Chapter 7: Mechanisms in Programs and Nature

Section 2: Three Mechanisms for Randomness

Sources of randomness

Two simple mechanical methods for generating randomness seem to have been used in almost every civilization throughout recorded history. One is to toss an object and see which way up or where it lands; the other is to select an object from a collection mixed by shaking. The first method has been common in games of chance, with polyhedral dice already existing in 2750 BC. The second—often called drawing lots—has normally been used when there is more at stake. It is mentioned several times in the Bible, and even today remains the most common method for large lotteries. (See page 969.) Variants include methods such as drawing straws. In antiquity fortune-telling from randomness often involved looking say at growth patterns of goat entrails or sheep shoulder blades; today configurations of tea leaves are sometimes considered. In early modern times the matching of fracture patterns in broken tally sticks was used to identify counterparties in financial contracts. Horse races and other events used as a basis for gambling can be viewed as randomness sources. Children's games like musical chairs in effect generate randomness by picking arbitrary stopping times. Games of chance based on wheels seem to have existed in Roman times; roulette developed in the 1700s. Card shuffling (see page 974) has been used as a source of randomness since at least the 1300s. Pegboards (as on page 312) were used to demonstrate effects of randomness in the late 1800s. An explicit table of 40,000 random digits was created in 1927 by Leonard Tippett from details of census data. And in 1938 further tables were generated by Ronald Fisher from digits of logarithms. Several tables based on physical processes were produced, with the RAND Corporation in 1955 publishing a table of a million random digits obtained from an electronic roulette wheel. Beginning in the 1950s, however, it became increasingly common to use pseudorandom generators whenever long sequences were needed—with linear feedback shift registers being most popular in standalone electronic devices, and linear congruential generators in programs (see page 974). There nevertheless continued to be occasional work done on mechanical sources of randomness for toys and games, and on physical electronic sources for cryptography systems (see page 969).

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