Topic XIV. Fermi Problems
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LEARNING GOALS
 B. CONCEPT ACQUISITION
 Fermi Estimates: A systematic estimate of a quantity based on what you know. The typical goal is to get within an order of magnitude of the right answer. (This often proves possible even for topics about which you know very little.)

EXAMPLES
 Exemplary Quotes
 “He’s suggesting that the Federal budget deficit is due to the money we spend on job training programs. But that’s ridiculous! Even if every single person out of work  let’s imagine that it is 10% of the workingage population (say 10 million people out of work)  went to a job training program that cost as much as a year of college at a good university (say, $40,000), that would cost 400 billion dollars. Hmm... well that’s not quite as small as I expected, but it’s still not trillions of dollars, and furthermore I am sure we aren’t spending that much on each person for job training. Let see, can I estimate that cost per person in some more realistic way than using college costs...”
 Cautionary Quotes: Mistakes, Misconceptions, & Misunderstandings
 "I don't know how many pianos there are in Chicago so I can' t estimate how many piano tuners are currently working there."
 "Keyla asked me how many firecrackers were shot last night. I tried googling it, but couldn't find out. I guess we'll never know now, will we?"
LEARNING GOALS
 B. CONCEPT ACQUISITION
 Fermi Estimates: A systematic estimate of a quantity based on what you know. The typical goal is to get within an order of magnitude of the right answer. (This often proves possible even for topics about which you know very little.)
 Steps:
 a. Decompose the problem into multiple components that you can estimate. (Break down unfamiliar components into familiar components).
 b. Estimate components using approximations.
 c. Combine estimated components to calculate Fermi estimate.
 d. Compute upper and lower bounds (maximum and minimum quantities above/below between which you are fairly confident the correct estimate should be).
 C. CONCEPT APPLICATION
 Identify quantities that would and would not be appropriate to estimate with a Fermi calculation.
 Provide rough estimates for realworld quantities using “backoftheenvelope” (Fermi) approximations.
 Evaluate the credibility of quantitative statements using “backoftheenvelope” approximations.
 Use Fermi estimates to identify first, second, third order causes for example problems, and estimate their effect sizes.