On Growth and Form and Constructal Theory

November 13, 2008 2:17 AM

On Growth and Form (1917) was D'Arcy Wentworth Thompson's pioneering effort to explore the mathematical principles that underlie biological form. He studied the similarity between the shapes of a jellyfish and a drop of ink, a splash and a hydroid, between dragonfly wings and bubble froth, the growth of radiolaria and snowflakes, the spirals of nautilus and mollusk shells and sheep horns. More recently, Adrian Bejan's Constructal Theory aims to explain all biological shape from one thermodynamic principle. This month there is an interview with Bejan for the layman.

The central principle of Constructal Theory - for a finite system to persist in time (to live) it must evolve so currents can flow easier through it - has been used by Bejan and his coworkers to predict the structure of trees and other natural networks (such as why a river looks like a tree), to understand running, swimming, and flying (PDF), to explain why university rankings won't change, and generally, to think about the design of every thing that flows and moves.

You can learn more about Constructal theory from TreeHugger's four articles, from the Constructal Portal, and from Bejan's books. Bejan's website lists his (over 450) academic publications.

posted by twoleftfeet (16 comments total)

Alan Turing did some interesting work on morphogenesis, inspired and influenced by Thompson.
posted by Phanx at 2:29 AM on November 13, 2008 [3 favorites has favorites]

Is there a smaller (than 57 MB) PDF somewhere?
posted by pracowity at 3:20 AM on November 13, 2008

Which PDF are you talking about? For me, the "running, swimming, and flying" PDF is under 1 meg.
posted by twoleftfeet at 3:28 AM on November 13, 2008

Sorry, I get now that you're talking about the 57 MB B/W "On Growth and Form". That book was monumental in more than one sense; it's around 1000 pages. But try the Internet Archive's streaming Flip Book.
posted by twoleftfeet at 3:34 AM on November 13, 2008

Hi,
Can I double-favorite posts?
Thanks.
posted by krilli at 3:52 AM on November 13, 2008

Cool, I've been meaning to read On Growth and Form for awhile now. This random evolution week on Mefi is great.
posted by afu at 4:31 AM on November 13, 2008

@afu:
Yeah, this ... randomly evolving random evolution week is very interesting.
posted by krilli at 5:37 AM on November 13, 2008

Thanks for this, twoleftfeet!

If I may add, D'Arcy Wentworth's stately prose is beautiful. He "grows" his arguments in cadences that develop seemingly organically.
posted by subatomiczoo at 6:24 AM on November 13, 2008 [1 favorite has favorites]

The beauty of Thompson's prose could have come from his experience as a classics scholar. For example, he translated Aristotle.
posted by twoleftfeet at 6:42 AM on November 13, 2008 [1 favorite has favorites]

A true gentleman, it seems.
posted by krilli at 6:45 AM on November 13, 2008

On Growth and Form is my favorite snobby science book EVER, my copy requires a strong classical education since Thompson includes untranslated quotations in German, French, Latin and Greek in the introduction. I think I inherited it from my grandfather, maybe the modern edition includes footnotes.
posted by garbanzo at 8:38 AM on November 13, 2008

yuk. explaining why trees form like rivers is one thing, but to explain elite/power relations that flow through culture (like university rankings) through mathematics is very distasteful to me.
posted by yonation at 8:42 AM on November 13, 2008

yuk. explaining why trees form like rivers is one thing, but to explain elite/power relations that flow through culture (like university rankings) through mathematics is very distasteful to me.

Why do you find sociology distasteful? I'm not sure if this particular theory holds water, but you can describe a lot of things in culture through scientific thought.
posted by demiurge at 10:41 AM on November 13, 2008 [2 favorites has favorites]

demiurge, i'm an anthropologist. a lot of our work revolves around questioning the modeling, quantitative, and postivist basis of sociology. this is not because it doesn't have its merits, but its usefulness in describing (and intepreting) culture and cultural change is not only rife with errors, it is part of a very particular western tradition. people, for instance, may preserve university rankings not just because of modelable issues. you have to account for how power transmits, how elites preserve their cultural status, what kind of branding certain kinds of rankings have (and therefore why they are respected), how much students believe in them as their sustaining power, etc.
posted by yonation at 3:05 PM on November 13, 2008

...it is part of a very particular western tradition.

And therefore evil?

...not just because of modelable issues. you have to account for how power transmits, how elites preserve their cultural status, what kind of branding certain kinds of rankings have (and therefore why they are respected), how much students believe in them as their sustaining power, etc.

And why are these necessarily unmodelable?
posted by DU at 5:17 AM on November 14, 2008

I love the headline on that university rankings thing:

Physics Explains Why University Rankings Won't Change
Constructal theory of flows governs social phenomena like rankings

Uh-huh, sure. Bejan's popsci explanation seems ridiculous enough:

According to the theory, the hierarchy of university rankings -- in which few schools consistently land at the top and many more contend for lesser spots -- persists because that structure supports the easiest flow of ideas, Bejan reported..."This hierarchy is here to stay," Bejan said in an interview. "The schools at the top serve everybody well because they serve the flow of ideas. We're all connected."

There's been a lot of this kind of overreaching in the past, DU, and while I admit I can't do a detailed critique without reading the full article or his new book, I'm leaning heavily toward skepticism about any "Constructal Theory of Social Dynamics" that actually explains complex social phenomena like "business, crowd dynamics, legal systems and written languages, among other human endeavors." We are nowhere close to being able to identifying all of the variables in that kind of social complexity, let alone model them accurately. Dejan's work with nature is fascinating to this former biology/anthropology major, but the leap he seems to be making has been made by many other folks before him, and pretty much all of them have fallen far short of the mark.

After studying a few decades - hell, centuries - of that, you start to look at this stuff very, very skeptically.

Great post, though.
posted by mediareport at 8:47 AM on November 16, 2008