How Many Licks and Other Fermi Problmes

You might remember the classic old commercial that poses the question "How many licks does it take to get to the center of a Tootsie Pop?" The wise old owl licks twice, bites one and proclaims the answer is three.

Now author Aaron Santos has taken a stab at the question in his new book How Many Licks? Or How to Estimate Damn Near Anything.

He takes on what are commonly called Fermi problems. Fermi problems are basically exercises in estimation. You take a problem, make a few quick reasonable assumptions, and try to figure out a reasonable (although not exact) answer. The legendary Fermi problem is Fermi estimating the strength of the atomic blast at Trinity by observing how far the blast wave blew some paper. Knowing how far away he was, he got a pretty good estimate of the strength of the blast.

I heard about this book on the podcast the Naked Scientists. Naturally, they had to estimate how many people are having sex in the world at any given moment (a question sure to get the attention of high school students!)

I used these when teaching. They are great exercises in creative thinking. You can probably do some if you give it a shot. How many gallons of gasoline are used each year in the U.S. by automobiles? Well, you have an idea of how many cars there are, how far the average U.S. driver drives per year (my car insurance statement tells me this!) about what the average fuel economy is and you can get a reasonable number with a basic four function calculator (and if you are only interested in the nearest power of 10, you might be able to do it in your head).

One of my favorites was when my students asked me if there was a google (a 1 followed by 100 zeroes) of atoms in the universe. I didn't know the answer but quickly started jotting down some figures on the board (average density of the universe, size of the universe), got out my four function calculator, and quickly pronounced no. Off by many powers of 10. I got about 10^79 atoms which puts me nicely in the range of accepted estimates.

Fermi problems also serve as a good B.S. detector. Earlier this year with Obama's stimulus plan, a bunch of chain emails proposing other solutions that were allegedly cheaper. One such email proposed giving everyone over 50 $1 million to retire to solve unemployment. Well, a quick check of the math (that I could do without a calculator) put the cost of this proposal at about $40 trillion (which is a lot more than $787 billion). For reference, the entire U.S. economy is about $14 trillion per year. Obviously people need to be able to estimate things a little bit better before passing on chain emails! Another one claimed that the stimulus package amounted to more than $1 million per day every day since Jesus was born. I heard this, estimated the number of days in 2,000 years, and that one turned out to be true.

Fermi problems have a wide variety of applications. You can use them to figure out if you are being charged too much at the store or to see if the chain email your crazy uncle sent you is total nonsense. They are easy and one of the more powerful and useful tools that everyone should have in their mathematical toolbox.

Reprinted with permission from the Half-Astrophysicist Blog.