During his forty-year association with the Los Alamos National Laboratory, mathematician Stanislaw Ulam wrote many Laboratory Reports, usually in collaboration with colleagues. Some of them remain classified to this day. The rest are gathered in this volume and for the first time are easily accesible to mathematicians, physical scientists, and historians. The timeliness of these papers is remarkable. They contain seminal ideas in such fields as nonlinear stochastic processes, parallel computation, cellular automata, and mathematical biology. The collection is of historical interest as well, During and after World War II, the complexity of problems at the frontiers of science surpassed any technology that had ever existed. Electronic computing machines had to be developed and new computing methods had to be invented based on the most abstract ideas from the foundations of mathematics and theoretical physics. To these problems and others in physics, astronomy, and biology, Ulam was able to bring both general insights and specific conceptual contributions. His fertile ideas were far ahead of their time, and ranged over many branches of science. In fact, his mathematical versatility fulfilled the statement of his friend and mentor, the great Polish mathematician Stefan Banach, who claimed that the very best mathematicians see "analogies between analogies." Introduced by A. R. Bednarek and Francoise Ulam, these Los Alamos reports represent a unique view of one of the twentieth century's intellectual masters and scientific pioneers. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1990.

Metaphors show students how to make connections between the concrete and the abstract, prior knowledge and unfamiliar concepts, and language and image. But teachers must learn how to use metaphors and analogies strategically and for specific purposes, helping students discover and deconstruct effective comparisons. Metaphors & Analogies is filled with provocative illustrations of metaphors in action and practical tips.

Teaches how to distinguish between correct and incorrect analogies, such as "mouth is related to eat as teeth are related to chew" (correct) versus "mouth is related to eat as stomach is related to liver" (incorrect).

How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

From World War I to Operation Desert Storm, American policymakers have repeatedly invoked the "lessons of history" as they contemplated taking their nation to war. Do these historical analogies actually shape policy, or are they primarily tools of political justification? Yuen Foong Khong argues that leaders use analogies not merely to justify policies but also to perform specific cognitive and information-processing tasks essential to political decision-making. Khong identifies what these tasks are and shows how they can be used to explain the U.S. decision to intervene in Vietnam. Relying on interviews with senior officials and on recently declassified documents, the author demonstrates with a precision not attained by previous studies that the three most important analogies of the Vietnam era--Korea, Munich, and Dien Bien Phu--can account for America's Vietnam choices. A special contribution is the author's use of cognitive social psychology to support his argument about how humans analogize and to explain why policymakers often use analogies poorly.

Approach analogies as puzzles. To solve them, students need to use cognitive processes and critical-thinking skills. These exercises present word and/or picture relationships in several different ways. The goal is to develop skills in visual imagery, reading comprehension, vocabulary development, reasoning and test-taking.

A multiple analogy is a structured comparison in which several sources are likened to a target. In Multiple analogies in science and philosophy, Shelley provides a thorough account of the cognitive representations and processes that participate in multiple analogy formation. Through analysis of real examples taken from the fields of evolutionary biology, archaeology, and Plato's Republic, Shelley argues that multiple analogies are not simply concatenated single analogies but are instead the general form of analogical inference, of which single analogies are a special case. The result is a truly general cognitive model of analogical inference.Shelley also shows how a cognitive account of multiple analogies addresses important philosophical issues such as the confidence that one may have in an analogical explanation, and the role of analogy in science and philosophy. This book lucidly demonstrates that important questions regarding analogical inference cannot be answered adequately by consideration of single analogies alone.

During his forty-year association with the Los Alamos National Laboratory, mathematician Stanislaw Ulam wrote many Laboratory Reports, usually in collaboration with colleagues. Some of them remain classified to this day. The rest are gathered in this volume and for the first time are easily accesible to mathematicians, physical scientists, and historians. The timeliness of these papers is remarkable. They contain seminal ideas in such fields as nonlinear stochastic processes, parallel computation, cellular automata, and mathematical biology. The collection is of historical interest as well, During and after World War II, the complexity of problems at the frontiers of science surpassed any technology that had ever existed. Electronic computing machines had to be developed and new computing methods had to be invented based on the most abstract ideas from the foundations of mathematics and theoretical physics. To these problems and others in physics, astronomy, and biology, Ulam was able to bring both general insights and specific conceptual contributions. His fertile ideas were far ahead of their time, and ranged over many branches of science. In fact, his mathematical versatility fulfilled the statement of his friend and mentor, the great Polish mathematician Stefan Banach, who claimed that the very best mathematicians see "analogies between analogies." Introduced by A. R. Bednarek and Francoise Ulam, these Los Alamos reports represent a unique view of one of the twentieth century's intellectual masters and scientific pioneers. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1990.

Shows how analogy-making pervades human thought at all levels, influencing the choice of words and phrases in speech, providing guidance in unfamiliar situations, and giving rise to great acts of imagination.