# Presentation: 073748

## FERMI’S PIANO TUNER

***Mr. K.,NASA/GRC/LTP***

***Mr. K. NASA/GRC/LTP***
***Edited by Ruth Petersen***

**Notes:**
Fermi’s Piano Tuner
Sometimes we must attempt to estimate important scientific and/or engineering values based on scanty or apparently non-existent information. Experimental science seeks its answers from Nature; but, before an experiment can be designed, some idea/estimate of the parameter space involved must already be in hand. We must make an initial guess.
How do we proceed? We use what we already know, of course. Most people could do far more than they think if only they really knew how to use their heads. Enrico Fermi, hailed by some as, “the last universal scientist,” had a unique way of initiating his graduate students into this important discipline...

## Preliminary Activities

***1. ******Do a www search on the keyword *****“*****Enrico Fermi.” Be prepared to discuss who Enrico Fermi was and what he accomplished.***
***2. ******Do a www search on the keyword “Manhattan Project.” Why was this project significant?***
***3.******Solve the following problem: A particular city has a population of four million people. How many cars will be on the streets at rush hour? *****(***Just an estimate--you do not need to be exact!*** )**

**Notes:**
Please complete these activities before we meet. What follows will be much more fun and meaningful if you do! DO NOT GUESS!!! REASON THINGS OUT!!!

## 4. You are sitting by a railroad track. A train goes by so that one car passes you each second. How fast is the train moving?

***5. ******How would you estimate the energy in an atomic bomb that detonates (****explodes****) some distance away from you? ****(Just suggest a method--nothing elegant, but something fairly accurate!)*
***6. ******Why do you think I am asking you these bizarre questions? Be prepared to discuss your answer!***

**Notes:**
DITTO...

## Slide 4

**Notes:**
Enrico Fermi, the Italian physicist of Manhattan Project fame, knew only too well that physicists are often confronted by situations in which they are forced to reason from minimal information. Therefore, he taught his students how to think in such a world by using a strange type of problem...
But before we go any further, let’s first discover a little about who Fermi was and why the Manhattan Project was so important.

## Stag Field, Chicago (1942)

**Notes:**
“Manhattan Project” was the code name of a secret research project, conducted in Stag Stadium during the Second World War. As leader of this project, Fermi built and operated the first atomic pile (nuclear reactor) and showed that nuclear fission could be harnessed to produce energy. New theories of atomic and nuclear structure had already suggested the very clear possibility that enormous amounts of energy might be produced by relatively small amounts of fissionable material. The problem, of course, was to moderate the nuclear reactions and to control the energy released.
After successfully completing his dangerous experiment, the head of the National Defense Research Committee was notified via the coded message, “The Italian navigator has landed in the new world.” 

## Slide 6

**Notes:**
Work on nuclear fission in the U.S. was first prompted by a letter, written in 1939 by Leo Szilard and signed by Albert Einstein, warning President F. D. Roosevelt of German covert activities that could possibly lead to the development of powerful new atomic weapons. In one of history’s many sad ironies, Einstein was subsequently denied access to any and all U.S. information connected with nuclear energy because of his German heritage. After the war, Einstein and others became devoted to the cause of abolishing the use of atomic weapons in favor of world peace.

## Slide 7

**Notes:**
The first nuclear reactor was built in the basement of Stag Stadium, Chicago. It incorporated 400 tons of graphite and 22,000 pellets of metallic uranium stacked in 57 layers. Cadmium sheets nailed to flat wooden strips served as control and safety rods. While they could be withdrawn manually, they were set to automatically slam home should reaction rates get too high. As work progressed, graphite dust coated everything, making the work area extremely hazardous and slippery.

## Trinity,New Mexico

***Trinity,New Mexico***
*** ******1945***

**Notes:**
Many people contributed to the final test of “The Gadget” at Trinity, New Mexico, on July 15, 1945, at exactly 5:29:45 a.m. Although weather had threatened to postpone the test, the decision was finally made to proceed. When “The Gadget” worked, it became clear to project personnel, military and non-military alike, that the war was essentially over. A new era of human history began that fateful morning.

## So...

***...******What has all this***
***to do with***
***piano tuners?????***

**Notes:**
 Sometimes we can use a commonplace example to explain a very uncommon process!

## Do you remember all those bizarre questions I asked in the preliminary activities?

***Well, Fermi and his team were faced with bizarre questions,too. They had to determine things that had never been determined before--life and death things like how to safely run a nuclear reactor in a stadium in the middle of Chicago!***
***They ******HAD****** to know how to use their mental resources to the MAX!***
***Fermi used the piano tuner problem *****(*****and others like it*****)***** to force his students to ***_***think***_*** ******rather than merely to ***_***recite***_***.***
***So, if you’re ready, ******here it is******...***

**Notes:**
 Fermi was the archetypical thinker and scientist. He knew how to use the most commonplace resources to arrive at the most profound conclusions. In fact, he was a virtuoso! For example, when the gadget was tested at Trinity, Fermi estimated the blast strength by dropping small pieces of paper and noting their displacement. When the shock passed, the pieces of paper were displaced 2.5 m. Fermi thereby estimated the blast strength at 10 and 20 thousand tons of TNT.
As a professor, Fermi wanted his students not only to know about physics, but to know physics. So, along with teaching them physics, he sought to teach them how to think. The paper episode illustrates the same pattern of thought as the piano tuner problem that we are about to discuss!

## If 3,000,000 people live in Chicago,  how many of them are piano tuners?

***You have 2 minutes to complete this problem.***

**Notes:**
 Stop right here and see if you can work this problem through. Do not use any other resources than paper, pencil, and your own intuition. Above all, DO NOT GUESS!!! REASON IT OUT!!!

## First, simplify: Estimate just the number of pianos in Chicago...

***( Yeah, right! ). Any ideas? Well...***

**Notes:**
Before we can estimate the number of piano tuners, we must first have some idea about the number of pianos that require tuning. If you have not been able to get started yet, does this simplification give you any ideas?

## Reason and Calculate:

***If an ******average family****** has, say, ******4 members******, then there must be about***
_***             ***_*** ************ ***_***     ***_*** ******= ***_***             ***_*** Families***
***in Chicago***
***And ... if ******1****** ******in 5 families owns a piano******, there will be***
_***             ***_*** ************ ***_***     ***_*** ******= ***_***             ***_*** Pianos***
***in Chicago***

***  ******3,000,000      4       750,000***

***     ******750,000      5       150,000***

**Notes:**
Use what you know about family, friends, and neighbors. Perhaps throw in a school or concert hall or two. The idea is to get into the ballpark, not to produce an exact answer!

## Now, estimate the number of piano tuners . . .

**Notes:**
OK. Now that we have an idea of how many pianos there are, the rest should be simple...yes?!?!?!?

## ANOTHER HINT:

***Consider the work load of piano tuners. How many pianos do you think a person could tune in one***
***normal work ***_***day?***_*** A normal work ***_***week***_***? Work ***_***year***_***? And don’t forget vacations!***

***Another 2 Minutes***

**Notes:**
Before we estimate the number of tuners, we need to consider what a single tuner is capable of doing. Since weekends and holidays must factor into his/her productivity, we will take a baseline of one year for our calculation. The assumption here is that any given year is, more or less, like any other. Is this assumption reasonable?

## If the average piano tuner

***1. Serviced ******4 pianos every day of the week for 5 days******,***
***2. Rested****** on weekends******, ******and***
***3.****** ******Had a 2-week vacation****** during the summer******,***
***then in one year****** (52 weeks) ******the piano tuner would service***
_***   ***_*** ************ ***_***   ***_*** ************ ***_***   ***_*** ******= ***_***         ***_*** Pianos***

***	******    ******4     5    ****** ******50    1,000***

**Notes:**
This schedule is probably typical...

## So, how many piano tuners must there be?

***Just shout it out!!!***

**Notes:**
We now have an estimate of the total number of pianos in Chicago, and the number of pianos that one tuner can tune in a year. Assuming that every piano gets tuned once a year, the conclusion should be obvious!

## 150 piano tuners

***( Give or take a few  . . . )***

***150,000 Pianos/(1,000 Pianos/Tuner) ***
***or***
***150 piano tuners***
***living & working in Chicago!!***

**Notes:**
Bingo! We have arrived at the desired estimate. We may be off by a factor of 2, but certainly not by a factor of 5 or 10. Common sense should tell us that much. Thus, there may be anywhere from 75 – 300 piano tuners in Chicago (factor of 2 error), but not 30 – 750 (factor of 5) or 15 – 1,500 (factor of 10).
Do you think it more likely that the actual number of piano tuners is as low as 75 or as high as 300? Or do you think that the truth lies somewhere in between?

## QUESTIONS for DISCUSSION

***1.****** Are the assumptions made above reasonable?***
***2.****** How accurate do you think the result is?***
***3.****** Would you trust it to within a factor***
***of 2?***
***4.****** What different assumptions might YOU make?***
***5.****** Rework the *****‘*****piano tuner’ with your new assumptions.***

***5 Minutes***

**Notes:**
Please take a little time to work with these questions!

## 1. An error factor of 2 is often acceptable in rough physics calculation.

***2. ******For my estimate of 150 piano tuners, an error factor of 2 would give a range of anywhere from 75 – 300 piano tuners.***
***3. ******Is your estimate within this range?***
***4. ******Which assumption had the greatest effect on your result?***

## Can you suggest a Fermi-type problem that we might work on?

## Post Conference Activity

***Are there events in your daily life that you could examine using Fermi’s method of making logical assumptions, estimating, reasoning, and calculating? How many interesting problems can you invent for yourself? Use common  sense to solve them, and, where appropriate, use books or the www to check your accuracy and see how close you got to the truth!***
***Have fun!!!***

## For those interested in talking more, contact me at:

***joseph.c.kolecki@grc.nasa.gov ***

**Notes:**
Please feel free to contact me at NASA/GRC. I will be happy to correspond with you!