Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
We suggest an original physical approach to describe the mechanism of market pricing. The core of our approach is to consider pricing at different time scales separately, using independent equations of motion. Such an approach leads to a…
Experimental and empirical data are often analyzed on log-log plots in order to find some scaling argument for the observed/examined phenomenon at hands, in particular for rank-size rule research, but also in critical phenomena in…
In this paper we revisit an idea originally proposed by Mandelbrot about the possibility to observe ``negative dimensions'' in random multifractals. For that purpose, we define a new way to study scaling where the observation scale $\tau$…
In the eyes of a rationalist like Descartes or Spinoza, human reasoning is flawless, marching toward uncovering ultimate truth. A few centuries later, however, culminating in the work of Kahneman and Tversky, human reasoning was portrayed…
The logic of abduction involves a collision between deduction and induction, where empirical surprises violate expectations and scientists innovate to resolve them. Here we reformulate abduction as a social process, occurring not only…
The Goedelian approach is discussed as a prime example of a science towards the origins. While mere selfreferential objectification locks in to its own byproducts, self-releasing objectification informs the formation of objects at hand and…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…
Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed that partial derivatives in the study of various natural…
Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…
Defining similarity is a fundamental challenge in information science. Watanabe's Ugly Duckling Theorem highlights diversity, while algorithmic information theory emphasizes depth through Information Distance. We propose a…
In 2007 an international conference engaged a reflection on the present conditions for sciences and scientific practice, to initiate a dialogue between science, philosophy, epistemology and sociology. Starting from many examples taken from…
In light of the emergence of big data, I have advocated and argued for a paradigm shift from Tobler's law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and - more importantly -…
Human language offers a powerful window into our thoughts -- we tell stories, give explanations, and express our beliefs and goals through words. Abundant evidence also suggests that language plays a developmental role in structuring our…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and…
We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo)…
This paper pays a tribute to Loet's work in a specific way. More than 20 years ago Loet Leydesdorff and myself designed a programme for future innovation studies 'Measuring the knowledge base - a programme of innovation studies'. Although,…
This work presents a brief and non-technical description of the main results and concepts of the modern scientific cosmology, viewing it from an epistemological perspective which allows a dialog with other modes of thinking like e.g.…
There are ongoing divisions in the learning sciences between perspectives that treat cognition as occurring within individual minds and those that treat it as irreducibly distributed or situated in material and social contexts. We contend…