A Subjective Evaluation of Bode's Law and an ‘Objective’ Test for Approximate Numerical Rationality

Abstract Bode's law has usually been evaluated subjectively by means of overall judgment and opinions differ regarding its significance. Here we analyze it in some detail, with use of the axioms of probability, but still subjectively. The subjective Bayes factor in favor of Bode's law's being not a mere accident is given as between about 300 and 700. More tentatively, the existence of Bode's law seems to provide a factor of about 20 in favor of a non-cataclysmic origin of the solar system and hence in favor of there being an extremely large number of planetary systems in the galaxy. These factors would I think be much increased by taking into account “Dabbler's Law,” which is concerned with the mean distances of the saturnine satellites. It is pointed out that Dabbler's law has had predictive value and can be used for a further prediction. An “objective” test is given for whether a number is “nearly rational”. The ratios of the sidereal periods of pairs of solar bodies, for a given primary, are found not ...

[1]  I. J. Good,et al.  Some statistical methods in machine intelligence research , 1970 .

[2]  I. Good.  Discussion of Bruno de Finetti’s Paper ‘Initial Probabilities: A Prerequisite for any Valid Induction’ , 1969 .

[3]  I. Good,et al.  Utility of a Distribution , 1968, Nature.

[4]  I. Good.  Corroboration, Explanation, Evolving Probability, Simplicity and a Sharpened Razor , 1968, The British Journal for the Philosophy of Science.

[5]  I. Good,et al.  Coding Theorems and Weight of Evidence , 1968 .

[6]  I. Good.  A Bayesian Significance Test for Multinomial Distributions , 1967 .

[7]  I. Good.  The White Shoe is a Red Herring , 1967 .

[8]  I. Good.  On the Principle of Total Evidence , 1967 .

[9]  I. J. Good,et al.  How to Estimate Probabilities , 1966 .

[10]  F. Low,et al.  Infra-Red Observations of a Preplanetary System , 1966, Nature.

[11]  Irving John Good,et al.  The Estimation of Probabilities: An Essay on Modern Bayesian Methods , 1965 .

[12]  Cedric A. B. Smith,et al.  Personal Probability and Statistical Analysis , 1965 .

[13]  I. J. Good,et al.  Speculations Concerning the First Ultraintelligent Machine , 1965, Adv. Comput..

[14]  I. Good.  How Rational Should a Manager be , 1962 .

[15]  I. Good,et al.  THE PARADOX OF CONFIRMATION (II) , 1961, The British Journal for the Philosophy of Science.

[16]  I. Good.  A CAUSAL CALCULUS (I)* , 1961, The British Journal for the Philosophy of Science.

[17]  J. Romain,et al.  The earth, the planets, and the stars , 1961 .

[18]  Cedric A. B. Smith,et al.  Consistency in Statistical Inference and Decision , 1961 .

[19]  Y. Hagihara.  The Stability of the Solar System , 1961 .

[20]  W. Smart.  Text-Book on Spherical Astronomy , 1962 .

[21]  I. Good.  Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments , 1960 .

[22]  I. J. Good,et al.  Effective Sampling Rates for Signal Detection; or Can the Gaussian Model be Salvaged? , 1960, Inf. Control..

[23]  I J Good,et al.  Kinds of Probability: Although there are at least five kinds of probability, we can get along with just one kind. , 1959, Science.

[24]  I. Good.  Significance Tests in Parallel and in Series , 1958 .

[25]  I. J. Good,et al.  Which Comes First, Probability or Statistics? , 1956 .

[26]  W. Leveque.  Topics in number theory , 1956 .

[27]  H. Alfvén.  The Origin of the Solar System , 1982 .

[28]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[29]  A. Roy,et al.  On the Occurrence of Commensurable Mean Motions in the Solar System , 1954 .

[30]  R. Carnap.  Logical foundations of probability , 1951 .

[31]  L. J. Savage,et al.  Probability and the weighing of evidence , 1951 .

[32]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[33]  Wilfred Perks,et al.  Some observations on inverse probability including a new indifference rule , 1947 .

[34]  P. Blackett.  The Magnetic Field of Massive Rotating Bodies , 1947, Nature.

[35]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[36]  Martin Davidson.  An easy outline of astronomy , 1946 .

[37]  E. C. Kemble,et al.  Is the Frequency Theory of Probability Adequate for All Scientific Purposes , 1942 .

[38]  B. O. Koopman.  The bases of probability , 1940 .

[39]  B. O. Koopman.  The Axioms and Algebra of Intuitive Probability , 1940 .

[40]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[41]  J. Uspensky.  Introduction to mathematical probability , 1938 .

[42]  J. Keynes.  Essays in biography , 1933 .

[43]  B. Russell,et al.  A Treatise on Probability , 1921 .

[44]  M. A. Blagg.  On a Suggested Substitute for Bode's Law. (Plate 12.) , 1913 .

[45]  W. R..  Introduction to Astronomy , 1906, Nature.

[46]  H. Jeffreys.  The Theory of Probability , 1896 .

[47]  G. F. Chambers.  The sun, planets, and comets , 1889 .

[48]  J. Lockyer.  Elements of Astronomy , 1870 .

[49]  G. F. Chambers.  A handbook of descriptive and practical astronomy , 1861 .

[50]  Siméon-Denis Poisson.  Recherches sur la probabilité des jugements en matière criminelle et en matiére civile, précédées des règles générales du calcul des probabilités , 1837 .