RANDOMNESS Mechanisms of Chance

These are just a few of the many devices people have invented during the course of history to meet the ever-increasing demand for random outcomes.

Dice

Dice "The earliest six-sided dice known have come from the East. Made of baked clay and dating circa 2750 B.C., one die was found in excavations of ancient Mesopotamia in Northern Iraq, Tepe Gawra. Dice dating from about the same period and made from the same material were found in all strata at the Mohenjo-Dam excavation in the Indus valley--including rectangular prism stick dice and triangular stick dice, as well as cubical dice. At both sites, the faces of the six-sided dice were marked with pips (dots). In those times pips were used probably because there was as yet no system of numerical notation, but the tradition of using pips rather than numbers has been retained in most modern dice.1"

--page 18, Randomness
1. The die found in excavations in Northern Iraq is described in "Ancient die," 1931. See also Mackay, 1976, and Bhatta, 1985. That pips were used because there was no numerical notation system was suggested by Davidson, 1949, and David, 1962.

The Astragalus

"Six-sided dice have been found in Egypt from excavations dating to 1320 B.C., but dice-like bones used as chance devices have turned up in much earlier Egyptian sites. These particular bones, found also in the later Greek and Roman civilizations, are from the heel of a hoofed animal such as a deer, calf, sheep, or goat and are called tali (Latin) or astragali (Greek). The astragalus has four distinctly different long flat faces, the only ones on which it will rest when tossed, and two small rounded ends. Of the four flat faces, two are narrow and flat and two are broad, with one broad side slightly convex and the other slightly concave. Since each side of the astragalus looked different, it was not necessary to mark the sides. If they were marked with pips, the sides were scored 1, 3, 4, and 6. Greek and Roman games of chance were played with four astragali. The lowest throw, known as "the dogs," resulted when all ones were thrown. In the highest throw, called the Venus throw, four different sides came up."

An astragalus
The astragalus and its four different faces

--page 19-20, Randomness

Random Number Tables

"As Alfred Bork has pointed out, 'A rational nineteenth-century man would have thought it the height of folly to produce a book containing only random numbers.' Nevertheless, in 1927 Cambridge University Press did indeed publish a table of 41,600 digits that had been randomly arranged by [Leonard H.C.] Tippett.2...Rejecting the effectiveness of cards, tickets, balls, and dice, Pearson [Tippett's mentor] contended that statistical experimenters "who have had to deal with the problems of random sampling" might benefit by 'a single system of numbers'...A mere ten years after its publication, Tippett's table of over 40,000 Random Sampling Numbers was deemed inadequate for very large sampling experiments. In 1938 the mathematicians R. A. Fisher and F. Yates published 15,000 additional random digits...In 1939 M. G. Kendall and B. Babington-Smith published a table of 100,000 digits...In 1949 the Interstate Commerce Commission published a table of 105,000 random digits,...[and] in 1955 the RAND Corporation published a document entitled 'A Million Random Digits with 100,000 Normal Deviates.' RAND stated that the purpose of producing such large tables was to meet the growing need for random numbers in solving problems by experimental probability procedures.3"

--pages 132-135, Randomness
2. Bork, 1967; Tippett, 1927 (pp. iii-iv).
3. RAND, 1955.

The Quincunx

A quincunx "In 1873-74 Sir Francis Galton (Charles Darwin's cousin) designed an apparatus that he later named the quincunx. This machine was a clever physical model of the theory of errors, which he believed was applicable to many phenomena in biology as well as physics. Enclosed behind glass was a cross section of a funnel opening onto a pyramid of equally spaced pins, with vertical compartments below the pins. Pellets, once released from the funnel, would bounce helter-skelter, left or right, against the pins (representing, in Galton's theory, the independent random disturbances of nature), to ultimately gather in the lower compartments in a pile which resembles a normal curve. Galton called this phenomenon the law of deviation. Galton believed that the important influences that acted upon an inherited characteristic, such as height, were a 'host of petty disturbing influences' (represented by the pins) and that the law of genetic deviation was purely numerical, universally following the single law of the normal distribution. Devices similar to the quincunx can be seen in science museums; sometimes they are enormous, with tennis balls serving as pellets."

--page 104, Randomness

Computer Algorithms

"As larger and larger tables of random digits were needed in computer models to solve nonprobabilistic problems, not to mention the wide range of probabilistic applications, storage of the random number tables in computers began to consume far too much memory. The use of a preprogrammed formula that allowed the computer to generate a random digit at the time it was needed in a calculation seemed to be the ideal solution...And so the search began for algorithms that could be computer-coded into programs generating random digits. The digits were called pseudorandom numbers, and the programmed formulas, or algorithms, were called pseudo-random number generators--for how could truly random numbers be generated through a formula and a machine?"

--page 139, Randomness

    RELATED LINKS:
    How to Generate Pure Random Numbers
    This site discusses uses for and methods for obtaining numbers generated by a truly random process, rather than an algorithm.

    Yahoo: Randomized Things
    The site links to many different generators that provide anything from random web links to random quotes.

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