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Math Trek

Flight of the Bumblebee

4:39pm, September 9, 2004
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"Like the bumblebee, they said it could never fly."

This statement appeared a few years ago in Popular Science, starting off an article about drag racing.

Indeed, the venerable line about scientists having proved that a bumblebee can't fly appears regularly in magazine and newspaper stories. It's also the kind of item that can come up in a cocktail party conversation when the subject turns to science or technology.

It's even the title of a book, Bumblebees Can't Fly by Barry Siskind, which offers self-help strategies for staying productive in busy, changing times. And Robert Cormier echoes the same idea in the title of his teen book The Bumblebee Flies Anyway.

Often, the statement is made in a distinctly disparaging tone aimed at putting down those know-it-all scientists and engineers who are so smart yet can't manage to understand something that's apparent to everyone else.

And the morals drawn from the tale are many, including the notion of persisting with a new idea in the face of dogmatic adherence to old standards and maxims.

Obviously, bumblebees can fly. On average, a bumblebee travels at a rate of 3 meters per second, beating its wings 130 times per second. That's quite respectable for the insect world.

How did this business of proving that a bumblebee can't fly originate? Who started the story?

One set of accounts suggests that the story first surfaced in Germany in the 1930s. One evening at dinner, a prominent aerodynamicist happened to be talking to a biologist, who asked about the flight of bees. To answer the biologist's query, the engineer did a quick "back-of-the-napkin" calculation.

To keep things simple, he assumed a rigid, smooth wing, estimated the bee's weight and wing area, and calculated the lift generated by the wing. Not surprisingly, there was insufficient lift. That was about all he could do at a dinner party. The detailed calculations had to wait. To the biologist, however, the aerodynamicist's initial failure was sufficient evidence of the superiority of nature to mere engineering.

Some accounts associate the story with students of physicist Ludwig Prandtl (1875–1953) of the University of Göttingen in Germany. Others identify the researcher who did the calculation as Swiss gas dynamicist Jacob Ackeret (1898–1981).

However, another thread of evidence points to French entomologist Antoine Magnan. In 1934, Magnan included the following passage in the introduction to his book Le Vol des Insectes:

Tou 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.

Magnan's reference is to a calculation by his assistant André Saint-Lagué, who was apparently an engineer.

What isn't clear is how this brief note in a scholarly book made its way into popular culture and how it came to be associated specifically with bumblebees.

Whatever its origins, the story has had remarkable staying power, and the myth persists that science says a bumblebee can't fly. Indeed, this myth has taken on a new life of its own as a piece of "urban folklore" on the Internet.

In some sense, the story has done its share to inspire further research. In recent years, scientists have tackled the problem of insect flight from a number of different angles and gained new insights into the complexities of powered flight.

Some of these researchers inevitably refer to the "bumblebees can't fly" story in their own remarks to the press and even in published reports, while pointing to the "new, improved" model to describe insect flight.

The persistence of the bumblebee myth also highlights a misunderstanding about science, models, and mathematics. The real issue isn't that scientists can be wrong. The real issue is that there's a crucial difference between a "thing" and a mathematical model of the "thing."

The distinction between mathematics and the application of mathematics often isn't made as clearly as it ought to be. In the mathematics classroom, it's important to distinguish between getting the mathematics right and getting the problem right.

It's quite possible, for instance, to calculate correctly the area of a rectangular piece of property just by multiplying the length times the width. Yet you can still get the "wrong answer" from a practical point of view, maybe because the measurements of the length and width were inaccurate or there was some ambiguity about the plot's boundaries or shape.

The word problems typically found in textbooks often serve as rudimentary models of reality. Their applicability to real life, however, depends on the validity of the assumptions that underlie the statement of the problem.

So, no one "proved" that a bumblebee can't fly. What was shown was that a certain simple mathematical model wasn't adequate or appropriate for describing the flight of a bumblebee.

Insect flight and wing movements can be quite complicated. Wings aren't rigid. They bend and twist. Stroke angles change. New, improved models take that into account.

Originally posted: March 29, 1997

Updated: Sept. 11, 2004

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