# Memorizing the following logarithm values is a good place to startJanuary 20, 2017 9:43 AM   Subscribe

Physicist Enrico Fermi famously arrived at the approximate strength of the Trinity test explosion by dropping pieces of paper and watching how far they drifted. Estimates with little or no data are now called Fermi problems, including the famous "How many piano tuners are there in Chicago?" and the Drake equation. Fermi Questions has been an event in the Science Olympiad, a competition in American K-12 schools, where competitors must estimate amounts such as the number of playing cards it would take to equal the mass of Betelgeuse (2x10^34, or twenty decillion). Practice your wild estimates at FermiQuestions.com (tutorial here).
posted by Etrigan (47 comments total) 55 users marked this as a favorite

You gotta start by realizing how many out-of-tune pianos there are that no one hires a tuner for
posted by thelonius at 9:51 AM on January 20, 2017 [11 favorites]

As a physicist, and a U of C graduate especially, this problem solving technique is deeply ingrained in my being. Not only did I learn this in Stat Mech and the undergrad lab courses, it came up again during qualifier exams in grad school. In fact, the one that sticks in my head was "How many dentists are there in Ann Arbor, MI? Show your work."
Go Blue
posted by cyclotronboy at 9:54 AM on January 20, 2017 [8 favorites]

I bought a house from a guy who spent his retirement as an itinerant piano tuner, flying around the country to tune pianos in a small, general aviation plane that he piloted himself. So, for the piano tuners in Chicago question, I'm going to answer: at most one.
posted by tobascodagama at 9:55 AM on January 20, 2017 [10 favorites]

(I just glanced at Wikipedia's proposed solution to the piano tuner question, but I think it drastically overestimates what proportion of pianos are tuned regularly rather than left gathering dust in people's living rooms.)
posted by tobascodagama at 9:57 AM on January 20, 2017 [6 favorites]

Right! That's the problem with these as test questions. I don't know how many patients a dental practice serves, or how many people don't go to the dentist, or only go once every three years. I don't even know how many people there are in Ann Arbor. So how can I Fermi-ize in any meaningful way, unless I am allowed to do a little research?
posted by thelonius at 10:02 AM on January 20, 2017 [4 favorites]

Not knowing the answer to any of those questions, I quickly cooked up an answer of 30 dentists. I'm probably not off by an order of magnitude.
posted by figurant at 10:08 AM on January 20, 2017 [5 favorites]

I don't know how many patients a dental practice serves

How long do you think the dentist spends with you? Does that sound high or low? How many times do you think the dentist can repeat that each day? It's about turning "How many dentists are in Ann Arbor?", a question you cannot possible answer, into a bunch of questions that you can come pretty close to. And you're probably wrong, but you're probably wrong about the other questions in that bunch too, and you're likely wrong in opposite ways, so your various wrongnesses can cancel each other out.
posted by Etrigan at 10:12 AM on January 20, 2017 [16 favorites]

I bought a house from a guy who spent his retirement as an itinerant piano tuner, flying around the country to tune pianos in a small, general aviation plane that he piloted himself.

Someone get Werner Herzog on the line; I think we've found the subject for his next film.
posted by Atom Eyes at 10:12 AM on January 20, 2017 [18 favorites]

congratulations on ruining productivity today for the entire engineering staff.
posted by Dr. Twist at 10:16 AM on January 20, 2017 [10 favorites]

I don't even know how many people there are in Ann Arbor.

I know *of* Ann Arbor, but not much about it. That says to me that it's under a million, but more than 100,000. So say 500,000 people.

Google says 117,025. So I was off, but within the order of magnitude of Fermi questions.
posted by Quindar Beep at 10:17 AM on January 20, 2017 [7 favorites]

Every time I think of fermi questions, I feel like I've seem a wormhole into the origins of mansplaining.
posted by advicepig at 10:21 AM on January 20, 2017 [32 favorites]

Otherwise known as "fucking annoying questions for job interviews."
posted by rokusan at 10:28 AM on January 20, 2017 [7 favorites]

At work we call these "WAGs" (wild-ass guesses). If you have some data, it might be a "SWAG" (scientific wild-ass guess).

The point of doing an exercise like this isn't to get the "right" number. It's really to formalize, in a way, your intuition. Based on some things I can assume or have a rough idea about, I can come up with a number that's probably correct to within an order of magnitude. If the analytical solution ends up being wildly out of proportion to what I originally guessed, then either a) my assumptions about the system are wrong or b) my calculations are wrong.
posted by backseatpilot at 10:33 AM on January 20, 2017 [8 favorites]

As I understand it, the Fermi method is more a matter of coming up with a decent estimate to use as a starting point, than as a final answer.

For example, you have an item you want to market to dentists in Ann Arbor. Is it even worth your while to court that market? Well, you estimate that you'd have to sell 5000 of that item to break even, and if you come to a Fermi estimate of 1000 or 10,000 dentists, maybe you do more research. If you estimate 20, maybe you move on.
posted by explosion at 10:52 AM on January 20, 2017 [6 favorites]

If you're interested in Fermi problems, you should really look at Caltech's Physics 101 course, Order of Magnitude Physics. (Many other places do something similar, of course - this is the one I'm familiar with. And you can follow the link to Purcell's useful OoM numbers.)
posted by RedOrGreen at 10:58 AM on January 20, 2017 [2 favorites]

4 out of 5 Ann Arbor dentists disagree about how many dentists there are in Ann Arbor.
posted by Atom Eyes at 11:00 AM on January 20, 2017 [14 favorites]

Pretty sure it's 3 out of 4.
posted by Etrigan at 11:14 AM on January 20, 2017 [2 favorites]

If I understand Fermi problems correctly, it's 1 out of 1 dentists.
posted by logicpunk at 11:18 AM on January 20, 2017 [17 favorites]

It's about turning "How many dentists are in Ann Arbor?", a question you cannot possible answer, into a bunch of questions that you can come pretty close to. And you're probably wrong, but you're probably wrong about the other questions in that bunch too, and you're likely wrong in opposite ways, so your various wrongnesses can cancel each other out.

One of the most irritating presentations I've ever been to was put on by a former employer, who brought the author of "The Wisdom of Crowds" in to give us all a pep talk about how you can crowdsource your problems and somehow magically triangulate answers through the law of averages and people generally being wrong by the same magnitude in all directions. As proof of this, he offered as his principal evidence a single case of a shipwreck that was located after a bunch of high-ranking people with no technical knowhow pushed pins into a map with their own uninformed guesses, and when they took the geometric average of the coordinates, it ended up being about 100 yards from the actual correct location.

I don't want to draw a cause-and-effect arrow between the ensuing Q&A session for this talk and the fact that I am no longer employed by this company, but I can tell you that the audience was largely engineers, and we* had a lot of fun talking about standard deviations, random number distribution, selection bias, and the absurdity of the idea that wild-ass guesses are going to be wrong within a known margin of error.

In conclusion, these questions are largely exercises in showing you can bullshit in the right kind of way, and coaching people to even try to answer them is, as advicepig so astutely notes, one of the reasons why people have engineer's disease.

* for certain values of "we" that did not include the keynote speaker
posted by Mayor West at 11:25 AM on January 20, 2017 [20 favorites]

A few weeks ago my wife and I were discussing how many punchbugs (and similar, like slugbug) each VW Beetle instigates during a car's average lifespan.

So if you want to have a guess at that one, let me know what you come up with. Otherwise I might take it to Askme.
posted by ardgedee at 11:27 AM on January 20, 2017 [3 favorites]

It's about turning "How many dentists are in Ann Arbor?", a question you cannot possible answer

Oh, that's easy. I just ask Wolfram Alpha, which tells me there's 70 general dentists in Ann Arbor (average salary 112k per year) . Might be missing a few specialists, though.

posted by effbot at 11:31 AM on January 20, 2017 [4 favorites]

Enrico Fermi - OG SWAG*

*Scientific Wildass Guess
posted by tommasz at 11:44 AM on January 20, 2017

It's about turning "How many dentists are in Ann Arbor?", a question you cannot possible answer

Oh, that's easy.

Yes, I'm ever so sorry that I didn't include "without looking it up or whatever". Want to get on me about mistyping "possibly" while you're making my eyes roll so hard they're making audible popping sounds?
posted by Etrigan at 11:51 AM on January 20, 2017 [2 favorites]

So the dentist sees me once every three to four visits, otherwise, I'm dealing with a hygienist. I go more often than most people, so people go to the dentist once every four years or so. When I see the dentist it's for 5-20 minutes. So let's say 10 minutes a patient. So a dentist can see 6 patients an hour. 6*8 *5*52=12500 people visit each dentist a year. Let's given them a month off. So there are 12 dentists in Ann Arbor. Go sell elsewhere.
posted by Hactar at 11:52 AM on January 20, 2017

I am fond of Fermi estimates because if it turns out I am completely wrong, setting it down will let me know -why- I am completely wrong.
posted by solarion at 11:55 AM on January 20, 2017 [2 favorites]

Missed the every four years. So 3 dentists in Ann Arbor. Or 1, by the Fermi method.
posted by Hactar at 11:59 AM on January 20, 2017

I'm reestimating my coefficents for the Drake equation on an hourly basis nowadays.
posted by RobotVoodooPower at 12:04 PM on January 20, 2017 [6 favorites]

I tried the first 10 questions and was pleased to see that I got about half of them dead on and the rest of them were off by 1 order of magnitude (except the last question where I was tired and couldn't be bothered to come up with some plausible size for a red blood cell and just guessed. I was off by 2 orders of magnitude).

posted by It's Never Lurgi at 12:27 PM on January 20, 2017

Guys, I think I might have found a new cottage industry: we become consultants to Fortune 500 companies, teaching them how to ask questions that LOOK like Fermi problems, but are actually sneaky ways to ferret out people's assumptions about mundane things. People are now used to answering inane questions in interviews, so this'll let us run detailed personality analyses to figure out which applicants are sociopaths/instigators/high risk for insurance risk pool.

For example:

Q. How many proctologists would it take to serve Ann Arbor, Michigan?
A. Well, let's say Ann Arbor has 100K people, and each one can see 8 patients a day, and each doctor works 220 days a year, and the average person goes to the proctologist once a year--
Q. AH-HA! Most people go once every FOUR years. If that's your wild-assed guess, you must be basing it on personal experience, so you must visit unusually frequently, and are probably a high colon cancer risk. Don't call us, we'll call you.
posted by Mayor West at 12:29 PM on January 20, 2017 [15 favorites]

In focussing so intently on his little experiment, Fermi rather neatly obviated the aghast 'what have we done?' moment we have accounts of from some of the other physicists who were also present.

Perhaps not entirely coincidentally, anticipation of such a moment -- as he anticipated so much else in physics -- has been adduced as a possible reason behind the disappearance of and abandonment of physics by Fermi's most brilliant student, Ettore Majorana.
posted by jamjam at 12:30 PM on January 20, 2017 [2 favorites]

Mayor West, that wild-assed guess about asses is just wild, I guess.
posted by Four Ds at 12:39 PM on January 20, 2017 [3 favorites]

From 2000-2002 I worked for a Very Large Internet Hosting Provider where one of the things we did for our managed hosting clients was analytics. Our contract with every analytics client specified that we retained their logs for 90 days. We actually only retained them for 7, but luckily nobody ever asked for really old logs.

When we needed to upgrade the analytics platform I was tasked with figuring out how we could get into compliance with the contracts at the same time. We pulled a bunch of metrics for the logs we had, started tracking how much things varied from day to day and week to week, and I did a sloppy sort of Fermi estimate and went to the people responsible for ordering our hardware to price out 90 day retention.

We rewrote our contracts instead. Turned out 30 day retention was economically viable with then-current hardware, but 90-day retention required more expensive hardware than we could justify. Luckily we gave our clients enough new, shiny stuff with the new analytics platform that nobody really complained about the change to the retention policy.
posted by fedward at 12:54 PM on January 20, 2017 [2 favorites]

Fermi thought about more than just how many piano tuners there were in Chicago.

There is no evidence of any piano tuners residing in Chicago now, and though we believe there were piano tuners residing in Chicago then, the fact remains that none are making themselves known to us at this time. Surely there must be many more now than there were in the past; and yet we see no evidence. This is an example of the Fermi Paradox.

It is as if there was some mass culling of piano tuners at some point before we noticed. Musicians who study the Fermi Paradox call the apparent cull names like The Not-So-Great Silence or the Analog Filter. This has concerning implications for the continued use and spread of other instruments on Earth.

A recently popular work by Chinese SF author Cixin Liu has brought another possibility to the mainstream consciousness, another possibility ; that of the Dark Stage. It requires its own axioms, to wit:

1. Piano tuners will do whatever it takes to ensure their own survival.
2. The number of musical instruments perpetually increases, but the individuals and organizations with the resources to own and care for pianos remains finite.

Thus, any other musical instrument or musician who is not a pianist is a threat to piano tuners everywhere. At the very least, a Casio CZ-series keyboard occupies a place where a piano might thrive instead. At the worst, Yamaha's DX-7 piano presets and its descendants are "good enough" to completely displace actual pianos, and thus piano tuners.

This state of affairs quickly leads to the following conclusion: it is only logical for piano tuners to hide their existence from other non-piano musicians. That way, piano tuners can use precious time and resources to scour the universe of these other musicians and replace their instruments with pianos, which will one day require tuning.

The universe of music, then, is very much like a dark stage, with each musician quietly murdering any others they encounter in the orchestra pit, to ensure their own survival and dominance.

As I tweak the filter cutoff on my Arturia Minibrute while I write, I pray the piano tuners never notice my post.
posted by infinitewindow at 1:05 PM on January 20, 2017 [27 favorites]

At least Fermi didn't play the goddamn bongo drums
posted by thelonius at 1:17 PM on January 20, 2017 [14 favorites]

It's about turning "How many dentists are in Ann Arbor?", a question you cannot possible answer, into a bunch of questions that you can come pretty close to. And you're probably wrong, but you're probably wrong about the other questions in that bunch too, and you're likely wrong in opposite ways, so your various wrongnesses can cancel each other out.

This sounds substantially similar, though not identical, to how quantum computers arrive at solutions (in this layperson's understanding). Specifically the bit about many solutions canceling each other out based on their amplitude of rightness/wrongness and the solution coming from the leftover magnitude measurement.
posted by smokysunday at 1:34 PM on January 20, 2017

(I just glanced at Wikipedia's proposed solution to the piano tuner question, but I think it drastically overestimates what proportion of pianos are tuned regularly rather than left gathering dust in people's living rooms.)

And if you follow the references, the "actual" number they cite of 290 (in comparison to their Fermi estimate of 225) is a Wolfram Alpha search that returns the total number of musical instrument repairers and tuners. I would guess less than half of those are piano tuners, but I'd also guess there are some piano tuners who aren't included in whatever numbers Wolfram Alpha is using.

Even if the actual number is more like 100-150 piano tuners, I'd say their Fermi estimate of 225 is still pretty darn close.
posted by straight at 1:49 PM on January 20, 2017

I just got this question: How many US dollar bills would it take to make a replica of the Empire State Building?

I don't understand it. Should I think of this as kind of how much surface area is there that I would have to paper with dollar bills (that's not technically making replica because without some other structure, it wouldn't stand.). So maybe I'm pasting these dollar bills into some kind of cardboard-like material and building a replica out of that? But again, am I just interested in the outside surface area. I can't imagine a full-sized empire-state-building-shaped box would stand up. So then maybe I'm folding/origami-ing these bills together?

Ok, I just took a guess and then clicked the citations they pull up. I think they're asking how many one dollar bills would fill an empire-state-building-sized contaier. So 'How many dollar bills equals the volume of the empire state building?" would have been a much clearer phrasing.
posted by If only I had a penguin... at 1:56 PM on January 20, 2017 [1 favorite]

For anyone interested, I made an interactive Drake Equation a few years back. Its default inputs are a bit out of date, especially the estimated number of stars having planets, but of course you may enter whatever values you like.
posted by Hot Pastrami! at 2:30 PM on January 20, 2017 [3 favorites]

Fermi was not always a fan of approximations:
Segrè and Hoerlin tell the story of Freeman Dyson’s encounter with Fermi. Dyson was then a professor at Cornell University, and had to provide dissertation problems for his students there. He decided to use a then-fashionable approximation method to try to reproduce Fermi’s results. I am quite familiar with the method, since I used it in my own thesis. Its virtue is that it is fairly easy to calculate with and seems to give sensible answers. Its flaw is that the terms you leave out may be as big or bigger than the ones you include. In any event, Dyson and his students got results that seemed to agree with Fermi’s experiment. Dyson then went to Chicago to see Fermi. It was not a long meeting. Fermi objected to the method and then asked how many free parameters Dyson had used to make the fit. Dyson said four. Fermi told him that John von Neumann had often said “with four parameters I can fit an elephant and with five I can make him wiggle his trunk.” That was the end of that.
posted by dephlogisticated at 3:52 PM on January 20, 2017 [2 favorites]

Vulcan Science Academy on Vulcan: So... you guess?
Starfleet Academy. On Earth, In the Bay area: No, we solve Fermi questions!
Vulcan Science Academy: So... you guess?
VSA: And how accurate are these... guesses?
SFA: Within an order of magnitude. Usually. Depending on the metric.
VSA: Ah. Understood.
SFA: Are you mad at us?
VSA: You turned a sun into a torus.
SFA: It was an educated guess...
VSA: Fermi Problem.
SFA: Yeah. We guess we did, and guess we did, and now there is a sun that's a Torus. A human had to hit an alternate-universe human with his hand to make the experiment a success, and he's not sorry he did it, as it was himself.
VSA: Let us drink of synth-ale and attend a Klingon Opera. Not even Klingons want to attend a Klingon Opera, synth-ale or not. It's the logical thing to do to keep the arts alive in our alliance.
SFA: LET'S DO THIS THING! We love Shakespeare in the original Klingon!
posted by Slap*Happy at 7:12 PM on January 20, 2017 [5 favorites]

I had a friend during grad school who got lobbed a Fermi question during the oral of their research exam. Word quickly spread and turned into a slightly excited, slightly worried discussion of how to answer instances of it.

Like a lazy computer scientist, my instinct was to think that arithmetic is boring and what's much more interesting is the general idea of how it works, qualitatively that the error grows slowly in an order of magnitude analysis just like the constants in the Big-O notation that every computer science student is taught. But I don't think I could have handled the risk and stress of giving that as an answer during an actual exam.
posted by polymodus at 7:29 PM on January 20, 2017

The wiki page covers the practical uses a bit, but the test is misleading for being purely about mental gymnastics utterly divorced from reality. There's not much you can do with a piggy bank the size of Betelgeuse.

These sorts of things are very valuable. It can let you do a sanity check on an "exact" calculation by using a completely independent method and see if you're still in the ballpark. You can use it to identify and avoid wasting time with concern trolls or their dupes. Put a solid upper and lower bound on some number and decide if the difference is actually important before you waste time trying to get the exact number. Think about the factors in your estimate and realize most of the uncertainty is coming from just one thing and find that out, or perhaps that the uncertainty is high in every thing and realize no one will get an answer in your lifetime.

In focusing so intently on his little experiment, Fermi rather neatly obviated the aghast 'what have we done?' moment we have accounts of from some of the other physicists who were also present.

Don't know which ones you're thinking of exactly, but the most famous such account--Oppenheimer's "I am become Shiva"--was pretty clearly retconned. Accounts of his reaction at the time were along the lines of "It worked."
posted by mark k at 9:53 PM on January 20, 2017 [2 favorites]

Anyone want to check their work? I work with dentists, and therefore I have a relevant spreadsheet from the ADA. As of 2015, there are 6,056 dentists in Michigan. There are also 61.03 dentists per 100,000 in Michigan. Ann Arbor's population is 117,070 (vs 344,791 for Wastenaw metro).

The better question is, where are Fermi Problems in a world of readily available big data?

GO BLUE! I MISS ZINGERMANS!
posted by leotrotsky at 4:32 AM on January 21, 2017 [1 favorite]

Where are Fermi problems in a world of big data.

Totally agree with this. I feel like there should be "assisted Fermi problems" where you have intuition + problem solving + what you can quickly find on the google.
posted by TheShadowKnows at 7:31 AM on January 21, 2017 [1 favorite]

Don't know which ones you're thinking of exactly, but the most famous such account--Oppenheimer's "I am become Shiva"--was pretty clearly retconned. Accounts of his reaction at the time were along the lines of "It worked."

Well, now I'm wondering how many failed atomic bombs are lying around in the Nevada desert unexploded.
posted by pwnguin at 8:02 AM on January 21, 2017

There's not much you can do with a piggy bank the size of Betelgeuse.

Use it for saving Ningis?
posted by Insert Clever Name Here at 9:57 AM on January 21, 2017 [2 favorites]

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