Chapter 7: Mechanisms in Programs and Nature

Section 3: Randomness from the Environment

Mechanical randomness

It takes only small imperfections in dice or roulette wheels to get substantially non-random results (see page 971). Gaming regulations typically require dice to be perfect cubes to within one part in a few thousand; casinos normally retire dice after a few hundred rolls.

In processes like stirring and shaking it can take a long time for correlations to disappear—as in the phenomenon of long-time tails mentioned on page 999. One notable consequence were traces of insertion order among the 366 capsules used in the 1970 draft lottery in the U.S. But despite such problems mixing of objects remains by far the most common way to generate randomness when there is a desire for the public to see randomization occur. And so for example all the state lotteries in the U.S. are currently based on mixing between 10 and 54 balls. (Numbers games were instead sometimes based on digits of financial data in newspapers.)

There have been a steady stream of inventions for mechanical randomness generation. Some are essentially versions of dice. Others involve complicated cams or linkages, particularly for mechanical toys. And still others involve making objects like balls bounce around as randomly as possible in air or other fluids.

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From Stephen Wolfram: A New Kind of Science [citation]