Related papers: Bertrand's paradox: a physical solution
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as "Schrodinger's cat," has long posed an apparent paradox because the state resulting from a measurement appears to…
The arrival time problem for the free particle in one dimension may be formulated as the problem of determining a joint probability for the particle being found on opposite sides of the $x$-axis at two different times. We explore this…
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…
How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…
In this note we present a method to bound gaps between primes via the divergence of the series of reciprocals of the prime numbers, a consequence of a version of the Bertrand's test for convergence of series of positive numbers and a…
The reason for recalling this old paper is the ongoing discussion on the attempts of circumventing certain assumptions leading to the Bell theorem (Hess-Philipp, Accardi). If I correctly understand the intentions of these Authors, the idea…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
The letter submitted is an executive summary of our previous paper. To solve the Einstein Podolsky Rosen 'paradox' the two boundary quantum mechanics is taken as self consistent interpretation of quantum dynamics. The difficulty with this…
We give a popular account of the Banach-Tarski paradox and its connections with the axiom of choice.
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
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…
I define a notion of local causality LOC closely modelled on the Bell principle, construed as the condition that single case probabilities cannot be modified by actions at spacelike separation. The new principle, like that of Bell, forces…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
In this paper three unrelated problems will be discussed. What connects them is the rich methodology of classical probability theory. In the first two problems we have a complete answer to the problems raised; in the third case, what we…