For a real fluid, it is fairly well represented by the van der Waals equation. It is the equation of a surface of the third degree, part of which must be replaced by straight isotherms at the « condensation temperature » (see post 89).

The equation of state of a fluid expresses its volume as a function of its temperature and its pressure. The volume is the conjugate variable of the pressure. One might as well have chosen the conjugate variable of the temperature which is the entropy. The reason for this choice is that it is easier to measure changes of volume rather than changes of entropy, because measuring the latter require a calorimeter. Calorimetric measurements show that the entropy of a fluid can be represented by a point on a surface quite similar to the van der Waals surface. In particular, it includes the same condensation zone within which the fluid appears under two different phases.

To facilitate my readers’ comprehension, I made a plaster model of this surface, which is pictured below in two different diagrams. On the first, the horizontal coordinate axes represent the pressure P and the temperature T of a fluid. The vertical coordinate axis represents either the volume V or the entropy S. This surface may be usefully compared to the portion of the surface which is near the critical point as described in post 89.

In the second diagram, the horizontal coordinate axes represent the potential P of the production (marked «demand») and the temperature T of the economy (marked «supply»). The vertical coordinate axis (marked «production») represents either the volume V of production or its monetary value M. It is important to realize that a point on this surface represents the state of the economy for a given production. Some products may be in the stagflation phase while others are still in the expansion phase. The general state of the economy is then a weighted average of all of the states of production.

One can see on this model that the monetary value M of production grows throughout the economic cycle up to some point above the Seneca cliff, at which it starts to decrease before falling abruptly along the cliff. As we have seen (post 87), the decrease begins when the state of production crosses the critical isotherm. From there, capital income no longer offsets expenses, and capital decreases. Failure can occur as soon as the state of the economy reaches the edge of the Seneca cliff.

The analogy with fluids suggests that one can observe the analog of a delayed condensation. It is indeed an abrupt phase transition and these require the presence of condensation nuclei. As a fluid can stay for a while in a supercooled state, an economy can remain in state of debt, as long as the creditors do not request their due. Only when they realize they will not be paid, chain bankruptcies occur forming a cascade of events typical of self-organizing systems (post 18).

In the same way that a fluid condenses, a company which collapses must reorganize itself. New structures are formed on a small scale within which collaborations are established. This implies a reduction of entropy. In a heat engine, this phase corresponds to the evacuation of burnt gas. This is the phase during which a steam engine returns to the cold source part of the heat it has received. It gives off an amount of entropy ΔS. For a fluid which condenses, the product T.ΔS represents the latent heat of condensation. It is the heat which is released by the condensation of the fluid.

In a society, evacuated entropy is measured in monetary terms. Since cash flows are of opposite sign to entropy flows, an evacuation of entropy represents the investment of a new capital. It is for example the capital necessary to develop new energy resources during the so-called energy transition. This capital for investment plays the role of the latent heat of condensation. Its amount often adds up to the outstanding debt of the previous organization. It makes transition phases very painful to go through: these are periods of crises. In a future post, I will describe in more detail the different phases of the economy.


90 – Economic cycles

The second law of thermodynamics, also known as the « Carnot principle » tells us that one cannot sustainably produce mechanical energy other than by means of transformation cycles extracting heat from a hot source and giving some of it back to a cold source.

By nature, a dissipative structure continuously produces mechanical energy in order to dissipate it. This implies that it must perform transformations cycles. So in order to dissipate solar energy, the earth’s atmosphere produces cyclones and anticyclones, but also cycles such as the water cycle. Chemical elements are constantly recycled through cycles, such as carbon, nitrogen or phosphorus. Finally life itself exists only through cycles in which plants are eaten by small animals, which in turn are eaten by larger animals, whose wastes feed bacteria which produce fertilizers for plants.

Among all dissipative structures on Earth, those that dissipate the most energy are by far human societies. The science that studies how human societies dissipate energy is called economics. The first evidence of economic cycles is generally attributed to a French physician and economist, Clément Juglar, to which he attributed a period of about 8 years. In the early twentieth century, Kondratiev has pointed to longer cycles of the order of half a century.

In this blog, I myself talked about the four seasons of the economy (articles # 72 and 73), each season being of the order of a generation. This also leads to cycles having a period of about a century. In their book entitled « Secular cycles (1) » Turchin and Nefedov highlight historical cycles of even longer periods, about 400 years (see the list of these cycles the bottom of this post). For each of them, Turchin and Nefedov clearly identify four phases to which they give the following names: the expansion phase, stagflation, crisis and depression.

Cycles séculaires
Secular cycles of Turchin and Nefedov

It appears natural to relate economic cycles to cycles of dissipative structures.The Danish physicist Per Bak has shown that they oscillate around a critical point. The different parts of a same structure oscillate at different frequencies. We can therefore see a full spectrum of oscillations whose magnitudes are ever greater as they are spread over a longer period of time.

In my presentation at the Shift Project (2), I identified economic cycles to Carnot cycles described by the traditional variables P, V, T, but for which P represents the Gibbs-potential I called economic potential, measuring what economists usually call « demand ». The variable V represents the « volume » of production (quantity of manufactured goods). Lastly, the T variable, which I called the « temperature » of the economy (see article # 49), can be identified with what economists call « supply ».

At any given time, the state of an economic system may be represented by a point in space (P, V, T). In my previous post, I showed that all the points lie on a surface described by an equation of the state of an economy. I showed the analogy between this equation of a state and that of condensable fluids. I deduced that, as a fluid, an economy can be condensed into two distinct phases that I have identified as an economy for rich people, and an economy for poor people. I have shown that, within a certain area shown in dark in the figure, the two economies are dissociated from one another.

The figure below is the same as the one in the previous post, but rotated 90 ° clockwise. The three coordinate axes are still P, T, V now referred to by their economic appellations of demand, supply and production. Economic production is an extensive quantity, it is now reported on a vertical axis as a function of the two intensive variables that are the supply (toward the back) and the demand (toward the left). The curves usually called « isothermals » are the lines along which the supply remains constant.

Economic output (production), as a function of supply (offre) and demand (Falaise de Sénèque = Seneca Cliff)

Economic output (production), as a function of supply (offre) and demand (Falaise de Sénèque = Seneca Cliff)

The circuit is an arbitrary economic cycle around the critical point C. Projected onto the output (production)/demand plane, its area represents the energy dissipated during a cycle. Being a positive value, the rotation is necessarily clockwise. By analogy with a fluid, the part of the cycle which is in the dark area has been represented by a « condensation isotherm », here a vertical line segment.

The dark area is in a vertical plane. It seems natural to identify it to a zone of collapsing economy, a zone called « Seneca Cliff » by Ugo Bardi (3). In this zone of instability, production collapses vertically, whatever the supply (temperature) or the related demand (pressure) is. We have seen (previous post) that, within this area, the economy separates into two phases, one for poor people and one for rich people, with no interactions between them. The collapse of output is accounted by the fact that supply can no longer meet demand because poor people cannot afford to buy what rich people produce. Gradually the whole population gets impoverished.

The economic cycle of the figure can be described and understood as follows: at the foot of the cliff, the economic output first goes to a minimum. This part of the cycle is characterized by a shortage of material goods and a growing demand. It is clearly identifiable as the depression phase of Turchin and Nefedov.

On the left-hand side of the cycle, the economic output begins to rise. This part is characterized by low wealth inequalities and an almost total absence of unemployment. The supply aims to meet the demand and the production increases. Peace and well-being increase, so populations tend to grow. This is the so-called expansion phase of Turchin and Nefedov.

Once satisfied, the demand tends to decline but, due to investments, supply continues. We arrive in the hot zone of the luxury economy. It follows laws that are similar to those of perfect gases. The supply maintains the demand in the same way that high temperatures maintain pressure in a boiler. Rich people are becoming more numerous, but gradually production stagnates and unemployment rises. This is Turchin and Nefedov’s stagflation phase.

Then we arrive at the top edge of the Seneca cliff where the economic output collapses. Companies go bankrupt, populations uprise and governments are overthrown. This is Turchin and Nefedov’s crisis phase.

Similar to Sisyphus, civilizations bear the burden of production along their economic ascension up to the top of the cliff, from where they see the fruits of their labor crumble. At the foot of the cliff, new civilizations take over.

(1) P. Turchin, S. Nefedov, Secular cycles, Princeton (2009). 
(2) See the video of the article # 75 and the text published in Res-Systemica, vol. 14, Article 01 (September 2015). 
See: http://www.theoildrum.com/node/8317 (Bardi’s Seneca Cliff)
For information, here is the list of the cycles described in the book of Turchin and Nefedov with the related period:
The Plantagenet cycle (1150-1485) 
The Tudor-Stuart cycle (1485-1730) 
The capétien cycle (1150-1450) 
The Valois cycle (1450-1660) 
Rome: The cycle of the republic (350-30 BC.) 
Rome: The cycle of the principate (30 av JC-285.) 
Russia: Moscow cycle (1460-1620) 
Russia: The Romanov cycle (1620-1922)