If differential equation theory was known and also studied by Galileo, so why he didn't manage to discover a normal distribution (its discovery had to wait for Laplace and Gauss)?

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    $\begingroup$ "differential equation theory was known and also studied by Galileo" ??? Where you have found this info ? $\endgroup$ – Mauro ALLEGRANZA Dec 20 '17 at 14:26
  • $\begingroup$ In the book titled: An Introduction to Probability and Stochastic Processes by Melsa and Sage, p.5. Actually I typed into Google this entry: "Galileo differential equations" and it popped up. $\endgroup$ – Lili Dec 20 '17 at 14:31
  • $\begingroup$ Ok, found. The law of motion used by Galileo was NOT a differential equation at all (at Galileo's time) because calculus was discovered by Newton and Leibniz. $\endgroup$ – Mauro ALLEGRANZA Dec 20 '17 at 14:37
  • $\begingroup$ Having said that what is the "link" from the laws of motion to normal distribution ? $\endgroup$ – Mauro ALLEGRANZA Dec 20 '17 at 14:38
  • $\begingroup$ The context is that I'm writing a work on normal distribution and the history of its discovery. The link is ... like... I need to find as much as possible about state of knowledge of that times to figure out why normal distribution emerged so late comparing its popularity in nature. $\endgroup$ – Lili Dec 20 '17 at 14:46

Even aside from the fact that Galileo knew nothing of differential equations, or derivatives for that matter (he lived before Newton and Leibniz), and that the normal distribution was not discovered by Laplace and Gauss but by De Moivre, why the connection? De Moivre discovered the bell curve not by solving differential equations but looking for a good approximation to binomial distributions with large n, Bernoulli's formula with binomial coefficients was not very practical for calculations. And Galileo could not do that either because even the simplest cases of the binomial distribution (or of any statistical distributions, for that matter) were not considered until the Fermat-Pascal correspondence 12 years after his death.

Laplace did try to derive the error curve using differential equations, but the curves he derived that way had cusps or vertical asymptotes at the origin and did not even look like the normal distribution, see Stahl's Evolution of the Normal Distribution.

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    $\begingroup$ Jaynes claims this: 'Moivre did not appreciate its [normal distribution] significance' (Probability theory, p.704). But 'appreciation' and 'discovery' are two different things. Anyway, Galileo couldn't do it himself. $\endgroup$ – Lili Dec 21 '17 at 13:41

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