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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| History of randomness | 2/4 | https://en.wikipedia.org/wiki/History_of_randomness | reference | science, encyclopedia | 2026-05-05T03:40:15.668742+00:00 | kb-cron |
For several centuries thereafter, the idea of chance continued to be intertwined with fate. Divination was practiced in many cultures, using diverse methods. The Chinese analyzed the cracks in turtle shells, while the Germans, who according to Tacitus had the highest regards for lots and omens, utilized strips of bark. In the Roman Empire, chance was personified by the Goddess Fortuna. The Romans would partake in games of chance to simulate what Fortuna would have decided. In 49 BC, Julius Caesar allegedly decided on his fateful decision to cross the Rubicon after throwing dice. Aristotle's classification of events into the three classes: certain, probable and unknowable was adopted by Roman philosophers, but they had to reconcile it with deterministic Christian teachings in which even events unknowable to man were considered to be predetermined by God. About 960 Bishop Wibold of Cambrai correctly enumerated the 56 different outcomes (without permutations) of playing with three dice. No reference to playing cards has been found in Europe before 1350. The Church preached against card playing, and card games spread much more slowly than games based on dice. The Christian Church specifically forbade divination; and wherever Christianity went, divination lost most of its old-time power. Over the centuries, many Christian scholars wrestled with the conflict between the belief in free will and its implied randomness, and the idea that God knows everything that happens. Saints Augustine and Aquinas tried to reach an accommodation between foreknowledge and free will, but Martin Luther argued against randomness and took the position that God's omniscience renders human actions unavoidable and determined. In the 13th century, Thomas Aquinas viewed randomness not as the result of a single cause, but of several causes coming together by chance. While he believed in the existence of randomness, he rejected it as an explanation of the end-directedness of nature, for he saw too many patterns in nature to have been obtained by chance. The Greeks and Romans had not noticed the magnitudes of the relative frequencies of the games of chance. For centuries, chance was discussed in Europe with no mathematical foundation and it was only in the 16th century that Italian mathematicians began to discuss the outcomes of games of chance as ratios. In his 1565 Liber de Lude Aleae (a gambler's manual published after his death) Gerolamo Cardano wrote one of the first formal tracts to analyze the odds of winning at various games.
== 17th–19th centuries ==
Around 1620 Galileo wrote a paper called On a discovery concerning dice that used an early probabilistic model to address specific questions. In 1654, prompted by Chevalier de Méré's interest in gambling, Blaise Pascal corresponded with Pierre de Fermat, and much of the groundwork for probability theory was laid. Pascal's Wager was noted for its early use of the concept of infinity, and the first formal use of decision theory. The work of Pascal and Fermat influenced Leibniz's work on the infinitesimal calculus, which in turn provided further momentum for the formal analysis of probability and randomness. The first known suggestion for viewing randomness in terms of complexity was made by Leibniz in an obscure 17th-century document discovered after his death. Leibniz asked how one could know if a set of points on a piece of paper were selected at random (e.g. by splattering ink) or not. Given that for any set of finite points there is always a mathematical equation that can describe the points, (e.g. by Lagrangian interpolation) the question focuses on the way the points are expressed mathematically. Leibniz viewed the points as random if the function describing them had to be extremely complex. Three centuries later, the same concept was formalized as algorithmic randomness by A. N. Kolmogorov and Gregory Chaitin as the minimal length of a computer program needed to describe a finite string as random. The Doctrine of Chances, the first textbook on probability theory was published in 1718 and the field continued to grow thereafter. The frequency theory approach to probability was first developed by Robert Ellis and John Venn late in the 19th century.
While the mathematical elite was making progress in understanding randomness from the 17th to the 19th century, the public at large continued to rely on practices such as fortune telling in the hope of taming chance. Fortunes were told in a multitude of ways both in the Orient (where fortune telling was later termed an addiction) and in Europe by Romanis and others. English practices such as the reading of eggs dropped in a glass were exported to Puritan communities in North America.
The term entropy, which is now a key element in the study of randomness, was coined by Rudolf Clausius in 1865 as he studied heat engines in the context of the second law of thermodynamics. Clausius was the first to state "entropy always increases". From the time of Newton until about 1890, it was generally believed that if one knows the initial state of a system with great accuracy, and if all the forces acting on the system can be formulated with equal accuracy, it would be possible, in principle, to make predictions of the state of the universe for an infinitely long time. The limits to such predictions in physical systems became clear as early as 1893 when Henri Poincaré showed that in the three-body problem in astronomy, small changes to the initial state could result in large changes in trajectories during the numerical integration of the equations. During the 19th century, as probability theory was formalized and better understood, the attitude towards "randomness as nuisance" began to be questioned. Goethe wrote:
The tissue of the world is built from necessities and randomness; the intellect of men places itself between both and can control them; it considers the necessity and the reason of its existence; it knows how randomness can be managed, controlled, and used.