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How Not to Be Wrong: The Power of Mathematical Thinking

Jordan Ellenberg

Last accessed on Sunday March 19, 2017

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There’s nothing wrong with the Laffer curve—only with the uses people put it to. Wanniski and the politicians who followed his panpipe fell prey to the oldest false syllogism in the book: It could be the case that lowering taxes will increase government revenue; I want it to be the case that lowering taxes will increase government revenue; Therefore, it is the case that lowering taxes will increase government revenue.

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The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we’d now call mathematics, things we’d now call religion, and things we’d now call mental illness. They believed that odd numbers were good and even numbers evil; that a planet identical to our own, the Antichthon, lay on the other side of the sun; and that it was wrong to eat beans, by some accounts because they were the repository of dead people’s souls.

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sometimes you know that the effect, if it exists, is small. In other words, a study that accurately measures the effect of a gene is likely to be rejected as statistically insignificant, while any result that passes the p < .05 test is either a false positive or a true positive that massively overstates the gene’s effect. Low power is a special danger in fields where small studies are common and effect sizes are typically modest.

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If you’ve ever used America’s most popular sort-of-illegal psychotropic substance, you know what it feels like to have too-flat priors. Every single stimulus that greets you, no matter how ordinary, seems intensely meaningful. Each experience grabs hold of your attention and demands that you take notice. It’s a very interesting mental state to be in. But it’s not conducive to making good inferences.

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Their approach was governed by a simple maxim: if gambling is exciting, you’re doing it wrong.

Note:sklut

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In the lottery, both the cost of the ticket and the size of the prize are denominated in dollars. It’s much less clear how to weigh the cost of the time we might waste sitting in the terminal against the cost of missing the flight. Both are annoying, but there’s no universally recognized currency of annoyingness.

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The standard economic story is that human beings, when they’re acting rationally, make decisions that maximize their utility.

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The answer is simple—eliminating waste has a cost, just as getting to the airport early has a cost. Enforcement and vigilance are worthy goals, but eliminating all the waste, just like eliminating even the slightest chance of missing a plane, carries a cost that outweighs the benefit.

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why handsome men are such jerks.

Note:true?

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Biologists are eager to think regression stems from biology, management theorists like Secrist want it to come from competition, literary critics ascribe it to creative exhaustion—but it is none of these. It is mathematics.

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We become like those pious people who, over time, accumulate a sense of their own virtuousness so powerful as to make them believe the bad things they do are virtuous too.

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Darwin showed that one could meaningfully talk about progress without any need to invoke purpose. Galton showed that one could meaningfully talk about association without any need to invoke underlying cause.

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correlation isn’t transitive. Niacin is correlated with high HDL, and high HDL is correlated with low risk of heart attack, but that doesn’t mean that niacin prevents heart attacks.

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Clinical researchers call this the surrogate endpoint problem. It’s time consuming and expensive to check whether a drug improves average life span, because in order to record someone’s life span you have to wait for them to die. HDL level is the surrogate endpoint, the easy-to-check biomarker that’s supposed to stand in for “long life with no heart attack.” But the correlation between HDL and absence of heart attack might not indicate any causal link.

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What’s going on? Here’s a hint: the small, dark pile of oats is playing the role of H. Ross Perot in this scenario. The mathematical buzzword in play here is “independence of irrelevant alternatives.” That’s a rule that says, whether you’re a slime mold, a human being, or a democratic nation, if you have a choice between two options, A and B, the presence of a third option, C, shouldn’t affect which of A and B you like better.

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In other words: the slime mold likes the small, unlit pile of oats about as much as it likes the big, brightly lit one. But if you introduce a really small unlit pile of oats, the small dark pile looks better by comparison; so much so that the slime mold decides to choose it over the big bright pile almost all the time. This phenomenon is called the “asymmetric domination effect,” and slime molds are not the only creatures subject to it. Biologists have found jays, honeybees, and hummingbirds acting in the same seemingly irrational way.

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The presence of a slightly dumber version of Adam made the real Adam look better; given the choice between dating Adam, Bill, and Chris, almost two-thirds of the women chose Adam. So if you’re a single guy looking for love, and you’re deciding which friend to bring out on the town with you, choose the one who’s pretty much exactly like you—only slightly less desirable.

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Post-Einstein, we understand that non-Euclidean geometry is not just a game; like it or not, it’s the way space-time actually looks.

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This is a story told in mathematics again and again: we develop a method that works for one problem, and if it is a good method, one that really contains a new idea, we typically find that the same proof works in many different contexts, which may be as different from the original as a sphere is from a plane, or more so.

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Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship. The examiner: Oh! This is very bad. This could not happen in this country. Gödel: Oh, yes, I can prove it. Fortunately, the examiner hurriedly changed the subject and Gödel’s citizenship was duly granted. As to the nature of the contradiction Gödel found in the Constitution, it seems to have been lost to mathematical history. Perhaps for the best!

Note:trump

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People like that, the quibblers and the naysayers and the maybesayers, don’t make things happen.

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It is not the critic who counts; not the man who points out how the strong man stumbles, or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again, because there is no effort without error and shortcoming; but who does actually strive to do the deeds; who knows great enthusiasms, the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.

Note:teddy Roosevelt speech on gsd

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the main theme, to which Roosevelt returns throughout the speech, is that the survival of civilization depends on the triumph of the bold, commonsensical, and virile against the soft, intellectual, and infertile.

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