相关论文: Maxwell's daemon, the Turing machine, and Jaynes' …

The halting probability of a Turing machine,also known as Chaitin's Omega, is an algorithmically random number with many interesting properties. Since Chaitin's seminal work, many popular expositions have appeared, mainly focusing on the…

Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…

I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…

Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…

Ce m\'emoire r\'ealis\'e \`a l'IUFM de Cr\'eteil en 1998 sous la direction d'Evelyne Barbin \'etudie l'histoire du d\'ebut du calcul des probabilit\'es. Sources: correspondance entre Pascal et Fermat, et Trait\'e du triangle arithm\'etique…

Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…

We discuss properties of recursive schemas related to McCarthy's ``91 function'' and to Takeuchi's triple recursion. Several theorems are proposed as interesting candidates for machine verification, and some intriguing open questions are…

Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…

This paper fails to derive quantum mechanics from a few simple postulates. But it gets very close --- and it does so without much exertion. More exactly, I obtain a representation of finite-dimensional probabilistic systems in terms of…

The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of…

I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…

In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…

The recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic and learning are both practices of the human brain, it leads to another…

This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…

We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…

This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to…

This book examines a number of problems of quantum mechanics, most of which are not usually discussed. What is the origin of probabilities in the mechanics of the microworld? What is the nature of Planck's constant h? What is the nature of…

We review the theory of neural networks, as it has emerged in the last ten years or so within the physics community, emphasizing questions of biological relevance over those of importance in mathematical statistics and machine learning…