How Not To Be Wrong

Jordan Ellenberg promises to share ways of thinking that are both simple to grasp and profound in their implications, and he delivers in spades. These beautifully readable pages delight and enlighten in equal parts.  Those who already love math will eat it up, and those who don’t yet know how lovable math is are in for a most pleasurable surprise.

(Rebecca Goldstein, author of Plato at the Googleplex)

How Not To Be Wrong comes out on June 3, 2014 from The Penguin Press.

Preorder it:

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Shiny new webpage about the book coming soon!

21 thoughts on “How Not To Be Wrong

  1. Tom McCarty says:

    Dr. Ellenberg,

    Just gave up waiting for the ebook version of “How Not To Be Wrong” through the Montgomery County Public Library system (Davis Library next to Walter Johnson HS). I was number 56 and not getting any closer. I went and bought it at Barnes and Noble in Bethesda. After reading it for a couple of chapters, especially the Baltimore Trader, I called my dad to see if he still maintained an interest in math (as he used to talk about when I was a kid). He is an retired accountant. He was interested and actually had read about it through NY Times. Nevertheless he was not sure he wanted to buy it and instead thought he would wait for it in his library in Virginia. Anyway his birthday is August 28th and I would love to buy him a copy but would like to ask if there was a way I could ship it to you to sign and possibly get it back to me near that date? I see how busy you are, but this would certainly be the more interesting birthday presents he’s gotten. Look forward to hearing from you and thanks.

    Tom McCarty

    ps. I read about the book in my last issue of On Wisconsin. I got my BS in Bacteriology in 1986. Go Badgers!

  2. John Baez says:

    Why is it called “How Not To Be Wrong” instead of “How To Be Right”?

  3. JSE says:

    Because the title was a big enough oversell as it was?

  4. Henry Bliley says:

    Well, I have the book and in the first few pages I was frustrated to the max over the geometry of the circles and squares, and never got beyond that portion, and am still unsatisfied ……..eventually lost interest and now can’t find the book. :-(

  5. delicateear says:

    I am really enjoying the book… but it sometimes leads to really misguided places (which is part of the theme, I think). For example, how can you demonstrate an expected value of >$2 for a powerball ticket and encourage people to participate when ‘the payout is high enough’? The fact is that ANY winning on the scale of millions blows the doors off of any reasonable investment, even a daily ticket. The payout does not matter. The greater fact is that you are almost certainly not going to win, and obfuscating this by applying the given analysis is pure folly! The $2 you have is very different from the millions you almost certainly will not have. The analysis does not take this into account, and it serves only as another example of how misguided math and statistics can be, confronted with human psychology. This should have been flagged harder in the text; it is dangerous for people who on the blunt end of the lottery tax. Yeesh.

  6. Nadia says:

    Your writing about “math” and “madness” was colorful in HNTBW, but not especially well informed. It was also very inconsiderate of people dealing with mental health problems. Several of my family members and friends deal with mental health conditions, and I volunteer with organizations that help mentally ill kids and teens.
    You present no evidence from medicine or behavioral science to support any of your assertions about Pythagoreans or mathematicians and mental health. You talk about being mad as it’s one of the worst things ever, and as though the people who stumble into it have just been indulging in bad thinking habits. Meditation and math are things that keep one from going crazy, as though it’s all a matter of making the right choices like those.
    Actually, people who have these conditions often have a strong innate predisposition towards their afflictions, and they commonly face hard social/family circumstances. A couple of areas where decent empirical work has been done reveal that physicians suffer from depression and commit suicide at rates higher than others. Soldiers also suffer from certain mental health conditions at higher rates than the population. These two groups definitely make mistakes, but they have advanced the well-being of people all around the world.
    Many individuals with mental health problems have a lot to offer as colleagues, citizens, parents, and friends—those are the things that should matter most. These people should be judged on their character, actions, and contributions, rather than denigrated because of their encounters with madness. The world is a worse place when the latter happens instead of the former. Personally, one of my friends with anxiety and depression, lost her dad to cancer when she was a child and she wants to be a nuclear engineer to help develop safe technologies.
    You say you might go crazy without math. But, are all mathematicians like that? Consider Birth of a Theorem. Stephen Muirhead noted the joy and fervor that the author got out of math, but also “frustration, pain and even depression that Villani suggests is the inevitable result of such passion.” Villani is not lesser than you or other mathematicians for that. He advances his field, reaches out to the public, and lovingly fulfills his responsibility as a dad. Recall that DFW suffered from depression and killed himself. The adolescents and kids I talk to who have struggled with suicidal thoughts actually do not experience them the way DFW did. They contemplate killing themselves, but they think about their parents, just as Villani described thinking about his kids when he wished to die.

  7. Artie Prendergast-Smth says:

    Just ordered 8 copies. I don’t know exactly how royalties work, but I assume you can now retire and live in unimaginable luxury!

  8. Gerard Weatherby says:

    p 34. “No one knew whether the area of a circle could be expressed using whole numbers alone.” (footnote: It can’t …) Not sure what that’s trying to say … a circle with diameter 1/sqrt(Pi) has area 1, does it not?

  9. David Scott says:

    It seemed pretty obvious (to me) that the chapter on lotteries was telling us that lottery players lose. It says expected value is not the value you should expect. (or something close to that).

  10. David Scott says:

    I think the footnote about whole numbers was referring to they wanted to find some whole number (or at least a rational) that could be multiplied by some measurement to get the area.

  11. Gerard Weatherby says:

    The thing to take away from highly improbable events applied to very large populations, in the context of lotteries, is 1) someone will win, and 2) it won’t be you!

  12. delicateear says:

    Yes, I agree with you guys that the message of the book is ultimately against lotteries. But there is this sentence, “So it sounds like the lottery might be a good idea after all – if you’re careful to play only when the jackpot gets high enough.” This chapter is all about the expected value on return from the lottery ticket price. However, for the average person buying a normal amount of tickets, the size of the jackpot does not matter. It could be a paltry $1 million, it could be $100 billion. For most people that play the lottery, the money they use to buy tickets has real value in their life. The chance to win ‘something big” – no matter how big – is astronomically small. They throw away real value and receive nothing at all in exchange. As GW says, 1) someone will win, and 2) it won’t be you! It does not matter how big the jackpot is.

  13. Narayan Ramanathan says:

    I cannot understand how the figures are arrived on page 259 (How not to be wrong); for example for the chance of ‘no deuces’ – this is mentioned in the book as 5.3%. The no. of non deuces are (35-12-1=22). The total possible nos. are 35. Is not the required probability for non-deuce of all the 7 tickets to be = (22*21*20*19*18*17*16) / (35*34*33*32*31*30*29) = 2.54% . I don’t know where I am goofing! Please help anybody!

  14. Ryan Jones says:

    I absolutely loved your book. I almost couldn’t put it down and read it in only a couple of days. I do, however, have a couple of complaints.
    My biggest complaint is that the asterisks weren’t big enough for me. I would often find myself reach the bottom of a page and see that there was a comment, and then go looking about the page in search of the asterisk to see just what the comment referred to. The second and third comments noted with the cross and double cross were much easier to note. It is true that my eyesight is not perfect but it is close enough to 20/20 with the help of my glasses that a can’t image that there weren’t some other readers had the same problem I did.
    My second complaint is much more personal. When I was first deciding whether or not to buy the book I happened to open it to the page at the end of chapter one where I in glancing
    read the false syllogism attributed to Wanniski; whatever his first name is. I instantly thought that this was what you believe conservatives in general think about taxes and almost didn’t buy the book. As to what Wanniski actually believed, you never really say, so I can’t tell if I agree with Mr. Wanniski or not. I can tell you that what I do believe is that taxes “only” at the rate of 35% are higher than optimum to raise the most taxes, given enough time for the effect of lowering those taxes to play out in the economy. Not that I want the government to raise as much taxes as possible. I am in favor, however, of the government raising enough money to keep the nation’s infrastructure ready for the demands of a growing national economy, to whatever extent that that infrastructure is most efficiently paid for with public money. I in general agree with the graph at the top of page 22, although I don’t think that it should be entirely linear and that the optimum graph would have some curve in it like the graph at the top of page 23. I may even agree with the statement that there should be a national minimum income, but that this income should be the bare minimum for what it takes for someone to have enough food and shelter to be reasonably comfortable, but I believe that this amounts to less money than what a typical welfare recipient is paid to a considerable degree, as to keep the desire to work for a living alive for as many people as possible. As for people who for whatever reason can’t work for a living, they should be paid more. I also think there should be no minimum wage and that public charity should be removed at a rate of one dollar for ever three dollars made from work. I further believe that there should be no taxes on any business, because businesses don’t pay taxes, they only pass there taxes along to whoever buys their products and services. As far as Social Security is concerned, I don’t think it should be modeled as some kind of retirement payment, but rather only used in the same why that a payment to someone who can’t work should be paid and that everybody should therefore get the same amount, regardless of how much money they have made while working. As far as health care is concerned, I think that it is the fact that the government has been so involved in it is the reason it is so unaffordable to the average person, and that under normal market forces it would be much more of a reasonable proposition. Preexisting conditions could be taken care of to a certain degree by insurance bought by parents for as yet unborn children, and to the rest of the way by the role of private charity in the much more affluent society we would have under the above bounds for government. The government also should obviously pay for an adequate military, in proportion to the risk to our freedom from our enemies. Overall, I think that taxes should have a nearly flat rate to the income distribution, because we are all equally citizens, despite however rich or poor we may be. Finally, although I believe the role of our government should be considerably less than it is, I still do not think there is any such thing as Libertopia. As to all that I have said, I hope that you wouldn’t call me nuts.

  15. w says:

    I noticed a mistake in my copy of the book(penguin paperback 2015 version). On page 332 in the section “the triumph of mediocrity in weather” The first table and first scatter plot of temperatures in January of 2011 and 2012 do not agree. The description in the text does (almost)agree with the table.

  16. Ben says:

    Dear Professor Ellenberg,

    Did you ever reply to Daniel J. Mitchell’s response to your critique of his reasoning about the US and Sweden? Seems like you were unfair to him and an apology may be due. You may not agree with his economics and perhaps the one blog post you cherry picked can be twisted to support your point, but it sure looks like Mr. Mitchell’s substantive approach to the government spending debate is clearly non-linear. See here: By the way, I like your book.


  17. Ryan Jones says:

    I’ve just begun rereading How Not To Be Wrong. I was going to write you about the same asterisk problem I didn’t know I wrote to you before on. I think it’s really Penguin’s problem to be fair.
    On rereading my own comments I now find that I think that my old self was a bit immature, and I have to tell you that I now find my old taxation position to be somewhat hypocritical. The truth is that it matters as much what we spend our tax money on and how much that spending helps people as how we are taxed. I try to be more careful of how I preach politics these days, and not so longwinded.

  18. Sandro Perrone says:

    Good morning,
    I am Sandro Perrone,
    a 63-year-old engineer from Turin with a passion for mathematical issues.
    I bought your book and I appreciated it very much, clear, smooth and pleasant to read.
    Since 6 years have passed since its publication, is another book of yours coming soon?
    Please “update” me.
    Sandro Perrone

  19. JSE says:

    New book, “Shape,” coming May 2021!

  20. Vijay Antharam says:

    Dear Dr. Ellenburg
    I just finished and purchased your book How Not to Be Wrong. I thoroughly enjoyed the book—-though I had to struggle with the Fano plane and some of the Hamming code translations—that has to do more with me than the book, which was excellent.

    Having said that, I was disappointed and saddened through the last pages about the depiction of the 2000 election and the “irrelevant alternative” Nader. I and my family voted to Nader and I feel he was (subtly) not directly caste as some sort of villain or a person with devious, nefarious intentions in that election. I was 24 (now I an 44) and what he stood for really resonated and felt special to me. It still does and my support only intensifies 20 years later—especially on how the country has changed vastly since then. Nader is someone who I (and my late parents) admired for his half-century of consumer, environmental, and political activism. He has a phenomenal record but has been demonized (wrongly) by democrats.

    This was such a nice book, but those passage kind of hurt me when I read them. There is debates on both sides and Gore slipped on so many banana peels–am sure I can argue with anyone about this and win them over (I actually did that to the editor of the Alligator newspaper (the college newspaper at the University of Florida where I did my studies), but seems like people have already made up their mind.

    Respectfully yours,

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