@quantabooks.org just released their first book, on the story of Lean by @kevinhartnett.bsky.social. It's a great story, about a pretty significant part of what's happening in math right now.
www.quantabooks.org/books/the-pr...
Suppose you wanted to reinvent the idea of Shannon Entropy for yourself. This puzzle is a good place to start (Full video on YouTube).
Video
www.quantabooks.org
The inside story of Lean, a computer program that answers the age-old question: How do you know if something is true?
Anyway, the video I was hoping to have out this day will be out closer to the 20th. Some call it “missing your deadline”, but I prefer to think of it as giving the L_{2.2} norm a little love.
This video was a complete joy to make. Here's a short preview, but next time you're looking to sit down for 45 minutes of math and art, take a look at the full version on YouTube: youtu.be/ldxFjLJ3rVY
Well, math terminology being what it is, something like this was bound to happen eventually.
(If you're curious about why these balls are so puny, the full talk is up on YouTube)
The Ladybug Clock puzzle
New video! Memorable for its delightfully absurd name, the Hairy Ball Theorem is extremely beautiful and has some surprising applications: youtu.be/BHdbsHFs2P0
Ah! Correction, as several have pointed out, it should be 4 in the taxicab metric. And the same correction, i.e., measuring the circle in the appropriate metric, the relevant date-shifting-joke-value to be closer to 2.6
Happy Pi Day! In a certain sense, π is not a constant, but a variable. Using our usual Euclidean distance, it is 3.14159… but applying other L^p norms on ℝ², half the unit circle's perimeter will give other values. For instance, at p=1 (taxicab geometry), “π” = 2√2. At p ≈ 2.2, it's 3.20.
