Whenever I got stuck on math homework while growing up, I would go looking for my mother. Often I would find her on the living-room couch unwinding after work, catching up on the news with both the local Cantonese news station blaring on the TV and The Economist open in her lap.“I don’t know how to do this,” I would complain, settling on the carpet by her feet.“Read me the question.”I would recite: “Sarah takes six hours to paint a fence, and John takes 12 hours to paint the same fence. How long will it take to paint a fence twice as long if they work together?”She wouldn’t even look at the page.“How many hours do you think it’ll take them?”“I don’t know, or I wouldn’t be asking you!”“Single digit? Tens of hours? Hundreds of hours?”“Mommm …”
I love Fermi problems, and making estimates. These days, I do it a fair bit for work, and I also do it a fair bit around chemical employment as well. How many professors do you think work on this problem? Maybe 1, maybe 10. How many working industrial medicinal chemists are there in the United States? I dunno, definitely 1000, definitely not 100,000, probably closer to 5,000. How many chemical plants are there in the United States? Well, that's probably a number less than 5000, but more than 100.
Readers, what are your favorite Fermi-type questions and how do you go about solving them?
No favorite Fermi question, but tangential story. Our undergrad gen chem professor used to call our calculators "crutches". He would force us to work through a rough calculation in our heads first, prior to doing the exact calculation, so we had a better sense for the magnitude of the answer.
ReplyDeleteThe classic one from management consulting interviews is to estimate how many piano-tuners there are in Chicago.
ReplyDeleteThe other day I found myself trying to estimate how many fibre Internet subscribers there are in my neighbourhood.
The twitter for one of the state fish and game departments had a Thanksgiving trivia question to guess how many feathers on a wild turkey. If a wild turkey weighs close to a domestic turkey, and if a 20 pound turkey was a sphere, and about as dense as water, and you guess a size of a single feather, you can get the right order of magnitude.
ReplyDeleteConsidering that the thing is going to have both big feathers and teeny little down feathers, I would have trouble getting the order of magnitude right.
DeleteCan't think of a favorite application off the top of my head. But working through the question in the article reveals how useful it would have been for me to apply the discipline mentioned by PD earlier in my studies.
ReplyDeleteIf C&E News releases an occasional report on total chemistry PhDs per year, and it also compiles an annual jobs report, and chemjobber tracks the total academic postings per year, just what is the statistical likelihood of those who want one getting a T/T job?
ReplyDeleteI was group-grading a Chem101 exam. Almost all the responses to the written answer sections could be codified by simple criteria into various levels of credit, but once in a while we would get an odd-duck answer that we would look at as a group. One such one that I found was a student who worked through the math, made a minor error, and wound up off by many orders of magnitude. The student then wrote something to the effect "I know this is wrong, the answer should be more like XXX", which was correct. We gave the student almost full credit for the problem.
ReplyDeleteI suspect these kinds of questions do a better job of measuring an interviewee's ability to think under pressure than they do of measuring reasoning skills. I've known a lot of people who would have come up with a well-thought-out answer in a low-pressure situation, but would have blanked during a job interview.
ReplyDeleteUnless this was a sales position (i.e. a scenario in which "logical reasoning under time pressure with verbal dexterity" was a key skill), I wouldn't be asking during an interview. When I wrote the post, I envisioned a beer with friends, etc.
DeleteJust over the weekend, my father asked me about how much soil he'd need to fill a depression in the yard. I quickly came up with the number, but it gave me pause as I imagined the size of a heap of soil that big(17 cubic yards, or so I thought). Then it struck me: I came up with the volume in cubic feet, not cubic yards. After correction, the number looked a lot more reasonable in my head.
ReplyDeletePart of the issue is also that what garden centres deliver as a cubic yard, is not always actually a cubic yard (they cheap out on buyers)
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