How Not to Be Wrong Quotes

“His most famous paradox goes like this. I decide to walk to the ice cream store. Now certainly I can’t get to the ice cream store until I’ve gone halfway there. And once I’ve gone halfway, I can’t get to the store until I’ve gone half the distance that remains. Having done so, I still have to cover half the remaining distance. And so on, and so on. I may get closer and closer to the ice cream store—but no matter how many steps of this process I undergo, I never actually reach the ice cream store. I am always some tiny but nonzero distance away from my two scoops with jimmies. Thus, Zeno concludes, to walk to the ice cream store is impossible.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Proving by day and disproving by night is not just for mathematics. I find it’s a good habit to put pressure on all your beliefs, social, political, scientific, and philosophical. Believe whatever you believe by day; but at night, argue against the propositions you hold most dear. Don’t cheat! To the greatest extent possible you have to think as though you believe what you don’t believe. And if you can’t talk yourself out of your existing beliefs, you’ll know a lot more about why you believe what you believe. You’ll have come a little closer to a proof.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances, and resist the lure of the Baltimore stockbroker; or you make a decision based not just on the most likely future, but on the cloud of all possible futures, with attention to which ones are likely and which ones are not; or you let go of the idea that the beliefs of groups should be subject to the same rules as beliefs of individuals; or, simply, you find that cognitive sweet spot where you can let your intuition run wild on the network of tracks formal reasoning makes for it; without writing down an equation or drawing a graph, you are doing mathematics, the extension of common sense by other means. When are you going to use it? You've been using mathematics since you were born and you'll probably never stop. Use it well.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“If something is true and you try to disprove it, you will fail. We are trained to to think of failure as bad, but it's not all bad. You can learn from failure. You try to disprove the statement one way, and you hit a wall. You try another way, and you hit another wall. Each night you try, each night you fail, each night a new wall, and if you are lucky, those walls start to come together into a structure, and that structure is the structure of the proof of the theorem. For if you have really understood what's keeping you from disproving the theorem, you very likely understand, in a way inaccessible to you before, why the theorem is true. This is what happened to Bolyai, who bucked his father's well-meaning advice and tried, like so many before him, to prove that the parallel postulate followed from Euclid's other axioms. Like all the others, he failed. But unlike the others, he was able to understand the shape of his failure. What was blocking all his attempts to prove that there was no geometry without the parallel postulate was the existence of just such a geometry! And with each failed attempt he learned more about the features of the thing he didn't think existed, getting to know it more and more intimately, until the moment when he realized it was really there.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Mathematics, mostly, is a communal enterprise, each advance the product of a huge network of minds working toward a common purpose, even if we accord special honor to the person who places the last stone in the arch.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“What you learn after a long time in math-and I think the lesson applies much more broadly-is that there's always somebody ahead of you, whether they're right there in class with you or not. People just starting out look to people with good theorems, people with some good theorems look to people with lots of good theorems, people with lots of good theorems look to people with Fields Medals, people with Fields Medals look to the "inner circle" Medalists, and those people can always look toward the dead. Nobody ever looks in the mirror and says, "Let's face it, I'm smarter than Gauss." And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“A scientist can hardly encounter anything more desirable than, just as a work is completed, to have its foundation give way.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“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.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“What can I say? Mathematics is a way not to be wrong, but it isn't a way not to be wrong about everything. (Sorry, no refunds!) Wrongness is like original sin; we are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions. There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we're still wrong about. 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.

I'll do my best to resist the temptation. But watch me carefully.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“The master group theorist John Conway, upon encountering the lattice in 1968, worked out all its symmetries in a twelve-hour spree of computation on a single giant roll of paper. These symmetries ended up forming some of the final pieces of the general theory of finite symmetry groups that preoccupied algebraists for much of the twentieth century.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“You can do linear regression without thinking about whether the phenomenon you’re modeling is actually close to linear. But you shouldn’t.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Tanya Latty and Madeleine Beekman of the University of Sydney were studying the way slime molds handled tough choices. A tough choice for a slime mold looks something like this: On one side of the petri dish is three grams of oats. On the other side is five grams of oats, but with an ultraviolet light trained on it. You put a slime mold in the center of the dish. What does it do? Under those conditions, they found, the slime mold chooses each option about half the time; the extra food just about balances out the unpleasantness of the UV light. If you were a classical economist of the kind Daniel Ellsberg worked with at RAND, you’d say that the smaller pile of oats in the dark and the bigger pile under the light have the same amount of utility for the slime mold, which is therefore ambivalent between them. Replace the five grams with ten grams, though, and the balance is broken; the slime mold goes for the new double-size pile every time, light or no light. Experiments like this teach us about the slime mold’s priorities and how it makes decisions when those priorities conflict. And they make the slime mold look like a pretty reasonable character. But then something strange happened. The experimenters tried putting the slime mold in a petri dish with three options: the three grams of oats in the dark (3-dark), the five grams of oats in the light (5-light), and a single gram of oats in the dark (1-dark). You might predict that the slime mold would almost never go for 1-dark; the 3-dark pile has more oats in it and is just as dark, so it’s clearly superior. And indeed, the slime mold just about never picks 1-dark. You might also guess that, since the slime mold found 3-dark and 5-light equally attractive before, it would continue to do so in the new context. In the economist’s terms, the presence of the new option shouldn’t change the fact that 3-dark and 5-light have equal utility. But no: when 1-dark is available, the slime mold actually changes its preferences, choosing 3-dark more than three times as often as it does 5-light!”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Nowadays, the Abrahamic argument—just look at everything, how could it all be so awesome if there weren’t a designer behind it?—has been judged wanting, at least in most scientific circles. But then again, now we have microscopes and telescopes and computers. We are not restricted to gaping at the moon from our cribs. We have data, lots of data, and we have the tools to mess with it.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“Big Data isn’t magic, and it doesn’t tell the feds who’s a terrorist and who’s not. But it doesn’t have to be magic to generate long lists of people who are in some ways red-flagged, elevated-risk, “people of interest.” Most of the people on those lists will have nothing to do with terrorism. How confident are you that you’re not one of them?”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“we’re not actually people at all, but simulations running on an ultracomputer built by other people.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“irrational behavior is as unacceptable to a certain species of economist as the irrational magnitude of the hypotenuse was to the Pythagoreans. It doesn’t fit their model of what can be; and yet it is.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“It takes a thousand men to invent a telegraph, or a steam engine, or a phonograph, or a telephone or any other important thing—and the last man gets the credit and we forget the others.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Clausewitz: Mathematics is the extension of common sense by other means.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“MATHEMATICS IS THE EXTENSION OF COMMON SENSE BY OTHER MEANS”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“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.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“It doesn’t, of course, have to be a single smooth hill like the one Laffer sketched; it could look like a trapezoid or a Bactrian camel’s back”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Look, I know this theory of general relativity sounds wacky, but that’s what they said about Galileo!”)”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“with the right mix of zeal and political canniness to get people to listen to an idea considered fringy even by tax-cut advocates.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“provocative”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“But formal mathematics without common sense—without the constant interplay between abstract reasoning and our intuitions about quantity, time, space, motion, behavior, and uncertainty—would just be a sterile exercise in rule-following and bookkeeping. In other words, math would actually be what the peevish calculus student believes it to be.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Without the rigorous structure that math provides, common sense can lead you astray.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Math is like an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

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― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking