Related papers: Complex and Unpredictable Cardano
As it is well-known, the year 2005 has been the centenary of the "annus mirabilis" (1905) during which Albert Einstein published four fundamental papers of his. But already in 1979, for the centenary of Einstein's birth, the world…
The paper {\it On the multifractal nature of fully developed turbulence and chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984 (vol {\bf 17}, page 3521) has been a starting point of many investigations on the…
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The most striking observable feature of our indeterministic quantum universe is the wide range of time, place, and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this…
This document is the first installment of three in the Cerro Grande Fire Series. It is a collection of letters written to various colleagues, most of whom regularly circuit this archive, including Howard Barnum, Paul Benioff, Charles…
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…
An account is given of an interesting but unknown theory by Majorana regarding scalar quantum electrodynamics, elaborated several years before the known Pauli-Weisskopf theory. Theoretical calculations and their interpretation are given in…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
This study examines the quantitative relationship between linguistic regularities and computational search complexity through a hybrid classical-quantum framework applied to Renaissance Italian texts. Using four representative works from…
Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s. Like Turing himself, it attracted less attention than it deserved beyond the confines of mathematics. Today our experiences in computer…
Two recent papers (Renou et al., arXiv:2101.10873, and Chen et al., arXiv:2103.08123) have indicated that complex numbers are necessary for quantum theory. This short note is a comment on their result.
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
The formalism of covariant quantum theory, introduced by Reisenberger and Rovelli, casts the description of quantum states and evolution into a framework compatable with the principles of general relativity. The leap to this covariant…
An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skilfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well.
In this paper we review Castagnino's contributions to the foundations of quantum mechanics. First, we recall his work on quantum decoherence in closed systems, and the proposal of a general framework for decoherence from which the…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…