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

We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…

This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its $\omega$-consistency. The system is called TP, for 'Truth and Paradoxicality'.

Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]

Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]

Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]

Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]

This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…

We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…

We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to…

We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…

The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…

We discuss the legacy of Alan Turing and his impact on computability and analysis.

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…

This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…

This paper discusses Maxwell's demon thought experiment. In recent years, there has been extensive research on Maxwell's demon. I first provide a detailed overview of important historical milestones of Maxwell's demon thought experiment.…

Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…

We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…

Laplace's views on randomness and determinism. The paper was written for "Cahiers rationalistes" and addresses a rather wide audience. It contains large quotations of Laplace, most of them coming from his introduction to the book…

I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…

Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…