wimagguc

Even the most "solo" proofs rest on a foundation built by others (notations, concepts, lemmas, entire frameworks invented decades or centuries earlier), so nothing really is created in isolation.

It's also right to point out that mathematics can be done in solitude — but in my experience, that solitude is anything but passive. It takes a kind of disciplined internal dialogue—working through examples, forming your own structures, asking endless questions. (I quite like the way Paul Halmos puts this: “Don’t just read it; fight it.”)

For anybody interested in this era of photography, the book "A Triumph of Genius" by Ronald K. Fierstein is such a brilliant documentation of the history around the Kodak vs Polaroid patent war.

A huge Duolingo fan and I play every day, but I wonder whether it's actually helping me to learn anything. I've been using it to study mandarin characters for the 3rd year now, but when I actually see Chinese text there's barely anything I recognize.

Admittedly, I spend maybe 5-15 minutes per day on average and most of that I do in a rush, but the expectation still sounds fair -- reading would be relatively passive knowledge too.

Pay attention to the camera & directing the next time you watch an episode, it's an absolute masterpiece.

One example to look out for is the back-and-forth between Columbo and the baddie. They would usually stand in opposite ends of the room and shot from two (sets of) cameras. One camera is closer to Columbo and the other is closer to the baddie, so when the detective is "winning" an argument, he'll look bigger on the screen and vice versa.

This usually starts with a shot where Columbo looks super small somewhere in the back of the room, then he'd ask his famous "just one last question", and then they switch the setup. Now Columbo is bigger in the front, and the baddie looks small while they are in trouble.

Interesting that she located the elements by tapping on the screen at certain positions, instead of using the left/right swipe _anywhere_ on the screen, which selects and reads the previous/next element.

Having seen a lot of these videos before (we've been working on making apps truly accessible), I never actually came across someone who didn't use the left/right swipe as a first plan of action, but hey ho, you always learn.

(I wonder if it depends on mental models, and whether you prefer building a 2D map of the screen to moving up and down in a 1-dimensional vector.)