Try to double or triple or even x10 the number of dots on your piece of paper and you get "patterns" forming. Repeat the experiment 1 million times and you might find other patterns appearing
But that's what I'm talking about
Randomness is all about patterns, even if those patterns are random on their own. With this in mind, you can try to exploit this property consciously once you definitely see or assume that you are dealing with random events, or if you know that beforehand (which is often the case in real life). In fact, we are all using this subtlety of randomness in everyday life without even thinking about it, without even being aware of it
The way a dealer shuffles. The way a casino card stack is cut, the way the roulette wheels are oiled. The way the metal ball hits when it's thrown on the wheel
I see what you are getting at, but in this topic I'm speaking mostly about the outcomes which are considered the representation of the built-in randomness of the world. Whether they are truly random in this sense is another question. Technically, our assumptions about these outcomes can just reflect our lack of knowledge (read, God doesn't play dice)
Then the answer is 42
Montgomery had found that the statistical distribution of the zeros on the critical line of the Riemann zeta function has a certain property, now called Montgomerys pair correlation conjecture. He explained that the zeros tend to repel between neighboring levels. At teatime, Montgomery mentioned his result to Freeman Dyson, Professor in the School of Natural Sciences.
In the 1960s, Dyson had worked on random matrix theory, which was proposed by physicist Eugene Wigner in 1951 to describe nuclear physics. The quantum mechanics of a heavy nucleus is complex and poorly understood. Wigner made a bold conjecture that the statistics of the energy levels could be captured by random matrices. Because of Dysons work on random matrices, the distribution or the statistical behavior of the eigenvalues of these matrices has been understood since the 1960s.
Dyson immediately saw that the statistical distribution found by Montgomery appeared to be the same as the pair correlation distribution for the eigenvalues of a random Hermitian matrix that he had discovered a decade earlier. His result was the same as mine. They were coming from completely different directions and you get the same answer says Dyson. It shows that there is a lot there that we dont understand, and when we do understand it, it will probably be obvious. But at the moment, it is just a miracle.
The unexpected discovery by Montgomery and Dyson at teatime in the 1970s opened a tantalizing connection between prime numbers and mathematical physics that remains strange and mysterious today. Prime numbers are the building blocks of all numbers and have been studied for more than two thousand years, beginning with the ancient Greeks, who proved that there are infinitely many primes and that they are irregularly spaced.
More than forty years after the teatime conversation between Dyson and Montgomery, the answer to the question of why the same laws of distribution seem to govern the zeros of the Riemann zeta function and the eigenvalues of random matrices remains elusive, but the hunt for an explanation has prompted active research at the intersection of number theory, mathematical physics, probability, and statistics. The search is producing a much better understanding of zeta functions, prime numbers, and random matrices from a variety of angles, including analyzing various systems to see if they reflect Wigners prediction that the energy levels of large complex quantum systems exhibit a universal statistical behavior, a delicate balance between chaos and order defined by a precise formula
https://www.ias.edu/ideas/2013/primes-random-matrices
This is the zero of riemann zeta function
