Introduction to Fermi Problems

1. Introduction to Fermi Problems

2. Enrico Fermi (September 29, 1901 – November 28, 1954) • An Italian-born physicist • Known for his work on the development of the first nuclear reactor, and contributions to quantum theory, nuclear and particle physics • Fermi was known for his ability to make good approximate calculations

3. Fermi Problems (akaFermi Estimates) • Named after Enrico Fermi, they are problems that require making educated guesses using estimation skills and prior knowledge • They are solved by breaking what seems like an impossible problem into smaller/simpler problems, and using estimation skills to continuously refine your answer • These problems often involve making justified guesses about quantities that seem impossible to compute given limited available information

4. How do I solve a Fermi Problem? • Most of the time, you will need to ask questions! • A Fermi question demands communication • A Fermi question utilizes estimation • Write these down! • A Fermi question might require you to make assumptions • Write these down! • A Fermi question emphasizes process rather than “the” answer. • Show how you got to your answer

5. The Classic Fermi Problem • “How many piano tuners are there in Chicago?”

6. Sample Solution to the Classic Problem • Typical solution involves multiplying a bunch of estimates that leads to the correct answer if the estimates are correct • Sample solution: • There are ~ 5 000 000 people living in Chicago • On average, there are 2 people in each household in Chicago • Roughly one household in 20 has a piano that is tuned regularly • Pianos that are tuned regularly are tuned once a year • Each piano tuner works 8 hours a day, 5 days a week, and 50 weeks a year

7. Sample Solution to the Classic Problem • Typical solution involves multiplying a bunch of estimates that leads to the correct answer if the estimates are correct • Sample solution: • There are ~ 5 000 000 people living in Chicago • On average, there are 2 people in each household in Chicago • Roughly one household in 20 has a piano that is tuned regularly • Pianos that are tuned regularly are tuned once a year • Each piano tuner works 8 hours a day, 5 days a week, and 50 weeks a year • With all of these assumptions…we get 125 piano tuners in Chicago. • See SAMPLE WRITE UP

8. Why do these ‘work’? • Fermi estimates generally work because… • The estimations of the individual terms are often close to correct • Over- and under- estimates help cancel each other out

9. So,if we can’t get the answer, what’s the point? • Looking for Fermi estimates of the answer to a problem before turning to calculations provides you with a useful check on your results • Although Fermi estimates are often not accurate (it depends on how good your estimates are), this type of analysis does tell us what to look for in order to get a better answer (e.g. is one of your estimates really off?) • Fermi estimates give us a rough idea of the answer… which may be enough in some cases

10. What’s the point (continued)… • They are good brain exercise • They often don’t have an exact answer, forcing you to… • Use your imagination • Think outside the box (sometimes)

11. Your task… • Work in groups to tackle a fermi problem • Do a written report (see sample report) • Present your solution to the class