Back-of-the-envelope calculations are one of our chief tools as scientists. When you spend most of your time wondering if your latest measurement is correct, having a tool to check if the numbers make sense is simply priceless. If you are lucky, a good estimate might just avoid a costly or laborious measurement — this is very common in disciplines like chemical engineering, which a friend described as “the art of estimating numbers and plugging them into some variation of Bernoulli’s continuity equation”. Unsurprisingly, these Fermi problems are now common interview questions at major consultancy and tech companies, and have even started to go viral.
Last week, I thought I would ask my biochemistry students to solve a back-of-the-envelope problem as part of their tutorial work. Disguised as an enzyme catalysis problem, I asked them to estimate the energy of a single hydrogen bond. Needless to say, they were puzzled. Some of them asked if I had forgotten to include some information in the problem sheet. For some reason, Fermi problems seem to be less common in chemistry and biology that they are in physics of engineering. Of course, estimating the energy of a hydrogen bond is in many ways much harder than guessing the number of ping pong balls that fit a Boeing 747. Nobody has seen a hydrogen bond in the flesh. And our minds struggle to grasp the vast numbers present at the molecular level. Nevertheless, guesstimates are incredibly useful
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