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How not to be wrong by Jordan Ellenberg

How not to be wrong (2014)

by Jordan Ellenberg

Other authors: Elise Craig (Fact checker)

Other authors: See the other authors section.

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English (17)  French (1)  All languages (18)
Showing 1-5 of 17 (next | show all)
This book has a lot going for it. It doesn't gets so un-mathematical as to be vacuous or offensive, but it is interesting to persons who are not interested in math for itself. It starts out compellingly with its argument that mathematics, or at least the mathematics in the book, is common sense, strengthened. Then it distinguishes between types of mathematics on two dimensions: profound vs. not-so-interesting, and simple vs. complex. This book is in the profound and simple quadrant, Ellenberg claims. Personally, I'm not so sure that I entirely agree about which things belong in which classification, but it is still a good way of thinking. That was just the introduction.

One real strength of this book is that it doesn't throw in dumb jokes to make the topic seem more accessible; it has many smart, rather snarky jokes about the actual subject matter. The hand drawn graphs are often quite clever, and sometimes funny, also.

Part I: Linearity

The first chapter is about the perils of the pitfalls of implicit linearity. It includes remarks on the Laffer curve and directed me toward an essay by Martin Gardner. Excellent points made. Now I'll be ready to tell someone "That implicit assumption of linearity is questionable." instead of just rolling my eyes.

The second chapter asks the question, "Why do so many people engage in simplistic linear thinking?" and answers that question by pointing out that all curves looks like straight lines when you get close to them. This is one of the more mathematical chapters. Discusses irrationality of root 2, Archimedes method of exhaustion for estimating pi, and Newton's derivatives/fluxions. Cauchy worked to put the calculus on a rigorous footing and this involves series. If we side with Cauchy, we must cease to believe that ever integer has only one decimal representation! Woah!

Chapter 3: Everyone is Obese
This chapter takes us back to foolish assumptions of linearity. It invites us to consider that fitting a straight line to some points using the method of least squares may be inappropriate. In fact, until you know that the relationship is linear, you might as well not do it. The graph of % of American's overweight vs. time is plotted. If current trends continue, 109% of Americans will be overweight of 2060! Now, that can't be right. Actually, the graph of an increasing proportion tends to flatten out as the proportion gets closer to 100%. This is because there are fewer and fewer items to convert.

Chapter 4: How Much is that in Dead Americans?
This is another discussion of linearity, but some of the remarks are a bit questionable. I decided to give this book a rest, because I wanted to think over some of the more questionable points. It starts out well with a graph of a 0.015 slope line where the y-axis is equivalent number killed and the x-axis is country population. It points out that this time, the assumption of linearity is not so much dumb as just not helpful. Then comes the point that proportions do, however, matter. Sometimes, absolute numbers are quite misleading. But proportions, while intuitively a bit fairer, can also be misleading when chance is involved. He asserts, without proof, that the reason South Dakota is top ranked among all 50 states for brain cancer deaths does not mean that if you live in South Dakota you are more likely to get brain cancer than if you lived elsewhere. This high rate of brain cancer, 5.7/100,000, nearly double the rate of 3.4/100,000 for the US as a whole, is probably just due to randomness. Instead of a direct argument, he uses a simple to understand analogy with coin tosses. A similar-to-the-brain-cancer-argument is made about test scores in small and large schools. This argument is certainly as valid as the brain cancer one. But then, Ellenberg introduces the normal distribution. As far as I understand, that is not a useful distribution when you're dealing with cancer rates, the probability of which is not 50/50. When the probability is not 50/50, the distribution is not symmetric. So, how can I be reasonably confident that the rate of cancer in South Dakota is most likely due to randomness. He is unable to give any help.
  themulhern | Feb 18, 2019 |
It’s basically the history and philosophy of math, similar to a biography of Bach that isn’t exactly music theory, but is still, you know, tangentially related.

I say this because I don’t know much math, and I can’t pretend that now I do. But if I did, I’d say, “See, this is why....”

And no book that is filled with things that are true is a waste of space, even if it’s naturally not a substitute for a completely different kind of book.


I did learn things from it.
  smallself | Dec 31, 2018 |
This book is extremely well-written and covers a diverse set of material related to applied mathematics (statistics particularly). However, it covers many disparate topics, and the only string I observed is various caveats and/or pitfalls when utilizing numbers to make decisions or process information more generally. ( )
  aevaughn | Mar 5, 2018 |
Really really good. That's why I took so long to read it. I had to make myself slow down. He does get caught up in chasing some geometric proofs which were less than interesting but overall a really strong argument for learning math in its totality. Probably should be used as a hs text in an ambitious academically rigorous school. ( )
  kallai7 | Mar 23, 2017 |
Obnoxious title aside, I found this informative and enjoyable. Ellenberg gets a little lost in the weeds deriving a few things where a two-sentence summary would do, but hey - his book, his call. Most of the content here was common sense - not all curves are linear, correlation doesn't imply causation, improbable things happen all the time, small sample sizes skew results, and so on - but common sense isn't really all that common, and it's important to keep these fundamentals in mind when you use numbers and patterns and trends to try to understand the world around you. My takeaway, at least. ( )
  steve520 | Dec 10, 2016 |
Showing 1-5 of 17 (next | show all)
Mr. Ellenberg's key point: Mathematics is not some strange language used by a few single-minded experts. Rather, it is a powerful extension of our common sense, one that anyone can employ to tackle real-life problems.
Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. He presents these in fluid succession, like courses in a fine restaurant, taking care to make each insight shine through, unencumbered by jargon or notation. Part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic, comparing slime molds to the Bush-Gore Florida vote, criminology to Beethoven’s Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics.

» Add other authors (7 possible)

Author nameRoleType of authorWork?Status
Ellenberg, JordanAuthorprimary authorall editionsconfirmed
Craig, EliseFact checkersecondary authorall editionsconfirmed
Dewey, AmandaDesignersecondary authorsome editionsconfirmed
Elewa, AdlyCover designersecondary authorsome editionsconfirmed
Rudels, MatsAuthor photosecondary authorsome editionsconfirmed
Villepique, GregCopy editorsecondary authorsome editionsconfirmed
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"What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement."

Bertrand Russell, "The Study of Mathematics" (1902)
for Tanya
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Right now, in a classroom somewhere in the world, a student is mouthing off to her math teacher. - When Am I Going To Use This?
A few years ago, in the heat of the battle over the Affordable Care Act, Daniel J. Mitchell of the libertarian Cato Institute posted a blog entry with the provocative title: "Why Is Obama Trying to Make America More Like Sweden when Swedes Are Trying to Be Less Like Swedenborg?" - Chapter
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Overview: The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn't confined to abstract incidents that never occur in real life, but rather touches everything we do-the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It's a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does "public opinion" really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman-minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia's views on crime and punishment, the psychology of slime molds, what Facebook can and can't figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is "an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength." With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.… (more)

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