E. T. Jaynes' resolution of Bertrand's paradox in terms of invariance principles is criticized. An experimental setup is considered which generates general solutions to Bertrand's problem by rotating a line around a point a distancer+d from a circle of radiusr. The general solution obtained is neither translationally nor scale invariant, but depends on the value ofr/d. Only in the limitr/d » 0, when the line is just translating across the circle, is the distribution translationally invariant and scale invariant. In this limiting case the distribution found is just that obtained by Jaynes.
KeywordsGeneral Solution Invariance Principle
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- 1.E. T. Jaynes,Found. Phys. 3, 477 (1973).Google Scholar