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Fermi's Piano Tuner ProblemAs a lecturer, Enrico Fermi used to challenge his classes with problems that, at first glance, seemed impossible. One such problem was that of estimating the number of piano tuners in Chicago given only the population of the city. When the class returned a blank stare at their esteemed professor, he would proceed along these lines:
This method does not guarantee correct results; but it does establish a first estimate which might be off by no more than a factor of 2 or 3--certainly well within a factor of, say, 10. We know, for example, that we should not expect 15 piano tuners, or 1,500 piano tuners. (A factor of 10 error, by the way, is referred to as being 'to within cosmological accuracy.' Cosmologists are a somewhat different breed from physicists, evidently!!!) |
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