I discuss the relations among four worlds: Reality, mathematical models, computer simulation, and models of computation. Pros and cons of two models of computation, the Turing machine and the real number model, are presented. The the intrinsic difficulty of solving a mathematical model, as...

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k1. For the Wiener measure occurring in many applications we have k=2. We want to...

Over the last sixty years there has been a stream of impossibility results from mathematics and theoretical computer science announcing undecidability, non-computability, and intractability. Should these impossibility results be of concern to physics? <p> Two of these impossibility results are...</p>

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low-discrepancy algorithms are sometimes superior. We report on numerical testing which compares low-discrepancy and Monte Carlo algorithms on the evaluation of financial derivatives. The...

At its first meeting in 1986 the Computer Science and Technology Board, National Research Council, identified six critical national issues. <p> I discuss these six issues as they appeared in 1986 and how they appear for my 1996 vintage. <p> There was a seventh critical issue which I did not want to...</p></p>

In this paper we build a spatial, aspiration-based model of learning in the context of Cournot oligopoly from which we want to explore the conditions that lead to the emergence of cooperation among firms. We consider an economy consisting of many identical duopolies; each duopoly is placed on a...

The paper discusses the role of self-organizing phenomena like emergence of infrastructure and self-organizing criticality in a spatial economy. Some theoretical models are discussed and reviewed. Computer models in the form of simple cellular automata, similar to the game "Life" and Schelling's...

This paper investigates the properties of a local economy in which personal connections are important in finding jobs. The complementarities in the model generate an interesting nonlinear relationship between the distribution of human capital in the economy, the characteristics of the social...

In Part I we provide a heuristic discussion of the motivation for the investigation of games of status. Here we confine our remarks to several alternative formulations of games of status and to exploring the relationship between these games and the class of simple games, in part using the...

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks such as the Internet, social networks or biological...