Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
Stephen Wolfram has recently outlined an unorthodox, multicomputational approach to fundamental theory, encompassing not only physics but also mathematics in a structure he calls The Ruliad, understood to be the entangled limit of all…
In a recent paper A.Beardon and I.Short proposed to use chains of tangent horocycles as an extended tool describing continued fractions. We review the origin of such construction from the Moebius transformations point of view. Related…
We argue that discrete dynamics has natural links to the theory of analytic functions. Most important, bifurcations and chaotic dynamical properties are related to intersections of algebraic varieties. This paves the way to identification…
In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to…
New insights into the combinatorial structure of the Mandelbrot set are given by `Correspondence' and `Translation' Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles…
We consider the "Mandelbrot set" $M$ for pairs of complex linear maps, introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and others. It is defined as the set of parameters $\lambda$ in the unit disk such that the…
Segregation is a widely recognised phenomenon with profound implications for societies worldwide. From political science and gender studies to anthropology and urban studies, it has garnered considerable attention across numerous scientific…
Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can…
Reasoning, a fundamental cognitive process integral to human intelligence, has garnered substantial interest within artificial intelligence. Notably, recent studies have revealed that chain-of-thought prompting significantly enhances LLM's…
Einstein was in many ways like a detective on a mystery trail, though in his case he was on the trail of nature's mysteries and not some murder mystery! And like all good detectives he had a style. It consisted of taking facts that he knew…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
Carl Gustav Hempel (1905-1997) formulated the dilemma that carries his name in an attempt to determine the boundaries of physics. Where does physics go over into metaphysics? The purpose of this contribution is to indicate how a recently…
Human language defines the most complex outcomes of evolution. The emergence of such an elaborated form of communication allowed humans to create extremely structured societies and manage symbols at different levels including, among others,…
We formalize the paradox of an omniscient yet lazy investor - a perfectly informed agent who trades infrequently due to execution or computational frictions. Starting from a deterministic geometric construction, we derive a closed-form…
Quantum mechanics challenges classical intuitions of space, time, and causality via the superposition principle, which allows systems to exist in multiple states simultaneously. Niels Bohr addressed these paradoxes through his…
One would not think that thought experiments could matter to nature, for they are a humble human device. Yet quantum mechanics very naturally frames thought experiments (as distinct from precisely defining what exists). They exemplify the…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less…