Joseph Tainter has an interesting essay titled Complexity, Problem Solving and Sustainable Societies. His thesis is that humankind, in order to solve practical problems, increases the complexity of the systems that go toward a solution. Over time this complexity needs to be subsidised by increasing energy - lest they collapse.

Tainter includes a discussion of Rome in his thesis. As Theophile Escargot argues, Rome hung around for so long that you can fit any model into its collapse:

[T]he Decline of Rome is a useful ground for arguing absolutely anything. Want to build up defence spending? Argue the Roman empire fell because it didn't secure its borders against the barbarians. Don't like immigration? Argue that their mistake was letting Visigoth asylum-seekers settle inside the Danube border after fleeing the Huns. Like free trade? Argue like Pirenne that the Arab restriction of trade routes did for it. Don't like religion? Follow Gibbon and say it was weak-minded Christianity that softened it up.

Tainter's argument is that complexity, and ability to problem solve with increasing complexity is a restraint on a society and economic system. The only way it can be overcome is with external energy inputs. Humans generally choose a simpler and easier method where they can, but often, there is no choice but to become more complex and usually through greater "differentiation, specialisation and integration".

Tainter describes complexity as an economic process as it "levies costs and yields benefits" and as such is an investment that has a quantifiable return. Humankind has generally chosen the cheapest, easiest and least complex solution first. But once that is exhausted increasingly complex solutions are found with diminishing returns. A good example is oil extraction. Most of the easy oil deposits have been found, so now we drill offshore and are even contemplating using the oil shale in Canada for energy.

In terms of Rome we have looked at Peter Turchin's model of Asabiya which describes the cycles of collective action. More recently Chalmers Johnson's thesis that empire leads to undemocratic forms which are inefficient and lead an empire into long decline. Not to forget Jared Diamond's ideas of social collapse.

Tainter describes Rome's increasing complexity and diminishing returns in terms of how the ruling class responded to military crisis. It taxed heavily, established greater bureaucracy, built more and more fortifications, doubled the army and devastated the economy:

The empire came to sustain itself by consuming its capital resources; producing lands and peasant population. The Roman Empire provides history's best-documented example of how increasing complexity to resolve problems leads to higher costs, diminishing returns, alienation of a support population, economic weakness, and collapse. In the end it could no longer afford to solve the problems of its own existence.

Interestingly he discusses industrialisation, which was the rise of the British Empire, though Tainter does not mention it that way. The overpopulation and denuding of forests for energy led to the use of coal. The easy deposits were mined, so deeper and deeper shafts were driven but that led to ground water issues. Which was solved with steam powered pumps. He writes:

What set industrialism apart from all of the previous history of our species was its reliance on abundant, concentrated, high-quality energy. With subsidies of inexpensive fossil fuels, for a long time many consequences of industrialism effectively did not matter. Industrial societies could afford them. When energy costs are met easily and painlessly, benefit/cost ratio to social investments can be substantially ignored (as it has been in contemporary industrial agriculture). Fossil fuels made industrialism, and all that flowed from it (such as science, transportation, medicine, employment, consumerism, high-technology war, and contemporary political organization), a system of problem solving that was sustainable for several generations.

So energy subsidises complexity, to the point that complexity's true cost and diminishing return on investment can be hidden. Such that Tainter writes that for our ability to solve problems with greater complexity, "the availability of energy per capita will be a constraining factor".

Robert Samuelson has an interesting op-ed in the WaPo on the issue of the poverty trap arguing that Gregory Clark's thesis of culture as being the rate determining step on the path to wealth (or more accurately the path out of poverty).

Clark suggests that much of the world's remaining poverty is semi-permanent. Modern technology and management are widely available, but many societies can't take advantage because their values and social organization are antagonistic. Prescribing economically sensible policies (open markets, secure property rights, sound money) can't overcome this bedrock resistance.

It is interesting to note the Deniehy and Harpur saw little difference between political and social organisation. To 19thC Republicans they were one and the same: as reduction of tyranny led to increased liberty and consequent greater individual moral expression.

The article continues:

"There is no simple economic medicine that will guarantee growth, and even complicated economic surgery offers no clear prospect of relief for societies afflicted with poverty," he writes. Various forms of foreign assistance "may disappear into the pockets of Western consultants and the corrupt rulers of these societies." Because some societies encourage growth and some don't, the gap between the richest nations and the poorest is actually greater today (50 to 1) than in 1800 (4 to 1), Clark estimates.

There may be another component in play where the ability of social organisation to harness and leverage complexity toward positive outcomes. Joseph Tainter has argued that fossil fuels and their incredible return of energy on burning have allowed our societies to increase in complexity and the consequent energy consumption without adverse affects.

But the use of fossil fuels has enabled social complexity as well not just physical complexity through technology. Farming is a pretty bare existence with the risk of crop failure being constant, not to mention poverty, hunger, taxes, and not having enough members in your family to do the manual labor on the farm.

Until you throw in fossil fuels and industrial nitrates. Suddenly tractors, irrigation and fertilisation lead to over-production. But that is useless until you have super-cargo ships to carry the over-production to city markets around the globe, and rail to transport the grain and livestock, and trucks, and roads, and shops, and malls, and just-in-time computing inventory systems, and credit cards, etc.

Without the social organisation able to underly that complexity then the bump is difficult. It may be that the physical analogy is friction where a scalar coefficient describes the force that has to be overcome. Alternatively it may be quotient where the present complexity off the social organisation is divided over a base organisation that represents the minimal level of complexity to sustain a prosperous economy.

Probably the closest thing to that which is being tracked these days is the corruption report.