Tree vs human. Photo by Gilly Stewart on Unsplash.

Milton Friedman and the surprising rationality of trees

In one of the most famous essays of 20th century economics, one of its most famous protagonists offers an astounding hypothesis on tree growth, just to dismiss it out of hand. Indeed, the dismissal is understood to be mutual between author and reader, as it sets up the author’s intellectual tour de force.

Even if the premise is wrong, the conclusion can still be correct as long as it is congruent with the empirical findings. There is no such thing as a false assumption, even if it is as outlandish as positing that trees are rational actors. There are only empirical discrepancies between prediction and reality.

The famous author is Milton Friedman, the essay is his famous The Methodology of Positive Economics, and his readership includes some 15,000 scholars who cite the essay, mostly approvingly. It changed modern economics.

Consider the density of leaves around a tree. I suggest the hypothesis that the leaves are positioned as if each leaf deliberately sought to maximize the amount of sunlight it receives, given the position of its neighbors, as if it knew the physical laws determining the amount of sunlight that would be received in various positions and could move rapidly or instantaneously from any one position to any other desired and unoccupied position. Now some of the more obvious implications of this hypothesis are clearly consistent with experience: for example, leaves are in general denser on the south than on the north side of trees but, as the hypothesis implies, less so or not at all on the northern slope of a hill or when the south side of the trees is shaded in some other way. Is the hypothesis rendered unacceptable or invalid because, so far as we know, leaves do not “deliberate” or consciously “seek,” have not been to school and learned the relevant laws of science or the mathematics required to calculate the “optimum” position, and cannot move from position to position?

— Milton Friedman, The Methodology of Positive Economics, 1953.

But do we actually know that trees are not rational actors in Friedman’s sense? Apart from accepting that trees didn’t go to school and didn’t learn calculus there, the observed behavior of grown trees matches his hypotheses remarkably well.

So we shouldn’t quite dismiss such a theory out of hand. And as it turns out, the literature in forestry about tree growth is quite voluminous, even if admittedly mostly younger than Friedman’s 1953 essay.

Circumnutation and trees as deliberate seekers

One of the basic laws of operations research is that in any optimization program, corner solutions are rarely optimal and interior solutions are often hard to locate.

This basic law has its equivalent in economics in Rudi Dornbusch’s overshooting model, which posits that exchange rate volatility is often driven by overeager attempts to reach such an interior market-clearing equilibrium.

Even human behavior outside the economic realm often exhibits this kind of circling around the equilibrium point, as mobility researcher have known for some time. Drivers don’t hold an “optimum” distance to the preceding vehicle, they cycle within a posited distance window.

Trees are rooted, so they don’t quite have the same range of motion as a human to optimize distance. But somewhat surprisingly they use whatever range they have to optimize growth in a process called circumnutation.

Circumnutation, the observable rotating motion of a growing single-stem plant, is still not fully understood, but its analysis goes back to a scholar even more famous than Friedman: Charles Darwin, who prominently described it in his penultimate book The Power of Movement in Plants.

It can’t escape notice that this spiralling motion might serve the purpose, if not of single leaves individually trying to optimize sunlight exposure, but the tree itself optimizing leaf placement in an recurring data collection process about the availability of resources (sunlight) and restrictions (other nearby plants).

So maybe Milton Friedman wasn’t as far off as he, and his readers, thought.

Canopy disengagement and forest growth as collective action

Moving from micro to macro analysis, the first question that should be asked is “why forests?”

We know that trees grow both solitarily and collectively, but it is not as apparently obvious why and where trees find it more convenient to congregate, given that competition between trees, and plants in general, can be quite intense.

The first approximate answer is that as always, the choice is one between tradeoffs. Solitary growth offers uncontested exposure to both sunlight and soil nutrients, but forest growth offers protetion from wind forces.

The happy compromise forest-dwelling trees have come up with is known as canopy disengagement, or crown shyness. For reasons that are also still somewhat mysterious, trees keep their distance from each other.

Existing hypotheses offer branch abrasion as the situational competitive answer, or circumnutation as the strategic collusive answer. By scanning the immediate environment, trees learn early on where they might have unimpeded access to sunlight, and where they face fierce competition.

The surprising realization that trees engage in such behavior also opens the possibility that they are not only strategic rational actors, but also collective actors who use their ability to anticipate conflict to optimize their growth schedule.

Biosphere 2 and the speed-vs-strength conundrum

Both famous 20th century scholars, Milton Friedman and Buckminster Fuller are rarely invoked in the same essay. Yet we can’t avoid invoking the author of Spaceship Earth and the controversial systems science experiment he inspired, in asking the question what trees are actually optimizing for.

Started in 1987, Biosphere 2 was the most ambitious attempt so far to create a fully closed social ecosystem, erected in rural Oracle, Arizona. In its two widely publicized runs it was either an astounding success or a total failure, depending on who you ask.

For our purposes the most important experiment concerned tree growth. An early observation revealed that under the geodesic domes of Biosphere 2 trees grow faster than outside, soon followed by the observation that the indoor trees fell over before they reached maturity.

The post mortem analysis concluded that Biosphere trees lacked wind and as a consequence, never developed the stress wood needed to withstand wind sheer.

An open question, as Biosphere 2 is not yet a long-run experiment, is whether the trees might eventually evolve to grow fast without stress wood as the lack of wind inside the domes would make such a strategy evolutionarily optimal.

The more important point for us is that trees take the constraints of their environment into account when they devise their growth strategy, even if sometimes a technological shock can throw their strategy out of balance. But we shouldn’t claim that this can’t happen to humans.

Strategic trees and the seat of rationality

The premise I hope we can all accept is that trees don’t go to school and never learn calculus, yet there are many observations which posit that in certain situations, they act as if they did.

Friedman’s main argument is that we shouldn’t care, but that we should focus on whether theories engender testable hypotheses that withstand empirical scrutiny. Elsewhere he cites, somewhat dismissively, Thorstein Veblen’s equally famous caricature of the rational actor.

The hedonistic conception of man is that of a lightning calculator of pleasures and pains who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift him about the area, but leave him intact.

— Thorstein Veblen, Why is Economics Not an Evolutionary Science, 1898.

The somewhat surprising realization is that Veblen describes exactly what we just learned about tree behavior: circumnutation as oscillation, except he attributes it to the criticized conception of homo oeconomicus.

The question left for us then is where exactly do trees, and by corollary humans, undertake these lightning calculations? The answer cannot be that it’s exactly the same location in the brain where we do the calculations required of us in school or in business, as trees don’t have that faculty.

In consequence the answer has to be that all of nature optimizes at a physiological level below the where brain scans detect excitation when we solve math questions. And indeed often enough humans act very much in accordance with that realization.

Emerging research posits that life is an exercise in optimization to avoid negative surprise. We should follow this research with curiosity, all the time remembering that moment when Milton Friedman came close to the truth, just to steer away from it at the very last moment.




I write about how technology shapes the world we live in.

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Oliver Beige

Oliver Beige

I write about how technology shapes the world we live in.

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