Related papers: De Divino Errore
This is a missing chapter from Hans Magnus Enzensberger's mathematical adventure The Number Devil (Henry Holt and Company, New York, 1997). In the book, a math-hating boy named Robert is visited in his dreams by the clever Number Devil, who…
The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…
We study the error calculus from a mathematical point of view, in particular for the infinite dimensional models met in stochastic analysis. Gauss was the first to propose an error calculus. It can be reinforced by an extension principle…
Galileo determined distances to stars based on the assumption that stars were suns, the apparent sizes of stars as seen through his telescope, and basic geometry. However, the apparent sizes that he measured were the result of diffraction…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
A mathematical conjecture is successfully identified, which is used for relativistic analysis of dielectric Einstein-box thought experiment in a Letter (Ramos, Rubilar, and Obukhov, Phys. Lett. A 375, 1703 (2011)), where the authors…
Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly)…
This note is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian…
Standard interpretations of Goedel's "undecidable" proposition, [(Ax)R(x)], argue that, although [~(Ax)R(x)] is PA-provable if [(Ax)R(x)] is PA-provable, we may not conclude from this that [~(Ax)R(x)] is PA-provable. We show that such…
A common flaw of astronomers is to believe that they know the truth even when data is scarce. I provide ten examples where this approach led to wrong strategic decisions in research plans, causing unnecessary delays in finding the truth. In…
withdrawed due to a substantial error.
This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example $1!-2!+3!-\text{etc.}$ and uses…
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent…
The Jeffreys-Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian…
In Plato's dialogues Republic and Laws, the most important disciplines for the best education of the rulers of the city are identified with arithmetic, geometry and astronomy. Those disciplines, however, are not intended for practical…
In 1975, G. P\'olya suggested that if two proofreaders found $a$ and $b$ errors in a text, of which $c$ errors were found by both of them, then a reasonable approximation of the unknown number $e$ of all errors is $e\approx ab/c$. We…
This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…
In spite of the wide range of his book, Cournot did not know some essential discoveries in natural sciences (William Herschel, Daniel Bernoulli, Humboldt) and his deliberations about measurement were almost useless. But he introduced the…
This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to…