I posted the first chapter of my book, "Making Sense of Worked Example Research." It starts like this: "Some of the dullest teaching on the planet comes courtesy of worked example abusers."
"Modeling Life" is a gorgeous mathematical biology text that opens with a fascinating retelling of mathematical history. In short, we teach students in calculus that if they have an equation describing how something changes we can get an equation for that thing. But in general, this is not possible. Sorry. In the 20th century, we invented ways of visualizing those change equations anyway.
I was wondering how much of the real numbers we could get rid of while holding on to calculus. From wikipedia: "computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm." Seems from the article that maybe you can restrict things to just these sorts of numbers?
Benjamin Dickman told me about the Semantle puzzle, which as far as I'm concerned is (sorry everybody) the one reliably interesting Wordle-inspired puzzle. It uses a measure of word similarity to tell you how close you are to guessing the day's secret word. It is quite hard.
Here's country musician Roy Clark playing "Racing the Mule" on guitar. It's great. But as soon as I heard it I realized that I'd heard it before, in Diaspora Yeshiva Band's "David Melech Yisrael." The second half is basically a long quote of Roy Clark. I don't expect anyone else to care but this was basically earthshattering to my ears.
For no particular reason, I wanted to reread the George Saunders piece "Manifesto" this week: "Last Thursday, my organization, People Reluctant To Kill for an Abstraction, orchestrated an overwhelming show of force around the globe. At precisely 9 in the morning, working with focus and stealth, our entire membership succeeded in simultaneously beheading no one."
OK here's more from "Manifesto": "During Phase IV, just after lunch, we were able to avoid bulldozing a single home. Furthermore, we set, on roads in every city, in every nation in the world, a total of zero (0) roadside bombs which, not being there, did not subsequently explode, killing/maiming a total of nobody. No bombs were dropped, during the lazy afternoon hours, on crowded civilian neighborhoods, from which, it was observed, no post-bomb momentary silences were then heard. These silences were, in all cases, followed by no unimaginable, grief-stricken bellows of rage, and/or frantic imprecations to a deity. No sleeping baby was awakened from an afternoon nap by the sudden collapse and/or bursting into flame of his/her domicile during Phase IV."
Also for no particular reason, I wanted to rewatch Bruce Springsteen and the E Street Band perforing "Badlands" at the No Nukes concert. Poor man wanna be rich, rich man wanna be king, king aint satisfied till he rules everything.
From the always interesting Futility Closet: "In 1983, University of British Columbia physicist Lorne Whitehead noted “a simple and dramatic demonstration of exponential growth, as in a nuclear chain reaction.” He determined that one domino can knock down another that’s about half again as large in all dimensions; since the gravitational potential energy of an upright domino is proportional to the fourth power of its size, this means that one tiny domino can set off a graduated chain reaction with impressively thunderous results."
From my four year old: Why did the Elephant like to eat hair?
Because he was hairable.