Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial…
One of the fundamental properties of the Mandelbrot set is that the set of postcritically finite parameters is structured like a tree. We extend this result to the set of quadratic kneading sequences and show that this space contains no…
Fractals are ubiquitous in nature, and since Mandelbrot's seminal insight into their structure, there has been growing interest in them. While the topological properties of the limit sets of IFSs have been studied -- notably in the…
Three thinkers of the 19th century revolutionized the science of logic, mathematics, and philosophy. Edmund Husserl (1859-1938), mathematician and a disciple of Karl Weierstrass, made an immense contribution to the theory of human thought.…
The Sapient Paradox is the apparently unexplainable time delay of several ten thousand years following the arrival of Homo sapiens in Asia and Europe and before the introduction of impressive innovations with the agricultural revolution.…
This article challenges the conventional reading of Francis Ysidro Edgeworth by reconstructing his intellectual project of unifying the moral sciences through mathematics. The contribution he made in the first phase of his writing,…
Newton's centuries-old wisdom of standing on the shoulders of giants raises a crucial yet underexplored question: Out of all the prior works cited by a discovery, which one is its giant? Here, we develop a novel, discipline-independent…
This is the English version of my inaugural lecture at Coll\`ege de France in 2021, available at https://www.youtube.com/watch?v=bxktplKMhKU. I reflect on the difficulty of multi-disciplinary research, which often hinges of unexpected…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument…
Even though Plato's philosophy in ancient times was always closely associated with mathematics, modern Platonic scholarship, during the last five centuries, has moved steadily toward de-mathematization. The present work aims to outline a…
In an increasingly polarized world, demagogues who reduce complexity down to simple arguments based on emotion are gaining in popularity. Are opinions and online discussions falling into demagoguery? In this work, we aim to provide…
Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…
The motivation of this article is to estimate multifractality classification and model selection parameters: the first-order scaling exponent $c_1$ and the second-order scaling exponent (or intermittency coefficient) $c_2$. These exponents…
Einstein's distinction between principle theories and constructive theories is methodological rather than metaphysical. Principle theories such as thermodynamics and relativity articulate empirically distilled constraints that delimit…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
In this paper, a solution to Zeno's paradox of motion was offered and a possible, based on observations and empirical viewpoint, interpretation. A gedanken experiment was proposed in accordance to our empirical and experimental paradigm,…
In the paper we look into the epistemology of quantum theory. The starting point is the previously established mathematical ambiguity. The perspective of our study is the way that Schroedinger described Einstein s idea of physics…
Apparently random events in nature often reveal hidden patterns when analysed using diverse and robust statistical tools. Power-law distributions, for example, project diverse natural phenomenon, ranging from earthquakes1 to heartbeat…
`Philosophy' was speakable for John Bell but is not for many physicists. The border between philosophy and physics is here illustrated through Brownian motion and Bell experiments. `Measurement', however, was unspeakable for Bell. His…