The power tower puzzle | Ep. 8 Lockdown live math

Описание: 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