Kneading Dough is Chaotic

Why does kneading dough mix it? In this video, we learn what it means to "mix" from a mathematical perspective. We'll learn the basics of chaos theory, we'll learn about the baker's map, the dyadic map, and the bit-shift map, and we'll learn what chaos means for computers. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds 0:00 Introduction 1:33 Chaos Theory 4:40 An equation for kneading 6:40 Proof that kneading mixes 10:48 Shuffling is basically kneading 12:20 Fractals 13:15 Computers can't do irrationals 15:24 Irrational numbers don't exist Shift Map is Chaotic: https://astro.pas.rochester.edu/~aquillen/phy256/lectures/shift_map.pdf More on Chaos, Baker's Map, Shift Map: Chaos and Fractals: New Frontiers of Science, Peitgen and Jürgens and Saupe Shuffling a Deck of Cards: The Theory of Gambling and Statistical Logic, Epstein I estimated the number of particles in Play-Doh assuming that it was mostly flour (patent here: https://patents.google.com/patent/US6713624) using estimates of starch density https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/starch-granule and size https://www.sciencedirect.com/science/article/abs/pii/S0733521084710587