## The Well-Posed Problem (1973)

Venue: | Foundations of Physics |

Citations: | 28 - 0 self |

### BibTeX

@ARTICLE{Jaynes73thewell-posed,

author = {Edwin T. Jaynes},

title = {The Well-Posed Problem},

journal = {Foundations of Physics},

year = {1973},

volume = {3},

pages = {477--493}

}

### Years of Citing Articles

### OpenURL

### Abstract

distributions obtained from transformation groups, using as our main example the famous paradox of Bertrand. Bertrand's problem (Bertrand, 1889) was stated originally in terms of drawing a straight line "at random" intersecting a circle. It will be helpful to think of this in a more concrete way; presumably, we do no violence to the problem (i.e., it is still just as "random") if we suppose that we are tossing straws onto the circle, without specifying how they are tossed. We therefore formulate the problem as follows. A long straw is tossed at random onto a circle; given that it falls so that it intersects the circle, what is the probability that the chord thus defined is longer than a side of the inscribed equilateral triangle? Since Bertrand proposed it in 1889 this problem has been cited to generations of students to demonstrate that Laplace's "principle of indifference" contains logical inconsistencies. For, there appear to be many ways of defining "equally possibl

### Citations

298 | The Classical Groups - Weyl - 1946 |

178 | Papers On Probability
- Jaynes
- 1983
(Show Context)
Citation Context ...tally. We conclude that probability theory has a wider range of useful applications than would be supposed from the standpoint of the usual frequency definitions. 1. Background In a previous article (=-=Jaynes 1968-=-) we discussed two formal principles---maximum entropy and transformation groups---that are available for setting up probability distributions in the absence of frequency data. The resulting distribut... |

51 |
Introduction to Mathematical Probability
- Uspensky
- 1937
(Show Context)
Citation Context ...of the circle. These assignments lead to the results p A = 1=2, p B = 1=3, and p C = 1=4, respectively. Which solution is correct? Of the ten authors cited (Bertrand 1889, Borel 1909, Poincar'e 1912, =-=Uspensky 1937-=-, Nortrup 1944, Gnedenko 1962, Kendell and Moran 1963, von Mises 1957 and 1964, THE WELL-POSED PROBLEM 2 and Mosteller 1965) with short quotations, in the appendix only Borel is willing to express a d... |

40 | Statistics and Truth - Mises, Probability - 1957 |

24 | Calcul des probabilités - Bertrand - 1889 |

5 |
Fifty challenging problems in probability
- Mosteller
- 1965
(Show Context)
Citation Context ...correct? Of the ten authors cited (Bertrand 1889, Borel 1909, Poincar'e 1912, Uspensky 1937, Nortrup 1944, Gnedenko 1962, Kendell and Moran 1963, von Mises 1957 and 1964, THE WELL-POSED PROBLEM 2 and =-=Mosteller 1965-=-) with short quotations, in the appendix only Borel is willing to express a definite preference, although he does not support it by any proof. Von Mises takes the opposite extreme, declaring that such... |

5 |
Calcul des probabilitiés
- Poincaré
- 1912
(Show Context)
Citation Context ...e interior area of the circle. These assignments lead to the results p A = 1=2, p B = 1=3, and p C = 1=4, respectively. Which solution is correct? Of the ten authors cited (Bertrand 1889, Borel 1909, =-=Poincar'e 1912-=-, Uspensky 1937, Nortrup 1944, Gnedenko 1962, Kendell and Moran 1963, von Mises 1957 and 1964, THE WELL-POSED PROBLEM 2 and Mosteller 1965) with short quotations, in the appendix only Borel is willing... |

4 | Lady Luck. The Theory of Probability - Weaver - 1982 |

2 |
Éléments de la Théorie de Probabilités. Hermann 1909. 2nd edition 1910, 3rd edition 1924. New revised ed. published
- Borel
- 1965
(Show Context)
Citation Context ...hord over the interior area of the circle. These assignments lead to the results p A = 1=2, p B = 1=3, and p C = 1=4, respectively. Which solution is correct? Of the ten authors cited (Bertrand 1889, =-=Borel 1909-=-, Poincar'e 1912, Uspensky 1937, Nortrup 1944, Gnedenko 1962, Kendell and Moran 1963, von Mises 1957 and 1964, THE WELL-POSED PROBLEM 2 and Mosteller 1965) with short quotations, in the appendix only ... |

1 |
The Theory of Probability, Chelsea Publ
- Gnedenko
- 1962
(Show Context)
Citation Context ...nts lead to the results p A = 1=2, p B = 1=3, and p C = 1=4, respectively. Which solution is correct? Of the ten authors cited (Bertrand 1889, Borel 1909, Poincar'e 1912, Uspensky 1937, Nortrup 1944, =-=Gnedenko 1962-=-, Kendell and Moran 1963, von Mises 1957 and 1964, THE WELL-POSED PROBLEM 2 and Mosteller 1965) with short quotations, in the appendix only Borel is willing to express a definite preference, although ... |

1 | Riddles in mathematics - Northrup - 1944 |