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| Borel E. — Probability and certainty. A sun book |
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| Предметный указатель |
Absolute zero 54
Alphabetical numeration 73—77
Alphabetical numeration, illusion in 77 78
Alphabetical numeration, normal numbers in 75—77
Alphabetical numeration, vs. decimal numeration 75
Annals of Eugenics 139
Annals of Mathematical Statistics 139
Assessments, estimated 48
Astronomical numbers 81—83
Average speed of molecules 53—54
Bernoulli, Jacques 27 52 71
Bertrand, Joseph 94 95 96 132
Biometrics 139
Births, male, probability of 37— 40 113
Bohr, Niels 85
Boltzmann 52 54
Broglie, Louis de 85
Brownian movement 58
C.G.S. units 81 83 86
Calculus of probability, applied 39 52
Calculus of probability, assumptions in 12
Calculus of probability, derivations from 52
Calculus of probability, restrictions in use of 40 125 126
Calculus of probability, use of in polls 40 42
Camot — Clausius principle 121
Carnot, Sadi 59
Causes, probabilities of 34—51
Centimeter-Gram-Second (C.C.S.) units 81 83 86
Certainty, and error 114—18
Certainty, characteristics of 122—24
Certainty, in elections 5
Certainty, in natural events 5 6
Certainty, invalidation of 5
Certainty, negative 5
Certainty, positive 4
Certainty, practical 117—18 123
Chance, games of 14—18
Chance, imitation of 48—51
Closed system, definition of 61
Common sense 60
Composite probabilities 31 n.
Computable probabilities, theory of 30
Continuity, physical 103 104—9
Couderc, Paul 63 n.
Decimal numbers, non-normal 71 72
Decimal numbers, normal 71 72
Decimal numbers, “frequency” in 71
Decimal probabilities 69
Denominator of probability 74
Density, average, of galaxy 88
Density, average, of matter within the sphere 87
Density, average, of stars 82 88 89 90
Density, average, of universe 88
Deviation 20—23
Deviation, as zero 46
Deviation, exceptional 35 36
Deviation, law of 21 29
Deviation, probability of 23 24
Deviation, real 23
Deviation, relative 23 26
Deviation, unit of 20—23
Deviation, unit of, in a million trials 25 35
Deviation, unit of, in predicting composition of urn 42 43
Diffusion of liquids 61
Discontinuity, physical 101 104
Discontinuity, physical, introduction of 108
Distances, astronomical 81—83
Distances, astronomical, minute 84 85
Distribution of speeds, law of 54 55
Earth, age of 83
Earth, heating of 59
Energy sources 65 66
Entropy, and certainty 114—18
Entropy, definition of 63
Entropy, degrees of 67 68
Entropy, disregard of 68
Entropy, percentage 48
Entropy, principle of 59—61
Equalities, false 67—69
Erosion 64
Error, average, in polling 46—48
Errors of observation 109—11
Expansion of universe 63
False equalities 67—69
Galaxy, average density of 88
Galaxy, dimensions of 82 83 89 90
Galaxy, of first order 89
Galaxy, of second order 89
Galileo 14
games of chance 14—18
Gases, kinetic theory of 52
Gases, mixing of 54—57
Gibbs 55
Great numbers, law of 27—30
Heads or Tails, in Petersburg Paradox 92
Heads or Tails, unit of deviation in 25 34—36
Heads or Tails, ways of winning 16—17
Illusion in alphabetical numeration 77—78
Infinite number 71
Jeans’ experiment 91
Jeans’ miracle 60 (see also Jeans’ experiment)
Jeans’ miracle, improbability of 120 121 123 124
Journal of the American Statistical Association 139
Journal of the Royal Statistics Society 139
K (body of knowledge) 8 9 30
K (body of knowledge), erroneous 11 12
K (body of knowledge), incomplete 10 11
Keynes, John Maynard 8
Kinetic theory of gases 52
Laplace-Gauss law of deviation 53 n. 110 112
Large numbers, law of 71 (see also Great numbers law
Law of deviation 21 29 110
Law of distribution of speeds 54 55
Law of errors 110
Law of great numbers 27—30 137
Law of Large Numbers 71
Law of universal attraction 63
Life, appearance of 124—26
Light, speed of 81
Logarithm of probability 63
Male births, probability of 37— 40 113
Mass, minute 84—86
Mass, minute, in average speed of gas molecules 53
| Mathematical expectation 18—21
Mathematical expectation, calculation of 128—130
Mathematical expectation, equal to unity 70 134
Mathematical expectation, in a fair game 133
Mathematical expectation, in the Petersburg Paradox 93 96
Mathematical expectation, infinite 135
Mathematician’s illusion 77—80
Maxwell, James Clerk 52 53 54
Mere, Chevalier do 15 16
Mises, van 112
Molecular hypothesis 52
Molecules, average speed of 53 54
Molecules, movement of 53—59
Monkeys, typewriting 91
Mortality, of girls 38
Multiple births, sex in 39 40
Multiple trials 30 31
Natural phenomena, in probability 3
Natural resources, dissipation of 65 66
Numbers, astronomical 81—83
numbers, decimal 71 72
Numbers, infinite 71
Numbers, superastronomical 88 89
Numerical calculation, of probability 4
Opinion, public, on “pile of wheat 99 100
Opinion, public, polls of 40—43
Pascal, Blaise 15 16
Pascal’s triangle 17 18
Pascal’s triangle, wager 138
Perrin, Jean 52 84
Petersburg Martingale 127—38
Petersburg Paradox 92—97 127— 38
Petersburg Paradox, solution of 95—97
Petersburg Paradox, statement of 92—94
Phenomena, irreversible 64
Phenomena, natural 3
Physical continuity, definition of 104—7
Planck, Max 85
Poincar , Henri 67 (see also Poincar’s formulas)
Poincar’s Formulas 104
Poincar’s Formulas, as logical solution 109
Poincar’s Formulas, objection to 106 107
Poisson, Simon Denis, formulas of 70
Poll, public-opinion 40—43
Poll, public-opinion, predicting results of 42 43
Poll, public-opinion, validity of 40 41
Principle of sufficient reason 72
Probabilities, disregard of 118 119
Probability vs. certainty 4
Probability, a priori 34
Probability, assessment of 9
Probability, assessment of, aleatory elements in 9 10
Probability, assessment of, statistics in 11
Probability, calculus of see Calculus of probability
Probability, categories of 3
Probability, decimal 69
Probability, evaluation of 98—101
Probability, logarithm of 63
Probability, numerical calculation of 4
Probability, statistical 111—13
Probability, subjective nature of 7—9
Probability, subjective, defined 8 9
Probable gain 19 20
Public opinion, polling 40—43
Public opinion, polling, in “pile of wheat” 99—100
quantum mechanics 52 85
Quantum mechanics, theory 52
Radiation, solar 64 83
Random choice, advantages of 48 51
Random choice, and statistical probability 111—13
Random choice, from short pack of cards 12
Random choice, in alphabetical numeration 80
Random choice, in forming decimal numbers 68—72
Random choice, in polling 46—51
Random choice, in repeated trials 10 31
Random choice, theory of 23 30
Relativity, theory of 87
Repeated trials, series of 27 28
Ruin of players 24—27
Ruin of players, certainty of 24
Rulings by administration 101—4
Sampling, by categories 47 48
Sampling, in public-opinion polls 44—48
Sampling, random 47 48
Schrolinger 85
Series of figures 73
Series of figures, unlimited 89
Sex ratio, at birth 38
Sex ratio, in multiple births 39 40
Solar radiation 64
Solutions, molecules in 57 58
St. Petersburg Problem see Petersburg Paradox
Statistical probability 111—13
Subjective probability, definition of 8 9
Sun, cooling of 59
Temperature, in movement of molecules 53—55
Temperatures, equalization of 58 59
Theory, of composite probabilities 31 n.
Theory, of computable probabilities 30
Theory, of expanding universe 91
Theory, of relativity 87
Theory, of repeated trials 36
Theory, of total probabilities 31 n.
Thermodynamics 62
Time periods, astronomical 83 84
Time periods, shortest 86 87
Total probabilities, theory of 31 n.
Trials, repeated 14—33 42 43
Trials, theory of 36
Truth, mathematical 115
Twins, sex of 39 40
Typewriting miracle 120 121 123 typewriting)
Unit of deviation 20—23
Universe, expanding, theory of 91
Universe, finite vs. infinite 87 88
Urn, determining composition of contents 42—47
Valry, Paul 60
Wave mechanics 53 85
Wider Universe, The (Couderc) 63 n.
Zeno the Eleatic 136
“Certain,” common usage of 3—6
“Maxwell’s demon” 62
“Pile of wheat” 98—113
“Probable,” common usage of 3—4
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