Energizing Exchange: Learning from Econophysics’ Mistakes

Let’s talk econophysics. If you’re not familiar, ‘econophysics’ is an attempt to understand economic phenomena (like the distribution of income) using the tools of statistical mechanics. The field has been around for a few decades, but has received little attention from mainstream economists. I think this neglect is a shame.

As someone trained in both the natural and social sciences, I welcome physicists foray into economics. That’s not because I think their approach is correct. In fact, I think it is fundamentally flawed. But it is only by engaging with flawed theories that we can learn to do better.

What is important about econophysics, is that it demonstrates a flaw that runs throughout economics: the idea that we can explain macro-level phenomona from micro-level principles. The problem is that in all but the simplest cases, this principle does not work. Yes, complex systems may be reduced to simpler pieces. But rarely can we start with these simple pieces and rebuild the system. That’s because, as physicist Philip Anderson puts it, more is different.

What follows is a wide-ranging discussion of the triumphs and pitfalls of reduction and resynthesis. The topic is econophysics. But the lesson is far broader: breaking a system into atoms is far easier than taking atoms and rebuilding the system.

Let there be atoms!

To most people, the idea that ‘matter is made of atoms’ is rather banal. It ranks with statements like ‘the Earth is round’ in terms of near total acceptance.1 Still, we should remember that atomic theory is an astonishing piece of knowledge. Here is physicist Richard Feynman reflecting on this fact:

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that … all things are made of atoms.

(Richard Feynman, Lectures on Physics)

Feynman spoke these words in the 1960s, confident that atoms existed. Yet if he’d said the same words a century earlier, they would have been mired in controversy. That’s because in the 19th century, many scientists remained skeptical of the atomic hypothesis. And for good reason. If atoms existed, critics observed, they were so small that they were unobservable (directly). But why should we believe in something we cannot see?

Today, of course, we can see atoms (using scanning transmission electron microscopes). But long before we achieved this feat, most scientists accepted the atomic hypothesis. Why? Because multiple lines of evidence pointed to atoms’ existence. Here’s how Richard Feynman put it:

How do we know that there are atoms? By one of the tricks mentioned earlier: we make the hypothesis that there are atoms, and one after the other results come out the way we predict, as they ought to if things are made of atoms.

(Richard Feynman, Lectures on Physics)

One of the first hints that atoms existed came from chemistry. When combining different elements, chemist John Dalton discovered that the masses of the reactants and product always came in whole-number ratios. This ‘law of multiple proportions’ suggested that matter came in discrete bits.

Another line of evidence for atomic theory came from what is today called ‘statistical mechanics’. This was the idea that macro properties of matter (such as temperature and pressure) arose from the interaction of many tiny particles. The key inductive leap was to assume that these particles obeyed Newton’s laws of motion. At the time, this assumption was a wild speculation. And yet it turned out to be wildly successful.

A gas of billiard balls

By the mid-19th century, the properties of gases had been formulated into the ‘ideal gas law’. This was an equation that described how properties like pressure, volume and temperature were related. But what explained this law?

Enter the kinetic theory of gases. Suppose that a gas is composed of tiny particles that collide like billiard balls. Next, assume that these collisions obey Newton’s laws. Last, assume that collisions are elastic (meaning kinetic energy is conserved). What does this imply?

It turns out that these assumptions imply the ideal gas law. So here we have the reasoning that Richard Feynman described: we hypothesize that there are atoms, and then the “results come out the way we predict, as they ought to if things are made of atoms.” What was exciting about this particle model was that it gave a micro-level definition of temperature and pressure. Temperature was the average kinetic energy of gas particles. And pressure was the force per area imparted by particles as they collided with the container.

As the mathematics of this kinetic model were developed further, there came another surprise. From equality came inequality. The ‘equality’ here refers to the underlying process. In the kinetic model, each gas particle has the same chance of gaining or losing energy during a collision. One might think, then, that the result should be uniformity. Each particle should have roughly the same kinetic energy. The mathematics, however, show that this is not what happens.

Instead, when James Clerk Maxwell and Ludwig Boltzmann fleshed out the math of the kinetic model, they found that from equality arose inequality. Due only to random collisions, gas particles should have a wide distribution of speed.

Figure 1 illustrates this counter-intuitive result. The top frame shows a simple model of a gas — an ensemble of billiard balls colliding in a two dimensional container. The collisions are uniform, in the sense that each particle has the same chance of gaining/losing speed. And yet the result, shown in the bottom frame, is an unequal distribution of speed.

Figure 1: The random collision of gas particles gives rise to a wide distribution of speeds. [Source: Wikipedia]

The blue histogram (in Figure 1) shows the distribution of speeds found in the modeled gas particles. Because there are relatively few particles (a few hundred), their speed distribution jumps around with time. But if we were to add (many) more particles, we expect that the speed distribution would converge to the yellow curve — the Maxwell–Boltzmann distribution.

This particle model demonstrates how a seemingly equal process (the random exchange of energy) can give rise to wide inequalities. If econophycisists are correct, this model tells us why human societies are mired by inequality. It’s just basic thermodynamics.

Energized particles, monetized humans

After Maxwell and Boltzmann, statistical mechanics gave rise to a long string of successes that bolstered the atomic hypothesis. The icing on the cake came in 1905, when Albert Einstein used the kinetic model to explain Brownian motion (the random walk taken by small objects suspended in a liquid). It’s hard not to be impressed by this success story.

Now let’s fast forward to the late 20th century. By then, statistical mechanics was a mature field and the low-hanging fruit had long since been picked. And so physicists widened their attention, looking for other areas where their theories might be applied.2

Enter econophysics. In the 1990s, a small group of physicists set their sites on the human economy. Perhaps, they thought, the principles of statistical mechanics might explain how humans distribute money?3

Their idea required a leap of faith: treat humans like gas particles. Now, humans are obviously more complex than gas molecules. Still, econophysicists highlighted an interesting parallel. When humans exchange money, it is similar to when gas particles exchange energy. One party leaves with more money/energy, the other party leaves with less. Actually, the parallel between energy and money is so strong that physicist Eric Chaisson describes energy as “the most universal currency known in the natural sciences” (emphasis added).

With the parallel between energy and money, ecophysicists arrived at a startling conclusion. Their models showed that when humans exchange money, inequality is inevitable.


When econophysicists began publishing their ‘kinetic-exchange models’ of income and wealth, social scientists greeted them with skepticism. People, social scientists observed, are not particles. So it is inappropriate to use the physics of inanimate particles to describe the behavior of (animate) humans.

In the end, I think this criticism is warranted … but for reasons that are probably different than you might expect. Before I get to my own critique, let’s run through some common objections to econophysics models of income.

Exchange is not ‘random’

If I told you that your last monetary purchase was ‘random’, you would protest. That’s because you had a reason for purchasing what you did. When you gave money to Bob, it wasn’t because you ‘randomly’ bumped into him (as envisioned in econophysics world). It was because Bob was selling a car that you wanted to buy. So the effect (the exchange of money) had a definite cause (you wanted the car).

When econophysicists use ‘random exchange’ to explain income, many people are horrified by the lack of causality. It’s an understandable feeling — one that was actually shared (a century earlier) by Ludwig Boltzmann. A founder of statistical mechanics, Boltzmann was nonetheless tormented by his own theory. Like most physicists of the time, Boltzmann wanted his theory to be deterministic. (He thought effects should have definite causes.) Yet to understand the behavior of large groups of particles, Boltzmann was forced to use the mathematics of probability. The resulting uncertainty in cause and effect made him uneasy.4

Ultimately, Boltzmann’s unease was warranted. Quantum mechanics would later show that at the deepest level, nature is uncertain. But this quantum surprise does not mean that probability and determinism are always incompatible. In many cases, the use of probability is just a ‘hack’. It is a way to simplify a deterministic system that is otherwise too difficult to model.

A good example is a coin toss. When you toss a coin, most physicists believe it is a deterministic process. That’s because the equations that describe the toss (Newton’s laws), have strict cause and effect. Force causes acceleration. So if we had enough information about the coin and its environment, we could (in principle) predict the coin’s outcome.

The problem, though, is that in practice we don’t have enough information to make this prediction. So we resort to a ‘hack’. We realize that there are only two possible outcomes for the coin: heads or tails. If the coin is balanced, both are equally probable. And so we model the coin toss as a random (non-deterministic) process, even though we believe that the underlying physics are deterministic.

Back to econophysics. When social scientists complain that econophysics models invoke ‘randomness’ to explain income and wealth, they are making a philosophical mistake. Econophysicists (correctly) respond that their models are consistent with determinism. When you spend money, you know exactly why you did it. But that doesn’t stop us from modeling your exchange with a statistical ‘hack’. Regardless of why you did it, the end result is that you spent money. So like a coin toss, econophysicists think we can treat monetary exchange in probabilistic terms. That’s a reasonable hypothesis — one that social scientists too readily dismiss.

Where is the property?

In his article ‘Follow the money’, journalist Brian Hayes argues that econophysicists don’t model ‘exchange’ so much as they model theft. He has a point.

When you spend money, you usually get something back in return — namely property. That property could be a physical thing, as when you buy a car. Or it could be something less tangible, as when you buy shares in a corporation. But either way, the exchange is two-sided. You lose money but gain property.5

In econophysics, however, there is no property. There is only money. So when you ‘bump’ into Bob (in econophysics world) and give him money, you get nothing in return. Of course, this type of one-sided transaction does happen in real life. But we don’t call it ‘exchange’. We use other words. If you gave the money to Bob, we call it a gift. Or if Bob just took the money, we call it theft. Either way, the gift/theft economy is a tiny part of all real-world monetary transactions. So it would seem that econophysics has a problem.

Or does it?

Econophysicists do not (to my knowledge) deny the importance of property. They just think we can model the exchange of money without understanding property transactions. Here’s why.

Regardless of what you bought from Bob, you leave the transaction with less money, he leaves with more money. We can lump the corresponding property transaction into the ‘causes that are too complex to understand’ column. Despite this (unexplained) complexity, the end result is still simple: money changes hands. Why can’t we model that transfer of money alone? Again, this is a reasonable hypothesis.

Bottoms up

Having defended econophysics models, it’s time for my critique. By appealing to statistical mechanics, econophysicists hypothesize that we can explain the workings of the economy from simple first principles. I think that is a mistake.

To see the mistake, I’ll return to Richard Feynman’s famous lecture on atomic theory. Towards the end of the talk, he observes that atomic theory is important because it is the basis for all other branches of science, including biology:

The most important hypothesis in all of biology, for example, is that everything that animals do, atoms do. In other words, there is nothing that living things do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics.

(Richard Feynman, Lectures on Physics)

I like this quote because it is profoundly correct. There is no fundamental difference (we believe) between animate and inanimate matter. It is all just atoms. That is an astonishing piece of knowledge.

It is also, in an important sense, astonishingly useless. Imagine that a behavioral biologist complains to you that baboon behavior is difficult to predict. You console her by saying, “Don’t worry, everything that animals do, atoms do.” You are perfectly correct … and completely unhelpful.

Your acerbic quip illustrates an important asymmetry in science. Reduction does not imply resynthesis. As a particle physicist, Richard Feynman was concerned with reduction — taking animals and reducing them to atoms. But to be useful to our behavioral biologist, this reduction must be reversed. We must take atoms and resynthesize animals.

The problem is that this resynthesis is over our heads … vastly so. We can take atoms and resynthesize large molecules. But the rest (DNA, cells, organs, animals) is out of reach. When large clumps of matter interact for billions of years, weird and unpredictable things happen. That is what physicist Philip Anderson meant when he said ‘more is different’.

Back to statistical mechanics. Here we have an example where resynthesis was possible. To develop statistical mechanics, physicists first reduced matter to particles. Then they used particle theory to resynthesize macro properties of matter, such as temperature and pressure. That this resynthesis worked is a triumph of science. But the success came with a cost.

In all fairness to Maxwell and Boltzmann, their equations describe systems that are utterly boring. The math applies to an ideal gas in thermal equilibrium. At the micro scale, there’s lots going on. But at the macro scale, literally nothing happens. The gas just sits there like a placid lake on a windless day. Boring.6

Water, reduced and resynthesized

When we move beyond ideal gases in thermal equilibrium, the mathematics of resynthesis quickly become intractable. Let’s use water as an example, and try to resynthesize it from the bottom up.

At the most fundamental level, water is described by quantum mechanics. According to this theory, chemistry reduces to the bonding of electrons between atoms. We can use this ‘quantum chemistry’ to predict properties of the water molecule (H2O), such as the bond angle between the two hydrogen atoms. We can also predict that, because of this bond angle, the water molecule will have electric poles. These poles cause water molecules to attract one another, a fact that explains properties of water like its surface tension and viscosity.

When we move to larger-scale properties of water, however, we have to leave quantum mechanics behind. Suppose we want to explain a simple vortex, as shown in Figure 2. To create the vortex, all you need is a tube filled with water and a hole in the bottom. Pull the plug and a vortex will form. (We add the pump to sustain the system.) Now the question is, how do we explain the whirlpool?

Figure 2: A setup for making a vortex.

Quantum physics is no help. It’s a computational chore to simulate the properties of a single water molecule. But our vortex contains about 1024 molecules. So quantum physics is out.

What about statistical mechanics? It’s not helpful either. Physicists like Maxwell and Boltzmann made headway explaining the properties of gases, because when matter is in this state it’s valid to treat molecules like billiard balls. But in a liquid, this assumption breaks down. Rather than a diffuse cloud of billiard balls, a liquid is analogous to a ball-pit filled with magnetized spheres. The molecules don’t zoom around freely. They roil around in a haze of mutual attraction. It’s a mess.

So to make headway modeling our vortex, we abandon particle theory and turn to a higher-level approach. We treat water as a continuous liquid, defined by macro-level properties such as density and viscosity. We determine these properties from experiment, and then plug them into the equations of fluid dynamics. If we have enough computational power, we can simulate our vortex.

To model larger systems, we need still more computational power. Climate models, for instance, are basically large fluid-dynamics simulations. Presently, such models cannot resolve weather below distances scales of 100 km. Doing so would take too long on even the fastest supercomputers.

Back to water. The point of this story is to show the difficulty of resynthesis. We cannot take water molecules and resynthesize the ocean. Doing so is computationally intractable. So we introduce hacks. We do a partial resynthesis — water molecules to properties of water. We then put these properties in simpler equations to simulate the macro-level behavior of water.

This partial resynthesis is an important achievement. But it pales to what we ultimately wish to do. In a famous segment from Cosmos, Carl Sagan depicts the evolution of life from primordial ooze to humans. He concludes by noting: “those are some of the things that molecules do given four billion years of evolution.”

Sagan’s evolution sequence illustrates the scale of the resynthesis problem. We can easily reduce life to its constituents — primarily water and carbon. And yet we cannot take these components and resynthesize life. Unlike with water alone, with life there are no simplifying hacks that allow us to get from molecules to mammals. That’s because in mammals, the fine-scale structure defies simplification. Baboons are mostly sacks of water. But modeling them as such won’t explain their behavior. If it did, we would not have behavioral biology. We would have behavior fluid dynamics.

A foolhardy resynthesis

Social scientists often rail against the plight of ‘reductionism’. I think this is a mistake. To understand a complex system, we have no choice but to reduce it to simpler components. But that’s just the first step. Next, we must understand the connections between components, and use these connections to resynthesize the system. It is this second step that is filled with pitfalls. So when social scientists criticize ‘reductionism’, I think they are really criticizing ‘foolhardy resynthesis’.

And that brings me back to econophysics. When social scientists hear that econophysicists reduce humans to ‘particles exchanging money’, they are horrified. But when you have a close look at this reduction (as I have above), it’s not so terrible. Certainly humans are more complicated than molecules. But we do exchange money much like molecules exchange energy. The physicists who developed statistical mechanics were able to take energy-exchanging particles and resynthesize the properties of ideal gases. Why, say econophysicists, can’t we do the same with humans? Why can’t we take simple principles of individual exchange and resynthesize the economy?

The problem is that by invoking the mathematics of ideal gases, econophysicists vastly underestimate the task at hand. Explaining the human economy from the bottom up is not like using particle theory to explain the temperature of a gas. It is like using particle theory to explain animal metabolism.

Let’s dig deeper into this metaphor. We can certainly reduce metabolism to energy transactions among molecules. But if you try using these transactions to deduce (from first principles) the detailed properties metabolism, you won’t get far. The reason is that animal metabolism involves an ordered exchange of energy, defined by complex interconnections between molecules. Sure, the chemical formula for respiration is simple. (It’s just oxidizing sugar.) But when you look at the actually mechanisms used in cells, they’re marvellously complex. (Check out the electron transport chain, the machine that drives cellular respiration.)

What econophysicists are trying to do, in essence, is predict the properties of animal metabolism using the physics of ideal gases. The problem is not the reduction to energy exchange between molecules. The problem is a foolhardy resynthesis. In gases, the exchange of energy is unordered. So we can resynthesize properties of the gas using simple statistics. But we cannot apply this thinking to animal metabolism. When you ignore the ordered connections that define metabolism, you resynthesize not an animal, but an amorphous gas.

Money metabolism

The metaphor of metabolism is helpful for understanding where econophysicists go wrong in their model of the economy. Take, as an example, the act of eating.

Suppose a baboon puts a piece of fruit in its mouth. What happens next is a series of energy transactions. We might think, naively, that we can understand these transactions using the physics of diffusion. So when the fruit hits the baboon’s tongue, the energy in the fruit starts to ‘diffuse’ into the tongue. Unfortunately, that is not how metabolism works. The fruit touches the baboon’s tongue, yes. But the tongue cells don’t get any energy (yet). Instead, the tongue passes the fruit down the throat, where a long and complicated series of energy transactions ensue (digestion, circulation, respiration). Eventually, some of the fruit’s energy makes it back to the cells of the tongue. But the route is anything but simple.

Something similar holds in the human economy. Suppose you want to buy a banana. One option would be to purchase the fruit from your neighbor. If you do, things are much as they appear in econophysics models. You ‘bump’ into your neighbor Bob, and give him $1. He gives you a banana. It’s a particle-like transaction.

The problem is that (almost) nobody buys fruit from their neighbors. If you want a fruit, what you actually do is go to a grocery store … say Walmart. And there the transaction is different.

True, in the Walmart things start out the same. You find some bananas and head to the check out. There you meet Alice the cashier. You give her money, she lets you leave with the bananas. It’s still a particle-like transaction, right?

Actually no. The problem is that when you hand your money to Alice the cashier, it’s not hers to keep. The hand-to-hand transfer of cash is purely symbolic. As soon as Alice receives the money, she puts it in the cash register.7 Later, a low-level manager collects the cash and deposits it in a Walmart bank account. From there, mid-level managers distribute the money, working on orders from upper management. Eventually, some of your money may end up back in Alice’s hands (as a pay check). But the route is anything but simple.

Think of this route as ‘money metabolism’. Alice ‘touches’ your money much like tongue cells ‘touch’ the energy in food. But like the tongue cells, which simply pass the food down the digestive tract, Alice passes your money into Walmart’s ‘accounting tract’. As with the food energy, the result is a complex web of transactions governed by many layers of organization.

Yes, you can cut out this organization and observe that the end result is that money changes hands. But that’s like taking animal metabolism and reducing it to diffusion. When you cut out the details, you effectively convert the organism to a placid pool of matter. Similarly, when you cut out the ordered web of transactions that occur within organizations, you convert the economy to an inert gas. It is a foolhardy resynthesis.

Resynthesizing mud

Many econophysicists will grant that their models oversimplify the economy. But they will defend this simplification on the grounds that it ‘works’. Their models reproduce, with reasonable accuracy, the observed distribution of income.

The appropriate response should be “Good, your model passes the first test. Now open the hood and keep testing.” The problem is that econophysicists often do not keep testing. They are content with their ‘good results’.8

To see why this is a bad idea, let’s use an absurd example. Suppose that a biology lab is trying to synthesize life. The scientists combine elements in a test tube, add some catalysts, and then look at the result. They first test if the atomic composition is correct. They look at the abundance of hydrogen, carbon and oxygen to see if it is consistent with life. Lo and behold, they find that the test tube has the same atomic composition as humans!

“We’ve synthesized a human!” a lab tech shouts euphorically. The other scientists are less optimistic. “We’d better do more tests,” they caution. Their skepticism is well founded. Looking further, they see that the test tube contains no tiny human. It contains no organs, no cells, no DNA. It’s the right composition of elements, yes. But the test tube contains nothing but mud.

Kinetic exchange models of income/wealth, it pains me to say, are the equivalent of mud. Yes, these models replicate the macro-level distribution of income and wealth. But they ignore all other social structure. That’s okay, so long as the model is just a stepping stone. But the tendency in econophysics is say: “Look! My kinetic-exchange model reproduces the distribution of income. Therefore, inequality stems inevitably from the laws of thermodynamics.”

Sure … just like humans stem inevitably from mud.

How far down?

One of the central tenets of the scientific worldview is that the universe has no maker. It is a system that has self assembled. The consequence of this worldview (if it is correct) is that complexity must have arisen from the bottom up. After the Big Bang, energy condensed to atoms, which formed molecules, which formed proteins, which formed cells, which formed humans, who formed global economies. (For an epic telling of this story, see Eric Chaisson’s book Cosmic Evolution.)

The ultimate goal of science is to understand all of this structure from the bottom up. It is a monumental task. The easy part (which is still difficult) is to reduce the complex to the simple. The harder part is to take the simple parts and resynthesize the system. Often when we resynthesize, we fail spectacularly.

Economics is a good example of this failure. To be sure, the human economy is a difficult thing to understand. So there is no shame when our models fail. Still, there is a philosophical problem that hampers economics. Economists want to reduce the economy to ‘micro-foundations’ — simple principles that describe how individuals behave. Then economists want to use these principles to resynthesize the economy. It is a fool’s errand. The system is far too complex, the interconnections too poorly understood.

I have picked on econophysics because its models have the advantage of being exceptionally clear. Whereas mainstream economists obscure their assumptions in obtuse language, econophysicists are admirably explicit: “we assume humans behave like gas particles”. I admire this boldness, because it makes the pitfalls easier to see.

By throwing away ordered connections between individuals, econophysicists make the mathematics tractable. The problem is that it is these ordered connections — the complex relations between people — that define the economy. Throw them away and what you gain in mathematical traction, you lose in relevance. That’s because you are no longer describing the economy. You are describing an inert gas.

So what should we do instead? The solution to the resynthesis problem, in my view, is to lower our expectations. It is impossible, at present, to resynthesize the economy from individuals up. So we should try something else.9

Here we can take a hint from biology. To my knowledge, no biologist has ever proposed that organisms be understood from atomic ‘first principles’. That’s because thinking this way gets you nowhere. Instead, biologists have engaged in a series of ‘hacks’ to try to understand life. Each hack partially reconstructs the whole.

Biologists started with physiology, trying to understand the function of the organs of the body. Then they discovered cells, and tried to reconstruct how they worked. That led to the study of organelles, and eventually the discovery of molecular biology. Along the way, biologists tried to resynthesize larger systems from parts — bodies from organs, organs from cells, cells from organelles, etc. They met with partial success.

When economists try to reconstruct the economy from ‘micro principles’, they are doing the biological equivalent of resynthesizing mammals from molecules. (Yes, the human economy is that complex.) The way to make progress is to do what biologists did: take baby steps. First look at firms and governments to see how they behave. Look at the connections between these institutions. Then look inside these institutions and observe the connections among people. Resynthesize in small steps.10

As we try to ‘hack’ our way to a resynthesis, we will probably fail. But we will fail less badly than if we tried to resynthesize society from individuals up. And hopefully, from our failure we will learn something. That’s science.

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  1. Interestingly, there are still people who deny that the Earth is round. (Check out the Flat Earth Society.) But where are the atom deniers? If they exist, they have no presence on the internet.
  2. It was around this time (the late 1990s) that physicists became obsessed with power-law distributions (which occur everywhere in the natural world, including in the economy). Joking about this obsession, computer scientist Aaron Clauset wrote in 2010:

    Look for me soon in Boulder drinking my coffee from a mug that advertises “I went to a physics conference and all I got was a lousy power law.”

  3. A historical note. After econophycists developed their ‘kinetic-exchange’ model of wealth and income, they discovered that a social scientist had beat them to the punch. In 1986, the sociologist John Angle had developed an identical model. Well, identical in mathematics at least. The narrative behind Angle’s model was quite different than the physicists’ appeal to gas particles. Angle’s model was based on the idea of surplus production proposed by Karl Marx. See Angle’s paper The Surplus Theory of Social Stratification and the Size Distribution of Personal Wealth.
  4. In his review of David Lindley’s book Boltzmann’s Atom, Leo Kadanoff writes:

    To treat many-particle systems, one must use a probabilistic approach and thereby give up elements of accuracy, specificity, and determinism. As pointed out by Lindley, and previously by Thomas Kuhn, Boltzmann was extremely reluctant to wed concepts of probability with those of mechanics.

    (Kadanoff, 2001)

  5. Technically it is not property per se that is bought and sold, but rather property rights. Whether you end up with something tangible is irrelevant. What you are actually buying is the right to exclude others from using/controlling what you own.
  6. I am being glib here to make a point about the simplicity of the system. The flip side is that Maxwell and Boltzmann were ingenious precisely because they focused on something ‘boring’. When most people see a gas in thermal equilibrium, they think nothing of it. That’s why for eons, no one thought to explain equilibrium. The key insight of thermodynamics is that thermal equilibrium (i.e. a boring system) needs an explanation.
  7. With digital transactions, the cashier never even touches your money. It goes straight to Walmart’s bank account.
  8. This ‘look at my results, not my assumptions’ sentiment is ubiquitous in economics. It was formalized by Milton Friedman in his essay The Methodology of Positive Economics. Friedman writes:

    … theory is to be judged by its predictive power for the class of phenomena which it is intended to “explain.”

    So far so good. But then comes the whopper:

    … a theory cannot be tested by comparing its “assumptions” directly with “reality.” Indeed, there is no meaningful way in which this can be done.

    This torturous reasoning cleared the way for economists to build models that gave ‘good results’, but were based on absurd assumptions. (Sidenote: George Blackford has a good piece that debunks Friedman’s reasoning. I’m sure there are many others.)

  9. By avoiding going ‘all the way down’ to individuals, I don’t mean to disparage all attempts to do so. Agent-based models, for instance, are useful thought experiments. That’s largely because when agents interact, simple assumptions about behavior often lead to unexpected results. We should absolutely investigate these assumptions. On that front, economist Tim Gooding is doing interesting agent-based work. See his book Economics for a Fairer Society.
  10. To be fair, there are empirical economists who study connections between and within institutions. But most economists are still taught (in Econ 101) that the ‘first principles’ of microeconomics explain the economy.

Further reading

Angle, J. (1986). The surplus theory of social stratification and the size distribution of personal wealth. Social Forces, 65(2), 293–326.

Chatterjee, A., Chakrabarti, B. K., & Chakraborti, A. (2007). Econophysics and sociophysics: Trends and perspectives. Milan: John Wiley & Sons.

Chatterjee, A., Yarlagadda, S., & Chakrabarti, B. K. (2007). Econophysics of wealth distributions: Econophys-kolkata I. Springer Science & Business Media.

Gallegati, M., Keen, S., Lux, T., & Ormerod, P. (2006). Worrying trends in econophysics. Physica A: Statistical Mechanics and Its Applications, 370(1), 1–6.

Hayes, B. (2002). Follow the money. American Scientist, 90, 400–405.

Kakarot-Handtke, E. (2013). Toolism! A critique of econophysics. Social Science Research Network.


  1. […] Figure 1 illustrates this counter-intuitive result. The top frame shows a simple model of a gas — an ensemble of billiard balls colliding in a two dimensional container. The collisions are uniform, in the sense that each particle has the same chance of gaining/losing speed. And yet the result, shown in the bottom frame, is an unequal distribution of speed. […]

  2. […] Figure 1 illustrates this counter-intuitive result. The top frame shows a simple model of a gas — an ensemble of billiard balls colliding in a two dimensional container. The collisions are uniform, in the sense that each particle has the same chance of gaining/losing speed. And yet the result, shown in the bottom frame, is an unequal distribution of speed. […]

  3. Well, in general the criticism is right, but I would not agree that econophysicists are happy with their results and stopped at there. And econophysics is not only about kinetic exchange, as I discussed in my recent book entitled “Income Distribution Dynamics of Economic Systems: An Econophysical Approach”, Cambridge University Press (2020), ISBN 9781107092532. There is more to econophysics modelling than just kinetic exchange.

  4. I tend to differentiate between chance and random events. If a dice is rolled, it is going to land on one of the six faces. As you mention, if all the variables are known it can be predicted. Since we do not have all the information we just say one particular face has a chance of 1 in 6 to turn up.
    On the other hand, we can not predict the mutation(s) that is going to happen in a DNA chain even though we have a good knowledge of all the chemical reactions causing a mutation. it is a random event and evolution is possible only because of it being random.

  5. Blair,

    Would it be okay if we reposted your work as often as once a week? We may not do it every week because we want to keep our readers from “taking you for granted”. We receive a Google Analytics report every week and so far you are getting a lot of page reads and the average reader is spending several minutes on your articles. Last week one of your articles received 57 page-read-hours. That was from 419 page-reads with an average of 8 minutes 11 seconds each. A “page” is the full article. Last week was the second week for that article; the first week was 22 page-read-hours with an average time of 2 minutes 10 seconds each for 619 page-reads. It is quite possible that some of the second-week page-reads were from people who bookmarked it the first week and returned to read it thoroughly.

    We increase intervals for authors if there seems to be a declining reader trend at the interval we have been using so we try to avoid “over-exposure”. We have between 20k and 25k unique individual visitors most months and that is not a huge audience.

    So, may we continue to repost your blogs?


    John B. Lounsbury Ph.D. CFP

    Managing Editor Econintersect.com

    Senior Contributor TheStreet.com

    Highly ranked author Seeking Alpha


    • Hi John,

      Yes, repost as often as you would like. I’ve been meaning to put Creative Commons licenses on my posts to indicate that they are freely shareable. It’s on my to do list.


  6. This is a fairly excellent article if combined with your previous ones–it sort of ‘fills in some gaps’ (or rather , takes the history closer to the present).

    Its excellently written, but still leaves some things out, and may ‘misrepresent’ a few ideas.

    (My articles, in contrast never leave anything out nor misrepresent anything.
    Maybe this is why haven’t been published —
    I just need to find the right publisher and someone to write my articles.)



    1. One of the 2 formal (as student or employee ) mathematical biology projects I (partially) did was to apply to a biological system (on the immune response ) a model for ‘phase transitions in water’ (ie freezing or boiling)

    (The model was s not one of the 2 main ones—
    which are by people at Cal Tech and U Chicago which use quantum field theory.

    The model i was using (which had already been used in immunology) was classical and ‘simplistic’ —
    basically a form of random graph theory–with complications.

    The water model was basically one step up from Boltzmann’s ideal gas model

    ie the ‘water atoms ‘ dont just ‘collide;’ they also ‘stick together’ at times—eg freeze into a solid —
    or fall apart into a ‘gas’–based on temperature. So they are special ‘temperature dependent’ atoms.
    In winter they freeze, in summer sun they turn into air.

    Immunology is another few steps up—
    antibodies and antigens are not ‘point particles’ , an ‘ideal gas’. or ‘water atoms’.

    Its more like DNA—which is not a random assemblage of ‘codons’ or ‘nucleotides’.

    Most books and human communication are closer to Boltzmann’s ideal gas model is my impression.

    Very occassionaly one notices a pattern in books and spoken communication —
    eg as if there is ‘meaning in the message’
    —but these seem to be just statistical outliers in a power law, exponential, gaussian or related distribution.

    In psychiatry one labels this ‘hearing voices’ or ‘seeing things that are not there’ or ‘making things up’.
    These conditions are treatable with expert help.


    2. The Brian Hayes article i think may be the best popular article on ‘econophysics’ written.

    I’d add that econophysics in math form goes back to P Samuelson in 1970’s , and a few other economists
    and physicists in same period. However only a few dealt of those dealt with income–others dealt with other parts of ieconomics.

    Some oif Yakovenko’s papers cite papers going even further back to maybe 1930’s .


    3. I personally live in a non-capitalist gift economy –similar to a hunter -gatherer or barter economy (adam smith, marx and engels, ricardo, proudhon …) but we have money and view it as a kind of gift or commodity .

    I think it grows on the money trees some plant to stop the global cooling or shield you from the wind and snow.
    (My relatives in N Dakota planted trees as ‘wind breaks’–these would be almost the only trees in the area. There are some (usually spruce , fir , cedar or a few others) trees which will keep out 80-99% of any snow or rain that is falling.
    money treess are like a fruit bearing treee–a cash crop.

    you can cut dthem down and sell the wood, but you can wait entil they grow mo0re money on them and then just collect it with a rake in the fall. and use it for fires, or give it away, or uby stuff

    –some people collect money .


  7. What is really behind this whole discussion is in fact theory assessment. This is a problem that is increasingly faced by theoretical physicists dealing with particle field theories, but it is also acutely present in economics, although most economists are not aware of that.

    On this respect I would like to call the attention to paper I wrote in collaboration several years ago regarding Ludwig Boltzmann’s epistemological viewpoints on the nature of scientific theories, entitled “Boltzmann’s Concept of Reality.” This paper is publicly available in the arXiv by following the link below.


    I extensively used Boltzmann’s viewpoints in the first chapter of my book “Income Distribution Dynamics of Economic Systems: An Econophysical Approach”, Cambridge University Press (2020), ISBN 9781107092532, to argue that economics needs urgently an epistemological perspective in order to avoid its theories going astray.

  8. Nice discussion. Perhaps it underestimates the complexity of an ideal gas and how diffusion works?

    Interactions between molecules in a gas are absurdly complicated. Even a supercomputer would get stuck past a few once accounting for the detailed quantum mechanics of molecular interactions. Just a horrible mess, no less horrible than interactions between, say, people.

    Yet, stat mech, works.

    I think it is extremely helpful to get a good handle on the equipartition principle and why it works, that in the end, by whatever means, all available degrees of freedom have the same energy density. This is important because it implies many poor and few rich, again by whatever means, and so inequality. It has to be this way because at equilibrium there are no pressure gradients to drive net diffusion of energy from one mode to another and create an imbalance. (Some invoke entropy maximization here, but meh…). Expressed in terms of kinetic energies the M-B distribution gets molecular inequality right – even before quantum mechanics was understood.

    Of course, equilibria are fictions, and systems evolve, but evolutionary timescales are longer typically than equilibration timescales, so equipartition still generally works. For people our daily timescales are much shorter than the approximately 30 year doubling timescale of our collective energy demands.

    As for diffusion, take a look at turbulent diffusion. Insanely complex again in its detailed filamented structure, but still described using such physical constructs as diffusivity, and linear equations for fluxes from high pressure to low pressure (or density, or temperature, but most generally pressure).

    In sum, people are complicated. Physical systems are complicated. And stat mech + simple diffusion theory take you where you need to go achieving the right results.

  9. @Tim Garrett The problem is that the Boltzmann distribution depends on certain statistical properties to obtain it: in particular, independent, identically distributed (IID) events as responsible for redistributing the energy. Collisions. That is, there are no noticeable correlations (“independent”) between different events, and the probability distributions for each event are the same every time. Even if you don’t know the exact derivation, you could almost catch that just by looking at the form – in momentum space, it’s a normal distribution, and while its converse is not necessarily true, that’s a good hint at least that the central limit theorem is likely involved. Each molecule receives an independent and identically distributed amount of momentum. Those all get added up, by conservation of momentum. You get a normal distribution in each of the three dimensions of space. Now do |p|^2/(2m) and voila, you get the energy distribution.

    What OP is saying is effectively that that is exactly what is blown out of the water. The following of a regular procedure by the actual individual agents in their store example, is the exact opposite of “independent” – in fact the whole idea of procedure is to maximize statistical dependence: if I must pass the money on to my manager, that means the three “people-molecules” – the customer, me, and the manager – involved are undergoing not just correlated, but ideally (i.e. I’m not feeling deceitful and pocket the money) maximally correlated, so totally dependent, sequences of exchange events! If you want a molecular analogy, biology’s a good one that the OP brought up; think of the electron transport process in the mitochondrion, those electrons are not being moved randomly.

    Hence, generally speaking, the IID assumption that would be required to treat “people as gas molecules” and derive inequality therefrom correctly, simply is absurdly false. Yes, the IID premise leads to the correct conclusion (inequality), but that doesn’t justify taking it: an argument can start from a false premise and still lead to a true conclusion.

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