Home > math, math education > How Not To Be Wrong by Jordan Ellenberg

How Not To Be Wrong by Jordan Ellenberg

May 29, 2014

You guys are in for a treat. In fact I’m jealous of you.

I had a little secret about my survival in grad school, and that secret has a name, and that name is Jordan Ellenberg. We used to meet every Tuesday and Thursday to study schemes at the CallaLily Cafe a few blocks from the Science Center on Kirkland Street, and even though that sounds kind of dull, it was a blast. It was what kept me sane at Harvard.

You see, Jordan has an infectious positivity about him, which balances my rather intense suspicions, and moreover he’s hilariously funny. He’s really somewhere between a mathematician and a stand-up comedian, and to be honest I don’t know which one he’s better at, although he is a deeply talented mathematician.

Screen Shot 2014-05-29 at 7.21.14 AMThe reason I’m telling you this is that he’s written a book, called How Not To Be Wrong, and available for purchase starting today, which is a delight to read and which will make you understand why I survived graduate school. In fact nobody will ever let me complain again once they’ve read this book, because it reads just like Jordan talks. In reading it, I felt like I was right back at CallaLily, singing Prince’s “Sexy MF” and watching Jordan flirt with the cashier lady again. Aaaah memories.

So what’s in the book? Well, he talks a lot about math, and about mathematicians, and the lottery, and in fact he has this long riff which starts out with lottery math, then goes to error-correcting codes and then to made-up languages and then to sphere packing and then arrives again at lotteries. And it’s brilliant and true and beautiful and also funny.

I have a theory about this book that you could essentially open it up to any page and begin to enjoy it, since it is thoroughly enjoyable and the math is cumulative but everywhere so well explained that it wouldn’t take long to follow along, and pretty soon you’d be giggling along with Jordan at every ridiculous footnote he’s inserted into his narrative.

In other words, every page is a standalone positive and ontological examination of the beauty and surprise of mathematical discovery. And so, if you are someone who shares with Jordan a love for mathematics, you will have a consistently great time with this book. In fact I’m imagining that you have an uncle or a mom who loves math or science, in which case this would be a seriously perfect gift to them, but of course you could also give that gift to yourself. I mean, this is a guy who can make nazi jokes funny, and he does.

Having said that, the magic of the book is that it’s not just a collection of wonderful mathy tidbits. Jordan also has a point about the act of scrutinizing something in a logical and mathematical fashion. That act itself is courageous and should be appreciated, and he explains why, and he tells us how much we’ve already benefited from people in the past who have had the bravery to do so. He appreciates them and we should too.

And yet, he also sends the important message that it’s not an elitist crew of the usual genius suspects, that in fact we can all do this in our own capacity. It’s a great message and, if it ends up allowing people to re-examine their need for certainty in an uncertain world, then Jordan will really end up doing good. Fingers crossed.

That’s not to say it’s a perfect book, and I wanted to argue with points on basically every other page, but mostly in a good, friendly, over-drinks kind of way, which is provocative but not annoying. One exception I might make came on page 256: no, Jordan, municipal bonds do not always get paid back, and no, stocks do not always go up, not even in expectation. In fact to the extent that both of those statements seem true to many people is the result of many cynical political acts and is damaging, mostly to people like retired civil servants. Don’t go there!

Another quibble: Jordan talks about how public policy makers make proclamations in the face of uncertainty, and he has a lot of sympathy and seems to think the should keep doing this. I’m on the other side on this one. Telling people to avoid certain foods and then changing stances seems more damaging than helpful and it happens constantly. And it’s often tied to industry and money, which also doesn’t impress.

Even so, even when I strongly disagree with Jordan, I always want to have the conversation. He forces that on the reader because he’s so darn positive and open-minded.

A few more goodies that I wanted to adore without giving too much away. Jordan does a great job with something he calls “The Great Square of Men” and Berkson’s Fallacy: it will explain to many many women why they are not finding the man they’re looking for. He also throws out a bone to nerds like me when he almost proves that every pig is yellow, and he absolutely kills it, stand-up comedian style, when comparing Ross Perot to a small dark pile of oats. Holy crap he was on a roll there.

So here’s one thing I’ve started doing since reading the book. When I give my 5-year-old son his dessert, it’s in the form of Hershey Drops, which are kind of like fat M&M’s. I give him 15 and I ask him to count them to make sure I got it right. Sometimes I give him 14 to make sure he’s paying attention. But that’s not the new part. The new part is something I stole from Jordan’s book.

The new part is that some days I ask him, “do you want me to give you 3 rows of 5 drops?” And I wait for him to figure out that’s enough and say “yes!” And the other days I ask him “do you want me to give you 5 rows of 3 drops?” and I again wait. And in either case I put the drops out in a rectangle.

And last night, for the first time, he explained to me in a slightly patronizing voice that it doesn’t matter which way I do it because it ends up being the same, because of the rectangle formation and how you look at it. And just to check I asked him which would be more, 10 rows of 7 drops or 7 rows of 10 drops, and he told me, “duh, it would be the same because it couldn’t be any different.”

And that, my friends, is how not to be wrong.

Categories: math, math education
  1. May 29, 2014 at 10:11 am

    You are rapidly becoming one of my favorite bloggers. Thanks for this great recommendation.

    • Guest2
      June 2, 2014 at 11:57 am

      It was Jordan Ellenberg’s WSJ Sept 1-2, 2013 review that introduced me to “Liars and Outliers” (Bruce Schneier). Ellenberg’s grasp of current sociological and institutional challenges is amazing! Check out the review.

  2. cat
    May 29, 2014 at 10:21 am

    The kindle version is $14.95 which is $5 over my limit on kindle books. However you do recommend it so I’m tempted because I love books for nerds by nerds.

    Whats holding me back is I’m skeptical someone who is proven wrong by the first hit on “do municipal bonds always get paid back” google search can be trusted to have an informed position on any subject outside of their PhD.

    • May 29, 2014 at 10:24 am

      Worth $15 IMHO. And my quibbles were on one page of a big book.

      • cat
        May 29, 2014 at 11:22 am

        Let me just leave this here http://xkcd.com/793/

        and maybe it will make my point better.

        • June 2, 2014 at 9:22 am

          The thing is, if you read Jordan’s book, you’ll be struck by the depth and subtlety of his engagement with topics outside his official job description — it’s *exactly* the opposite of the xkcd comic. I’m a (politically liberal) academic economist, and his discussions of taxation and stock prices are better than most undergraduate teaching by professionals. When he glosses over some details, I’m pretty sure he is making a pedagogical choice as opposed to being unaware that bonds don’t all get paid. (Otherwise why would the interest rates on different bonds bonds be different? This is exactly the sort of thing even a silly mathematician can figure out.)

          I guess the broad point is that when teaching a conceptually subtle thing like expected utility theory, *it is acceptable to “lie” a little bit* about the real world, and treat a “bond” as a shorthand for “a sure thing” in a toy model, without feeling like one is slighting real-world pensioners who are left out in the cold. It’s easy to hold the contrary view only if you don’t have to teach these sorts of things.

  3. josh
    May 29, 2014 at 12:47 pm

    Thanks very much for the recommendation. I’ll get it.

    Amazon is not the only bookseller in the world. But it might be some day soon.
    http://bits.blogs.nytimes.com/2014/05/23/amazons-tactics-confirm-its-critics-worst-suspicions/

    Please don’t advertise for them.

    If you can afford it, buy it from an independent bookseller, If you can’t, ask your public library to get it. Admittedly, that’s a slow approach, at best) but you’ll be doing a public service. If you are in between, B&N is competitive with Amazon and not as evil (or, at least, not as big).

    • May 29, 2014 at 12:48 pm

      Agreed! And I’ll stop linking to Amazon from now on, they’re evil.

  4. David18
    May 30, 2014 at 9:37 am

    Looks like a fun book :-) You can download the kindle sample and read about a Nazi refugee shielding planes from bullets during WWII.

  5. JSE
    May 31, 2014 at 2:46 pm

    I’ll say this, though, Cathy — very often (as in the case of tobacco, which I write about in the book) industry and money are the ones most strongly promoting uncertainty and pushing back against the idea of making any formal recommendation, let alone imposing a regulation!

  6. June 2, 2014 at 9:10 am

    “no, stocks do not always go up, not even in expectation”

    How could you ever be sure of such a proposition, Cathy? I’m not saying that they do always go up in expectation, but how do you know Nature’s probability measure to know that Jordan is wrong on this?

    • June 2, 2014 at 9:12 am

      Anybody who’s lived through a stock market crash knows this.

      • June 2, 2014 at 9:23 am

        How do you know the expectations were wrong, as opposed there just being a low-probability realization of aggregate uncertainty? That is, how do you know the beliefs were wrong ex ante, and not just ex post?

        • June 2, 2014 at 9:27 am

          Let me put it this way. I don’t, and neither do you. It’s a fantasy to think there’s a mathematical argument to be made there. And more to the point, I don’t think anyone should give advice to people about where to put there money with a mathematical argument. If you wanna put your money there and you get that you might lose your money, then fine, but don’t think that being a math genius is going to help.

          On Mon, Jun 2, 2014 at 9:23 AM, mathbabe wrote:

          >

        • June 2, 2014 at 9:49 am

          I now see more clearly what you mean. Your critique of Jordan’s remarks on stock prices was NOT that you know the correct probabilistic model of their evolution, and you checked that E[ price tomorrow | knowledge today] is sometimes a negative number, and you are here to set the record straight. Instead, what you are saying is that: “E[ price tomorrow | knowledge today]” is not even a legitimate thing (at least not for giving financial advice). It is some kind of ill-founded burble, and so statements like “this burble is always positive” are not even wrong — they are just nonsense that is pretending we can mathematically discuss things we shouldn’t.

          Or maybe you are saying something more modest. Namely: Statements like “stock prices go up in expectation” are only valid in certain narrow (wrong?) models, and so talking about those models as if they were about ACTUAL STOCKS is misleading to lay readers.

          The first position seems extreme and wrong to me, but I have some sympathy with the second, more modest claim. Again, I think pedagogical license is okay here. It *is* valuable to think about finance probabilistically, no matter what your politics. And the simplest toy model DOES have all stock prices rising in expectation, and it’s fine to work with it and tentatively accept its fictions before moving to its critiques. The contrary view is like saying that treating rods as incompressible in a pop physics book is dangerous, since real-world bridges have collapsed because of compressible rods.

        • June 2, 2014 at 9:57 am

          I’m gonna say something in between the two. But yes, I think you’ve articulated my position better than I did. Thanks!

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