Demi’s Reviews > How Not to Be Wrong: The Power of Mathematical Thinking > Status Update

"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... Believe whatever you believe by day, but at night, argue against the propositions you hold most dear."

last chapter, "How to be Right": pit Theodore Roosevelt against "Soonest Mended" poem by John Ashbery. action vs. acknowledgement of uncertainty? "Math gives us a way of being unsure in a principled way"

section “genius is a thing that happens” is a mildly digressive, but surprisingly refreshing, debunking of the glorification of genius. genius is a thing that happens (as the result of a village / teamwork / persistence and grit), not a person. the glorification of genius is esp prominent in math, but debunking it is a refreshing reminder for many other fields too!

kind of 🤯 at all the voting systems and how they can yield different results. mostly florida 2000 as an example, if only this book came out after 2016... the irrelevant alternative and asymmetric domination effect, instant runoff voting and its difficulty for centrists, giving up on the search for truth and settling for a definition

“public opinion doesn’t exist” ... the majority preference doesn’t always meld into a definitive stance

a nice caveat to the uncertainty around correlation and causation: in terms of policy, you can’t wait until you’re certain to make the policy. if there is a possibility of saving lives in the case that the causation is true, then the policy is worthwhile. “it’s not always wrong to be wrong” “if you never give advice until you’re sure it’s right, you’re not giving enough advice”

slow buildup to “correlation =/= causation” (surprised he didn’t say it outright. “the non-transitivity of correlation is somehow obvious and mysterious at the same time.” he recommends the “blood relation” analogy - the correlated variables may “share part of their DNA”, but you can’t conclude one causes the other. esp tricky for medical scenarios; lots of factors at play!

must be remarked that Galton was an unapologetic eugenicist, and Ellenberg pushes back on his own title. “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.” timely to note with recent discussions around AI and racial stereotypes!