Of Bees and Spherical Chickens

In tackling problems in science and engineering, a vital tool in the problem-solving arsenal is making assumptions which simplify the calculations by ignoring or minimizing the contributions of factors which have little or no impact on the outcome. Examples of such simplifying assumptions include ignoring friction and air resistance, or, in the case of particle physics, ignoring the effects of gravity. So pervasive is the use of such simplifying assumptions, that it has spawned a joke which eventually made its way into an episode of CBS' "The Big Bang Theory." (Finally, a series about My People!) This practice of simplification even became fodder for an xkcd comic.



This practice of making simplifying assumptions can be extremely useful. It can transform calculations which might ordinarily require a supercomputing cluster into something that can literally be calculated on the back of an envelope. But it can be taken too far. There is something of an art to knowing what can be safely ignored and what actually has an impact, and it is largely experience which provides the proper guidance. When BP recently attempted to place a collection dome over the gushing well-head in the Gulf of Mexico, the effort failed because BP engineers had failed to take into account the fact that methane does not behave the same at such great depths as it does as standard temperature and pressure. As a result, the methane (at high pressures and low temperature) combined with seawater to form methane hydrate, essentially a methane ice, thus clogging the collection pipe.

There is another example of oversimplification and its consequences which is even more broadly known among the populace, the popular bit of folklore which states that science had once proven that bees cannot fly (despite obvious evidence to the contrary). Everyone has heard this little nugget, which has become so pervasive in our culture as to become a cudgel  for science-bashing, and several scholars have dug into the history of this tale to determine where it originated.

In the October 1996 issue of Physics World, an article appeared entitled "The strange case of the bumble-bee that flew" by Ken Zetie. In it, he wrote:

But how did the myth about bees not being able to fly start? When does the story date back to? J McMasters states that the story was prevalent in the German technical universities in the 1930s, starting with the students of the aerodynamicist Ludwig Prandtl at Gottingen. The story goes that a noted Swiss aerodynamicist, whom McMasters does not name, was talking to a biologist at dinner. The biologist asked about the flight of bees and the Swiss gentleman did a "back-of-the-napkin" calculation of the kind I described earlier, assuming a rigid, smooth wing and so on. Of course, he found that there was insufficient lift and went off to find out the correct answer. 

In the meantime, the biologist put the word around that bees could not fly, presumably to show that nature was greater than engineering, and the media picked up the story. The truth, then as now,  wasn't newsworthy, so a correction was never publicized. The people I meet, therefore, continue to tell me that science is a load of crock because it once proved that bumblebees cannot fly. And they will not hear otherwise, especially not from a scientist.

This "J McMasters" as it turns out was a Boeing aerospace engineer named John H. McMasters, who had earlier published an article about this very topic in the journal American Scientist: "The Flight of the Bumblebee and Related Myths of Entomological Engineering" (Am. Sci., Vol. 77, pp. 164-8). In an e-mail exchange discussing this article, McMasters reveals that he had been told that the Swiss aerodynamicist in question was one Jacob Ackeret, a well-established figure in the field of supersonic aerodynamics, but this could not be verified, so Ackeret's name was left out of the article. McMasters goes on to relate that, following the publication of his article, he was inundated with mail, including Xerox copies of page 8 of a French monograph on insect flight by the famed entomologist August Magnan, Le Vol Des Insects (Hermann and Cle, Paris, 1934), which contains the following line:

Tout d'abord poussé par ce qui fait en aviation, j'ai appliqué aux insectes les lois de la résistance de l'air, et je suis arrivé avec M. SAINTE-LAGUE a cette conclusion que leur vol est impossible.

En anglais, this reads:

Driven by the fact of aviation, I have applied the laws of the resistance of air to insects, and I arrived, with Monsieur Sainte-Lague, at the conclusion that their flight is impossible.

Mr. Sainte-Lague appears to be the mathematician André Sainte-Laguë, who was no light-weight in his field. Whoever originated this meme regarding the inability of bees to fly, whether it was Jacob Ackeret or the team of Magnan and Sainte-Laguë, we are talking about knowledgeable, credible scientists and engineers. How could such individuals reach such bizarre conclusions?

First of all, it should be pointed out that the account given by McMasters clearly depicts Ackeret (or whatever other Swiss engineer it might have been) clearly proclaiming his result with tongue firmly planted in cheek. He obviously recognized that assumptions he made in performing his back-of-the-napkin computations presented an overly-simplified analysis of an horrendously complex topic, thus leading to a clearly preposterous conclusion.  As for Magnan and Sainte-Laguë, no information is provided regarding their analysis, but it is fairly safe to assume (if you will pardon the conceit) that they also made the mistake of oversimplifying the problem. If one tries to analyze the wings of a bee as if they operated like aircraft wings, the lift they generate is clearly too low to allow flight. But bee wings don't work like aircraft wings.  Thanks to high-speed photography and more detailed analysis (taking into account the complexities of how bees actually fly, such as the constantly changing angle of attack of the wings), modern scientists have a very clear understanding of the dynamics of bee flight.

Yes, scientists and engineers do make mistakes, being human beings after all. (For a rather dramatic example, one need look no further than early 20th century naysayers of rocketry who illustrated their lack of understanding of Newton's Third Law and the Law of Conservation of Linear Momentum by claiming that rockets could not possibly work in space since they would have no atmosphere against which to react.) But the beauty of it all is that science, by its very nature, is a self-correcting mechanism.