Title: Physics Toolbox 1: Logarithms and Fermi estimation Date: 14/09/2020 Category: Physics

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One of the interesting perceptions “hard sciences” tend to feature from outside is that they’re extraordinarily precise.

That’s certainly true, sometimes - but the thing is, that’s only when it has to be. Physics has a dirty secret: often, you don’t have to be, and sometimes it’s actively detrimental.

The best example of this is what are known as “Fermi problems” or Fermi estimations. You may have heard them in interviews. Essentially, you’re given a question you’d never have thought of before - how many piano tuners in great britain? say - and you’ve got to estimate it somehow. Really, even getting within a factor of two is unlikely, but that means you don’t need to sweat the details.

Eventually, you’ll end up with something like:

Pianos in the UK: 100,000 Frequency of tuning: 1/5 years. Time taken to tune: 1 day (including travel)

• maybe 2 a week, assuming it’s probably not a viable business to be a piano tuner if you’re doing less.

100000 * 1/5 * 104

You could round, but rounding and logarithms makes it even easier:

10^(5) + 210^(-1) / 10^2 = 210^(5-2-1) = 200 tuners. Alternatively:

cars in the UK: 3.610^7 mileage: 810^3 economy: 4*10^2

fuel: 3.6*8/4 * 10^(7+3-2) gal/year.

Let’s round 7.2 to 10, and keep a brief mental note that we’ve currently overestimated:

10^9 gal/year / 8.640010^4 * 3.6510^2 ~ 10^9 / 2.4 * 10^(4+2+1) 50 gals/s.

So, who cares? But the thing is, this on-the-fly stuff does matter. Yes, if you work for shell, you’ll have better data. But you may not. If, say, climate change matters to you, quick and dirty estimates of the yield per km2 of a solar farm, and the demands of the country you’re in, let you know if it’s feasible, marginal, or fantasy. That’s important, because there is no value in doing more detailed calculations on ideas that are not viable.