*Warning: Slightly excessive pedantry.*

You’ve probably read about or heard of Enrico Fermi at some stage in life. Italian physicist that moved to Columbia University to escape Fascism in the 1930’s and engineered the first nuclear pile at the University of Chicago. There is an element and a national laboratory named after him. He became a part of the Manhattan project and the Los Alamos tests.

An intriguing story though is the tale of Enrico Fermi dropping bits of paper one by one, as the blast wave passed by about 9 km away from the Trinity epicenter on July 16, 1945. The bits of paper (dropped from a height of about 6 ft) displaced horizontally by about 2.5 meters when the wave passed. The blast wave reached Fermi about 40 seconds after detonation. From those observations, he estimated the TNT equivalent of the first nuclear detonation at 10 kilotons of TNT. He was close. The estimate from calculations stemming from results of several instrumental readings is about 20 kilotons.

It is difficult to know whether Fermi made that estimate from purely theoretical calculation or from extrapolating empirical measurements from smaller tests done at Los Alamos. He did not say. Might have been just a wild hair.

You can read some folks attempts at rationalizing his calculations at this site.

That sort of order-of-magnitude estimate has become known as a Fermi estimate or calculation. There are a few books and essays on the subject.

It is probably a skill that can be taught, but it is also probably a skill that is learned by almost everyone that works in one particular field for a while; it is the human brain distilling something down to something a little simpler. Just takes a little motivation.

Perhaps one of the more famous Fermi calculation demonstrations is to ask the question “How many piano tuners are there in Chicago?” So you inquire “How many people are there in Chicago?”, “What fraction of those folks own pianos?”, “How often do pianos need tuning?”, “What fraction of piano owners are dedicated?” You can tweak the calculation, but that gets you started.

Another of the more famous estimation discussion concerns the existence of extraterrestrial, intelligent life. That topic is often called the Fermi Paradox.

The famous quote is “Where is everybody?”

**Order-of-Magnitude Estimation**

Doing simple arithmetic on a napkin is cool. Doing it with a machine is cool. Doing it in your head without even trying is cooler. Fermi probably excelled at the latter.

Although being able to do the arithmetic in your head is probably a good thing, it is also fun to have certain numbers at ready. All of the following quantities can be estimated in a somewhat Fermi–like fashion. So see if you can get within a factor of 100 for each of them.

**Number of Water molecules in a human body: 10**^{27}

* 70 kg body that is mostly water; water molecules with 18 g/mole; *

* Avogadro’s number*

**Number of stars in the universe: 10**^{22}

^{ }100 billion galaxies x 100 billion stars/galaxy

**Number of neurons in a human brain: 10**^{11 }

* About a 1 liter brain with neurons that are 100 µ**m by 10 µ**m x 10 µ**m*

It is useful in those sorts of calculations to have a familiar relationship with the idea that adding exponents is like multiplication and that subtracting exponents is like division. That sort of thing is the basis of the lost art of using a slide rule or logarithm tables. I just recovered a slide rule from a box that was my father’s. I myself was sort of on the cusp of the slide rule / calculator ages. Perhaps a waste of time to play with, but slide rules hardly ever malfunction.

** Recommended Additional Reading**