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The Physics of Inequality

May 11, 2017

Economics has been known as "the dismal science" since this phrase was used by Thomas Carlyle (1795-1881) in an anonymous 1849 essay. As he wrote,
"Not a gay science... no, a dreary, desolate and, indeed, quite abject and distressing one; what we might call, by way of eminence, the dismal science."
Carlyle thought that Economics was dismal, since it reduced the essential principle of the world to supply and demand, making laissez-faire the proper way of governance. Laissez-faire governance, of course, means no governance at all. Thus, Economics is not called dismal, as many students might think, because it's a science that was always overloaded with mathematical equations.

I studied introductory Economics from the preeminent textbook of my era, Economics, by Paul Samuelson (1915-2009). Samuelson went on to become the first recipient of the Nobel Memorial Prize in Economic Sciences in 1970. This prize was a late addition to the Nobel Prizes established by Alfred Nobel.

As I remember, the mid-1960s edition of Samuelson's book had a single equation. This might be the earliest example of an author heeding the principle that every equation in a book reduces its readership by half. This rule is mentioned by Stephen Hawking in the acknowledgements section of his 1988 book, A Brief History of Time, that contained a single equation (E = mc2).

In its early days, Economics was not mathematical, and it was mostly philosophical. An example of this can be seen in the work of Thorstein Veblen (a.k.a., Torsten Veblen), an economist who flourished in the late nineteenth, and early twentieth, century. Veblen is best known for his 1899 book, The Theory of the Leisure Class,[1] in which he coined the term, conspicuous consumption.

Thorstein (Torsten) Veblen

Thorstein (Torsten) Veblen (1857-1929).

Veblen's "The Theory of the Leisure Class" introduced the term, "conspicuous consumption."

(Wikimedia Commons image, modified for artistic effect)

Conspicuous consumption is the purchase of lavishly expensive, or ephemeral and impractical, goods and services simply as a way of displaying income or wealth. A quick reading of Google News will show that conspicuous consumption is as alive, today, as it was more than a century ago. Veblen's 184 page book has no equations, and a quick perusal of some recent papers in Economics on arXiv will show that Economics has changed quite a bit since Veblen's time.

Economic equation (arXiv 1703.08807

An equation pulled from a recent paper on Economics at arXiv.[2]

They say that money is power. The physical definition of power is the rate of doing work; that is, it's the amount of energy consumed per unit time. Since time is money, we arrive at the dubious equation that energy E is proportional to money squared,
E = k($)2
All this is tongue-in-cheek, although some business guru could likely sell thousands of copies of a book based on this idea. However, it does introduce the intimate connection between wealth and energy. The physical basis of the connection between a country's economic activity and energy consumption has been analyzed in a recent paper in the Journal of Applied Physics.[3-5] The paper reveals, also, the underlying principles that foster wealth inequality in the world.

Any casual observation will prove that income inequality exists, but a more pressing question is why it seems to increase and it's so difficult to erase.[3-4] Adrian Bejan, a professor of mechanical engineering at Duke University, and Marcelo Errera, a professor of environmental engineering at the Federal University of Paraná, Brazil, write that such a hierarchical distribution of wealth happens naturally; and, since hierarchy is persistent and unavoidable, it's difficult to erase.[3]

The essential idea is that wealth, like many physical quantities, flows, and it's addressable by aspects of fluid mechanics. This is an application of Bejan's Constructal Law that I discussed in a previous article (Scaling Laws, March 31, 2016). His law, simply stated, is that "For a finite-size system to persist in time, it must evolve in such a way that it provides easier access to the imposed currents that flow through it."[6] Flowing system will trend toward an architecture that allows for an easier flow.

Map of US highways.

Go with the flow...

Map of United States highways.

(Via Wikimedia Commons.)

It appears to be a fundamental principle of physics that flow systems evolve over time to increase flow access. That's why so many branching, tree-shaped flow patterns appear in nature, with examples in river basins, neural networks, lightning bolts, the human vascular system, and the movement of freight.[4-5] Says Bejan, "Social organization is more complicated, but it's all physics."[4] As Bejan explains,
"From physics, it's actually easy... You may have noticed that annual wealth, a.k.a. gross domestic product (GDP), is essentially proportional to the useful energy or 'work and movement' generated by a group or territory, so you can think of wealth as movement. Also recognize movement (wealth) as inequality that is hierarchical."[4]

As shown in the figure, the Gross Domestic Product of a country is proportional to the amount of fuel consumed annually, which is a correlate of physical movement, such as fueling the human body with food, or powering vehicles.[3,5] At this fundamental level, there's a link between economics and physics; and, as Bejan states, "If movement is hierarchical, naturally, then so is the wealth.[5]

Graph of GDP vs energy

Graph of gross domestic product as a function of annual fuel consumption.

More economic activity is correlated with greater fuel consumption.

(American Institute of Physics image by Bejan and Errera.)

In the early days of human society, everything was local, and everyone was equally wealthy (or equally poor). A greater connectivity in society led to wealth inequality, a scenario that's exacerbated by today's globalization.[5] This creates a greater inequality in wealth distribution, a fact that's explained in Bejan's model.[5] Such inequality had an early origin. As Bejan states, "Relatively modest complexity is required for the nonuniformity in the distribution of movement (wealth) to be evident."[4]

Eradication of wealth inequality seems as if it will be a losing battle. When laws are enacted to favor more equality, inequality emerges again in other pathways. In an historical example, Bejan cites the Bolshevik Revolution.
"Indeed, some governments have tried to impose equality overnight, leading to tragic results... Just look at the Bolshevik Revolution. Within days of trying to install universal equality, there were already government insiders and party leaders who had enormous power and wealth. Today in Russia, oligarchs have the wealth. Physics always wins."[5]

This research was supported by the National Science Foundation.[5]


  1. Thorstein Veblen, "The Theory of the Leisure Class," 1.4 MB PDF File, via Law in Contemporary Society Web Site, Columbia Law School.
  2. Anuj Bhowmik and Jiling Cao, "Ex-post core, fine core and rational expectations equilibrium allocations," arXiv, March 26, 2017.
  3. Adrian Bejan and Marcelo R. Errera, "The physics basis of inequality in wealth and movement," Journal of Applied Physics, vol. 121, no. 12 (March 28, 2017), Article No. 124903, DOI: 10.1063/1.4977962.
  4. Physics can predict wealth inequality, American Institute of Physics Press Release, March 28, 2017.
  5. The physics of wealth inequality, Duke University Press Release, March 28, 2017.
  6. Adrian Bejan, Constructal Law Web Site at Duke University.

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