Related papers: PC4 at Age 40
We build on the empirical finding that a human being's mental age is normally distributed around the chronological age. This opposes the frequent societal assumption "mental = chronological" which is known to be false in general but…
The paper presents a counterexample to the Hodge conjecture.
This Note describe my own recollection of the first 30 years of Category Theory, it is not the result of any historical investigation. The choice of concepts and its evaluation is my own, necessarily subjective. It follows a chronological…
In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincar\'{e} inequality plays…
In the half century since the 1950s computer simulation has transformed our understanding of physics. The rare, expensive, slow, and bulky mainframes of World War II have given way to today's millions of cheap, fast, desksized workstations…
According to Karl Popper assumptions are statements used to construct theories. During the construction of a theory whether the assumptions are either true or false turn out to be irrelevant in view of the fact that, actually, they gain…
This paper is a faithful description of the author's career as a scientist, which often intersected that of Yves Couder. The emphasis of this paper is a true description of how the science that the author has been associated with really…
Reminiscence, the act of revisiting past memories, is crucial for self-reflection and social interaction, significantly enhancing psychological well-being, life satisfaction, and self-identity among older adults. In HCI and CSCW, there is…
We analyze the statistical properties of Poincar\'e recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincar\'e…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
In this paper, the origin of discrete dynamics is stated from a historical point of view, as well as its main ideas: fixed and periodic points, chaotic behaviour, bifurcations. This travel will begin with Poincar\'e's work and will finish…
Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…
Jean-Marc Ginoux's recent book, "Poincar\'e, Einstein and the Discovery of Special Relativity: An End to the Controversy" (2024), seeks to close the debate over the respective roles of Poincar\'e and Einstein. Yet what is presented as an…
The year 2024 marks two anniversaries: The 70th anniversary of CERN and the 50th anniversary of the $J/\Psi$ discovery. At this occasion I have been asked to give review talks on the significance of these anniversaries. This article is an…
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
This paper provides a systematic response to the criticisms raised by Jean-Marc Ginoux in response to my review of his book on the history of relativity. Whereas my review was written in a strictly academic manner, Ginoux's commentary…
This is the announcement of an alternative approach to the 3-dimensional Poincar\'e Conjecture, different from Perelman's big and spectacular breakthrough. No claim concerning the other parts of the Thurston Geometrization Conjecture, come…
When PageRank began to be used for ranking in Web search, a concern soon arose that older pages have an inherent --- and potentially unfair --- advantage over emerging pages of high quality, because they have had more time to acquire…