I Bet You Haven't Seen This Proof of Central Limit Theorem Before

BLOG: https://tomasmiskov.com/quincunx.html

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This video explains the Central Limit Theorem through the lens of entropy and information theory. The animation depicts a quincunx toy (Galton board) in which the traditional interpretation says that the balls at the base are distributed according to the Binomial distribution which converges to the Normal one as the number of balls grows. This is a nice purely statistical interpretation but it doesn't fully translate to the real world/simulation. Thus this video and the accompanying blog post explains the resulting normal distribution at the base of the Galton board through the principal of Maximum Entropy. I think this is a very interesting lens to look at Central Limit Theorem that is not frequently thought in regular frequentist statistical courses.

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Tools:
Animation: Cavalry (https://cavalry.scenegroup.co)
Graphics: Affinity Designer
Video edit: DaVinci Resolve

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Sources:
Find at the end of the blog post
https://tomasmiskov.com/quincunx.html

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Credits:
Intro music:    • AdhesiveWombat - Night Shade ♫ NO COPYRIGH...   by ‪@AdhesiveWombat‬
Second track:    • Mystery | Free mystery music for YouTube v...   from ‪@weefreemusic‬
Sound effects from ZapSplat: https://www.zapsplat.com

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Chapters:
0:00 Why is it normal?
0:49 Binomial explanation
1:34 Entropy explanation
2:27 Maximum Entropy Principle