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Thursday, May 28, 2009

"Fermi Problems"

My oral exam was a bit different from this:

Fermi problems, by Steve Hsu: Princeton University Press sent me a copy of Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin, by professors Lawrence Weinstein and John A. Adam. The book is a compendium of Fermi problems -- that is, problems which are simply stated and whose answers can be estimated at the order of magnitude level through simple logic from a few factual inputs.

The classic Fermi problem is: How many piano tuners are there in Chicago?

When I took my oral exam as a first year graduate student at Berkeley, theoretician Geoff Chew (a former student of Fermi's) asked me:

1. How many blades of grass are on your front lawn?

2. What is the ratio of paved to unpaved surface area in Iowa? (He had earlier asked where I grew up.)

Luckily I got them both right. The experimentalist in the examining pair, Paul Richards, held up a cylindrical metal device of some sort and asked me what it was -- to this day, I still don't know :-) I suppose I was destined to be a theorist!

Physicists are constantly solving Fermi problems in the course of their work, because it's the first step in sizing up any potential project, theoretical or experimental. ...Watching someone work out a Fermi problem in real time reveals a lot about their brainpower. Wall Street firms, consultancies like McKinsey, Microsoft and even small startups have been known to ask these kinds of questions of job applicants. This book discusses similar problems in a business context.

The difficulty of most Fermi problems is limited, unless the problem requires some specialized knowledge. But I like them slightly better than puzzles or brain teasers which rely on esoteric tricks that the solver either gets or doesn't get. A former collaborator of mine came up with the following (slightly broadening the genre) one evening while I was visiting U Chicago:

1. If the sun stopped radiating energy, what temperature would the surface of the Earth cool to?

2. In the above scenario, could humans survive using current technology if given enough time to prepare?

Weinstein and Adam's book is a nice collection. ...

Here are some you can try, e.g.:

  1. In the 1989 Loma Prieta earthquake in California, approximately 2 million books fell off the shelves at the Stanford University library. If you were the library administrator and wanted to hire enough part-time student labor to put the books back on the shelves in order in 2 weeks, how many students would you have to hire? (You may assume that the books just fell off the shelves and got a bit mixed up but books in different aisles did NOT get shuffled together.)

  2. Estimate the total number of sheets of 8.5 x 11 inch paper used by all the students in one semester. 

  3. How many notes are played on a given radio station in a given year?

  4. How many drops of water are there in all of the Great Lakes?

  5. If you drop a pumpkin from the top of a ten story building what is the farthest a single pumpkin seed can land from the point of impact?

  6. How many flat tires are there in the US at any 1 time?

Suppose I want to ask a Fermi problem the next time I give an oral exam, what are some good questions related to economics? 

[Oops - I thought I was saving a draft - I didn't mean to publish this yet as it wasn't quite ready - oh well, I lost part of a post last night on health care costs, so this is par for the course lately.]

    Posted by on Thursday, May 28, 2009 at 10:36 AM in Economics | Permalink  TrackBack (0)  Comments (33)


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