Eiffel’s Tower and the Lesson from the Trees

David Klinghoffer

Eiffel Tower.jpg

When Thomas Edison visited the Eiffel Tower in Paris, not long after it first opened in 1889, he left a memorable inscription in the guestbook. Edison paid tribute to the tower’s designer, engineer Gustave Eiffel, for devising “so gigantic and original specimen of modern Engineering, from one who has the greatest respect and admiration for all Engineers including the Great Engineer, the Bon Dieu” — that is, the “good God.”
The Eiffel Tower was in the news last week, if tangentially, when NPR noted a curious fact about the inspiration the lies behind its design. Eiffel himself drew on a biomimetic theory going back now 500 years to Leonardo da Vinci. Biomimetics, as Casey has pointed out here on more than one occasion, is the approach to human technology and engineering that looks to models in nature for superior structures even as, by a rigid convention and in defiance of all intuition, nature’s brilliance is always attributed to unplanned and unenvisioned causation — evolution — rather than to intelligent design.
No one sensible would say that the striking fruitfulness of this approach “proves” ID but it is, well, striking. Why pretend that that’s not so?
Eiffel wanted to make sure his 1063-foot tower, commemorating the 100th anniversary of the French Revolution, would be resistant to high winds. The best design for wind resistance comes to us from trees and, in particular, the mathematical relationship of surface area between mother and daughter branches, a very specific relationship first worked out by Leonardo da Vinci. That’s the conclusion of UC San Diego physicist Christophe Eloy, whose recent article in Physical Review Letters is the occasion for NPR’s report.
Writing under the title “Leonardo’s Rule, Self-Similarity, and Wind-Induced Stresses in Trees,” Eloy put Leonardo’s rule succinctly this way: “When a mother branch branches in two daughter branches, the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch.”
Don’t miss this wonderful irony: In engineering his now iconic monument, built to celebrate a revolution that sought to displace any idea of a designing being behind nature or anything else, Eiffel looked to Leonardo who looked to the trees. In commenting on the startling source of inspiration, NPR’s reporter, Joe Palca, chose not to go with the usual attribution to mindless evolution, trite and unconvincing as it is.
He opted instead for a jokey references to trees designing themselves:

From an engineering point of view, if you wanted to design a tree that was best able to withstand high winds, it would branch according to Leonardo’s rule.
Apparently, trees have figured out the sophisticated engineering principles all on their own.

Which is a punt if ever there was one, but understandable. What else what was he going to say? That trees, like the Eiffel Tower, are…engineered?
Photo credit: Simon Forsyth.