# XKCD's brilliant explanation of Fermi Estimation

Aw geez. I hear my mathematician wife talking about the Fermi Estimation and until today I was blissfully ignorant of what it meant.

The end of an era, thanks to XKCD.

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Phineas & Ferb did itâ€¦

Speaking of covering the earth in paint, each time I see the Sherwin Williams logo, I wonder when theyâ€™ll change it. I mean, in this day and age, this image isnâ€™t exactly â€śgreen.â€ť

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That logo is hilariously ominous. Not only the phrase â€ścover the Earth,â€ť but the way itâ€™s set in bold, uniform, almost fascistic characters not unlike the â€śKeep Calmâ€ť poster, and on top of that plastered over red dripping paint thatâ€™s indistinguishable from cartoon blood.

Freshman year physics, my first homework problems was a set of Fermi estimates. Ah, memories.

Then, in my 2nd semester math class, my professor told us about a time he went to buy paint for his living room. He accidentally calculated the volume instead of the surface area, and bought enough paint to cover 9,000 square feet of wall (30x30x10) instead of 1000 (30104). Unrelated, until now.

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I just noticed that Fermium is element #100. Fitting.

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All joking aside, a Fermi estimate is one of the most powerful techniques an amateur or professional physicist can have. By bounding a question between orders of magnitude, you can determine if it needs to be investigated with more rigor or dismissed outright.

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I remember an ancient, drunken, and animated discussion about how much the space shuttle weighted, in Caterpillar D-9 tractor units. I finally looked the answer up just today. We were very surprisingly far off, or maybe itâ€™s just the answer thatâ€™s very surprising.

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Memories of going down to Rippon, WI for the Science Olympiad, but that was a billion parsecs agoâ€¦

Most of these estimates seem like they could be pretty far off. The average price per square meter of the worldâ€™s real estate is probably way lower than the average price per square meter of a US house. The number of cans of paint or light bulbs you see in a store in your area probably has more to do with selection than overall quantity. At any rate, people use paint and light bulbs at different rates: in the UK a lot of people use wallpaper, in Germany rented houses need to be freshly painted in white before you leave them (and are probably often painted in other colors shortly afterward once the new tenants arrive). Most paint for large buildings wonâ€™t come from duty As Randall mentioned, many things that arenâ€™t buildings are painted. When I worked on a ship, we were constantly painting the steel with multiple coats, each of which were a lot thicker than house paint. When we cover the earth with paint, are we assuming that itâ€™s a prepared, uniform and non-absorbant surface (i.e. a fictional area of plastered wall the size of the earthâ€™s surface area)? Heâ€™s probably right that there hasnâ€™t been enough paint to cover the earth, but I think even with the Fermi estimation youâ€™d need to base it on less local data and be clearer about the amount of paint per unit area you actually need.

Doing my physics degree we spent a surprisingly large amount of time on estimates, there was even exam questions where you would be penalised for being too precise in your working.
We always tended to use the first significant figure rather than just nearest order of magnitude, slightly more precise but still almost as easy to calculate quickly.

â€śWithin and order of magnitudeâ€ť is the physicist version of â€śclose enoughâ€ť.

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BP has been trying to buy this logo for years.

Thus proving the old adage, â€śItâ€™s a small world, but I wouldnâ€™t want to have to paint it.â€ť

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