Experimental tests of Bertrand's question and the DuhemQuine problem
Abstract
In this paper we report on an experimental test of Bertrand's question on the probability to find a random chord drawn inside a unitradius circle with length greater than sqrt{3} 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 experimentally unattainable limit of infinite straw length, tilde{d}=2R/L> 0 d ∼ = 2 R / L → 0 . In addition, we observe a systematic discrepancy in the limit, tilde{d}=2R/L> 1 d ∼ = 2 R / L → 1 , where a large number of events are rejected. We conclude that the experimental test of Bertrand's paradox provides a good illustration of the DuhemQuine problem: that hypothesis testing is always conditional on a bundle of real auxiliary assumptions.
 Publication:

European Journal of Physics
 Pub Date:
 November 2019
 DOI:
 10.1088/13616404/ab39bd
 arXiv:
 arXiv:1806.00308
 Bibcode:
 2019EJPh...40f5801L
 Keywords:

 Bertrand’s paradox;
 Duhem–Quine problem;
 probability;
 experimental physics;
 Physics  History and Philosophy of Physics
 EPrint:
 5 pages, 6 figures