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I think I added How Not to Be Wrong: The Power of Mathematical Thinking to my to-read list after seeing a review in the paper. The thing is, I don’t think it was this particular review. I say that because one of the first examples from the book was entirely familiar to me and I’m feeling like it wasn’t that example which I read about when being sold on this book.

The author of How Not to Be Wrong, Jordon Ellison, starts out with his experience, as a teacher of mathematics, with answering the perpetual question of his students (forced to take his math course as a graduation requirement): “When will I ever need this in real life?” As part of the answer, he tells the classic story of survivorship bias and the United States Army Air Corps in World War II.

At this risk of retelling a tale that is already everywhere on the internet, I’ll briefly summarize. Abraham Weld was a Hungarian-born mathematician of Jewish decent. This background and the discrimination it engendered caused him to flee the National Socialism of Austria (now annexed by Germany) in 1938. Once the U.S. entered the war, he aided the war effort as part of the Statistical Research Group centered at Columbia University.

That group was presented with a problem to be solved by advanced mathematics. The Air Corps had notice that the distribution of damage to aircraft as a result of combat was uneven. It occurred to the brass that, rather than burden aircraft with heavier armor all-around, if they could focus the hardening where most needed, they could both improve survival and maintain higher performance. Their proposal was to armor the areas receiving the most damage and asked the number guys (and gals) at the Statistical Research Group to optimize armor placement.

Wald’s great insight was that the location of the damage on returning planes only showed you where damaged could be sustained without bringing down an aircraft. It was where the bullet holes weren’t that was much more interesting, because these were locations where the planes that had not returned had taken damage. One might even presume a casual relationship between the damage that nobody could see and the lethality of that damage to the planes.

I have to admit it is just as likely that I saw Wald’s story in another context, as supposed to in a review for this very book. It has been featured at the center of at least one other mass-market book on statistics and any number of recent internet and blog posts. The subject has become particularly popular over the last few months as we engage in never-ending arguments about the merits of thinking, analysis, scientific inquiry, and SCIENCE!tm.

Similarly, I’ve been wondering about the possibility that I missed the book reviews entirely and was drawn simply to the title. How Not to Be Wrong. Holy cow! I long to not be wrong anymore and the temptation of that would have been enough to draw me in. Unfortunately, the book does not actually instruct one on how to avoid mistakes in all endeavors to life. Fortunately, this marketing sensationalism is the weakest feature of what is, otherwise, a fairly enjoyable, enlightening, and incredibly timely book.

The real theme of the book is that “real life” question. What are some practical applications of (reasonably) advanced mathematics? The author guides us through some meanderings involving, mostly, probabilities and non-Euclidean geometries, with clear and present applications to actual issues. In doing so, he also explains the historical significance of the concept at hand, including the work of the mathematicians themselves. That the last consists of proofs rather than calculations might be a surprising revelation for the non-academics in his audience. The result is an advocacy for math; as a school subject, as an avocation, and as a body of knowledge which anyone might admire. The book is less about being right or wrong than it is about understanding how civilization has come to make sense of the universe over our natural (human) resistance, a tendency to be blind to its reality.

The book is a little more than five years old but it could have been written for this very moment. Of course, the “how not to be wrong” lessons are intended to be timeless. Understanding that highly improbably things happen all the time would help us eliminate irrationality when making sense of anything at any time. Understanding that today, in a 2020 that already has us all on edge, highly improbably things are bound to happen on top of what has already driven us to the brink – well that might help us keep our sanity and keep us from irrational and dangerous miscalculations.

The story of Wald and his bullet holes is not the only anecdote about which I’ve read before. The fact that several of his mathematical tales seem familiar is a function of 2020. He writes a good bit about medical studies and cites a paper by John P. A. Ioannidis titled Why Most Published Research Findings Are False. As we struggle to understand contradicting Wuhu Flu studies, a bit of understand of the nexus between probabilities and Journal publishing requirements help get us away from the “you know nothing – just do what we tell you to do” admonishments that are causing such anguish.

Even the discussion of proofs turns out to be surprisingly practical. Ellison suggests, near the end of the book, that we apply the methodology of mathematical proofs (essentially, the scientific method) to our every day life. Do you fervently hold a particularly-decisive political position but can’t convince society as a whole of its rightness and righteousness? Consider giving equal time to trying to prove yourself wrong rather than simply trying to prove yourself right! He also applies a groundbreaking mathematical insight, introduced at the beginning of his book but applied at the end, to the question of election results. In a nutshell, we believe our institutions (the law, the vote, etc.) exist to seek the pure, honest truth. In fact, they are highly-structured, rule-based system intended to produce self-consistent results. That the two might sometimes diverge (a clearly guilty criminal walks free or a President is elected after losing the popular vote) is not quite the failure that we might assume it to be*.

The sections on elections merely amplified a sense of unease I felt from the book’s beginning, where it uses the Laffer Curve as an example of simple non-linearity. Perhaps it my own particular sensitivity but I was acutely aware of Ellison’s politics and noticed them creeping into his writing. This isn’t to say that I found the book biased or misleading – any of his politically-charged commentary would seem to be independent of the underlying lessons. It does make me wonder what’s behind it. Is this part of the skew that we often read about – that because supermajority of academics are liberal their work products will tend to reflect the bubble in which they are developed? Could it be more? Perhaps authors now feel a need to signal, through political statements, that they are one of the “good ones.” Or maybe I’m reading too much into it. Maybe this is just one man’s center-left views coming through as he connects the theoretical to the personal. Like I said, I don’t actually see it as a problem – just observance of something that stood out.

The political aspect reminds me of a personal story. Ellison wrote his book with the Bush/Gore election panic in mind but not yet aware of Donald Trump’s election. In particular, as we approach an election that is more likely to be decided by lawyers and lawsuits than it is by voters and ballots, the temptations of gaining better understanding seem all the more appealing. In How Not to Be Wrong he explains that, from a practical and scientific standpoint, the Bush versus Gore election was a tie. The courts were not trying to determine the “winner,” as if there were at the bottom of it all a true and indisputable preference of the people for their choice for President. Instead, the courts try to insure a fair application of all the rules so that the result is consistent with the way we have declared it should be done. Ellison proposed to decide very close elections by coin toss rather than recounts. He is mathematically correct but emotionally wrong. Imagine being able to eek out a win and then losing it again over the toss of a coin! It would feel more wrong than the wrongness we’re dealing with today.

Back before the Florida situation came to a head, I had a friend who was pretty liberal. Turned out, I had no idea about his politics because before Bush defeated Gore, most people didn’t feel the need to flaunt their political leanings throughout their every day lives. Or maybe I was just more immune to the anti-Reagan screaming than I have become to the anti-everyone-else-that-followed insanity. In any case, my friend and I were prone to some wild conversations, often delving** into the political. When the ballot counting in Florida began to produce contradictory results, he proposed (perhaps even in a letter to the editor of a national paper) a solution whereby the Presidency be shared between the two of them. His was actually a superior solution to Ellison’s, although even less practical.

The problem with close votes goes beyond the inability to accurately determine the winner. It demonstrates that the “people” are hopelessly divided. As Ellison explains, mathematician Nicolas de Condorcet saw democracy as a means of using the “wisdom of the crowds” to produce superior leadership and policy. Truths that were impossible to scry for the individual could be determined by the collective. Right or wrong, this theory flops when the electorate produces a statistically-inconclusive results. I think my anti-Bush friend was right. The answer is not to determine the winner but, in close cases, declare that there was no winner.

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*Although it may suggest a path towards ways that the system can be improved. Think Newtonian physics versus Einstein.

**He proposed that Manhattan should secede from the Union and become an independent City State along the lines of Hong Kong which, back then, was still a thing. I wholeheartedly supported that proposal although probably for entirely different reasons than he had proposed it.