Part I: Bayes Estimators and the Shannon Entropy. <p> This paper is the first of two on the problem of estimation a function of a probability distribution from a finite set of samples of that distribution. In this paper a Bayerian analysis of this problem is presented, the optimal properties of the...</p>

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...

This paper provides a unified framework for studying the effects of economic (and other) institutions on the evolution of preferences, taking account of conformist cultural transmission, social segregation, and the simultaneous operation of selection processes at the individual and group level....

We use game theory and the Santa Fe Artificial Stock Market, an agent-based model of an evolving stock market, to study the properties of strategic Nash equilibria in financial markets. We discover two things: there is a unique strategic equilibrium in the market, and this equilibrium in...

Genetic relatedness is a central concept in the study of social evolution. Though originally defined in terms of genealogy, the modern version of relatedness accommodates genetic similarity of any origin. This paper examines relatedness in group structured models, in which a trait affects the...

Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as the noise strength. The presence of this slowly...

The immune system is a complex system of cells and molecules that can provide us with a basic defense against pathogenic organisms. Like the nervous system, the immune system performs pattern recognition tasks, learns and retains a memory of the antigens that it has fought. The immune system...

Can we build computers that are intelligent and alive? This question has been on the minds of computer scientists since the dawn of the computer age and remains a most compelling line of inquiry. Some would argue that the question makes sense only if we put scare quotes around "intelligent" and...

The notion of ``evolvability''---the ability of a population to produce variants fitter than any yet existing---is developed as it applies to genetic algortithms. A theoretical analysis of the dynamics of genetic programming predicts the existence of a novel, emergent selection phenomenon: the...

I raise questions regarding the unknown and the unknowable in science. I also briefly address two topics which have been much in the news in 1996, and which might erroneously be confused with my topic. These are, first, the book by John Horgan, called The End of Science, and second, the great...