# Randomness

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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.

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- How dare we speak of the laws of chance? Is not chance the antithesis of all law?
- Joseph Bertrand,
*Calcul des probabilités*, 1889

- Joseph Bertrand,

- The generation of random numbers is too important to be left to chance.
- Robert R. Coveyou, Oak Ridge National Laboratory, 1969
^{[specific citation needed]}

- 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.**"

- Albert Einstein, letter to Max Born, 4 December 1926; commonly paraphrased "

- 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)

- Stephen Jay Gould,"Chance Riches" in

- 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

- Stephen Hawking in a 1994 debate with Roger Penrose, as transcribed in

- 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

- Brian Hayes (scientist),

- 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

- Brian Hayes (scientist),

- Random chance was not a sufficient explanation of the Universe — in fact, random chance was not sufficient to explain random chance.

- 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

- Donald Knuth,

- 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

- Donald Knuth,

*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

- Maimonides,

- 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

- John von Neumann, "Various techniques used in connection with random digits" by John von Neumann in

- 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)

- Walter A. Shewhart and W. Edwards Deming,

- While in theory randomness is an intrinsic property, in practice, randomness is
*incomplete information*.- Nassim Nicholas Taleb,
*The Black Swan*(2007)

- Nassim Nicholas Taleb,