How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.

Dakota, Hawaii, and the District of Columbia. Now this is strange. Why should South Dakota be brain cancer central and North Dakota nearly tumor free? Why would you be safe in Vermont but imperiled in Maine?

Cant believe I fell for this - started theorizing causes!

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.

calculator doesn’t have a button for this. Because

have it on good assurance that one new father from a secular Jewish family waited until the Statistical Science paper was officially accepted before deciding to circumcise his son. (For the kid’s sake, I hope the refereeing process was on the speedy side.)

THE BALTIMORE STOCKBROKER

I figured this out!

without any input from the Torah, scientists and statisticians have already been worrying about them for quite some time. SEVEN DEAD FISH DON’T READ MINDS Because here’s the thing: the Bible code kerfuffle is not the only occasion on which the standard statistical tool kit has been used to derive a result that sounds like magic.

P-hacking

The more chances you give yourself to be surprised, the higher your threshold for surprise had better be.

Well put!

that mathematics demands there must be a god, on the grounds that a godless world would be highly unlikely to look like the one we

The Case for Faith, e.g.

ratios

The thinking behind COVID vax for kids

The truth is, the null hypothesis, if we take it literally, is probably just about always false. When

Hmm

THE MYTH OF THE MYTH OF THE HOT HAND

Love the point/counterpoint of over and under statisticizingcthe null hypothesis

Joseph Berkson, the longtime head of the medical statistics division at the Mayo Clinic, who cultivated (and loudly broadcast) a vigorous skepticism about methodology he thought shaky,

I'm sure he was fun at parties!

balls drop out of the cage. Don’t be that person.

Haha, yup

But it’s all worth it for those moments of discovery, where everything works, and you find that the texture and protrusions of the liver really do predict the severity of the following year’s flu season, and, with a silent thank-you to the gods, you publish.

Great writer! Love the intro on haruspicy

They’re running the con on themselves. And

Good point

“torturing the data until it confesses.”

= p hacking

For one thing, crappy might be as good as it gets.

Is this datted in the age of LLMs

For human action we have no such model and may never have one.

I guess the author never heard of Hari Selden

spiky. We assign a lot of mental weight to a few theories, while others, like the RBRRB theory, get assigned a probability almost indistinguishable from zero. How do we choose our favored theories? We tend to like simpler theories better than more complicated ones, theories that rest on analogies to things we already know about better than theories that posit totally novel phenomena.

Evolutionary psychology?

“Yes,” he says, satisfied. “Eet ees obvious.”

Classic math story

What is this, but a reckoning of the costs and benefits of adopting faith? Even in the middle of ecstatic communion with his savior, Pascal was still doing math! I love this about him.

I love this too!

But now pretend for a moment that you’re not a character in a word problem in an economics textbook, but rather an actual person—an actual person who does not have $100,000 cash on hand.

This sums up soo omuch in life!

This is a mathematical way of formalizing a principle you already know: the richer you are, the more risks you can afford to take.

And rich doesnt just mean bank acct or trust fund, it also means social capital

!

I kind of thought the at drug trials were by definition causation, not correlation?

I think this turned out to be false?

More precisely, it exists sometimes, concerning matters about which there’s a clear majority view.

The classic 70/30 issue

both Wright and Kiss head to head. Maybe we should toss all these Borda counts and runoffs and just elect the candidate who’s preferred by the majority.

example, Gödel, whose theorem ruled out the possibility of definitively banishing contradiction from arithmetic, was also worried about the Constitution, which he was studying in preparation for his 1948 U.S. citizenship test.

On the spectrum?

These were “the instruments which increase the power and direct the exercise of [our] faculties” that Condorcet wrote about with such vigor in the Sketch.

But has all the expertise died?

statisticians

What a surprise! :-)