2. FERMI’S PIANO TUNER Mr. K.,NASA/GRC/LTP Mr. K. NASA/GRC/LTP Edited by Ruth Petersen

3. 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! )

4. 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!

6. Stag Field, Chicago (1942)

7. A Fateful Letter

9. Gen. Groves Oppenheimer Szilard “The Gadget” Trinity,New Mexico 1945

10. So… …What has all this to do with piano tuners?????

11. 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…

12. If 3,000,000 people live in Chicago, how many of them are piano tuners? You have 2 minutes to complete this problem.

13. First, simplify: Estimate just the number of pianos in Chicago... ( Yeah, right! ). Any ideas? Well...    PIANO ARCHIVES 2 3 JohnDanaAnn SueRuthMary MarkBethetc. BillJoeetc.etc. HINT: 1

14. 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

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

16. 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

17. 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

18. So, how many piano tuners must there be? Just shout it out!!!

19. ( Give or take a few... ) 150,000 Pianos/(1,000 Pianos/Tuner) or 150 piano tuners living & working in Chicago!!

20. 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

21. 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?

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

23. 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!!!

24. For those interested in talking more, contact me at: joseph.c.kolecki@grc.nasa.gov