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Fermi problems and b***sh*t filtration

By Robert Merkel - posted Wednesday, 9 January 2008


And how many pianos can a tuner service in a year? A tuner might tune five pianos a day; tuners work five days a week, 50 weeks a year (yes, 48 is more realistic, but you may as well round off); therefore one tuner would tune about 1,250 pianos a year.

Therefore, all we need to do divide the number of tunings required, by the number one tuner can do each year: 60,000÷1,250, do a bit more rounding-off, and get an estimate of about 50 piano tuners.

As it turns out, a check of the Yellow Pages website suggests that there are 137 piano tuners and repairers in Melbourne; clearly, my Fermi problem skills are not as good as Fermi’s! However, through a little bit of calculation, it was possible to get an estimate that was within a factor of three of the more precise figure - and, for many purposes, it’s good enough.

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If somebody came to me with a proposal to produce a full-color glossy magazine aimed specifically at the piano tuners of Melbourne, I’d be extremely sceptical of the feasibility of making money from it, just on the basis of my Fermi, or “back-of-the-envelope”, calculation.

In my own particular line of work, the quantities I am most interested in estimating are the amount of time it will take for a computer to do something, and how much RAM or disk storage will be required along the way.

Quite often, I just want to know whether I have to worry any further about the time taken or not. So this leads a particular kind of back-of-the-envelope calculation, the upper bound - where I calculate a figure that must be higher than the actual quantity (of course, sometimes you want the opposite - a lower bound). For instance, if I know that my computer program will take 0.001 seconds, at most, to get an answer, I don’t care whether the actual time is 0.0001 or 0.00001 seconds.

Of all the skills I learned in my years of education, the ability to tackle Fermi problems is one of the most useful in daily life; it’s also damn handy in blog arguments. More seriously, I don’t see how one can tackle a lot of public policy debates without it.

Numbers ain’t everything, but for a lot of contemporary issues - particularly environmental ones - they are one of the most important things. Should we throw out appliances before the end of their useful life to replace them with more energy-efficient ones? Does drinking French wine, shipped half way round the world, instead of the local variety make a significant difference to global warming? Can we cut the demands on our dams significantly with water tanks?

I wouldn’t for a moment claim that back-of-the-envelope calculations are a substitute for detailed quantitive studies. Nor, would I make the ridiculous assertion that everything can be reduced to numbers. But, to me, Fermi-style estimation is an essential bullshit-filtering tool.

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Which brings me to something I’ve always wondered about. How in the hell do people who haven’t done first-year uni physics cope without the immense utility of envelope backs?

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First published at Larvatus Prodeo on June 26, 2007.



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About the Author

Robert has a blog called The View from Benambra. He is a postdoctoral research fellow (in software engineering) at Swinburne University of Technology.

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