Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…
We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle…
Pierre Bourdieu discussed how an individual's taste relates o his or her social environment, and how the classification of \emph{distinct} and \emph{vulgar}, among others, arises from at the same time as shapes this taste in his work called…
In his Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, Rene Descartes sought ``clear and certain knowledge of all that is useful in life.'' Almost three centuries later, in ``The foundations of…
Instructors and researchers think "thinking like a physicist" is important for students' professional development. However, precise definitions and observational markers remain elusive. We reinterpret popular beliefs inventories in physics…
The combinatorial Mandelbrot set is a continuum in the plane, whose boundary can be defined, up to a homeomorphism, as the quotient space of the unit circle by an explicit equivalence relation. This equivalence relation was described by…
A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the…
There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical deterministic model doesn't contain any…
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…
In this course, we propose an elementary and self-contained introduction to canonical Mandelbrot random cascades. The multiplicative construction is explained and the necessary and sufficient condition of non-degeneracy is proved. Then, we…
Human behaviors, including scientific activities, are shaped by the hierarchical divisions of geography. As a result, researchers' mobility patterns vary across regions, influencing several aspects of the scientific community. These aspects…
The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic…
As far as human perceptions and rational thinking are concerned, contradictions constitute a non negligible part of our reality. We often refer to these phenomena, in a more informal way, as the chicken or the egg causality dilemma.…
In his interviews with Eckermann in the 1820s, Goethe referred to his Theory of Colors as his greatest and ultimate achievement. Its reception following publication in 1810 and subsequent reviews throughout the history of physical science…
The historical development has lead to the decay of Natural Philosophy which until 19th century included all of our knowledge about the physical world into the growing multitude of specialized sciences. The focus on the in-depth enquiry…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
Investigating NLP through a philosophical lens has recently caught researchers' eyes, as it bridges computational methods with classical schools of philosophy. This paper introduces a philosophical framework inspired by the Hegelian…
A longstanding puzzle in urban science is whether there's an intrinsic match between human populations and the mass of their built environments. Previous findings have revealed various urban properties scaling nonlinearly with population,…
Quantum mechanics is a theory that is as effective as it is counterintuitive. While quantum practices operate impeccably, they compel us to embrace enigmatic phenomena like the collapse of the state vector and non-locality, thereby pushing…
Mandelbrot set is a closure of the set of zeroes of $resultant_x(F_n,F_m)$ for iterated maps $F_n(x)=f^{\circ n}(x)-x$ in the moduli space of maps $f(x)$. The wonderful fact is that for a given $n$ all zeroes are not chaotically scattered…