You’re one of the world’s greatest physicists, a Nobel Prize winner while still in your thirties. You built the first nuclear fission reactor in the squash courts at the University of Chicago in 1942, a key event in the development of the nuclear weapon that’s about to be tested. For better or worse, the world is about to profoundly change forever, and you are as responsible as any single person alive for it. The blast goes off; from your vantage point ten miles away, the remote New Mexico desert glows brighter than day through your welding glasses. Your boss, Robert Oppenheimer, is moved to think of a line in the Bhagavad Gita - “Now I am become Death, the destroyer of worlds”. What do you do?
If you’re Enrico Fermi, you start dropping little bits of paper and noting where they land.
Why?
As Fermi explains here, he was trying to estimate how powerful the explosion had been:
About 40 seconds after the explosion the air blast reached me. I tried to estimate its strength by dropping from about six feet small pieces of paper before, during and after the passage of the blast wave. Since at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2 1/2 meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T.
Fermi’s answer was not precise - in the end, weeks of calculations by a number of different people taking advantage of all the instrumentation set up to monitor the test resulted in a final estimate of a blast a little under twice the size. But in a couple of minutes, with the most primitive of instruments, Fermi calculated an estimate that a) indicated that the bomb had worked roughly as designed, and b) was sufficiently accurate to serve as a check against gross errors in other, later calculation.
Fermi was reknowned for these estimation abilities, and thus the practice of making preliminary calculations with rough, estimated data has become known as a Fermi problem, or, alternatively, a back-of-the-envelope calculation. It’s a fundamental skill for scientists and engineers, and one of the very first things taught in physics classes. But it’s not just restricted to strictly physics-related problems. Consider this classic Fermi problem, a generic variant of one usually attributed to Fermi himself: how many piano tuners are there in your state capital?
To tackle this, one approach would be first to estimate how many pianos there are in the appropriate city, guess how often they get tuned, estimate how many pianos a piano tuner can tune per year, and from there compute an estimate of how many tuners there would need to be. Each of these subsidiary quantities would need to be broken down and estimated in turn. For the first question:
- there are about 3.6 million people Melbourne,
- assume there’s roughly 2 people per household,
- making 1.8 million households.
- maybe 1 in 30 households have a piano (though this is perhaps the weakest guess so far)
- so, at a guess, there’s 60,000 pianos in Melbourne.
As far as piano tunings go:
- let’s take a guess and say that a piano will be tuned once a year
- so there’s 60,000 piano tunings to be conducted annually in Melbourne.
And how many pianos can a tuner service in a year?
- a tuner might tune 5 pianos a day.
- Tuners 5 days a week, 50 weeks a year (yes, 48 is more realistic, but you may as well round off), therefore,
- one tuner would tune about 1250 pianos a year.
Therefore, all we need to do divide the number of tunings required, by the number one tuner can do each year: 60,000 / 1250, do a bit more rounding-off, and get an estimate of roughly 50 piano tuners.
As it turns out, a check of the Yellow Pages website suggests that there are 137 piano tuners and repairers in Melbourne; clearly, my Fermi problem skills are not as good as Fermi’s! However, through a little bit of calculation, it was possible to get an estimate that was within a factor of 3 of the more precise figure - and, for many purposes, it’s good enough. If somebody came to me with a proposal to produce a full-color glossy magazine aimed specifically at the piano tuners of Melbourne, I’d be extremely skeptical of the feasibility of making money from it, just on the basis of my Fermi, or “back-of-the-envelope”, calculation.
In my own particular line of work, the quantities I am most interested in estimating are the amount of time it will take for a computer to do something, and how much RAM or disk storage will be required along the way. Quite often, I just want to know whether I have to worry any further about the time taken or not. So this leads a particular kind of back-of-the-envelope calculation, the upper bound - where I calculate a figure that must be higher than the actual quantity (of course, sometimes you want the opposite - a lower bound). For instance, if I know that my computer program will take 0.001 seconds, at most, to get an answer, I don’t care whether the actual time is 0.0001 or 0.00001 seconds.
Of all the skills I learned in my years of education, the ability to tackle Fermi problems is one of the most useful in daily life; it’s also damn handy in blog arguments. More seriously, I don’t see how one can tackle a lot of public policy debates without it. Numbers ain’t everything, but for a lot of contemporary issues - particularly environmental ones - they are one of the most important things. Should we throw out appliances before the end of their useful life to replace them with more energy-efficient ones? Does drinking French wine, shipped half way round the world, instead of the local variety make a significant difference to global warming? Can we cut the demands on our dams significantly with water tanks?
I wouldn’t for a moment claim that back-of-the-envelope calculations are a substitute for detailed quantitive studies. Nor, would I make the ridiculous assertion that everything can be reduced to numbers. But, to me, Fermi-style estimation is an essential bullshit-filtering tool.
Which brings me to something I’ve always wondered about. How in the hell do people who haven’t done first-year uni physics cope without the immense utility of envelope backs?
I can see the extreme usefulness of this skill in relatively fast-paced intellectual exchanges, such as those taking place in the blogosphere. I can also think of a few places in everyday life where this skill, or something similar, would be pretty handy. To answer your question, I’d say that most people have developed some ‘ball park’ system of estimation in areas of interest to them, but that it seems like a slightly more disciplined approach might be a really useful thing to get a handle on. Great post…
One could use a Fermi problem to calculate how many policemen might be needed to stamp out indigenous child abuse in the Northern Territory, given the number of indigenous people and how widely they are dispersed. It might be a tad more than the 60 or so proposed by the Prime Minister.
Standing in the teeth of atomic blast, incidentally, while a good way to hone intuitive calculation skills, probably was not good for Fermi’s health. He died of cancer aged just 53.
Beautiful post, Robert - the best you’ve ever written. And I’d like to see it applied to Spiros’ problem, too. There’s a partial answer to the more police = less crime poser in Freakonomics; it may offer a clue as to the sort of numbers required.
Mind you, this stats major tends to do something similar when it comes to similar problems, just a little more guiltily…
Outstanding post. Not only fascinating in substance, but also ingeniously written. Well done!
The concept of numerical scale is indeed a very useful bullshit filter, to say nothing of the simple mechanics of how to break down and pose a problem. Might I suggest, f’rinstance, that one of the reasons you were off in your calculation of piano tuners was that you indexed only by household, forgetting, say, that institutional piano ownership (schools, churches, hospitals, recording studios) is a big factor in this problem.
Also, a bit of anecdotal nonsense to further complicate the matter. For instance, when I wuz a kid, my piano teacher was this young guy who was a working session player, jazz and-rock-band gigger, and part-time instructor. Because he also had perfect pitch and was a good mechanic, he also did piano tuning on the side. He managed all these careers strictly through word of mouth and reputation; wasn’t ‘listed’ for any of this stuff. Assuming such people are “one in a million” (although they are probably more like one in 50 thousand), this brings your Melbourne contingent to about 141.
And what about the electric pianos? Melbourne must be a very musical city! Wouldn’t it be great to get, say 5,000 Melbourne pianists to all do “Benny the Bouncer” simultaneously on some bright Saturday afternoon?
Something to dream about…
j_p_z: you raise an interesting point - the act of doing a back-of-the-envelope calculation also explicitly draws out assumptions. In this case, that the overwhelming majority of Melbourne’s pianos were in private homes, an assumption that may well be wrong.
“How in the hell do people who haven’t done first-year uni physics cope without the immense utility of envelope backs?”
I guess that’s why so many people peddling BS…. now all we need to do is get more kids learning physics!
(nb: author may be biased…)
How many piano tuners does it take to change a light bulb?
great post - very interesting….. a crucial skill….. thankfully I did do 1st year Uni physics, but probably a more useful course was 1st year Uni statistics… damn lies!
You have missed the area I find this most useful - financial mathematics. Some of the spreadsheet models we see are hugely complicated. The first thing I normally do is apply a back of the envelope to it - does the answer make sense? Is it roughly within an order of magnitude of the answer I would expect? Sometime my expectations are wrong; but not too often.
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Michael D - apply it to something practical, like money, and they soon get a good handle on where they store their used envelopes.
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SL - on the police / crime thing you may find this interesting. A move to NYC or LA to get away from crime may be in order.
I have a piano, which I had tuned last year for the first time in about 15 years, when my son started having lessons. (For the previous 15 years, it had hardly been played.) I found a piano tuner from the Yellow Pages, a middle aged man who told me that he was always busy. He tunes piano in private houses as well as in public places eg schools.
I have since noticed that many people whose kids are learning to play, rent a piano.
Which makes me wonder a) what proportion of private domestic pianos are rented and B) how this impacts on the regularity with which they get tuned.
PS: the piano tuner advised me to have it tuned about once a year. I doubt I’ll be doing that - unless it develops an obvious problem.
suz,
We had a piano and even with my awful ear for music I could hear it out of tune after about a year. My advice would be to book him in for a tune next year.
If you’re Richard Feynman you take off the glasses you’ve ben instructed to wear so that you can see it directly…
Great post, Robert.
Actually, this piano tuner question sounds like the sort of thing that management consultants apparently ask their potential recruits at job interviews on the spot.
Fantastic post.
Catering is the only area I’ve really relied on this kind of thing, where the number of variables and ranges of variation cooking for 25 culinarily diverse people are occasionally mind-boggling - though no doubt not compared with the physics of a nuke explosion. Experience plays a huge part though. I’m over- and under- catering much less than I used to, and can only surmise this is because my back-of-envelope methodology is getting better.
I wonder if it would be useful to do a Fermi calculation on how many blog posts are paraphrases of wiki articles, and similarly, how many responses are based on, and contain quotes from wiki.
The corollary would be, if there was no wiki, would the blogosphere content look very different from what it is?
Lazarus: if it weren’t for Wikipedia, I’d actually go have to look up some books.
That said, I also have to give credit to LP blogger Mick, who when I mentioned I was doing a post on this, pointed me to the story about the bits of paper.
I estimate a whole lot more pianos. I’m guessing more than 1 in 30 in homes.
In schools: At least 1 piano per 400 students, while 1/6 residents are school students: Over 1000 more pianos.
In churches: 1 church per 2000 residents, and one piano per church, is nearly 2000 pianos.
OK, so neither of them affect the total very much.
But most pianos don’t get tuned that often. Maybe 3 years is the average.
A question in a computer science exam: Estimate the number of paving bricks in Rundle Mall.
The other one that came to me a few years ago was when I left a back door unlocked and got quietly burgled during the night. I reckon the doors are locked at least 95% of the nights. So if the burglar came only once or a few times, he fluked it - more likely he’s visited a number of times. And multiply by all the other homes, and on an average night how many people are going round checking random back doors to try and steal stuff!
Two houses in our street have been burgled in the past year (a year apart) from having left keys in letterbox (or under a potplant). Which indicates to me that there’s quite a lot of key-searching going on.
Robert,
That was a brilliant post. You are the only Larva-Prodder whose opinions I cannot guess from looking at the header. Thats a compliment, BTW.
My father, being Italian and a partisan sapper during the war, was fiercely proud of Fermi’s explosive achievements. So Fermi was a hero to me from an early age.
One thing that you should stress about Fermi is the importance of the follow up test, with predictions and corrections. Always distrust people who are unwilling to stick their neck out and make a prediction. Your back-of-the envelope formula should be taken into the world and the numbers should be given a run.
I always try to derive predictions from my theories. Of course luck and unanticipated complexity can sometimes confirm a prediction, despite theory being unsound. And refute a prediction, despite theory being sound. So you do need properly controlled and accurately measured quantitative tests.
Robert says:
You do not need to have great mathematical ability (diff calc and stats 101 was my limit) to get along way. Just basic algebra and commonsense. I got the first from doing Economics. It is not for me to comment on the second.
A while back I noticed the AEI making absurd sounding claims about declining European productivity. I forwarded it to Pr Q who remarked that “the numbers just did not stack up”. I found (cf “Jack did the sums…” in the Quiggin link) that the AEI’s numbers did not support the conclusions they were drawing.
I have an ironic application of the Fermi method: use it to solve the “Fermi paradox“: where are they? “They” being the alien civilizations that physcists predicted would populate the universe.
Drake developed an equation to provide a Fermi problem solution to the Fermi paradox! It attempts to predict the frequency of earth-style alien civilizations based on applying anthropomorphic knowledge to cosmological data.
But the Drake equation predicts multitudes of alien civilizations. And yet, as Fermi observed, we have not heard a single peep out of any of them.
A number of explanations have been forwarded to explain this puzzling discrepancy. The most obvious one is that Drake equation massively overestimates the probability of intelligent life emerging. As SJ Gould remarked, if we were to replay the evolutionary tape again it is most unlikely that H.Sapiens would successfully evolve. It is likely that we are alone, at least in this time and accross space.
I would be interested to see Robert using the Fermi approach to have a crack at the Fermi paradox. And any other Larva-Prodders who are sick of trying to prove that black is white and up is down on politico-cultural matters.
Excellent post.
Just on pianos, Robert, once a year is wildly optimistic was my thought. I know of two in households that were tuned once in 20 years. I asked my wife how often her preschool piano was tuned. Answer: “Never”. She said she had some people there from the Con once and they said it was “OK”.
(She’s not an idiot with music, had lessons with Max Olding, got her letters and played Mozart concertos and stuff.)
I’m doing rough numbers all the time and only did school maths. I think proportion is particularly important.
Eg, when people say we shouldn’t give ex-PMs a secretary and a car etc they don’t realise what a piffling amount of money is involved in terms of the Commonwealth budget. Very rough back of the envelope - 4 times whatever, definitely less than $10m, maybe even less than $1m. How many schools do you get for $10m. Think of the cost of a domestic house as an indicator of building costs. Probably less than one high school, maybe only a building or two.
Conclusion: A few mill out of $200b plus. It’s not worth the trouble figuring out the correct answer.
Another one. The cost overrun on the Goodwill Bridge in Brisbane was about $8m from memory. How much is that as a proportion of a $5 billion plus works budget. Again, it’s not worth working out.
Funny to gradually watch the back of the envelope slowly turn into the back of a massive postpak.
Once you decide to do a “proper” investigation of piano tuning demand, you have to factor in the average build quality, average range of temperature exposure, average frequency of transportation (even rolling it across the room affects tuning, but as always the amount is a factor of build quality), purpose of use (the Legions’ club is likely to be more tolerant of “character” than a music department), frequency of use. Starts to look like ecology before too long - so many variables interacting you’re tempted to run back to the clunky estimates you started with.
Instead, let’s estimate how often pianos are tuned.
- same number of pianos, 60,000
- 137 piano tuners
- (guess) a tuneup costs $150
- (guess) a piano tuner needs to be grossing $50K/year to bother advertising
So (137 * 50K)/150 = 45,000 tuneups per year — so they are getting tuned around once per year.
As an ex-physicist I’d like to add a “me too” to the chorus of praise. Though I think just getting most people to not be afraid of using any math at all would be the real breakthrough!
Jack: the Drake equation is a grand name for a concatenation of many numbers and probabilities, most of which are poorly known. (In astro we used to joke about the ecstasy of getting an observation to agree with theory to within a factor of 10 … which is harsh but not entirely unfair
So it’s not really true to say that the DE itself predicts anything; it depends upon the assumptions you make in plugging the numbers in. In fact, it is itself just an exercise in orders-of-magnitude/back-of-the-envelope thinking, of the kind Robert is talking about. The primary value of this (in line with Robert’s comment above) is that it makes explicit your assumptions about the size of the habitable zone or the communicative lifetime of a civilisation (and makes you think about how to refine them); secondarily it gives you some massively ballpark figures for the number of civilisations in the galaxy, just as something to guide your thinking. But no SETI astronomer says anything like “The Drake equation predicts one million civilisations, therefore …”, because it’s almost as easy for it predict 1 civilisation. It’s understood to be primarily a heuristic tool.
By the way, I met Frank Drake a few years ago, at a SETI conference. He was happy to pose for photos, sign a copy of one of his books and answer some follow-up questions I had by email. A very nice chap!
FDB, I was looking at something similar recently on global warming. Don’t hold me to the figures.
The sea level rose 15cm last century or an average of 1.5mm pa. But at the end of the century it was rising about 3.4mm pa. Anyone can see (except Turnbull/Howard and mates) that the IPCC forecast of 18-59cm for the 21st cent was based on the notion that the rate wouldn’t increase further, which is wildly unrealistic. Stefan Rahmstorf and mates at Potsdam did some very complicated mathematics (actually just before the IPCC latest) and came out with the notion that the better answer was 1 metre (midpoint), provided the process was linear and the ice sheets behaved.
That seems sensible, it looks right (forget about the envelope).
Then Hansen and 47 mates, including Rahmstorf, ran their models etc but in the end they looked and behold in the last interglacial the sea level was 5-6 metres higher than now, with a temperature 1-2C higher. Worse still when the temperature was 2-3C higher 3 million years ago the water was 25 metres (plus or minus 10) higher. If they built complicated mathematical models they’d have to conform with this or they wouldn’t believe them.
But they don’t have any idea about the timing. So the 1m becomes the lower bound and their best guestimate is 1-5m by 2100. Makes sense to me. Better tell the pollies.
Hmmm. Lots of enthusiasm from people with a scientific bent.
What I’m really curious about is those who come from the humanities side of the fence.
Well, I started out on the science side of the fence and later lept over to the humanities side, does that count?
Is it allowable to cut up a poorly tuned piano with a well tuned chainsaw. I have a well tuned chain saw, however not a piano. I have written yes on the back of an envelope, just need confirmation. Would this cover both science/humanities?.
Lol, Lang Mack.
I’m a humanities person, and in the literary/philosophical/cultural studies end also, without formal statistics training, or physics past a certain point in high school. Revealing assumptions is what it’s all about for me, so I’m all for honing the back of envelope as a skill. I’ve just added ‘Remember Enrico Fermi’ on my imagined list of useful things to remember.
I think it will come in handy next time I try to get myself into debt. A quick back of envelope will probably give me an idea of whether I’ll actually be able to pay it off in this lifetime, or if it might make two. Maybe a useful tool against self-deception, then?
“If you’re Enrico Fermi, you start dropping little bits of paper and noting where they land.
If you’re Richard Feynman you take off the glasses you’ve been instructed to wear so that you can see it directly…” Martin B at 1:11 pm
Strictly speaking he didn’t look directly at it, he watched it through a car windscreen to filter out the UV rays. Standard glass filters UV. Look along the edge of the glass, if it has a slight green tint then it filters UV, but if it is tint-free (rare, usually specialised glass) then it allows UV through. The green tint comes from an iron compound (I think).
“Is it allowable to cut up a poorly tuned piano with a well tuned chainsaw.” Lang Mack at 5:01 pm
Allowable, if it is your piano, but highly unadvisable. Chainsaws and piano wire won’t mix very well.
Adam, well thank you very much, um, for the non answer, that was sort of an answer, bit Rupert Shelldrake,however a lot deeper, I think.
I can buy an out of tune piano cheap, and cut it up with the well tuned saw and put the results on the back of an envelope and note the lilt. Maybe to help you when you ‘try’ (it approaches me by stealth) to get yourself in to debt, you could become wealthy by chain sawing up pianos,and I can be your man here to do the ground work and supply you with envelope backs, with info;.
Opens up a whole world, angle grinders on Bassoons, fencing pliers on Harps, a Kelpie as a Bag Pipe tuner. I even have a brew made from corn flour and cement that knocks over Rodents like you would not believe.
“How in the hell do people who haven’t done first-year uni physics cope without the immense utility of envelope backs?”
Not terribly well - which may go some way to explaining why people travel ridiculous distances to their primary place of work, sitting behind inefficient internal combustion engines which depreciate at alarming rates, & spew vast amounts of pollutants. All of which is paid for by indebtedness, requiring the average employed Australian to work a minimum of 41 hours a week. Not to mention the poorly designed homes with no regard for climatic realities, stuffed full of energy inefficient consumer goods - all of which is also paid for by a lifetime of debt. A couple of hours of envelope logic would benefit most of us. Ah but we now espouse educational philosophies delivered by our grand poohbahs that worship at the font of wrote learning, rather than the development of logic skills.
I remember reading about this some 20 or 30 years ago, probably in something Martin Gardiner wrote in the Scientific American.
The problem with it (as I think may have been pointed out in the same article) is that most people don’t know the necessary data and are completely useless at estimating it.
Some people are able do back of the envelope calcs and make educated guesses about things, primarily because of the knowledge and education that informs the calcs and the guess.
Subsequent sound research and calculation will either confirm or rebut the initial guess.
Other people do the back of the envelope calcs, and determine, eg, that the US will be greeted with flowers and candy when it invades Iraq.
Garbage in, garbage out.
Well its an interesting self-exploration.There are many types of bullshit,that simply require nothing less than to listen watch or read the ensuing flow. I have physics books and have been reading science mags for a long time,and often find myself ,knowing….. I am indeed deficient in quick calculus. But there are many ways also of reasoning why your piano tuner calculations will be always inefficient. Because you maybe characterising the problem mathematically. If you looked at the problem from an individual piano players perspective that is the real problem of a a real circumstance ,where a tuner maybe needed. And if your computer skills were better,or as good as maybe your maths you would find a computer programming function for the piano players at home. Not scolding you here,but pointing out, the failure of assuming that a quick calculation would derive a sense of reality ,where a telephone call to a piano player may derive a sense of availability of the tuners and ,hence something close to an instinct.,about numbers in the requirement of this subject. To assume that an accuracy will be less definitive as measure,by other means other than quick calculations,really denies,the reality of a subject. A logical enquiry would not necessarily make one chose the quick calculation,or indeed,the telephone call,depending on the necessity of the final numbers. With much talk of emotional intelligence,which surely could make one precise about bullshit,but not necessarily with a chosen heuristic as support…your blog subject is still quite worthy. If you have evidence that someone public is a real bad judge of character,could it be that you may then believe this will bring axiomatic realities about calculations too.? What disappoints me about most people with some type of University training,is how limited they sometimes are under pressure,and, within the field of their studies,but not necessarily studied as working tangible examples. And there may well be self trained piano tuners,not cheating,musical teachers who tune pianos, apprentice piano tuners who still are plainly not being paid,and pianos themselves rarely played,by,their owners today,because an wasted amount of time is spent earning an income,without a piano in sight.Perhaps you need to combine your interests in Fermi with the piano and let others see the result in some way.
Umm, yeah. The rest of that one was supposed to be a reply to Robert earlier in the thread, but I guess I didn’t make that clear =)
I think the Kelpie is a very good idea…
Lang Mack - I was so inspired by your theories I drew a ‘67 Strat on the back of an envelope and hit it with a Stilson wrench last night.
When can I expect the money to start rolling in?
” Robert Merkel on 26 June 2007 at 4:19 pm
Hmmm. Lots of enthusiasm from people with a scientific bent. What I’m really curious about is those who come from the humanities side of the fence.”
Robert, as a completely unqualified autodidact, I’d like to commend you on your thought provoking post. I’ll never be able to view a return address the same way again.
The Strocci Hypothesis:
“It is likely that we are alone, at least in this time and accross space.”
So……. it’s just us, and of course, Jack, at the centre of The Strocciverse. I guess this is how String Theorists define a no ‘braner.
Yes - the purpose of the glasses was to filter out the UV - so why not look at this colossal explosion, probably as hot as the centre of the sun - something you’d devoted years to achieving? I wonder how many people have looked at a nuclear explosion (not counting the sun, ok?)
As a total aside to the discussion, the Bhagavad GItA passage often quoted by Oppenheimer (11:32) is better translated as: “I am TIME, the destroyer of worlds.” The context of the passage is actually often cited in support of the Hindu just-war theory.
(11.33) … These warriors are already slain by Me; you are only my proxy, Arjuna.
(11.34) You (should) kill … other brave warriors; who are already killed by Me. Have no fear! You will certainly defeat the enemies in this war. Hence, fight!
Antonio; I gathered it was a bit of a mistranslation.
Incidentally, Oppenheimer never actually said it until a decade afterward - his claim was that he was thinking of it at the time. His immediate response to the test was apparently the rather more prosaic “it worked”.
I’ve always found the quote pretty banal. “Time” is far more evocative and interesting.
Thanks Antonio.
FDB, a cheque (on the back of an envelope) for a large amount payable to me will answer that question…….
Okay, LM, I tried that but nothing’s happened.
Should I hit the cheque with a piano?
If so, do I need to tune it first?
If so, should I tune the piano or the cheque?
You see my problem.
Fantastic post Robert! I completely love Fermi problems. I remember back as a young undergrad some 10 years ago now learning about Fermi problems. One of the things that struck me was how easy it was to use very simple math to get some sort of answer to very hard problems.
One of the things that used to get me down about physics was how hard the math can be for even very simple problems. What struck me about Fermi problems was the beautiful fact that very hard problems can become very easy if you are willing to sacrifice some accuracy. Indeed, this concept emerges frequently in theoretical computer science (which is kinda what I do nowadays), problems that are almost impossible to solve by a computer quickly CAN be solved quickly if you are willing to sacrifice some accuracy in the solution. Now sometimes this lack of accuracy can burn you, but in many “real world” problems estimates are more than enough.
Thoroughly understanding how these trade-offs work, that is the trade-off between a quick and rough solution and an impossibly slow accurate solution, is now regarded one of the key questions in computer science, mathematics and physics.
FDB, hit the cheque with a stamp,stuff the piano, and post it to me, double the amount as I can see you need a mentor.Then again, FDB, means a cheque in total for $4.00.Sigh.
Robert Merkel on 26 June 2007 at 4:19 pm
What I’m really curious about is those who come from the humanities side of the fence.
Well you have a whole blog roll full of them on your side of the webmasters fence. They cant say they werent told!
Humanitiarians tend to be poor at numbers because they are attracted towards subjects heavy on literacy instead of numeracy. NOt that theres anything wrong with that.
I experience some frustration with the more “humane” Larva Prodders who seem unwilling to put numbers on theories. Something about the uniqueness and complexity of social events. And an unwillingness to admit cherished beliefs are flat wrong. Bottom lines are unkind to people with their head in the clouds.
Speaking of woolly thinking, a Fermi approach, had I taken it, to forecasting Iraq-attack would have saved me much embarassment. The experts worst case scenarios low-balled it. Obvoiusly General Shinseki had a pretty good ball park figures in mind before he blew the whistle and fell on his sword.
Unfortunately Fermi methods are not so useful in circumstances where hard data are difficult to ascertain, relationships are complicated and forecasting horizons are lengthy. The paradigm case for this is the greenhouse effect, which has only been sorted after exhaustive data collection and extensive theoretical consensus.
Enemy Combatant on 27 June 2007 at 11:22 am
So……. it’s just us, and of course, Jack, at the centre of The Strocciverse. I guess this is how String Theorists define a no ‘braner.
THis “Strocchi-verse” trope is looking weaker by the minute, especially as most non-insane, non-corrupt, non-comatose members of the Left tilt towards Howard’s way. In fact the actual universe seems to be asymptoting towards the “Strocchi-verse”, going by the bi-partisan response to Howard’s authoritatian nationalism in many formerly contested areas.
BTW, what testable predictions has Enemy Combatant put out there? Or even Fermi approaches to curly problems? Or anything apart from running the Howard-hatred macro installed on all Larva-Prodder computers, which automaticly transforms a single keystroke into a pre-compiled script - no thinking required.
Instead of indulging in puerile piss-takes you should be re-examining the moral and intellectual bankruptcy of you and your comrades left-liberal ideological programs. That means testing and rejecting ideas as judged by their conseequences. Or do Left-liberals regard a generation of rock-spiders crawling all over defenceless children as success?
Great post - I never knew that and didn’t know about Fermi (or even the term).
Well I’ve always worked in human services - but probably don’t cut it as a humanities person (got slagged off here last week re: bad grammar).
I use ‘back of the envelope’ stuff all the time except I’d nearly always use a spreadsheet. I’ve kind of forgotten how to do things like long division by hand!
EC, Jack, stoushing over the alleged decline of the wets or the concept of the Strocchiverse is offtopic for this thread.
Thank you.
Jack, “from the non-humanities side of the fence”, lets rip.
“Instead of indulging in puerile piss-takes you should be re-examining the moral and intellectual bankruptcy of you and your comrades left-liberal ideological programs. That means testing and rejecting ideas as judged by their conseequences.(sic) ”
Jack, for goodness sake man, will you kindly submit your invective to a spell-check before posting. It does tend to diminish you as a rhetorician.
“BTW, what testable predictions has Enemy Combatant put out there? Or even Fermi approaches to curly problems? Or anything apart from running the Howard-hatred macro installed on all Larva-Prodder computers, which automaticly transforms a single keystroke into a pre-compiled script - no thinking required.”
If this is the best that you can do, Jack?
I’m afraid you’re going to have to lift your game, son. Taking liberties by grouping me with all LPers, as if each of us is tarred with the same Mauve Brush of Left Liberalism is a bridge too far, mister. Surprised you havn’t sussed what hues of the political spectrum rest most comfortably with me since we first began exchanging tentative pleasantries many threads yore. Perhaps Oz blogdom’s Energiser Bunny, like the Carrollian White Rabbit, is just far too busy to absorb such detail.
But Jack, since you HAVE generally been putting in an effort lately, I think it’s only fair that your request for me to “put a testable prediction out there”, be met. Are you paying attention? Good.
When “the pieces of paper(ballots) that were(will be) in the process of falling while the blast was passing(the next election)”, actually fall; I predict that The Howards will require the services of a piano tuner after they move out of Kirribilli.
Got any Fermi figures on Sydney Steinway stretchers, Jack?
OK, Robert, been away from the keyboard. Point taken.
“Well I’ve always worked in human services - but probably don’t cut it as a humanities person (got slagged off here last week re: bad grammar).”
Angharad, I think grammar is pretty low on my list of potential disqualifiers for being a ‘humanist’, if that’s any consolation. The forgetting of long division sounds suspiciously like a humanities-related syndrome to me, but then again, you do use spreadsheets. Personally, I’d define a humanities person as somebody who prefers to look at a great big block of text to a set of equations.
My favourite Enrico Fermi story is how shortly before the Trinity test, he was caught offering side bets on whether the blast would cause a chain reaction to ignite the atmosphere and so destroy all life on the planet. No word on how he planned to pay out in such an event.
Nabs, you haven’t finished your anecdote. What happened next? Did all life get obliterated, or not?
Similar to this, some people have been worrying about the Large Hadron Collider being constructed in Switzerland, which maybe will generate a black hole that will swallow Planet Earth for lunch.
At any rate, that’s what these folks seem to think — they’ve done a back of the envelope calculation and concluded that “If we add all the risks for the LHC we could estimate an overall risk between 11% and 25%!”
http://www.risk-evaluation-forum.org/anon1.htm
Is this an example of the dangers of envelope calculations? Or do these guys have a point?
I wouldn’t sweat it Paulus.
The Swiss banking system has long experience of managing black holes into which money vanishes and from which no information returns.
Oh, okay. Most of us probably want to keep quiet about stuff we don’t know much about, but I thought this was fascinating. (And I do a crude version of the envelope back thing a lot.)
I’d not heard of Fermi, but I’ve read the Bhagavad Gita and I’ve got a piano. And from the amount of time the tuner spends here when he comes, I’d say one of the reasons you turned up more piano tuners than you were expecting was that five a day is probably too many. Three, maybe four on a good day, might be closer to it. (Piano tuning is of course also about physics, is it not?)
And vice versa, Jack. And vice versa.
I normally treat Enemy Combatant’s two cents worth with lofty disdain. Sorry to bring the tone of the place down by breaching my rule.
On-Topic: I think the Fermi method is part of a range of handy scientific tools that even humanitarians can bring to bear in the solution of intellectual problems. These are in the nature of “fallacy detectors” that any witted person can apply to save time:
Occam’s Razor: dont unnecessarily multiply explanatory entities. It is to the theoretical as Fermi’s method is to the empirical: a way to control for outlandish postulates.
Eliminationism: deducing implications and controlling by observation. Popper comes in for some well-deserved flak for underrating the scientific utility of statistical probability in providing positive support for a theory. But his “logical negativism” - the continual search for flies in the ointment - is a pretty good way of screening out obviously nutty ideas.
There are several techniques to avoid howlers, which steve sailer handily summarised here. I have precied below:
Man bites Dog: the fallacy that any exception disproves the usual rule. Statistics deals with tendencies which have coefficients somewhat less than unity.
Arguments from Anecdote: the fallacy that any instance proves an unusual rule. So an example of a lazy or dumb NE Asian should not deter Microsoft from switching their R&D headquarters to Bejing.
Fuzzy social causes: attributing causal powers to one favoured factor amongst many. Otherwise known as spin.
The Devil Made Us Do It: The opposite of fuzziness. Attributing demonic powers to some reliable hate-figure eg Howard and conservative tendencies in the public.
Point and Splutter: Just repeat an opponents position and add moral outrage, as if indentification is commensurate with refutation.
Anyone else got any bright ideas about making social science commentary less ideological and less ball-busting?
“Anyone else got any bright ideas about making social science commentary less ideological and less ball-busting?”
I dunno… howsabout not reducing everything to a page in your grand wet/dry narrative?
You left out false dichotomy:
Oh boy, this is a beaut (from the Steve Sailer post):
Is the actual point of Sailer’s piece to demonstrate a range of argumentative howlers by example?
Parsing it and applying my own Fermi-like test of whether Sailer is talking sense or nonsense, I find five questionable assertions in succession - factual content zero. Ergo, I am 95% confident that the whole lot is B-U-L-L-S-H-I-T.
Great post Robert.
P.S. If you haven’t done first year physics you would survive if you did year 12 physics in my home state at the time I was finishing high school (because you couldn’t pass the dreaded section C of your final physics exam without it)
Not where I was in high school.
Joan Kirner was still working out her rage at being pushed through a selective government high school. The consequent dumbing-down of the VCE physics curriculum meant that you could get through Year 12 physics knowing the solutions of Newtonian mechanics for constant acceleration (translation: you needed to remember four simple equations and that was about it).
Lovely post Robert. I’ve not read all comments, but you should mention that Keynes was a dab hand at the same kind of thing and back of the envelope or BOTE models are critical in policy economics. Not that the skill is taught in economics schools of which I’m aware - sadly and not surprisingly.
Economists are often shy of offering BOTE models, often preferring precise and elaborate models with a range of implausible assumptions to something much simpler and more intuitive. Sad, but true.