Lecturing Birds on How to Fly Fallacy

The Evidence Staring at Us

It turned out that engineers, too, get sandbagged by historians.

I presented the joint paper I had written with Haug on the idea of lecturing birds on how to fly in finance at the London School of Economics, in their sociology of science seminar. I was, of course, heckled (but was by then very well trained at being heckled by economists). Then, surprise. At the conclusion of the session, the organizers informed me that, exactly a week earlier, Phil Scranton, a professor from Rutgers, had delivered the exact same story. But it was not about the option formula; it was about the jet engine.

Scranton showed that we have been building and using jet engines in a completely trial-and-error experiential manner, without anyone truly understanding the theory. Builders needed the original engineers who knew how to twist things to make the engine work. Theory came later, in a lame way, to satisfy the intellectual bean counter. But that’s not what you tend to read in standard histories of technology: my son, who studies aerospace engineering, was not aware of this. Scranton was polite and focused on situations in which innovation is messy, “distinguished from more familiar analytic and synthetic innovation approaches,” as if the latter were the norm, which it is obviously not.

I looked for more stories, and the historian of technology David Edgerton presented me with a quite shocking one. We think of cybernetics— which led to the “cyber” in cyberspace—as invented by Norbert Wiener in 1948. The historian of engineering David Mindell debunked the story; he showed that Wiener was articulating ideas about feedback control and digital computing that had long been in practice in the engineering world. Yet people—even today’s engineers—have the illusion that we owe the field to Wiener’s mathematical thinking.

Then I was hit with the following idea. We all learn geometry from textbooks based on axioms, like, say, Euclid’s Book of Elements, and tend to think that it is thanks to such learning that we today have these beautiful geometric shapes in buildings, from houses to cathedrals; to think the opposite would be anathema. So I speculated immediately that the ancients developed an interest in Euclid’s geometry and other mathematics because they were already using these methods, derived by tinkering and experiential knowledge, otherwise they would not have bothered at all. The Greeks had developed a steam-powered device some two millennia before the Industrial Revolution. It is just that things that are implemented tend to want to be born from practice, not theory.

Now take a look at architectural objects around us: they appear so geometrically sophisticated, from the pyramids to the beautiful cathedrals of Europe. So a sucker problem would make us tend to believe that mathematics led to these beautiful objects, with exceptions here and there such as the pyramids, as these preceded the more formal mathematics we had after Euclid and other Greek theorists. Some facts: architects (or what were then called Masters of Works) relied on heuristics, empirical methods, and tools, and almost nobody knew any mathematics—according to the medieval science historian Guy Beaujouan, before the thirteenth century no more than five persons in the whole of Europe knew how to perform a division. No theorem, shmeorem. But builders could figure out the resistance of materials without the equations we have today—buildings that are, for the most part, still standing. The thirteenth-century French architect Villard de Honnecourt documents with his series of drawings and notebooks in Picard (the language of the Picardie region in France) how cathedrals were built: experimental heuristics, small tricks and rules, later tabulated by Philibert de l’Orme in his architectural treatises. For instance, a triangle was visualized as the head of a horse. Experimentation can make people much more careful than theories.

Further, we are quite certain that the Romans, admirable engineers, built aqueducts without mathematics (Roman numerals did not make quantitative analysis very easy). Otherwise, I believe, these would not be here, as a patent side effect of mathematics is making people over-optimize and cut corners, causing fragility. Just look how the new is increasingly more perishable than the old.

And take a look at Vitruvius’ manual, De architectura, the bible of architects, written about three hundred years after Euclid’s Elements. There is little formal geometry in it, and, of course, no mention of Euclid, mostly heuristics, the kind of knowledge that comes out of a master guiding his apprentices. (Tellingly, the main mathematical result he mentions is Pythagoras’s theorem, amazed that the right angle could be formed “without the contrivances of the artisan.”) Mathematics had to have been limited to mental puzzles until the Renaissance.

Now I am not saying that theories or academic science are not behind some practical technologies at all, directly derived from science for their final use (not for some tangential use)—what the researcher Joel Mokyr calls an “epistemic base,” or propositional knowledge, a sort of repository of formal “knowledge” that embeds the theoretical and empirical discoveries and becomes a rulebook of sorts, used to generate more knowledge and (he thinks) more applications. In other words, a body of theories from which further theories can be directly derived.

But let’s not be suckers: following Mr. Mokyr would make one want to study economic geography to predict foreign exchange prices (I would have loved to introduce him to the expert in green lumber). While I accept the notion of epistemic base, what I question is the role it has really played in the history of technology. The evidence of a strong effect is not there, and I am waiting for someone to show it to me. Mokyr and the advocates of such view provide no evidence that it is not epiphenomenal—nor do they appear to understand the implications of asymmetric effects. Where is the role of optionality in this?

There is a body of know-how that was transmitted from master to apprentice, and transmitted only in such a manner—with degrees necessary as a selection process or to make the profession more respectable, or to help here and there, but not systematically. And the role of such formal knowledge will be overappreciated precisely because it is highly visible.