Reality Rules, The Fundamentals (Volume 1) [Hardcover]

John Casti (Author)

Book Description

ISBN-10: 0471570214 | ISBN-13: 978-0471570219 | Publication Date: August 1992 | Edition: Volume 1

"Casti Tours offers the most spectacular vistas of modern applied mathematics" ???Nature
Mathematical modeling is about rules???the rules of reality. Reality Rules explores the syntax and semantics of the language in which these rules are written, the language of mathematics. Characterized by the clarity and vision typical of the author's previous books, Reality Rules is a window onto the competing dialects of this language???in the form of mathematical models of real-world phenomena???that researchers use today to frame their views of reality.

Moving from the irreducible basics of modeling to the upper reaches of scientific and philosophical speculation, Volumes 1 and 2, The Fundamentals and The Frontier, are ideal complements, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems.

Engagingly written and handsomely illustrated, Reality Rules is a fascinating journey into the conceptual underpinnings of reality itself, one that examines the major themes in dynamical system theory and modeling and the issues related to mathematical models in the broader contexts of science and philosophy. Far-reaching and far-sighted, Reality Rules is destined to shape the insight and work of students, researchers, and scholars in mathematics, science, and the social sciences for generations to come.

Of related interest . . .

ALTERNATE REALITIES

Mathematical Models of Nature and Man

John L. Casti

A thoroughly modern account of the theory and practice of mathematical modeling with a treatment focusing on system-theoretic concepts such as complexity, self-organization, adaptation, bifurcation, resilience, surprise and uncertainty, and the mathematical structures needed to employ these in a formal system.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Editorial Reviews

Review

Solutions Manual available. -- The publisher, John Wiley & Sons --This text refers to an out of print or unavailable edition of this title.

From the Publisher

An account of the grammar and syntax of the language in which reality rules are written--the language of mathematics. Coverage includes a discussion of computation and complexity running the gamut from Godel's Incompleteness Theorem and its work in artificial intelligence to the problem of NP-completeness and the complexity of numerical algorithms to the relation between chaos and stock-price fluctuations. Each chapter contains a significant amount of research problems and ends with discussion questions. Features an extended, annotated bibliography. --This text refers to the Paperback edition.

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Product Details

• Hardcover: 416 pages
• Publisher: Wiley-Interscience; Volume 1 edition (August 1992)
• Language: English
• ISBN-10: 0471570214
• ISBN-13: 978-0471570219
• Product Dimensions: 10.3 x 7.4 x 1.2 inches
• Shipping Weight: 2.2 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,201,804 in Books (See Top 100 in Books)

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1 of 2 people found the following review helpful:

5.0 out of 5 stars Models of the world based on more abstract concepts such as automata and chaos, November 10, 2008

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Reality Rules, The Fundamentals (Volume 1) (Hardcover)

Mathematical models of the world are the toolset that we use to build everything, from the simplest machine to the largest skyscraper. For example, when a large and tall building is being planned, the foundations are laid based on the models for the type of soil, width of the building, the weight of the materials and the height. It is all constructed in model form before the first shovel lifts the first piece of dirt. The fact that it is a rare occasion when a building or anything else spontaneously comes crashing down demonstrates how sound our mathematical models are.
In this book, Casti presents some of the more recent and abstract models of the world, these models are not nearly as precise. These are not basic equations, but generally ideas regarding how models can be constructed. The chapters are:

*) The ways of model making: natural systems and formal mathematical representations - this chapter introduces the idea of a system being modeled by a set of states and transitions between those states in response to events.
*) Catastrophes, dynamics and life: the singularities of ecological and natural resource systems - this chapter covers the models for systems that reach cusps of dramatic change, such as populations of living creatures where the model contains cusps. The most interesting graph in this chapter is on page 131. It is a graph of Scottish witchcraft trials from 1600 to 1700 plotted so the graph is linear.
*) Pattern and the emergence of living forms: cellular automata and discrete dynamics - in this chapter the models of cellular and finite automata are presented and used to describe some types of biological activity.
*) Order in chaos- the mathematics of chaos theory are presented and used to describe some situations such as population cycles, free markets and the spread of disease.

As the contents of the chapters demonstrate, this is not a book on simple modeling; the topics require a degree of mathematical sophistication. However, if your interest is in these models of the world, then this is an excellent resource. There is a small set of exercises at the end of each section and larger sets of discussion questions and problems at the ends of the chapters.