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Surprises in Numerical Expressions of Physical Constants

Ariel Amir, Mikhail Lemeshko and Tadashi Tokieda
The American Mathematical Monthly
Vol. 123, No. 6 (June-July 2016), pp. 609-612
DOI: 10.4169/amer.math.monthly.123.6.609
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Page Count: 4
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Surprises in Numerical Expressions of Physical Constants
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In science, as in life, “surprises” can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like π or e. The inverse problem also arises, whereby the measured value of a physical constant admits a “surprisingly” simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.

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