I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, are criticized.

1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of

Control theory traditionally has been focused on analysis and control of continuous systems with numerical characteristics. In the past decade, however, there has been a growing concern with the symbolic aspect of systems owing to the advances in computer engineering. As a result the discipline of Discrete-Event Systems (DES) is emerging from the system control community. In the framework of Ramadge and Wonham (RW), signals of interest no longer assume the form of continuously valued functions of numbers, but instead are discrete strings of symbols. The system is controlled by disablements of controllable events. In practice, RW control theory is found to be effective for systems of small size, but in the case of large systems, the computational complexity may become intractable. This thesis proposes a generalization of the RW framework. Systems are modeled as multilevel hierarchies in which high-level dynamics are obtained via abstraction of the low-level models, and this vertical mod...

Given the collapse hypothesis (CH) of quantum measurement, EPRtype correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that lorentz covariance along with the second law of thermodynamics imply a non-entropic version of ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the hilbert-space model of quantum mechanics have their origin in space-time structure. 1

Theoretical models are an important tool for many aspects of scientific activity. They are used, i.a., to structure data, to apply theories or even to construct new theories. But what exactly is a model? It turns out that there is no proper definition of the term “model ” that covers all these aspects. Thus, I restrict myself here to evaluate the function of models in the research process while using “model ” in the loose way physicists do. To this end, I distinguish four kinds of models. These are (1) models as special theories, (2) models as a substitute for a theory, (3) toy models and (4) developmental models. I argue that models of the types (3) and (4) are considerably useful in the process of theory construction. This will be demonstrated in an extended case-study from High-Energy Physics. ∗ I wish to thank M. Stöckler (Bremen) for many illuminating discussions and R. Müller and M. Schön (both Konstanz) for reading the manuscript. A slightly revised version of

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The biochemical attachment of photolyase to ultraviolet (uv) absorbed DNA molecules provides a method for registering whether a source has emitted photons. Here using laws of chemical kinetics and related experimental methods we argue that the instant after which this information becomes discernible can be empirically determined by retrodicting from relevant data when the photolyase binding to uv-absorbed DNA molecules has started occurring. Thus an empirically investigable twist is provided to the quantum measurement problem. If a system is initially in a state ψ(ψ = aψ1 + bψ2) which is a superposition of two states ψ1and ψ2 that are eigenstates of a dynamical variable which is measured, a general characteristic of its interaction with a measuring device is that it results in a final state of the form Ψ = aψ1Φ1 + bψ2Φ2 (1) where Φ1and Φ2 are mutually orthogonal and macroscopically distinguishable

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I propose a new concept of the evolutionary psychological imagination, to replace C. Wright Mills ’ half-century-old notion of the sociological imagination, as a way to link personal experiences with wider social phenomena. To illustrate, I discuss how one’s difficulty in dating might be connected to the current world war, and how the evolutionary psychological imagination sometimes allows us to see things that few others do.