From NYT: Good at approximation? Maybe you are the next math superstar!

Interesting article in the NYT science section on the power of approximation and how those folks who are the best at ball park guessing, may have a natural ability for advanced mathematics.
“When mathematicians and physicists are left alone in a room, one of the games they’ll play is called a Fermi problem, in which they try to figure out the approximate answer to an arbitrary problem,” said Rebecca Saxe, a cognitive neuroscientist at the Massachusetts Institute of Technology who is married to a physicist. “They’ll ask, how many piano tuners are there in Chicago, or what contribution to the ocean’s temperature do fish make, and they’ll try to come up with a plausible answer.”
“What this suggests to me,” she added, “is that the people whom we think of as being the most involved in the symbolic part of math intuitively know that they have to practice those other, nonsymbolic, approximating skills.”

So, I had an expensive lunch today. $10, plus $2 worth of iced tea and a $3 tip. But! Two kebabs, a pile of rice, a Greek salad and two lamb chops! It was late, I completed a big and miserable project and wanted to treat myself. Besides, who has lamb chops for lunch?! Anyway, back to the approximating. My lunch was about $15. AIG's bail-out loan from the Fed is estimated at $85 billion. So, that is about 5.6 billion kebab, lamb chop, Greek salad, rice and iced tea lunches.

My beloved San Fernando Valley has about 1.8 million people and, if it was a city, it would be the 6th most populous in the nation. If I got an $85 billion dollar loan from the federal government, I could buy about 3000 lunches for every person in the San Fernando Valley. From the equine estates of Chatsworth to the Tarzana chicken coop of Mark Frauenfelder, from the handmade carnitas of Carrillo's in San Fernando to the Walt Disney Studios in Burbank, I could buy 3000 lunches per resident. Let's face it, with two kebabs and two lamb chops, that is a dinner. So, an extremely hearty lunch, a sturdy dinner and I will add two egg McMuffins for breakfast so, let's see, that would raise the per day cost per resident to about $33. Perhaps that won't get you far in Londo but, in Los Angeles, that is an ample per diem!

At $33 per day, I could buy every resident in the Valley breakfast, lunch and dinner for, hmm, about 3 years? Or I could just buy everybody a new $50,000 Mercedes!

NYT: Gut Instinct's Surprising Role in Math (Registration required)
Also, from NYT, fun little game to check your mathematic gut instinct

(Mister Jalopy is a guest blogger!)


  1. I got 88% of the time. The key is to hold your breath, don’t blink, and look at the negative space not at any one particular dot.

  2. A professor I had would regularly pose such questions as “how many ping pong balls would it take to fill this auditorium?” or “how much does an average house weigh?”

    I regularly do a quick approximation when I hear things like figures touted on the news about schemes to power toll booths by harvesting the power of cars driving over spring loaded road sections or just about any statistic.

  3. Four kebabs, four lamb chops, and two Egg McMuffins a day. After the heart attacks, your beloved SFV may not have 1.8 million people. It sure sounds like a great meal to have once a week or so, though (the kebabs & chops, not the EggMacs).

  4. If an average “adult” gets it right 75% of the times while I’ve made no mistakes at all in 30 tests, I wonder how bad my brain is going to become in the next 15 years… :(

  5. This is kind of what Right-Wingers do when trying to explain societal changes they disagree with:

    “Why are people getting divorced? Must be gay people.”

    “Why does about half of society disagree with our policy and actions? They hate America, and are probably gay.”

    “Who is getting our kids hooked on drugs? Mexicans. No, we used Mexicans last year, go with Muslims, gay Muslims.”

  6. I have trouble when it’s different by 1 dot, or if the dots become a mass of dots. Good article, and a really fun game!

    (If I read this correctly, this means that Mister Jalopy owes us all a kebab, right?)

  7. Cathoo, the key to the mass of dots of both colors in the same area is to blur your vision so the size of the dots is not as recognizable. Since you will be looking at the background not the foreground, the colors can float in two directions and sort themselves out behind your sight.

    At least that’s the way I’m doing it.

  8. AIG’s bail-out loan from the Fed is estimated at $85 billion.

    If AIG is going to get a bail-out — because it’s so “inextricably woven into the global financial system” — how about we hit up some other governments beside the U.S. to help pay for it?

    Can’t say I’m really keen on seeing Americans working to pay for the massive transfer of wealth into the hands of criminal mortgage brokers and their shareholders and partners throughout the aforementioned global financial system.

  9. Different sizes can fool me. I would have thought I would test higher – doing this repeatedly I ended up in the high 80s. But given my overall math skills I would have expected more, probably close to 100%. Maybe it’s because I’m drunk.

    But no question, quick estimation skills are a good test – the ability to assess reality in purely numeric terms.

  10. Well after 100 attempts, I went down to only 86% from 88%. Still, that’s fairly accurate since most of my math scores have been in the B to A- range.

  11. 88% but that would have been higher if I hadn’t been second guessing my intuitive first call on about four of the screens. My match scores were never better than 65% if i worked very hard.

  12. While stocking water jugs at Wal-Mart, I used to try estimating how many Otter Pops (or milk gallons, etc) were produced in a year, and how much they weighed. In fact, I do this all the time. However, I’m ridiculously terrible at math.

  13. 90% of the time over 30 attempts. What I did find strange though was that about 80% of my incorrect guesses were in the first 40% of my attempts.

    With this reasoning I could assume that that I would either get better at the game as time goes on, or at the very least level out and after approximately 100 attempts (which I won’t do while I’m at work) I would expect an average of perhaps 95%.

  14. And another quick 10 attempts has supported my theory. 92% correct, no incorrect guess in those 10 attempts.

    Better close this window. Addictive.

  15. 90% over 30 attempts. Very addictive.

    It took way too long for me to adjust to the game. Often I would click yellow 4 times in a row because I was so sure that yellow appeared more even when I had that gut feeling that blue looked a bit more concentrated.

  16. If you’re an American taxpayer, for only one dollar a day (rounding up a bit), you too, will bail out the country’s largest insurance company! Isn’t that much better than saving a starving child in a third world country? Maybe we should be requesting that the US government send us a monthly story and picture of a disadvantaged CEO being helped by this program.

  17. Great article, thanks for bringing it to my attention. Based on the test, I estimate the probability of me becoming the next math superstar at about 140%. And with math chops like that, you know that’s a dead-on estimate.

  18. so what you’re saying is that we could pretty much make sure that , at least for a few months, no one in america would go to sleep hungry….

  19. Granted, this is a biased audience. “Half of all adults are above average”, and using the web/interested in learning random facts (ie, BoingBoing reader) is a self-selection filter. So I’m not surprised we’re scoring above the NYT stated average.

    On the other hand, I wouldn’t put it past the NYT to deliberately state a slightly low number, so their readers score above it, feel good about themselves, feel good about the NYT, and buy into the brand a bit more. That’s a classic bit of marketing psychology.

  20. Estimation is a good time, but I would be more inclined to believe self-selection in this. They know they “have to” practice these skills? No, this is the kind of thing that you do for a laugh, if you’re quick at using rough calculations to estimate something. If you’re excited enough about raw math to become a mathematician or physicist, you probably enjoy throwing numbers around.

    In other news, AIG has solid assets to back the loan up with, and is still profitable. I’m not happy that the bailout had to happen, but it could have been a hell of a lot worse.

  21. Most equations that pop out of physical theory are actually unsolvable. The world is nonlinear. So even the equations themselves or approximations and then most of the time you have to look for an approximate solution.

    I’ve been teaching my 10-year-old to do approximations prior to division: Just a ballpark so he can see whether his solution doesn’t have a major flaw. The same is done in physics, and for most things if your equations bring you in the ballpark then you know you are not super far off in terms of your assumptions.

  22. #25, Technogeek:

    Half of all adults are above average

    No, half of all adults are above median. I guess you’re not the next statistics superstar.

  23. TL;DR, however this chunk of the quote:

    “What this suggests to me,” she added, “is that the people whom we think of as being the most involved in the symbolic part of math intuitively know that they have to practice those other, nonsymbolic, approximating skills.”

    is nonsense. Mathematicians and physicists do this because it’s fun, period. They aren’t practising anything.

    I don’t know whether this sort of thing has any real relevance to actual math or physics research, but I tend to doubt it, since this is not science. It is well established that any basic numerical skills are a fairly good predictor of ability at doing real math and physics work, and that’s probably all there is to see here.

  24. I’m at 85% over 40 tests.

    But what I’d be really interested in seeing is whether there’s a systematic colour bias – do I overestimate the yellow, and underestimate the blue? (I suspect I often do, because the yellow’s just so much more vivid)

  25. Hm, 1 tril each for the wars and for the financial fuxx0redness, that’s 6 grand per capita. I used to live in Ithaca, NY, population 100,000. $600M could pay for the most excellent boondoggle project of a 3 mile subway running from Cornell, through downtown, to the forest of big box stores on Meadow Rd. On certain assumptions the wars will cost an additional 3 grand per capita, which could be used to pay for an extension up to the Pyramid Mall in Lansing, or to run a pair of commuter spurs into Cayuga Heights and West Hill!

  26. Meals at $33/day/person?
    You could easily stretch that to $33/2weeks/person
    or longer and they’d still eat well, maybe even better. But not at restaurants.

    The interest alone on $85B would probably provide meals for everyone in SF Valley forever. Anybody wanna do the estimates?

  27. We did Fermi questions in physics class in HS for our Physics Olympics. Questions like: how many gas stations are there in the Unuted States? Or, If you accelerated at g/2, how many seconds would it take to reach 0.1c? Answers had to be correct to the nearest power of 10.

    BTW, I got 100% through 25 tests.

  28. We had to do this in Engineering design 101 when i was at Uni and it is a great game but also essential skill for any engineer or scientist. You need to know if your carefully calculated computed complicated formula answer is vaguely in the right order of magnitude, as 38 says.

    The project we had to work on was to think of a machine to transplant a fullygrown oak tree. So how heavy, tall is the tree, what about the rootball and earth etc. How long does the crane jib need to be, what safe working load etc etc. Good practice.

    More recently when teaching Renewable Energy to a class of final year honours civil engineering students, I had them do something similar to figure out how much steel and concrete you would need to replace all the UK’s electricity production with wind turbines. They hated that because they were not used to assignments that did not have a precisely “right” answer. But real life is more like this than it is like an exam paper.

    My kids (not at all techy) and I sometimes do this game on long journeys and set each other loopy things to approximate, such as how long is a “piece of string”.

  29. Ok, I’m going to get vague here, but this reminds me of a book I heard about where the authors found that the average of a crowd estimate is usually pretty spot on. Say you have a contest where you guess the weight of a bull or how many gumballs are in a jar – if you ask everyone (or most everyone) and then take the average of the guesses – it’s a winning answer. It sounds like this study taken to the level of the individual. Judging from the response in the comments, it seems to be a pretty fair conclusion.

    On a non-related note, I used to amuse myself by asking random people the answer to points of contention brought up by conversations with my friends – like what’s the capital of Nebraska, say, or who played the crazy bitch in The Hand that Rocks the Cradle – it’s amazing what people don’t know they know when put on the spot.

  30. So how many gas stations are there in the US? I’d guess one station for every 5000 people based on the fact that there are three stations in my town of 16,000, then one per 500 to one per 50,000 should be OK, so ~300million/5000 = 60,000 gas stations. But that seems too low, so I’d revise to one station per 2000 people and get 150,000.

    I was at 88% after 40 games.

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