Empirical Encounters with Computational Irreducibility and Unpredictability

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines. We present the results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (all 3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function finder program. This massive experiment prompts an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments.Comment: 18 pages, 4 figure

Suspensions of prolate spheroids in Stokes flow. Part 2. Statistically homogeneous dispersions

The simulation method for prolate spheroids in Stokes flow introduced in a companion paper (Claeys & Brady 1993a) is extended to handle statistically homogeneous unbounded dispersions. The convergence difficulties associated with the slow decay of velocity disturbances at zero Reynolds number are overcome by applying O';Brien's renormalization procedure. The Ewald summation technique is employed to accelerate the evaluation of all mobility interactions. As a first application of this new method, the hydrodynamic transport properties of equilibrium hard-ellipsoid structures are calculated for aspect ratios ranging from 3 to 50. Calculated viscosities in the isotropic phase agree reasonably well with published experimental measurements

Integrating hot and cool intelligences: Thinking Broadly about Broad Abilities

Although results from factor-analytic studies of the broad, second-stratum abilities of human intelligence have been fairly consistent for decades, the list of broad abilities is far from complete, much less understood. We propose criteria by which the list of broad abilities could be amended and envision alternatives for how our understanding of the hot intelligences (abilities involving emotionally-salient information) and cool intelligences (abilities involving perceptual processing and logical reasoning) might be integrated into a coherent theoretical framework

Integrability and chaos: the classical uncertainty

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now named by the more fashionable term of deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical mechanics. Based on the Hamiltonian formalism, the main objective of this article is to provide, from the physicist's point of view, an overall and intuitive review of this broad subject (with some emphasis on the KAM theorem and the stability of planetary motions) which may be useful to both students and instructors.Comment: 24 pages, 10 figure