A Fermi Problem About Pharmaceuticals

6 January 2010 § Leave a Comment

Rebecca Skloot tweets the following question, which she asks on behalf of Melinda Wenner (@lindy2350):

Anyone know how I can find the # of people worldwide taking a particular class of drug?

This is an interesting problem, and as well it’s a nice example of what has come to be known as a “Fermi problem.” The physicist Enrico Fermi famously posed the question “How many piano tuners are there in Chicago?” to his students, to be answered without consulting any reference sources: the answer to the question must come entirely from “back of the envelope” calculations. A similar situation faces a scientist approaching a new problem. How much voltage will be required for a new apparatus, made for an experiment never performed before? What is the most critical quantity in a new, never-before-tested theory? How large an effect should be expected if our theory is correct? Even an estimate of the order of magnitude of the quantity of interest would be useful, since nothing is known about it. Fermi problems are intended to train a student to think about quantities whose values can be discovered and what their relationships are, so that the answer to the Fermi problem can be deduced.

I’d like to consider Melinda’s question, but first, I’d like to work through the piano tuners problem, direct readers to some more sites with Fermi problems, and describe an experiment conducted by Fermi with nothing more than scraps of paper and “back of the envelope” calculations—to measure the power of the first atomic bomb.

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