# Randomness

The term randomness is often used in statistics to signify well defined statistical properties, such as lack of bias or correlation. Random is different from arbitrary, because to say that a variable is random means that the variable follows a probability distribution. Arbitrary on the other hand implies that there is no such determinable probability distribution for the variable.

## Quotes

* How dare we speak of the laws of chance? Is not chance the antithesis of all law?
** Joseph Bertrand, Calcul des probabilités, 1889.
* He who believes this (atomism) may as well believe that if a great quantity of the one-and-twenty letters, composed either of gold or any other matter, were thrown upon the ground, they would fall into such order as legibly to form the Annals of Ennius. I doubt whether fortune could make a single verse of them.
** Marcus Tullius Cicero, De natura deorum, 2.37. Translation from Cicero's Tusculan Disputations; Also, Treatises On The Nature Of The Gods, And On The Commonwealth, C. D. Yonge, principal translator, New York, Harper & Brothers Publishers, Franklin Square. (1877).
* The generation of random numbers is too important to be left to chance.
** Robert R. Coveyou, Oak Ridge National Laboratory, 1969.
* The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He does not throw dice.
** Albert Einstein, letter to Max Born, 4 December 1926; commonly paraphrased "God does not play dice with the universe."
* Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved.
** Brain S. Everitt, Chance Rules (1999), Chapter 12, p. 175.
* Perhaps randomness is not merely an adequate description for complex causes that we cannot specify. Perhaps the world really works this way, and many events are uncaused in any conventional sense of the word.
** Stephen Jay Gould,"Chance Riches" in Hen's Teeth and Horse's Toes (1983).
* Randomness is a very, very subtle concept with its study properly belonging to statisticians more than mathematicians.
** Julian Havil, The Irrationals: A Story of the Numbers You Can't Count On (2012), Chapter 9, p. 229.
* Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen.
** Stephen Hawking in a 1994 debate with Roger Penrose, as transcribed in The Nature of Space and Time (1996) by Hawking and Penrose, p. 26.
* Fretting about a dearth of randomness seems like worrying that humanity might use up its last reserves of ignorance.
** Brian Hayes (scientist), Group Theory in the Bedroom (2008), Chapter 2, Random Resources, p. 23.
* The fact that randomness requires a physical rather than a mathematical source is noted by almost everyone who writes on the subject, and yet the oddity of this situation is not much remarked.
** Brian Hayes (scientist), Group Theory in the Bedroom (2008), Chapter 2, Random Resources, p. 35.
* Random chance was not a sufficient explanation of the Universe — in fact, random chance was not sufficient to explain random chance.
** Robert A. Heinlein, Stranger in a Strange Land (1960).
* Random numbers should not be generated with a method chosen at random.
** Donald Knuth, The Art of Computer Programming, Vol. II, 1969, section 3.1.
* The sun comes up just about as often as it goes down, in the long run, but this doesn't make its motion random.
** Donald Knuth, The Art of Computer Programming, Vol. II, 1969, section 3.3.2.
* A random sequence is a vague notion in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians and depending somewhat on the uses to which the sequence is to be put.
** Dick Lehmer (1951), cited by Julian Havil in The Irrationals: A Story of the Numbers You Can't Count On (2012), Chapter 9, p. 229.
* Quand une regle est fort composée, ce qui luy est conforme, passe pour irrégulier.
** When a rule is extremely complex, that which conforms to it passes for irregular (random).
** Gottfried Leibniz, Discourse on Metaphysics (1686), §6.
* For I do not believe that it is through the interference of Divine Providence … that the spittle of a certain person moved, fell on a certain gnat in a certain place, and killed it.
** Maimonides, Guide for the Perplexed, 12th century, Friedländer translation.
* Existence is random. Has no pattern save what we imagine after staring at it for too long. No meaning save what we choose to impose. This rudderless world is not shaped by vague metaphysical forces. It is not God who kills the children. Not fate that butchers them or destiny that feeds them to the dogs. It’s us. Only us.
   * Alan Moore, Watchmen
* Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.
** John von Neumann, "Various techniques used in connection with random digits" by John von Neumann in Monte Carlo Method (1951), ed. A.S. Householder, G.E. Forsythe, and H.H. Germond.
* One of us recalls producing a 'random' plot with only 11 planes, and being told by his computer center's programming consultant that he had misused the random number generator: 'We guarantee that each number is random individually, but we don’t guarantee that more than one of them is random.' Figure that out.
** William H. Press, Press, Numerical Recipes in Fortran 77: The Art of Scientific Computing (2nd ed), (1992). ISBN: 0-521-43064-X.
* The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term.
** Walter A. Shewhart and W. Edwards Deming, Statistical Method from the Viewpoint of Quality Control (1939).
* While in theory randomness is an intrinsic property, in practice, randomness is incomplete information.
** Nassim Nicholas Taleb, The Black Swan (2007).

## See also

* Probability
* Statistics