Activity III: FERMI PROBLEMS

Activity III: FERMI PROBLEMS

Enrico Fermi in a speech to physicists in the late 1940s talked about the use of numbers and measurement in science education. He proposed that the keys to understanding quantitative measures in science were to understand the process by which one arrives at numbers and the assumptions that underlie the numbers used in the process. He gave the example that any scientist should be able to estimate the number of piano tuners who work in a city, knowing only an estimate of the population of the city. Precision is not necessary in such an estimate; it is the process and the assumptions which are important. This agrees with Deming's philosophy:

Don’t Be Number Driven, Be Process Driven

In this case, the process refers to the thinking process used to arrive at an answer.

At work or in your personal life you will “encounter” numbers. Learn to question the trustworthiness of the quoted numbers. Does the source of the numbers have political motives or personal perspectives which make the numbers suspect? Can you evaluate the reasonableness of such values?

These problems were discussed in Chapter 3. What I want you to recognize is that any time you are presented with a number, you should ask two simple questions:

1. Please explain the assumptions that were made in arriving at this number. Clearly define this, this, and this . . .

1. Discuss the logic that was “used on" these assumptions and definitions to generate the final number.

We want you to spend no more than 15 minutes on each Fermi. DO NOT DO ANY RESEARCH for these problems. Simply make assumptions.

Once we have received the Fermi for the week from all students, we will share the results. When you compare thinking processes, note how different people think differently.

After doing the Fermi process to estimate values, think about how one could use @RISK to bring this uncertainty into the analysis.

"Keep in mind that the results of any computation are only as good as its most questionable step. This point is neatly illustrated by "Burns' Hog-weighing Method," generally attributed to Scottish poet Robert Burns:

Burns' Hog-weighing Method

1.Select a well-balanced board and place it symmetrically on a fulcrum.

2.Place the hog to be weighed on one end of the board.

3.Pile rocks on the other end of the board until they exactly balance the weight of the hog.

4.Carefully guess the weight of the rocks."

From "Lies, Damned Lies, and Spreadsheets," Ronald Pearson,

BYTE Magazine, December 1988. p.304.

Fermi 1: In New York City, what will the health care costs be in 2001 be for treating AIDS patients? Make an interval estimate, not just a point estimate. Assumption: New York City population is 10,000,000 people.

Fermi 2: In the world, how many people will die in the week of January 21-January 27 from diseases that are directly linked to smoking? Make an interval estimate, not just a point estimate. Assumption: World population is 6,000,000,000.

Fermi 3: A human is constantly losing hair, how many pounds of human hair are lost each year by everyone on the planet? Make an interval estimate, not just a point estimate. Assumption: World's population is 6,000,000,000.

Activity III - 1

Spring 2002