I had an insight the other day and I wonder if anyone has made a mistake like this. I once created a program to generate numbers for Powerball tickets. I would run the program to see if any numbers come up more often than others. I was surprised by the results, similar results can be viewed at:
Obviously some numbers do come up more often than others, and this at first seems to defy randomness. At first I thought it was something wrong with the way Basic generated random numbers or even the way computers were able to generate random numbers. It was a puzzle but last week it came to me in a flash of insight, I visualized an 8 by 8, two dimensional surface composed of cells containing the numbers 1-64, (a little more than the lottery numbers). I imagined running my program but this time the frequency would be depicted as either a bump for higher frequency or a dent for lower frequency. I realized that at any given sampling, say 100000 runs, some numbers would be at higher and lower frequencies, however I could see that if you watched the surface over time as the program ran, the cells would undulate up and down randomly. The numbers are random after all! My mistake was to think that running the program for ever larger generations of numbers would increase the accuracy but instead it simply shows randomness at a different scale.
This has implications for nature, lets simply take entropy; at any given time, in a particular place, at a certain scale, there could be a clump of order that seemed to violate entropy, being more ordered than the background but at the same scale. At the same time in a different place there would clump if disorder that was more disordered than the background. I believe it is related to the phenomenon of the rogue wave.