Comment on Buffon and response

The needle problem presented to the RAS by Buffon provides an empirical demonstration of stochastic geometry and probability theory. The probability of an intersection between the lines on the floor and the needle is directly related to (a) the length of the needles; and (b) the distance between the lines on the floor. If one only knows a or b, and does the simple experiment, i.e., determines the probability of an intersection based number of intersections (I) for a given number of tosses (N), the resulting probability (I/N) can be used to estimate the unknown quantity. The approach is unbiased because the more sampling that is done, hat is, the more tosses of the needle, the more closely the estimate converges on the true or expected value. Thus, Buffon’s Needle Problem as illustrated by the figure in question provides a prototypical example for the use of a probe with known parameters to estimate a unknown parameter by bringing the probe and object in random contact. Would the blogger like to suggest a better way to illustrate this concept? For more information on this topic, see<title withheld>,

 

The needle problem was one of at least problems solved correctly by Buffon. He provided a number of other calculations that were incorrect such as the 2 sets of orthogonal lines problem.

 

Buffon’s work assumes that a < b.

 

There is nothing about Buffon’s work that is unbiased since he did not sample, nor did he consider sampling. What distinguishes Buffon’s work is that it is the first probability problem solved for a non-discrete situation.

The idea of sampling with a needle comes from LaPlace. That comes well after Buffon’s death.

The image shows someone tossing needles. There is good reason that Buffon did toss coins to verify his derivation for Franc Carreau and he may have used bread sticks to test his needle computation, but he did this to verify the probabilities he derived. He was not sampling. He was not estimating. He did not employ a probe.

I believe the first known sampling using Buffon’s needle comes in 1901 with a faked math paper.

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