Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-10T00:02:46.194Z Has data issue: false hasContentIssue false
  • English
  • Français

Random Thoughts about Randomness

Published online by Cambridge University Press:  28 February 2022

Irving John Good
Irving John Good*
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Va
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper I shall bring together some philosophical and logical ideas about randomness many of which have been said before in scattered places. For less philosophical aspects see, for example [27].

When philosophers define terms, they try to go beyond the dictionary, but the dictionary is a good place to start and one dictionary definition of ‘random’ is ‘having no pattern or regularity’. This definition could be analyzed in various contexts but, at least for the time being, I shall restrict my attention to sequences of letters or digits, generically called ‘digits’. These digits are supposed to belong to a generalized alphabet; perhaps a new word should be used, such as ‘alphagam’, but I shall use the word ‘alphabet’ in the generalized sense so as to avoid a neologism. For simplicity I shall assume that the alphabet is finite and consists of the t digits 0, 1, 2,…, t — 1.

Type
Part III Symposium: Fundamental Problems in the Concept of Randomness
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1972 , 1972 , pp. 117 - 135
Copyright
Copyright © 1974 by D. Reidel Publishing Company

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Invited lecture in the symposium on the Concept of Randomness, dedicated to the memory of L. J. Savage, in the Biennial Meeting of the Philosophy of Science Association, Olds Plaza Hotel, Lansing, Michigan, October 27-29, 1972. The work was supported in part by H.E.W., N. I. H. Grant #R01 GM18770. I am indebted to Dr. L. S. Mayer for pointing out some obscurities.

References

Bohm, David, ‘A Suggested Interpretation of the Quantum Theory in Terms of ‘hidden’ Variables’, Physical Review 85 (1952) 166-193.10.1103/PhysRev.85.166CrossRefGoogle Scholar
Bunge, Mario, ‘Strife about Complementarity’ British Journal for the Philosophy of Science 6 (1955) 1-12 and 141-154.10.1093/bjps/VI.21.1CrossRefGoogle Scholar
Dickey, J. M., ‘Estimation of Disease Probabilities Conditioned on Symptom Variables’, Mathematical Biosciences 3 (1968) 249-265.10.1016/0025-5564(68)90083-7CrossRefGoogle Scholar
Everett, H. J., III, ‘Relative State’ Formulation of Quantum Mechanics’, Reviews of Modern Physics 29 (1957) 454-462.CrossRefGoogle Scholar
Finetti, Bruno de, ‘La prevision, ses lois logiques, ses sources subjectives’ Annales de Vlnstitut Henri Poincare 7 (1937) 1-68.Google Scholar
Godambe, V. P. and Sprott, D. A. (eds.), Foundations of Statistical Inference, proceedings of a symposium in Waterloo, Ontario, Canada in 1970; Holt, Rinehart and Winston of Canada, Toronto and Montreal, 1971.Google Scholar
Good, I. J., Probability and the Weighing of Evidence, Charles Griffin, London; Hafners, New York, 1950.Google Scholar
Good, I. J., ‘Contribution to the Discussion of G. A. Barnard's Paper on Information Theory’, Journal of the Royal Statistical Society, series B 13 (1951) 61-62.Google Scholar
Good, I. J., ‘On the Population Frequencies of Species and the Estimation of Population Parameters’, Biometrika 40 (1953) 237-264.10.1093/biomet/40.3-4.237CrossRefGoogle Scholar
Good, I. J., ‘Review of M. H. Quenouille “Design and Analysis of Experiment”’, Annals of Eugenics 18 (1953) 263-266.Google Scholar
Good, I. J., ‘Contribution to the Discussion in the Third (1955) London Symposium on Information Theory’, Information Theory (ed. by Cherry, Colin), Butterworth's, 1956, pp. 13-14.Google Scholar
Good, I. J., ‘On the Estimation of Small Frequencies in Contingency Tables’, Journal of the Royal Statistical Society, series B 18 (1956) 113-124.Google Scholar
Good, I. J., ‘Which Comes First, Probability or Statistics?’, Journal of the Institute of Actuaries 82 (1956) 249-255.10.1017/S0020268100046448CrossRefGoogle Scholar
Good, I. J., ‘Review of G. S. Brown “Probability and Scientific Inference”’, Longmans, London, 1957; British Journal for the Philosophy of Science 9 (1958) 251-254.CrossRefGoogle Scholar
Good, I. J., ‘Review of R. von Mises, “Probability, Statistics and Truth'”’ (2nd ed.), 1957, Journal of the Royal Statistical Society, series A 121 (1958) 238-240.10.2307/2343367CrossRefGoogle Scholar
Good, I. J., ‘Kinds of Probability’, Science 129 (1959) 443-447.10.1126/science.129.3347.443CrossRefGoogle Scholar
Good, I. J., ‘Review of K. R. Popper, “The Logic of Scientific Discovery”’, Hutchinson, London, 1959; Mathematical Reviews 21 (1960) 1171-1173.Google Scholar
Good, I. J., ‘A Causal Calculus’, British Journal for the Philosophy of Science 11 (1961) 305-318; 12 (1961) 43-51; 13 (1962) 88.10.1093/bjps/XI.44.305CrossRefGoogle Scholar
Good, I. J., ‘Contribution to the Discussion of a Paper by J. Neyman and Elizabeth L. Scott’, Journal of the Royal Statistical Society, series B 20 (1958) 35.Google Scholar
Good, I. J., ‘The Mind-Body Problem or Could an Android Feel Pain?’, in Theories of the Mind (ed. byScher, J. ), Glencoe Free Press and Macmillan, 1962, pp. 490-518.Google Scholar
Good, I. J., ‘Speculations Concerning Precognition’, in The Scientist Speculates (ed. by Good, I. J., Mayne, A. J., and Maynard-Smith, J.), Heinemann, London; Basic Books and Capricorn, New York, 1962/1965, pp. 151-157.Google Scholar
Good, I. J., The Estimation of Probabilities; and Essay on Modern Bayesian Methods, MIT Press, 1965.Google Scholar
Good, I. J., ‘Review of Richard von Mises, “Mathematical Theory of Probability and Statistics”’ (ed. by Geiringer, Hilda), Academic Press; 1964; Journal of the Royal Statistical Society, series A 128 (1966) 289-291.Google Scholar
Good, I. J., ‘A Bayesian Significance Test for Multinomial Distributions’, Journal of the Royal Statistical Society, series B 29 (1967) 399-431 (with discussion).Google Scholar
Good, I. J., ‘Corroboration, Explanation, Evolving Probability, Simplicity and a Sharpened Razor’, British Journal for the Philosophy of Science 19 (1968) 123-143.CrossRefGoogle Scholar
Good, I. J., ‘Discussion of Bruno de Finetti's paper ‘Initial Probabilities: a Prerequisite for Any Valid Induction’ ’, 1968 Salzburg Colloquium in Philosophy of Science, Synthese 20 (1969) 17-24. Reprinted in Induction, Physics, and Ethics (ed. by Weingartner, P. and Zecha, G. ), Reidel, Dordrecht, 1970, pp. 18-25.Google Scholar
Good, I. J., ‘How Random are Random Numbers?’, The American Statistician 23 (1969) 42-45.10.1080/00031305.1969.10481874CrossRefGoogle Scholar
Good, I. J., ‘The Probabilistic Explication of Information, Evidence, Surprise.Causality, Explanation, and Utility’, and ‘Twenty-seven Principles of Rationality’, in Foundations of Statistical Inference (see Reference [6]), pp. 108-141 (including discussion).Google Scholar
Good, I. J., ‘Review of Philip McShane “Randomness, Statistics, and Emergence”’, Gill and MacMillan, 1970, Times Literary Supplement, 18 September 1970, p. 1043.Google Scholar
Good, I. J., ‘The Baker's Oven, XV’, Mensa Journal and Bulletin, No. 150, October 1971, pp. 10-12.Google Scholar
Good, I. J., ‘46656 varieties of Bayesians’, Letter in The American Statistician 25 (1971) 62-63.Google Scholar
Good, I. J. and Gaskins, R. A., ‘Non-Parametric Roughness Penalties for Probability Densities’, Biometrika 58(1971) 255-277.CrossRefGoogle Scholar
Good, I. J., and Gover, T. N., ‘The Generalized Serial Test and the Binary Expansion of √2’, Journal of the Royal Statistical Society, series A 130 (1967) 102-107; 131 (1968) 434.10.2307/2344040CrossRefGoogle Scholar
Good, I. J. and Toulmin, G. H., ‘The Number of New Species, and the Increase in Population Coverage, when a Sample is Increased’, Biometrika 43 (1956) 45-63.10.1093/biomet/43.1-2.45CrossRefGoogle Scholar
Kendall, M. G., ‘A Theory of Randomness’, Biometrika 32 (1941) 1-5.CrossRefGoogle Scholar
Kolmogorov, A. N., ‘On Tables of Random Numbers’, Sankhya, series A 25 (1963) 369-376.Google Scholar
Martin-Löf, P., ‘The Literature on von Mises’ Kollektivs Revisited', Theoria 35 (1969) 12-37; Mathematical Reviews 39 (1970) 404.CrossRefGoogle Scholar
Mises, R. von Probability, Statistics and Truth (2nd revised edn., prepared by Geiringer, Hilda ), Allen and Unwin, London; Macmillan, New York, 1957.Google Scholar
Scott, Christopher, ‘A review of a book by G. S. Brown’, in Journal of the Society of Psychical Research 39 (1958) 217-234.Google Scholar
Turing, A. M., ‘On Computable Numbers, with an Application to the Entscheidung problem’, Proceedings of the London Mathematical Society, series 2 42 (1937) 230-265; 43 544.CrossRefGoogle Scholar
Vajda, S., Private communication, 1959.Google Scholar
Valery, P. A., ‘Eupalinos ou l'Architecte-Dialogue des morts’, La Nouvelle Revue Francaise, No. 90, 1921, pp. 237-285.Google Scholar
Wigner, Eugene P., ‘Remarks on the Mind-Body Question’, in The Scientist Speculates (ed. by Good, I. J., Mayne, A. J., and Maynard-Smith, J.), Heinemann, London; Basic Books and Capricorn Books, New York, 1962 and 1965, pp. 284-302.Google Scholar