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The history of randomness

from Ken Zimmerman

After the cognitive revolution, Sapiens invented questioning and then questions. And Sapiens questioned everything. What happens next? Why did this happen rather than something else? Will each human die, when, and why? Who invented humans? Why were humans invented? What are the answers? One of the answers humans invented to deal with this and similar questions is randomness. Other inventions to deal with Sapiens’ questioning are chance, mathematics, and probability. Let’ consider the history of randomness.

In the ancient world randomness was intertwined with fate. As it is frequently in Asia and Africa today. Often in these cultures, devices such as dice, animal entrails, smoke, etc. were used to determine what fate would bring. Often summed up in the term divination. The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance. And later the odds associated with human life generally. The invention of calculus changed the formal study of randomness. Allowing for consideration of the complexity of the random. In the 19th century the concept of entropy was introduced in physics. In the 20th century Sapiens invented the mathematics of probability, axiomizing it in the 1930s. In the mid-20th century Sapiens invented quantum mechanics, changing the notion of randomness in many ways. A little later Sapiens added even more dimensions to randomness with algorithmic randomness. In the last 50 years computer scientists began to incorporate randomness into the design of computer algorithms, believing this created better performing computers. In some cases, such randomized algorithms outperform the best deterministic methods.

But before Sapiens invented randomness, it invented the divine. The gods, whoever and wherever they are, controlled humans like puppets. Deciding humanity’s future based on no plan other than the whims of the gods. Ancient Greece is one example. The ancient Greeks also believed that events were part of an unbreakable sequence. In this setting randomness is simply impossible. Plus, as the Greeks saw it randomness is unprovable and uninteresting.

Dice are found throughout the history of humanity. The first use of dice was as a divination tool, used in religious ceremonies, even if the first dice were often bones (or ossicles). Their natural asymmetry poses problems of credibility: even the pious believer will wonder about the true will of the gods if the dice constantly fall on the same side. The neutrality of symmetrical dice quickly became apparent. This symmetry has also allowed the development of games of chance, making the games fair for the different players. Generating random numbers has become a popular technique today for researchers to deal with several problems, ranging from behavior at the molecular level to sampling a population, or solving certain equation systems. Actuaries use them daily to quantify uncertainty. Until a century ago, people who needed random numbers could throw coins, shoot balls at restless urns, or roll dice as we have seen before. But recently other techniques have been invented. Including using the final few digits of government created large numbers. One interesting alternative is British statistician Leonard Tippett’s use of the mid-point of the parish area in England.

In 1927, a Soviet statistician, Evgueni (Eugene) Slutsky used economic series to generate chance, and Slutsky showed that random series could be used to generate all kinds of economic series. At the beginning of the 20th century, many researchers believed that unpredictable events such as wars, crop failures or technological innovations should play a role in economic cycles. But no one really understood how crucial random processes (nowadays we call them “stochastic“) are to understanding how the economy works. Until Slutsky published his work on “cyclical phenomena” showing that very simple manipulations of random series (in this case numbers obtained from government lottery draws) could generate undulating models that could not be distinguished from economic cycles. Or, as Slutsky said, “any economic series could be seen as a stochastic process obtained as “the sum of random causes.”

The main issue facing us today, “is indeterminacy a problem of probability?” Many projected scientific “advances” are based on the answer being yes.


  1. May 16, 2019 at 1:14 pm

    Ken, some caveats from a pedantic mathematician.

    When Slutsky says that “any economic series could be seen as a stochastic process” this does not mean that such series ‘really are’ stochastic.

    When you claim (if I read you right) that the main issue facing us today is indeterminacy, which is a problem of probability, and that many projected scientific “advances” are based on this assumption, there is more to be said.

    In what sense are coins and dice ‘genuinely’ random? If we had some particular coin tossing machine which was actually fair, how would we prove it?

    Pedantically, all we can ever justify is something like Slutsky’s claim: that a particular series or mechanism fits a stochastic model, and this fit has been severely tested according to current best practice. But some (often unanticipated) scientific advances have come about when chance or insight leads to some new test which the old model fails, hence motivating a new model / theory. For example, the construction of a machine that would toss supposedly fair coins or dice with biased results would prompt physicists to investigate such mechanisms and potentially lead to a new theory of coins and dice. The failure to conceive of or construct such a machine does not prove that a particular coin really is ‘fair’.

    To mathematicians there is more to ‘the problem of probability’ than is commonly supposed. (Hence my blog djmarsay.wordpress.com.)

    My own view (in agreement with Keynes) is that coins, dice and economic series can often reasonably be thought of ‘as if’ they were stochastic, but not always. And sometimes this matters. (See https://www.youtube.com/watch?v=AYnJv68T3MM).

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