The Problem Newton Got Wrong

2020-05-26

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Isaac Newton was right about everything from gravity to the calculus, but he didn’t quite get it right on dice and probability.

The Newton-Pepys Problem represents Isaac Newton’s only documented foray into probability. Samuel Pepys sent him a letter asking whether it would be more likely to roll one six in 6 dice, two sixes in 12 dice, or three sixes in 18 dice. In terms of computing the answer, we’ve got it pretty easy in the 21st century, whether we do it the long way, whether we apply binomial distribution, or just run a Monte Carlo simulation. To us, it’s a relatively basic problem in probability.

But Newton had to work it all out himself, and as he did that, he missed a few things. He just… didn’t get it totally right even though his numbers were accurate. The *real* Newton-Pepys Problem is deciding how much that even matters, and the answer gives us insight into the complex relationship between math, numbers, and the realities of human thought.

*** SOURCES ***

“Diary and Correspondence of Samuel Pepys,” pg. 367: https://www.google.com/books/edition/Diary_and_Correspondence_of_Samuel_Pepys/72RCAQAAIAAJ?hl=en&gbpv=0

“Isaac Newton as a Probabilist,” Stephen Stigler, Statistical Science 2006, Vol. 21, No. 3, 400–403: https://projecteuclid.org/euclid.ss/1166642443

“John Smith’s Problem,” T. W. Chaundy and J. E. Bullard, The Mathematical Gazette Vol. 44, No. 350 (Dec., 1960), pp. 253-260: https://www.jstor.org/stable/pdf/3614890.pdf

“Newton and Pepys,” Nick Berry / DataGenetics: http://datagenetics.com/blog/february12014/index.html

“The Gentle Art of Mathematics,” by Dan Pedoe, pg. 43: https://www.google.com/books/edition/The_Gentle_Art_of_Mathematics/JAyRUwlMTZAC?hl=en&gbpv=0

“Probability and Random Processes,” by Venkatarama Krishnan and Kavitha Chandrapg, pg. 33: https://www.google.com/books/edition/Probability_and_Random_Processes/TsgvCgAAQBAJ?hl=en&gbpv=0

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