We investigate the relationship between two approaches to modeling physical systems. On the first approach, simplifying assumptions are made about the level of detail we choose to represent in a computational simulation with an eye toward tractability. On the second approach simpler, analogue physical systems are considered that have more or less well-defined connections to systems of interest that are themselves too difficult to probe experimentally. Our interest here is in the connections between the artifacts of modeling that appear in (...) these two approaches. We begin by outlining an important respect in which the two are essentially dissimilar and then propose a method whereby overcoming that dissimilarity by hand results in usefully analogous behavior. We claim that progress can be made if we think of artifacts as clues to the projectible predicates proper to the models themselves. Our degree of control over the connection between interesting analogue physical systems and their targets arises from determining the projectible predicates in the analogue system through a combination of theory and experiment. To obtain a similar degree of control over the connection between large-scale, distributed simulations of complex systems and their targets we must similarly determine the projectible predicates of the simulations themselves. In general theory will be too intractable to be of use, and so we advocate an experimental program for determining these predicates. the object of the natural history which I propose is...to give light to the discovery of causes and supply a suckling philosophy with its first food . Francis Bacon, The Great Instauration. (shrink)

In this essay, I examine the notion of a nondeterministic algorithm from both a conceptual and historical point of view. I argue that the intuitions underwriting nondeterminism in the context of contemporary theoretical computer science cannot be reconciled with the intuitions that originally motivated nondeterminism. I identify four different intuitions about nondeterminism: nondeterminism as evidence for the Church Turing thesis; nondeterminism as a natural reflection of the mathematician's behavior; nondeterminism as a formal, mathematical generalization; and nondeterminism as a physical process. (...) I shall argue that there are irreconcilable tensions among these intuitions and, moreover, that these tensions have not been acknowledged in the conceptual development of theoretical computer science. In fact, a careful review of the received history reveals a number of gaps and discontinuities. For instance, I examine the seminal writings of Turing and argue that the formal introduction of the nondeterminism is to be found there and not, as is often supposed, in the research of the late 1950s and early 1960s. I also examine the period after 1960 and argue that even the more recent developments concerning nondeterminism are hard to reconstruct. ;Although I firmly believe that a rigorous philosophical account of nondeterminism is needed, I am not sure that such an account will bring us any closer to a solution to any of the notoriously difficult theoretical problems that turn on the notion of a nondeterministic algorithm. I do believe, however, that a clear conceptual account of nondeterminism will shed light on many long-standing philosophical problems. I conclude by pointing to a number of philosophical questions that resonate with issues raised by the foregoing investigation of nondeterministic algorithms. (shrink)