From Enrico Fermi to Bill Bennett

June 1 -- How big? How many? Quickly getting an approximate idea of the magnitude of a number and of its relation to other numbers is often helpful when doing physics.

To further this skill, the Nobel Prize-winning physicist Enrico Fermi often asked his students to estimate various bizarre quantities. Answering these questions required that they think critically about the quantity, make reasonable assumptions, ascertain basic facts, and then perform the required calculations.

A classic Fermi question is "How much tea is there in China?" Let me sketch the process before discussing its usefulness when reading the daily newspaper or Web site.

Tea in China

So how much tea is in China? We assume the following:

That there are about 1.2 billion people in China. That each person drinks an average of two cups of tea per day. That about four grams of tea leaves (post drying & processing) make one cup of tea. And, that there may be three or four months of leaves stockpiled at any one time.

With these (debatable) assumptions, the amount of tea in China is 1.2 billion people x 2 cups per person per day x 4 grams of tea leaves per cup x 100 days, which equals about 1 billion kilograms (or 1 million tons) of tea leaves in China.

By making our assumptions explicit, we can revise one or more of them if we find them to be way off.

However obtained (and there are other approaches), the answer certainly won't be exact. But if we're careful, it will probably be correct to within a power of three. For many purposes that's close enough.

If you want to try a Fermi problem, here's one (answer below): If the entire land surface of the Earth were to be divided into parcels of equal area, one for each human on the planet, how big would these parcels be?

Bill Bennett's Gambling

The appeal of these problems is that often without much more than arithmetic and a few facts we can obtain the approximate magnitude of numbers important to, but not explicitly mentioned in the news stories that we read. One example: