In Martin Gardner's Mathematical Games column in the February 1960 issue of Scientific American, there appeared a simple problem that has come to be known today as the Secretary Problem, or the Marriage Problem. It has since been taken up and developed by many eminent probabilists and statisticians and has been extended and generalized in many different directions so that now one can say that it constitutes a "field" within mathematics-probability-optimization. The object of this article is partly historical (to give a fresh view of the origins of the problem, touching upon Cayley and Kepler), partly review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment. The contents of this paper were first given as the Allen T. Craig lecture at the University of Iowa, 1988.

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Who Solved the Secretary Problem

As the gateway to scientific thinking, an understanding of the scientific method is essential for success and productivity in science. This book is the first synthesis of the practice and the philosophy of the scientific method. It will enable scientists to be better scientists by offering them a deeper understanding of the underpinnings of the scientific method, thereby leading to more productive research and experimentation. It will also give scientists a more accurate perspective on the rationality of the scientific approach and its role in society. Beginning with a discussion of today's 'science wars' and science's presuppositions, the book then explores deductive and inductive logic, probability, statistics, and parsimony, and concludes with an examination of science's powers and limits, and a look at science education. Topics relevant to a variety of disciplines are treated, and clarifying figures, case studies, and chapter summaries enhance the pedagogy. This adeptly executed, comprehensive, yet pragmatic work yields a new synergy suitable for scientists and instructors, and graduate students and advanced undergraduates.

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Scientific method in practice

The work of Johannes Kepler offers clear examples of conceptual change. In this article, using Kepler's work as a case study, we argue that analogical reasoning facilitates change of knowledge in four ways: (a) highlighting, (b) projection, (c) rerepresentation, and (d) restructuring. We present these four mechanisms within the context of structure-mapping theory and its computational implementation, the structure-mapping engine. We exemplify these mechanisms using the extended analogies Kepler used in developing a causal theory of planetary motion.

Analogical Reasoning and Conceptual Change: A Case Study of Johannes Kepler

mappings (Clement & Gentner, 1991; Gentner, Rattermann, & Forbus, 1993; Holyoak & Koh, 1987). For example, when given analogies to use in solving problems, people are typically fairly selective about choosing analogies that have genuine structural overlap with the target problem (Bassok & Holyoak, 1989; Holyoak & Koh, 1987; Novick & Holyoak, 1991; Novick & Tversky, 1987; Ross, 1987; Ross, Ryan, & Tenpenny, 1989). We have simulated subjects' retrieval patterns with the MAC/FAC simulation (Many Are Called but Few Are Chosen), in which a first stage retrieval process carries out a wide, computationally cheap and structurally insensitive search for candidate retrievals and a later stage (the FAC stage, essentially SME) performs a structural alignment over these candidate analogues (Forbus, Gentner, & Law, 1995). This system does a good job of capturing the phenomena: Retrievals based on surface similarity or on overall similarity are common, and retrievals based on purely relational similarity-the purely analogical retrievals that strike us as clever and creative-also occur, but rarely. Thus we might be tempted to conclude that Kepler differs most radically from others in his fertile access to various prior analogues (Process a). It is certainly plausible that what most distinguishes highly creative thinkers is a high rate of spontaneous analogical retrievals. But another possibility worth considering is that it may be the mapping process (Process b) that most differentiates highly creative individuals. There are two reasons for this speculation. First, the more energetic the mapping process, the more each analogy is likely to reveal its full potential set of inferences. Second, and less obvious, we conjecture that intense mapping may promote fertile access. For if access to prior material depends on a common encoding (Forbus, Gentner, & Law, 1995), then the highlighting, inferencing, and re-representing carried out in the course of pushing analogies may benefit subsequent memory access, as such activities tend to increase the scope of common internal representations (Gentner, Rattermann, Markman, & Kotovsky, 1995 ). This account is consonant with Seifert, Meyer, Davidson, Patalano, & Yaniv's (1995) prepared-mind perspective on creativity, and also with Gruber's (1995) discussion of Poincare. Thus, we suggest that a major reason for Kepler's high rate of ana-

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Analogy and creativity in the works of Johannes Kepler

Testing Scientific Theories was first published in 1984. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.Since much of a scientist's work consists of constructing arguments to show how experiments and observation bear on a particular theory, the methodologies of theory testing and their philosophical underpinnings are of vital concern to philosophers of science. Confirmation of scientific theories is the topic of Clark Glymour's important book Theory and Evidence,published in 1980. His negative thesis is that the two most widely discussed accounts of the methodology of theory testing - hypothetico-deductivism and Bayesianism - are flawed. The issues Glymour raises and his alternative "bootstrapping" method provided the focus for a conference sponsored by the Minnesota Center for Philosophy of Science and for this book. As editor John Earman says in his preface, the papers presented in Testing Scientific Theories germinate so many new ideas that philosophers of science will reap the harvest for years to come.Topics covered include a discussion of Glymour's bootstrapping theory of confirmation, the Bayesian perspective and the problems of old evidence, evidence and explanation, historical case studies, alternative views on testing theories, and testing particular theories, including psychoanalytic hypotheses and hypotheses about the completeness of the fossil record.

Louis O. Kattsoff

Papers

Elements of Philosophy.

Johannes Kepler: Life and Letters

Man is the Measure of all Things

The Logic of Self-Involvement.

Malcolm on Knowledge and Certainty