Experimental tests of Bertrand’s question and the Duhem–Quine problem

  title={Experimental tests of Bertrand’s question and the Duhem–Quine problem},
  author={Zhenning Liu and Charles S. Adams},
  journal={European Journal of Physics},
In this paper we report on an experimental test of Bertrand’s question on the probability to find a random chord drawn inside a unit-radius circle with length greater than 3 . In an experiment performed by tossing straws onto a circle, we confirm a theoretical prediction that the answer depends on the ratio of the circle diameter, 2R, to the straw length, L, and that the special case, which follows from rotational and translation invariance using integral geometry, is only obtained in the… 
1 Citations



Bertrand's paradox: a physical way out along the lines of Buffon's needle throwing experiment

Bertrand's paradox (Bertrand 1889 Calcul des Probabilités (Paris: Gauthier-Villars)) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the

Solving the hard problem of Bertrand's paradox

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox

A Resolution of Bertrand's Paradox

Bertrand's random-chord paradox purports to illustrate the inconsistency of the principle of indifference when applied to problems in which the number of possible cases is infinite. This paper shows

Calcul des Probabilités

  • F. e.
  • Philosophy
  • 1889
Abstract“EVERYBODY makes errors in Probabilities at times, and big ones,” writes De Morgan to Sir William Hamilton. M. Bertrand appears to form an exception to this dictum, or at least to its severer

Uniform line fillings.

It is proved that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut.

The well-posed problem

Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of

Probability, geometry, and dynamics in the toss of a thick coin

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and

The Bayesian Treatment of Auxiliary Hypotheses

  • M. Strevens
  • Philosophy
    The British Journal for the Philosophy of Science
  • 2001
This paper examines the standard Bayesian solution to the Quine–Duhem problem, the problem of distributing blame between a theory and its auxiliary hypotheses in the aftermath of a failed prediction.

Quantum-Bayesian Coherence

It is argued that the Born Rule should be seen as an empirical addition to Bayesian reasoning itself, and how to view it as a normative rule in addition to usual Dutch-book coherence is shown.

Finitary probabilistic methods in econophysics

Econophysics applies the methodology of physics to the study of economics. However, whilst physicists have good understanding of statistical physics, they may be unfamiliar with recent advances in