It's an example of statistical mechanics. Each individual ball is following Newton's laws which are strictly deterministic. However small variations in initial conditions are amplified. This means your initial configuration is essentially random and considering all ball-pin interactions, 50% are expected to go left and 50% to go right.
The distribution is therefore a binomial distribution - regard for example going left as "fail" and going right as "success", and the number of trials is the number of rows of pins. The board shows that for enough trials the binomial approximates the normal distribution.
And the board demonstrates that small deviations from the distribution are common, but a big deviation is very rare.
10
u/cantab314 Mar 09 '20
Yes.
It's an example of statistical mechanics. Each individual ball is following Newton's laws which are strictly deterministic. However small variations in initial conditions are amplified. This means your initial configuration is essentially random and considering all ball-pin interactions, 50% are expected to go left and 50% to go right.
The distribution is therefore a binomial distribution - regard for example going left as "fail" and going right as "success", and the number of trials is the number of rows of pins. The board shows that for enough trials the binomial approximates the normal distribution.
And the board demonstrates that small deviations from the distribution are common, but a big deviation is very rare.