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The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
This ratio of densities, and other ratios (using four fundamental constants: speed of light in vacuum c, Newtonian constant of gravity G, reduced Planck constant ℏ, and Hubble constant H) computes to an exact number, 32.8·10 120. This provides evidence of the Dirac large numbers hypothesis by connecting the macro-world and the micro-world.
Unfortunately, extensive computer searching [8] has failed to find such a constant, and in fact it is now known that if exists and if it is an algebraic number of degree at most 25, then the coefficients in its minimal polynomial must be enormous, at least , so extending Apéry's proof to work on the higher odd zeta constants does not seem ...
A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator.
The eery coincidence of a contestant literally named Kovid making an outfit with a matching face mask less than a year before COVID-19 hit the U.S. was not lost on TikTok or Twitter, where a clip ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Luck. Fate. Blessing. A glitch in the matrix. Or, if you’re more skeptical, just a coincidence.. It’s a phenomenon that, from a statistical perspective, is random and meaningless.
Given a discrete-time stationary ergodic stochastic process on the probability space (,,), the asymptotic equipartition property is an assertion that, almost surely, (,, …,) where () or simply denotes the entropy rate of , which must exist for all discrete-time stationary processes including the ergodic ones.