Exploding Dots & Gödel's Incompleteness Theorem Explained 🧠

This video builds on the exploding dots experience, introducing folks to strings and the beginning of Kurt Gödel's first incompleteness theorem.

For an interactive exploration of these ideas, check out
https://wildthinks.org

For more exploding dots check out the following websites.

The exploding dots webpage

https://www.explodingdots.org

James Tanton's g'day math page
http://gdaymath.com

NOTES: Yeah, I took some major liberties in how I showed Gödel's definition of a proof number. I've never seen Gödel's original formula. He had a more complicated way of encoding proofs and statements as numbers. His final "Gödel Formula" must have been a monster. As a computer scientist we prefer to translate provability into computability and then write a first order formula for the existence of an accepting computation path of a particular Turing machine. But that is way too far afield for this video.

Anyway, I wanted viewers to get a visual sense that there is an actual arithmetic definition of provability, even if the actual definition was pretty cooked.