This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation (...) that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)

The central claim of this paper is that computer simulation provides (though not exclusively) a qualitatively new and different methodology for the physical sciences, and that this methodology lies somewhere intermediate between traditional theoretical physical science and its empirical methods of experimentation and observation. In many cases it involves a new syntax which gradually replaces the old, and it involves theoretical model experimentation in a qualitatively new and interesting way. Scientific activity has thus reached a new milestone somewhat comparable to (...) the milestones that started the empirical approach (Galileo) and the deterministic mathematical approach to dynamics (the old syntax of Newton and Laplace). Computer simulation is consequently of considerable philosophical interest. In view of further technical developments in the near future, computer experts suggest that we are at present only at the very beginning of this new era. (shrink)

Two decades of critique have sensitized historians and philosophers of science to the inadequacies of conventional dichotomies between theory and practice, thereby prompting the search for new ways of writing about science that are less beholden than the old ways to the epistemological mores of theoretical physics, and more faithful to the actual practices not only of physics but of all the natural sciences. The need for alternative descriptions seems particularly urgent if one is to understand the place of theory (...) in contemporary molecular biology, a science where, until now, no division between theory and experiment has obtained, and where distinctions between representing and intervening, and more generally, between basic and applied science, are daily becoming more blurred.Indeed, the very division between theory and experiment threatens to slight the extensive and sophisticated theoretical analyses on which experimental work in contemporary molecular biology so often depends. My aim in this paper is to find a way of talking about theoretical practices in biology that is directly rooted in the mix of conceptual and material work that biologists do. As an example of such theoretical practices, I choose for the focus of my analysis the development of a model for gene regulation out of the experimental work of Eric Davidson and his colleagues at Cal Tech. (shrink)

Two decades of critique have sensitized historians and philosophers of science to the inadequacies of conventional dichotomies between theory and practice, thereby prompting the search for new ways of writing about science that are less beholden than the old ways to the epistemological mores of theoretical physics, and more faithful to the actual practices not only of physics but of all the natural sciences. The need for alternative descriptions seems particularly urgent if one is to understand the place of theory (...) (and, in parallel, the role of modeling) in contemporary molecular biology, a science where, until now, no division between theory and experiment has obtained, and where distinctions between representing and intervening, and more generally, between basic and applied science, are daily becoming more blurred. Indeed, the very division between theory and experiment threatens to slight the extensive and sophisticated theoretical analyses (and even modeling) on which experimental work in contemporary molecular biology so often depends. My aim in this paper is to find a way of talking about theoretical practices in biology that is directly rooted in the mix of conceptual and material work that biologists do. As an example of such theoretical practices, I choose for the focus of my analysis the development of a model for gene regulation out of the experimental work of Eric Davidson and his colleagues at Cal Tech. (shrink)

In this paper we will discuss some of the issues related to the attempts of Ralph Howard Fowler and Nevil Vincent Sidgwick to create a legitimizing space for quantum and theoretical chemistry in Britain. Although neither Fowler nor Sidgwick made original contributions to quantum chemistry, they followed closely the developments in the discipline, participated in meetings and discussions and delivered lectures, talks and addresses, where methodological topics, ontological questions and implicitly the problem of autonomy of the new discipline vis-à-vis both (...) physics and chemistry were taken to be pressing issues. In particular, they encouraged young people to work within the nascent discipline. Viewing quantum chemistry as a branch of applied mathematics became an emblematic characteristic of the practice of the new discipline in Great Britain. (shrink)

The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions (...) made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand–Naimark–Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell’s electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics. (shrink)

Taking a critical stance towards the notions of dematerialization and inscription, this paper considers the role of physical molecular models in chemical research, specifically in the development of structural concepts and in the articulation of chemists' knowledge of molecular structures. The main argument, illustrated through specific historical case studies, is that the materiality of these models, their specific properties as material objects, is not simply incidental to the role they have played in the development of chemistry.

Computer simulation is shown to be philosophically interesting because it introduces a qualitatively new methodology for theory construction in science different from the conventional two components of "theory" and "experiment and/or observation". This component is "experimentation with theoretical models." Two examples from the physical sciences are presented for the purpose of demonstration but it is claimed that the biological and social sciences permit similar theoretical model experiments. Furthermore, computer simulation permits theoretical models for the evolution of physical systems which use (...) cellular automata rather than differential equations as their syntax. The great advantages of the former are indicated. (shrink)