Normal Distribution. Why Pure Randomness Always Makes a Bell Curve?

Drop one ball through a Galton board and nobody can tell where it will land. Drop 5,000 and you get the same bell curve, the normal distribution, every single time. Why does pure randomness keep drawing the same shape? Every simulation in this video is real: computed ball by ball, not drawn by hand. We simulate it from scratch: one ball as twelve coin flips, the 4,096 paths hiding in Pascal's triangle, dice and a lopsided spinner that still add up to a bell — the central limit theorem — and the places where the bell curve breaks: wealth, city sizes, earthquakes. Chapters 0:00 One ball vs 5,000 0:34 One ball = twelve coin flips 1:18 Counting the paths (Pascal's triangle) 2:09 The central limit theorem 3:12 Where the bell curve breaks 4:14 The supreme law of Unreason Sources [1] Galton board — Wikipedia. https://en.wikipedia.org/wiki/Galton_... [2] F. Galton (1889), Natural Inheritance, pp. 62–70 — galton.org. https://galton.org/books/natural-inhe... [3] Galton's quincunx — UCL Science Collections. https://collections.ucl.ac.uk/Details... [4] Francis Galton quotations — Today in Science History. https://www.todayinsci.com/G/Galton_F... [5] J. D. Cook, How the central limit theorem began. https://www.johndcook.com/blog/2010/0... [6] De Moivre–Laplace theorem — Wikipedia. https://en.wikipedia.org/wiki/De_Moiv... [7] Central limit theorem — Wikipedia. https://en.wikipedia.org/wiki/Central... [8] Normal distribution — Wikipedia (Occurrence and applications). https://en.wikipedia.org/wiki/Normal_... [9] P. M. Visscher et al. (2008), Heritability in the genomics era, Nat. Rev. Genet. 9, 255–266 [10] Pareto distribution / Heavy-tailed distribution — Wikipedia. https://en.wikipedia.org/wiki/Heavy-t...