The power tower puzzle | Ep. 8 Lockdown live math

A fun puzzle stemming from repeated exponentiation. Full playlist:    • Lockdown math   Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status... Play along on Desmos: https://www.desmos.com/calculator/nul... Related videos. Calculus series:    • Essence of calculus   In particular look at:    • The other way to visualize derivatives | C...   Numberphile on Grahm's constant:    • Graham's Number - Numberphile   Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ Video timeline (thanks to user "noonesperfect") 0:36 Question 1 1:13 Answer 1 1:29 Introduction to tetration 3:37 How exponentiation works in tetration 6:10 Python program for power tower iterations 8:40 Question 2 9:32 Python Program regarding question 2 10:37 Answer 2 and explanation 13:18 Power tower for infinite size converges or not? (Thumbnail question) 15:21 Question 3 16:28 Footage of Grant's setup arrangement problem due to construction-work back at home. 16:49 Answer 3 and explanation 17:40 Checking logic behind 2 different problems of power towers whose answer converges to the same value (Is it even possible?) 19:42 Checking same logic using Desmos graph tool i.e. Cobweb Graph (Desmos graph link in description) 28:12 Question 4 28:51 Questions from audience tweets 29:15 Knuth's Up Arrow Notation and Graham's Number (Check Numberphile video in description) 32:32 Answer 4 and explanation 37:29 Homework/Challenge Puzzle 39:20 Thumbnail question power tower logic 40:55 Audience questions from twitter 41:45 Power tower for complex numbers/Fractal set 45:19 Brainteaser 48:06 More questions from tweets 53:17 Notes for lock-down series in Grant's Tweeter ------------------ The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Reddit:   / 3blue1brown   Instagram:   / 3blue1brown_animations   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown