The Law of Flow is Everywhere

Once You See Bejan's Constructal Law in Action, You Will Always See It

Alex Diaz at Unsplash

The despot is not a man. It is the Plan. The correct, realistic, exact plan, the one that will provide your solution once the problem has been posited clearly, in its entirety, in its indispensable harmony.   - Le Corbusier

Adrian Bejan is a Romanian-American who grew up under Nicolae Ceaușescu’s brutal central planning regime. Trained in mechanical engineering, Bejan somehow bridged his love of physics and his yearning for freedom. He never lost that yearning after 1989—the year the Romanian people removed Ceaușescu.

Six years later, flying back to the US after attending a conference in France featuring the esteemed Ilya Prigogine, the penny dropped for Bejan.

It niggled Bejan that Prigogine had claimed the branching of dissipative structures is coincidental. But Bejan’s consternation and some cabin pressure led to an idea:

The universal tendency of flow systems is to morph into evolving configurations that provide greater and easier access over time.

Bejan’s now-famous “constructal law” operates in all living systems on earth. Its tell-tale sign is vascularization. Just imagine how the following systems are configured:

• River systems with tributaries, streams, and brooks.

• Human bodies with hearts, veins, and capillaries.

• Transportation systems with highways, roads, streets, and alleyways.

• Trees with trunks, limbs, branches, and twigs.

• Firms as large, medium, and small businesses.

All living systems, to continue living, have to accommodate energy flows.

The beauty of Bejan’s Law of Flow is that it explains the form and function of living systems in physical terms.

I appreciate the Law of Flow enough to open After Collapse thus:

In the Amazon, far below the rainforest canopy, a network of roots stabilizes a thick trunk. Mirroring the branches and twigs among the leaves above, the roots below split into smaller roots, which split into yet smaller roots, extending outward to absorb water. All that water gets stored in the tree's cells. 

A few miles away, a mighty river rushes. The river carries watercraft and fish, a few large and many small, inexorably toward a delta. What feeds the great river are smaller rivers, Apurimac and Mantaro, then tributaries, which are fed by streams, which are fed by brooks, which are fed by sources high in the Peruvian Andes. 

Navigating the river early in the morning, an old woman goes fishing. Her body contains a system of veins and arteries that carry blood, enriched or depleted, to nourish every cell in her body. Likewise, her brain and limbs are animated by information signals within a network of nerves. These signals have to be processed by an organ of fractal complexity, or the old woman will be unable to navigate much less fish.

Everywhere in the world, we see these sorts of living systems. They display the property researchers Adrian Bejan and Sylvie Lorente refer to as "few large, many small.” This stunning vascularization of everything means that even inorganic systems can have a kind of life, where life is defined as accommodating currents of flow and change. Living systems are thus flow systems. And if a system is no longer able to deal with currents of flow and change, it dies.

We can say the same of human systems. To the extent that a human system can accommodate flow is the extent to which it will persist in time--that is, to live. In some fundamental sense, this idea, strange and wonderful, is the guiding idea of this work.

This framing, of living systems as flow systems, has everything to do with collapse and renewal.

If Bejan is right, this is one of the world's most important—and, indeed, undeniable—features. It bundles Hayek's insights, Mandelbrot's mathematics, and Darwin's biology to a new, unified theory.

But how?

First, it means that evolution has directionality. That is to say, there is a tendency for systems to evolve in certain ways over time. This extends Darwinian evolution in ways that have implications for biology and society.

Second, it means that the “fractal” patterns in nature are not random as Prigogine thought. Natural fractals have explanatory backing in constructal theory, as fractal patterns tend to accommodate flow.

Third, market economics has a whole new functional justification rooted in physics. The idea of natural law has been something of a patch-quilt concept for classical liberals in their attempts to justify free markets. Hayekian spontaneous orders are familiar to us and offer a functional justification for free markets. But we can now build on Hayek.

This article by Ephrat Livni offers a concise overview of Bejan’s work as it applies to the distribution of wealth:

Recently [Bejan][ published a paper in the Journal of Applied Physics, arguing that wealth inequality is inevitable because of, and can even be predicted by, constructal law. That’s because the distribution of all things—across the social, political, and economic worlds—is determined by vascular patterns, like those of tree branches or river tributaries, Bejan says. They fork and morph to create new streams, naturally. And, naturally, these branches and tributaries are unequal.

That last point is vital. No living systems are “equal,” but instead evolve in organic hierarchies, that is, vascular systems. Livni continues:

Bejan illustrates that hierarchy is unavoidable using Horton’s law of stream numbers, which says that three to five tributaries emerge over the lifetime of a mother stream. As the mother streams calve and then the next generation of tributaries in turn calves again, uniformity disappears. When Horton’s law’s multiplier is applied to the movement of wealth in a society, Bejan says, even modest complexity—five families in a tiny village, for example—leads to a non-uniform distribution of wealth.

I wouldn’t want to derive an "ought" from an "is," but I do want to argue we have a new set of important reasons for questioning economic interventionists and egalitarians. Smith’s invisible hand designs a vascular flow system.

Bejan from his TEDx talk on Time and Beauty

Interventionists constrict, distort, or destroy economic flows, otherwise developing from the bottom up according to the Law of Flow. If you try to reconfigure a natural system according to some technocratic plan, you will likely kill it—as its vascularization keeps the ecosystem alive.

“Freedom is good for design,” writes Bejan.

Design in this context is a noun, not a verb. Livni, once more, thinks Bejan is an accidental Taoist:

The Tao advises we be like water and flow among currents instead of against them; in the Tao Te Ching, as in the constructal law, accommodating forces and morphing willingly is key to evolution. Resistance constricts flow and blocks growth.