Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
Statistical schools-such as Bayesianism and Frequentism-are often presented as competing frameworks, each claiming technical rigour and superiority. Frequentism emphasizes objective inferences through repeated sampling, while Bayesianism…
A dominant paradigm in visual intelligence treats semantics as a static property of latent representations, assuming that meaning can be discovered through geometric proximity in high dimensional embedding spaces. In this work, we argue…
Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's philosophical comments on mathematics and the natural sciences published in the middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl discussed…
Physicists and philosophers alike have pondered the measurement problem in quantum mechanics since the beginning of the theory nearly a century ago. Marcel Reginatto and I (2013) have made the case as have many others, Niels Bohr among…
We consider complex Mandelbrot multiplicative cascades on a random weigh\-ted tree. Under suitable assumptions, this yields a dynamics $\T$ on laws invariant by random weighted means (the so called fixed points of smoothing transformations)…
In the rapidly evolving field of Large Language Models (LLMs), there is a critical need to thoroughly analyze their capabilities and risks. Central to our investigation are two novel elements. Firstly, it is the innovative parallels between…
A theory of citations should not consider cited and/or citing agents as its sole subject of study. One is able to study also the dynamics in the networks of communications. While communicating agents (e.g., authors, laboratories, journals)…
The von Neumann attitude on such a deep interpretational question as the role of a human observer in order for the quantum description of measurement to be consistent has been long misrepresented. The large majority of the subsequent…
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…
An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling…
Research output and impact is currently the focus of serious debate worldwide. Quantitative analyses based on a wide spectrum of indices indicate a clear advantage of US institutions as compared to institutions in Europe and the rest of the…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three. We…
A mathematical model of the interaction mechanism for the intuitive-imaginative and heuristic-logical thinking responsible for the rift in the intellectual activity into two cultures has been suggested. The said model proceeds from the…
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
The finite-size behaviours of the homogeneous sine-Gordon models are analysed in detail, using the thermodynamic Bethe ansatz. Crossovers are observed which allow scales associated with both stable and unstable quantum particles to be…
Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can…
This paper investigates whether current large language models exhibit biases in logical reasoning, similar to humans. Specifically, we focus on syllogistic reasoning, a well-studied form of inference in the cognitive science of human…