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Learning cycles

Swings in the economy are related to waves of technological advance.  A new technology is invented, undergoes rapid improvement, then reaches a stage of maturity after which there is little further refinement. Meanwhile, the invention is incorporated into an innovative product that is adopted by users at an accelerating rate until almost everyone who wants one has one, and new customers are rare. The initial explosive growth of invention and innovation produces an economic boom. The subsequent stagnation results in a bust. Since the industrial revolution there has been a series of such waves. In each successive wave, the time from boom to bust has decreased by a factor of √2, but the centres of the waves have been regularly spaced. Cesare Marchetti. 1980. Society as a Learning System: Discovery, Invention and Innovation Cycles Revisited. Technological Forecasting and Social Change 18.

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Social macrodynamics

World population follows a hyperbolic curve that can be explained by a simple model. Let P = population and T = technology. Assume that population is limited by the technology, i.e. better technology makes possible a larger population. This can be expressed as P = a T, where a is some constant of proportionality. Assume the growth of technology is increased by both the population (more potential inventors) and the technology already in existence (facilitating the spread and recombination of ideas). This can be expressed as dT/dt = b P T, where b is a constant. We can therefore write dP/dt =a dT/dt = a b P T, and since a T = P, this becomes dP/dt = b P2. The solution to this equation is P = c / (t0  - t) where c = 1 / b, t0  = 1 / (b P0 ), and P0 = starting population. This is the equation of a hyperbola. With suitable estimates of c and P0, it fits the observed growth of world population to an accuracy of 99.6%.  Andrey Korotayev, Artemy Malkov & Daria Khaltourina. 2006. Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. URSS.

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Structural-demographic theory

Civil war and rebellion become likely when 3 conditions are met:
1. Popular discontent and volatility, due to falling incomes, urban growth and a youthful population
2. Intra-elite conflict, when there are more candidates for elite status (e.g. university graduates) than there are positions for them to occupy
3. A fiscal crisis, in which the state's credit has run out and it can no longer meet its financial obligations
There is a cycle. Population growth outstrips technology, causing general impoverishment. Elites exploit this cheap labour to expand, and divide into rival factions. Elite expansion increases the state's obligations while general impoverishment reduces its revenues, and its authority breaks down. Elite factions then mobilise the populace to fight over a new order. This produces social and economic innovation so that living conditions improve, and the cycle starts over. Jack Goldstone. 1991. Revolution and Rebellion in the Early Modern World. Univ. of California Press. Peter Turchin and Sergey Nefedov. 2009. Secular Cycles. Princeton Univ. Press.

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The generational cycle

People born in a similar era, and exposed to similar influences, develop similar attitudes and behaviours in later life. Since they partly emulate and partly react against their parents, the result is a cycle of generations in which the same attitudes come round roughly every 80 years, the length of a long human life. The cycle involves two forms of upheaval, a political-economic crisis and a cultural awakening, each returning as memory of the last one fades. Before the crisis is an unravelling and after it a high. The generations divide into four types, defined by their differing experiences of these phases:
Nomads: entrepreneurial survivors; neglected as children and in old age.
Heroes: can-do team players; young adults during the crisis.
Artists: efficient, cultured technocrats, with an ever-youthful outlook.
Prophets: radicals and visionaries; young adults during the awakening. 
Neil Howe and William Strauss. 1991. Generations: The History of America’s Future, 1584 to 2069. William Morrow & Company. Neil Howe and William Strauss. 1997. The Fourth Turning: What the Cycles of History Tell Us About America’s Next Rendezvous with Destiny. Broadway Books. 

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The hegemonic cycle

In The Peloponnesian War, the Greek historian Thucydides says that, while there were many specific reasons why war broke out, the ultimate cause was "the rise of Athens, and the fear this caused in Sparta". This was an example of a recurrent syndrome in international affairs: the rise of a challenger to the current hegemon, where the clash between the ambitions of the challenger and the desire of the hegemon to hold on to power eventually leads to a contest of arms. In recent history, this syndrome has followed a cycle with a period of about 100 years. Usually, the challenger is defeated in the war but the hegemon is so exhausted by it that it loses its leading position to a third party. The current cycle, with the United States as hegemon, began with the ending of World War 2 and is expected to culminate in the next few decades. George Modelski. 1999. From Leadership to Organization. In V. Borschier and C. Chase-Dunn (eds.), The Future Of Global Conflict. Sage.

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The dynastic cycle

The Arab historian, Ibn Khaldun (1332-1406) found that dynasties go through a rise and fall that lasts four generations or 120 years. The first generation comes to power on the basis of strong asabiya, Ibn Khaldun's word for 'solidarity' or 'social cohesion', among and with its supporters. Over time, the dynasty loses its war-like character and asabiya declines as the rulers take their position for granted and develop a taste for luxury. Early on, taxes are light and easily raised. Later, they become heavy and hard to raise. Overall tax revenues hardly increase, but a growing proportion is squandered. Asabiya disappears fastest at the periphery, where a new, more vigorous contender arises then comes to conquer the core, and the cycle begins again. There are 5 stages: conquest, consolidation, leisure, peace, waste. Ibn Khaldun, tr. F. Rosenthal. 2005. The Muqaddimah: An Introduction to History. Princeton University Press. Peter Turchin. 2003. Historical Dynamics: Why States Rise and Fall. Princeton University Press.

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Cultural dynamics

Fundamental cultural beliefs, as expressed in the works of artists, writers and philosophers, change over time. In just one of many examples, western civilisation since the Renaissance has seen an irregular swing between eternalism, the belief that change is an illusion, and temporalism, the belief that change is everywhere and all is change. Furthermore, the switch from temporalism to eternalism has been associated with civilisational crises that brought permanent changes in political, economic and social structures. Other kinds of belief show similar fluctuations, while different civilisations may be at different stages in these long-term dynamics. Pitirim Sorokin. 1957. Social and Cultural Dynamics: A Study of Change in Major Systems of Art, Truth, Ethics, Law and Social Relationships. Peter Owen.

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The civilisational year

According to Oswald Spengler (1880-1936), civilisations follow a lifecycle with seasons like the year, undergoing the same experiences in the same sequence. Once they have passed through all four seasons, over a period of 1000-2000 years, they enter an arrested, unchanging state, or they are swept away altogether. Each civilisation is formed around a core set of ideas that appears in all of its art, philosophy and science. Western civilisation is formed around the ideas of infinite extension and human autonomy, and this is seen in its invention of perspective, its cosmological picture of galaxies at vast distances, its adoption of the Faust myth, and its Darwinian belief in a natural world of struggle and competition. Arabian civilisation, of which Islam is a product, is  formed around the ideas of the cavern and human helplessness in relation to the divine will. While the West is entering its winter, Arabian civilisation has already ended and has no more potential for development. Oswald Spengler. 2014 (1926 and 1928). The Decline of the West. Random Shack.

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The lifecycle of civilisations

According to Arnold Toynbee (1889-1975), the history of a civilisation exhibits “three and a half beats”, i.e. three cycles of boom and bust, then one final peak before the civilisation fades away. The driving mechanism for this is challenge and response, which means that the civilisation has some characteristic problem—such as population pressure or a difficult climate—that underlies everything it does. Toynbee believes that every civilisation constructs a Universal State—i.e. it imposes on the world its monolithic vision of how society should be ordered—and a Universal Church—i.e. it adopts a dominant religion. Its growth phase is presided over by a creative minority, and its decline by a dominant minority. Furthermore, the civilisation’s development is affected not only by the behaviour of its internal proletariat but also by its relationship with the external proletariat, i.e. those outside the civilisation who are influenced by it and provide it with labour. Arnold Toynbee. 1972. A Study of History: The New One-Volume Edition. Thames and Hudson. Stephen Blaha. 2002. The Life Cycle of Civilizations. Pingree-Hill Publishing.

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Zipf's law

Many sociological quantities obey approximate power laws, whose signature is the tendency to produce a straight line on a logarithmic plot. For example, with cities there is a power law such that cities half as large as a given size are twice as numerous. This phenomenon is named after George Zipf (1902-1950) who studied it in city populations, linguistics, personal incomes and other areas. The power law tendency can be used to infer the whole from a part, and so to detect fraud or missing data. Deviations from power law behaviour may also highlight particular factors or processes that inhibit the normal tendency. For example, city sizes are the outcome of a historical evolution responding to political, economic and social forces, and the power law distribution tells us about these forces and evolutionary mechanisms. For a simple explanation of Zipf's Law, assume that the city size distribution is stable and unchanging while every city at each time step can either double or halve in size, with probabilities that are independent of its current size. Let the probability of doubling be p and the probability of halving be 1-p. If there are Ns cities of size S, after one time step these will have become p Ns cities of size 2 S and (1-p) Ns cities of size S/2. Since the distribution is stable, the total population must be the same, i.e. Ns S = (p Ns) x (2 S) +( (1-p) Ns) x (S/2), which can be solved to deduce that p = 1/3. Meanwhile, cities of size S after one time step consist of cities twice the size that halved (with probability 1-p = 2/3) plus cities half the size that doubled (with probability p = 1/3). Since the distribution is stable, this number must be constant, so Ns = (2/3) N2s + (1/3) Ns/2. This can be written as 1 = (2/3) (N2s/Ns) + (1/3)(Ns/2/Ns), and this must be true regardless of which size, S, we are considering. Hence, N2s/Ns = Ns/Ns/2. Call this value f. Then we have 1 =  (2/3) f + (1/3) (1/f), which has the solution f = 1/2. This means that, for cities of a given size, there are half as many cities of twice the size and twice as many cities of half the size, precisely as found empirically. George Zipf. 1949. Human Behavior and the Principle of Least Effort. Addison-Wesley Press. Gabaix, X. 1999. Zipf’s Law For Cities: An Explanation. The Quarterly Journal of Economics 114:3, 739-767.

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Cities and scaling

Some sociological quantities exhibit economies of scale: double the city size and you require less than twice as much, e.g. chemists, petrol stations, water pipes. Other sociological quantities exhibit returns to scale: double the city size and you get more than twice as much, e.g. crimes, inventions, incomes. More precisely, quantities showing sublinear scaling obey power laws with exponent 5/6, and quantities showing superlinear scaling obey power laws with exponent 7/6. For a simple explanation, assume that the economic output of a city is proportional to its population density, ρ = N/A, where N is the population size and A is the city area. Assume further that the costs of maintenance of the city are proportional to its linear size, l ~ A1/2. Finally assume that the output and the costs are equal, so we have N/A ~ A1/2. This implies N ~ A3/2 or A ~ N2/3. Now suppose that the amount of infrastructure (e.g. water pipes) per person is proportional to the average distance between people, d = ρ-1/2. Then total infrastructure, I ~ N d = N (N/A)-1/2 = N1/2 A1/2 ~ N1/2 N1/3 ~ N5/6, as found empirically. Next suppose that the amount of social activity (e.g. inventions) per person, s, is proportional to the number of people per unit of instrastructure (since it is at infrastructure like shops and roads where people meet), i.e. s ~ N/I = N1/6. The total social activity is N s = N7/6, again as found empirically. Luis Bettencourt. 2013. The Origins of Scaling in Cities. Science. Vol. 340, Issue 6139, pp. 1438-1441.

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Central place theory

Settlements form a central place hierarchy, with a large city surrounded by smaller satellite cities, which are surrounded by satellite towns, which are surrounded by villages. This creates roughly hexagonal patterns in the landscape. There are three kinds of pattern corresponding to different principles of organisation. Considered as markets, each central place has on average two satellite settlements (each central place has six satellites, but each satellite is shared with two other central places, so that a given central place has only a third of each satellite; a third share of six satellites amounts to two satellites). Considered as transport hubs, each central place has on average three satellite settlements (each satellite lies on the road between two central places, so each central place has a half share; a half share of six satellites amounts to three satellites). Considered as administrative centres, each central place has on average six satellite settlements (a given satellite can belong to only one administrative unit; all six satellites surrounding a central place belong to it). The different patterns are overlaid on each other, creating a complex picture. It is not just that the sizes of cities follow a definite pattern, as indicated by Zipf's Law, but they are also arranged in a particular way across the landscape, with cities of a given size class being evenly spaced out rather than placed at random. Richard L Morrill. 1970. The Spatial Organization of Society. Wadsworth Publishing Company. Wen-Tai Hsu. 2012. Central Place Theory and City Size Distribution. The Economic Journal, Vol. 122, Issue 563, pp. 903-932.

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Production principles

Technological and economic organisation has evolved through four great phases, embodying very different production principles. These are:
Hunter-Gatherer: 40,000 - 9000 BC (invention of farming): people lived directly off the land.
Craft-Agrarian: 9000 BC - AD 1430 (invention of the printing press): people lived by farming and relied on human and animal power.
Industrial: 1430 - 1955 (invention of the transistor): life became dominated by the machine.
Information-Scientific: 1955 - c. 2110; machines became intelligent, taking over human cognitive work.
While the production principles have been of successively shorter duration, they have each gone through the same six stages in the same relative time. The present Information-Scientific principle is currently in Stage 2 (Adolescence). Stage 2 of the Industrial principle was from 1600 to 1730, and witnessed breakthroughs in fundamental science. However, the real transformation of society came in Stage 3, when population was displaced from the countryside into the cities and the nature of work changed with the rise of factories and steampower. Stage 3 of the Information-Scientific principle will begin around 2030/2040, and will see displacement of population from the planet's surface into orbital factories along with changes in the nature of work as Artificial Intelligence takes over routine intellectual tasks. Leonid Grinin. 2012. Macrohistory and Globalization. Uchitel Publishing House.

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Kondratieff waves

Nikolai Kondratieff detected 60-year waves, dating back to at least 1800, in the vigour of capitalist economies. Each wave is associated with a particular key invention--steam engine, railway, electricity, motor car, electronics--which creates a boom as it spreads through the economy but eventually runs out of steam and turns to a bust. The Kondratieff wave is synchronised with fluctuations in the intensity of war. The causes of the 60-year cycle are negative feedbacks between critical variables: economic growth makes war more affordable, and war then dampens economic growth; innovation produces an economic boom, which decreases the pressure for innovation; growth creates rising prices and falling incomes, so consumer demand falls, undermining growth; a booming economy encourages investment in long-term capital projects, diverting money away from feeding the boom; the experience of war creates an aversion to war, which suppresses its occurrence until the rise of new generations who have no memory of it. Joshua Goldstein. 1988. Long Cycles: Prosperity and War in the Modern Age. Yale Univ. Press.

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Production zones

Johann von Thünen's 'isolated state' model explains the emergence of zones with different forms of production at different distances from a market centre. The original model focuses on agricultural production. Land nearest the market is the most valuable. It goes to the growers of produce that can fetch high prices in the market while also being costly to transport so that a more distant location quickly reduces profitability--typically fruit and vegetables. Land far from the market is cheap and goes to the growers of non-perishable produce that is not too costly to transport--typically firewood in von Thunen's day. In between, are zones with different products according to the shifting balance between prices and transport costs. Clearly, this is an idealisation. The model can be extended to take account of roads, rivers and seas that affect the cost of transport in different directions.  It can also be extended to cover non-agricultural products, and to situations where the central market is not a town but a region or a country, surrounded by suppliers and trading partners. To see why zones arise, suppose that the price of the ith product is pi and its transport cost is ci per unit distance. Suppose also that the outer limit of viability of a particular product is a distance r1 from the centre (we will see in a moment why a product has an outer limit). The next product to be viable will be the one that has the maximum value of pi - ci r1, since this is the amount of money left over, after deduction of transport costs, to pay rent, and therefore the growers of this product will have the most money to bid for the land. This product will be viable out to a distance r2, such that pi - ci r2 < pj - cj  r2 for some j. At this point, the product produces less profit than the other product j, and it will no longer win the bid for land. Hence the product is viable only within a zone between r1 and r2, its inner and outer limits. This argument makes the simplifying assumption that the market price of each product is fixed. In fact, it depends on supply and demand. We can extend the model by assuming that demand depends on price, say as D = D0 - d p, where D is demand, p is price and D0 and d are constants characteristic of the product. The amount produced of a given product is π(r22-r12)f, where r1 and r2 are the inner and outer limits of its zone and f is the amount of product produced per unit land area. For market equilibrium, supply and demand must balance, so we have D0 - d p = π(r22-r12)f. This gives us the price as p = (D0 - π(r22-r12)f)/d. The product that is most viable at r1 will be the one with the maximum value of D0/d - c r1, where c is transport cost as before. The outer limit of its zone occurs where there is some product for which D0'/d' - c' r2 > (D0 - π(r22-r12)f)/d - c r2. At this point, the other product generates more revenue. The model is more complex but it gives rise to zoning in the same way. Johann von Thünen. 1826. Der Isolierte Staat.

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Growth of world polities

The size of the world's largest polities has increased over time, from the Egyptian empire covering 0.1% of the earth's land mass in 2500 BC to the British empire covering 25% of the earth's land mass in 1925. Taking the combined area of the world's three largest empires, to smooth out some of the fluctuations, the chart of polity size against time divides into several phases. After the preliminary experiment of Egypt, the coming of bronze saw the combined size of the largest empires rise to hover a little below 1% of the earth's land mass. The coming of iron saw the combined size jump higher, to hover a little below 10%. The coming of industrialisation seems to have caused a further increase, to around 50-100%, though it is too early to be sure. (Note the logarithmic scale in the above chart.) The transition from bronze to iron was marked by a fall in the area of imperial control as the new technology changed the balance of power and the world order was drastically reconfigured through a period of chaos. The growth of world polities follows a logistic (S-shaped) curve, so that it is flattening out as it comes up against the limit of the earth's land mass. If the trend continues, by 3000, it will be routine for 50% of the world to belong to just three countries, while the first whole-earth government will come before that, a few centuries from now, only to break apart and later be re-formed. Rein Taagepera. 1978. Size and Duration of Empires: Systematics of Size. Social Science Research. Iss. 7, pp. 108-127.

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The one, the few, the many

At their simplest, political hierarchies consist of three elements:
The One: the ruler, be it a monarch or a political party.
The Few: the elite, with large holdings of wealth and property.
The Many: the ordinary people, the common masses.
Any two of these can dominate the other. If the ruler and the elite are united, they can always control the masses. Rulers who have the people on their side can overcome aristocratic rebellions. When the elite and the people are both dissatisfied with the prevailing order, the ruler will be overthrown. Understanding the attitudes of these three elements and the relationships between them is key to assessing the stability of a political system. Niccolò Machiavelli. 1513. The Prince. 

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The Russian political cycle

Over the last 120 years, Russian politics has exhibited a remarkably regular 36-year cycle, divided into three phases of 12 years each. These phases are:
Rejection of the past: e.g. the October Revolution and the establishment of communism.
Consolidation of a new regime: e.g. the rise of Stalin and his enjoyment of absolute power.
Fight against external and internal enemies: e.g. the German invasion and WW2, along with mass purges of dissidents.
The cyclical pattern began with the assassination of Alexander II in 1881 and does not appear to go back before that. Its discoverer relates it to astrological cycles, involving the movements of Saturn and Jupiter. Boris Romanov. 2011. Russia's Historical Cycles and Future: 1881-1917-1953-1989-2025.

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