MMacaulay001inforgottentheorieshashnodedev.hashnode.dev·May 11 · 6 min readI tested Bertrand's 1887 ballot formula on 648 vote splits and the answer was always (p-q)/(p+q).Part 100 of Forgotten Theories, a series re-testing old scientific claims with modern tools. Find the rest under the #forgotten-theories tag. In 1887 Joseph Bertrand sent a four-page note to the Comptes Rendus of the French Academy. The question he ...00
MMacaulay001inforgottentheorieshashnodedev.hashnode.dev·May 11 · 6 min readI tested von Mises's 1939 birthday claim with exact arithmetic and 10^5 Monte Carlo trials per group size. 23 people really is enough.Part 99 of Forgotten Theories, a series re-testing old scientific claims with modern tools. Find the rest under the #forgotten-theories tag. In 1939 Richard von Mises published a short paper with the unwieldy title Über Aufteilungs- und Besetzungswa...00
MMacaulay001inforgottentheorieshashnodedev.hashnode.dev·May 11 · 6 min readChebyshev's 1867 bound holds on every distribution I threw at it, and a two-point mix landed within 0.2% of saturating it.Part 98 of Forgotten Theories, a series re-testing old scientific claims with modern tools. Find the rest under the #forgotten-theories tag. In 1867 Pafnuty Chebyshev published a short proof of an inequality that any student of probability eventuall...00
MMacaulay001inforgottentheorieshashnodedev.hashnode.dev·May 11 · 6 min readI sampled a million coin flips with decaying probabilities. The 1909 dividing line showed up exactly where Borel said it would.Part 96 of Forgotten Theories, a series re-testing old scientific claims with modern tools. Find the rest under the #forgotten-theories tag. In 1909 Émile Borel was working through a problem about decimal expansions of real numbers, and he proved a ...00
MMacaulay001inforgottentheorieshashnodedev.hashnode.dev·May 11 · 6 min readI located the first 30 zeros of Riemann's zeta on the critical line. They all sat exactly where 1859 said they would.Part 95 of Forgotten Theories, a series re-testing old scientific claims with modern tools. Find the rest under the #forgotten-theories tag. In November 1859, Bernhard Riemann submitted an eight-page memoir to the Berlin Academy. The paper was about...00
