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In 1963-71, a group of people, myself included, formulated and perfected a new approach to physics problems, which eventually came to be known under the names of scaling, universality, and renormalization. This work formed the basis of a…
This article is a position paper written in reaction to the now-infamous paper titled "On the Dangers of Stochastic Parrots: Can Language Models Be Too Big?" by Timnit Gebru, Emily Bender, and others who were, as of the date of this…
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
In 1686 in his Discours de Metaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of "theory" becomes vacuous because there is always a theory. This idea is developed in the modern theory of…
Direct look at the celebrated "chaotic" Mandelbrot Set in Fig..\ref{Mand2} immediately reveals that it is a collection of almost ideal circles and cardioids, unified in a specific {\it forest} structure. In /hep-th/9501235 a systematic…
The hypothesis that philosophy is driven by difference/innovation is checked in a quantitative manner. This was performed by assigning grades to eight main philosophical features with respect to seven prominent philosophers, which allowed…
Statistics is a uniquely difficult field to convey to the uninitiated. It sits astride the abstract and the concrete, the theoretical and the applied. It has a mathematical flavor and yet it is not simply a branch of mathematics. Its core…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
Scientific communication is an essential part of modern science: whereas Archimedes worked alone, Newton (1676) acknowledged that "If I have seen a little further, it is by standing on the shoulders of Giants." How is scientific…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…
One often distinguishes between a line and a plane by saying that the former is one-dimensional while the latter is two. But, what does it mean for an object to have $d-$dimensions? Can we define a consistent notion of dimension rigorously…
Large language models (LLMs) have achieved remarkable successes on various tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs, which can be categorized into the…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of…
I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…
We consider Einstein's attitude with regard to religion both from sociological and epistemological points of view. An attempt to put it into a wider socio-historical perspective has been made, with the emphasis on his ethnic and religious…
Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and…
The explicit relationship among perception, communication, and design is being discussed in some detail, in order to relate it to characteristic details of the modeling of the world which defines the scientific and artistic activities of…
This paper explores the question of how accurately current large language models can perform logical reasoning in natural language, with an emphasis on whether these models exhibit reasoning biases similar to humans. Specifically, our study…