Risk Regulation and the Faces of Uncertainty

Dr. Walker addresses the difficulty of regulators\u27 working with potentially inaccurate information and clarifies related aspects of decision making by presenting a taxonomy for the kinds of uncertainty inherent in necessarily incomplete data

Eddington & Uncertainty

Sir Arthur Eddington is considered one of the greatest astrophysicist of the twentieth century and yet he gained a stigma when, in the 1930s, he embarked on a quest to develop a unified theory of gravity and quantum mechanics. His attempts ultimately proved fruitless and he was unfortunately partially shunned by some physicists in the latter portion of his career. In addition some historians have been less than kind to him regarding this portion of his work. However, detailed analysis of how this work got started shows that Eddington's theories were not as outlandish as they are often purported to be. His entire theory rested on the use of quantum mechanical methods of uncertainty in the reference frames of relativity. Though the work was ultimately not fruitful, in hindsight it did foreshadow several later results in physics and his methods were definitely rigorous. In addition, his philosophy regarding determinism and uncertainty was actually fairly orthodox for his time. This work begins by looking at Eddington's life and philosophy and uses this as a basis to explore his work with uncertainty.Comment: new version to appear in Physics in Perspective (either Sept. or Dec. issue

A New Principle in Physics: the Principle of "Finiteness", and Some Consequences

In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of "legitimate" laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory or principle in physics. I propose "finiteness" as a postulate (like the constancy of the speed of light in vacuum, "c"), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.Comment: 13 pages, 0 figure

Contextual Risk and Its Relevance in Economics

Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.Comment: 6 pages, 2 figure