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How Not to Be Wrong

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How Not to Be Wrong: The Power of Mathematical Thinking
Paperback edition
AuthorJordan Ellenberg
LanguageEnglish
GenreMathematics
PublisherPenguin Group
Publication date
May 29, 2014 (2014-05-29)
Publication placeUnited States
Media typePrint
Pages468 pp.
ISBN978-1594205224

How Not to Be Wrong: The Power of Mathematical Thinking, written by Jordan Ellenberg, is a New York Times Best Selling[1] book that connects various economic and societal philosophies with basic mathematics and statistical principles.[2][3]

Summary

How Not to Be Wrong explains the mathematics behind some of simplest day-to-day thinking.[4] It then goes into more complex decisions people make.[5][6] For example, Ellenberg explains many misconceptions about lotteries and whether or not they can be mathematically beaten.[7][8]

Ellenberg uses mathematics to examine real-world issues ranging from the fetishizing of straight lines in the reporting of obesity to the game theory of missing flights, from the relevance to digestion of regression to the mean to the counter-intuitive Berkson's paradox.[7][9]

Chapter Summaries

PART 1: Linearity

CHAPTER 1, LESS LIKE SWEDEN: Ellenberg encourages his readers to think nonlinearly, and know that “where you should go depends on where you are”. To develop his thought, he relates this to Voodoo economics and the Laffer curve of taxation. Although there are little to no numbers in this chapter, the point is that the overall concept still ties back to mathematical thinking.[10]

CHAPTER 2, STRAIGHT LOCALLY, CURVED GLOBALLY: This chapter puts an emphasis on recognizing that “not every curve is a straight line”, and makes reference to multiple mathematical concepts including the Pythagorean theorem, the derivation of Pi, Zeno’s paradox, and non-standard analysis.[10]

CHAPTER 3, EVERYONE IS OBESE: Here, Ellenberg dissects some common statistics about Obesity trends in the United States. He ties it into linear regression, and points out basic contradictions made by the original arguments presented. He uses many examples to make his point, including the correlation between SAT scores and tuition rates, as well as the trajectory of missiles.[10]

CHAPTER 4, HOW MANY IS THAT IN DEAD AMERICANS: Ellenberg analyzes statistics about the number of casualties around the world in different countries resulting from war. He notes that although proportion is these cases matters, it doesn’t always necessarily make sense when relating them to American deaths. He uses examples of deaths due to brain cancer, the Binomial Theorem, and voting polls to reinforce his point.[10]

CHAPTER 5, MORE PIE THAN PLATE: This chapter goes in depth with number percentages relating to employment rates, and references political allegations. He emphasizes that “actual numbers in these cases aren’t important, but knowing what to divide by what is mathematics in its truest form”, noting that mathematics in itself is in everything.[10]

PART 2: Inference

CHAPTER 6, THE BALTIMORE STOCKBROKER AND THE BIBLE CODE: Ellenberg tries to get across that mathematics is in every single thing that we do. To support this, he uses examples about hidden codes in the Torah determined by ELS, Equidistant Letter Sequence, a Stockbroker parable, noting that “Improbable things happen”, and wiggle room attributes to that.[11]

CHAPTER 7, DEAD FISH DON’T READ MINDS: This chapter touches on a lot of things. The basis for this chapter are stories about a dead salmons MRI, trial and error in algebra, and birth control statistics as well as basketball statistics. He also notes that poetry can be compared to mathematics in that it’s “trained by exposure to stimuli, and manipulable in the lab”. Additionally, he writes of a few other mathematical concepts, including Null hypothesis and the Quantic Formula. [11]

CHAPTER 8, REDUCTIO AD UNLIKELY: This chapter focuses on the works and theorems/concepts of many famous mathematicians and philosophers. These include but aren’t limited to the Reductio Ad Absurdum by Aristotle, a look into the constellation Taurus by John Mitchell, and Yitang “Tom” Zhangs “abounded gaps” conjecture. He also delves into explaining rational numbers, the prime number theorem, and makes up his own word, “flogarithms”. [11]

CHAPTER 9, THE INTERNATIONAL JOURNAL OF HARUSPICY: Ellenberg relates the practice of Haruspicy, genes that affect Schizophrenia, and the accuracy of published papers as well as other things to the “P value” or Statistical Significance. He also notes at the end that Jerzy Neyman and Egon Pearson claimed that Statistics is about doing, not interpreting, and then relates this to other real-world examples.[11]

CHAPTER 10, ARE YOU THERE GOD? IT’S ME, BAYESIAN INFERENCE: This chapter relates Algorithms to things ranging from God, to Netflix movie recommendations, and to terrorism on Facebook. Ellenberg goes through quite a few mathematical concepts in this chapter, which include Conditional probabilities relating back to “P value”, Posterior Possibilities, Bayesian Inference, and Bayes Theorem as they correlate to Radio Psychics and Probability. Additionally, he uses Punnett Squares and other methods to explore the probability of Gods existence.[11]

PART 3: Expectation

CHAPTER 11, WHAT TO EXPECT WHEN YOU’RE EXPECTING TO WIN THE LOTTERY: This chapter discusses the different probabilities of winning the lottery and expected value as it relates to lottery tickets, including the story of how MIT students managed to “win” the lottery every time in their town. Ellenberg also talks about the Law of Large numbers again, as well as introducing the Additivity of expected value and the games of Franc-Carreau or the “noodle/needle problem”. Many mathematicians and other famous people are mentioned in this chapter, including Georges-Louis LeClerc, Comte de Buffon, and James Harvey.[12]

CHAPTER 12, MISS MORE PLANES: The mathematical concepts in this chapter include Utility and Utils, and the Laffer curve again. This chapter discusses the amount of time spent in the airport as it relates to flights being missed, Daniel Ellsberg, Blaise Pascal’s Pense’s, the probability of God once more, and the St. Petersburg Paradox.[12]

CHAPTER 13, WHERE THE TRAIN TRACKS MEET: This chapter includes discussions about the Lottery again, and Geometry in Renaissance paintings. It introduces some things about coding, including Error Correcting Code, Hamming Code, and code words. It also mentions Hamming distance at it relates to language. The mathematical concepts included in this chapter are Variance, the Projective Plane, the Fano plane, and the Face centered cubic lattice.[12]

PART 4: Regression

CHAPTER 14, THE TRIUMPH OF MEDIOCRITY: This chapter discusses Mediocrity in everyday business according to Horace Secrist. It also includes discussions about Francis Galton’s “Hereditary Genius”, and baseball statistics about home runs.[13]

Scatter plot example

CHAPTER 15, GALTONS ELLIPSE: This chapter focuses on Sir Francis Galton, and his work on scatter plots, as well as the ellipses formed by them, correlation and causation, and the development from linear systems to quadratics. This chapter also addressed conditional and unconditional expectation, regression to the mean, eccentricity, Bivariate normal distribution, and dimensions in geometry.[13]

CHAPTER 16, DOES LUNG CANCER MAKE YOU SMOKE CIGARETTES: This chapter explores the correlation between smoking cigarettes and lung cancer, using work from R.A Fisher. It also goes into Berkson’s Fallacy, and uses the attractiveness of men to develop the thought, and talks about common effect at the end.[13]

Reception

Bill Gates endorsed How Not to Be Wrong and included it in his 2016 "5 Books to Read This Summer" list.[14][15]

The Washington Post reported that the book is “brilliantly engaging… 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.”[16]

The Wall Street Journal said, “Mr. Ellenberg writes, a kind of 'X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.”[17] The Guardian wrote, “Ellenberg's prose is a delight – informal and robust, irreverent yet serious.”[18] How Not to Be Wrong has also garnered reviews from The New York Times, Kirkus Reviews, Times Higher Education, Salon, Scientific American, Publishers Weekly, among others.[19][20][21][22][23][24]

References

  1. ^ "Hardcover Nonfiction Books - Best Sellers - June 22, 2014 - The New York Times". Retrieved 2018-04-25.
  2. ^ Crace, John (2014-06-08). "How Not to Be Wrong: The Hidden Maths of Everyday Life by Jordan Ellenberg – digested read". The Guardian.
  3. ^ "Review of 'How Not to Be Wrong: The Power of Mathematical Thinking' by Jordan Ellenberg – The Boston Globe". The Boston Globe.
  4. ^ Times, Los Angeles. "In 'How Not to Be Wrong' Jordan Ellenberg makes math meaningful". LA Times.
  5. ^ Bird, Review by Orlando (2014-06-13). "'How Not To Be Wrong: The Hidden Maths of Everyday Life', by Jordan Ellenberg". Financial Times. ISSN 0307-1766.
  6. ^ Ellenberg, Jordan (2014-06-13). "How I Was Wrong". Slate. ISSN 1091-2339.
  7. ^ a b "Thinking Inside the Box | On Wisconsin". OnWisconsin.
  8. ^ "How to Get Rich Playing the Lottery | Mathematical Association of America". www.maa.org.
  9. ^ "Mathematician Explains How To Figure Out What Time To Get To The Airport Before Your Flight". Business Insider.
  10. ^ a b c d e Ellenberg, Jordan (2014). How Not To Be Wrong: The Power of Mathematical Thinking. Penguin Books. pp. 21–85. ISBN 978-0-14-312753-6.
  11. ^ a b c d e Ellenberg, Jordan (2014). How Not To Be Wrong: The Power of Mathematical Thinking. Penguin Books. pp. 89–191.
  12. ^ a b c Ellenberg, Jordan (2014). How Not To Be Wrong:The Power of Mathematical Thinking. Penguin Books. pp. 196–291.
  13. ^ a b c Ellenberg, Jordan (2014). How Not To Be Wrong:The Power of Mathematical Thinking. Penguin Books. pp. 295–362.
  14. ^ Gates, Bill. "How Math Secretly Affects Your Life". www.gatesnotes.com.
  15. ^ Gates, Bill. "5 Books to Read This Summer". www.gatesnotes.com.
  16. ^ Suri, Manil (2014-06-13). "Book review: "How Not to Be Wrong: The Power of Mathematical Thinking," by Jordan Ellenberg". The Washington Post. ISSN 0190-8286.
  17. ^ Livio, Mario (2014-06-13). "Book Review: 'How Not to Be Wrong' by Jordan Ellenberg". Wall Street Journal. ISSN 0099-9660.
  18. ^ Bellos, Alex (2014-06-13). "How Not to Be Wrong: The Hidden Maths of Everyday Life by Jordan Ellenberg – review". The Guardian.
  19. ^ Ouellette, Jennifer (2014-08-01). "Jordan Ellenberg's 'How Not to Be Wrong,' and More". The New York Times. ISSN 0362-4331.
  20. ^ HOW NOT TO BE WRONG by Jordan Ellenberg | Kirkus Reviews.
  21. ^ "How Not to Be Wrong: The Hidden Maths of Everyday Life, by Jordan Ellenberg". Times Higher Education. 2014-06-04.
  22. ^ Miller, Laura. ""How Not to Be Wrong": What the literary world can learn from math". Salon.
  23. ^ Lamb, Evelyn. "How Not to Be Wrong (Book Review)". Scientific American.
  24. ^ "Nonfiction Book Review: How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg". Publishers Weekly.
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