This page contains brief descriptions of the books I have published. For a list of articles and other publications, please consult my curriculum vitae.
(Beyond Reason, John Wiley and Sons, New York, 2004)
Some will find the plunge from the media-inspired we-can-do-anything spin into the cold water of mathematical reality somewhat bracing. There are things we cannot do and things we cannot know. The book explores eight examples, altogether. We cannot square the circle, nor can we travel faster than light. We cannot compute some functions quickly, or others at all. We cannot have perpetual motion machines and we cannot predict the behaviour of a chaotic system (including the weather). Finally, we cannot prove some theorems, even if they happen to be true, and we cannot predict the positions and speeds of elementary particles at all! The reasons for all these impossibilities lie in mathematics itself.
(The Planiverse: Computer Contact with a Two-dimensional World. Poseidon Books/Simon & Schuster, New York, 1984.)
The tale of Yendred, a two-dimensional being who inhabits a two- dimensional world. Here is a truly exotic alternate world in which the details have been worked out to a degree not to be found in any other work of science fiction. Period. Would that all SF authors followed the implications of their premises this closely. Of course, what happens to Yendred in his search for the mysterious Drabk on his home planet of Arde not only reveals the implications of two-dimensionality at every step, but illustrates the challenges that face all beings, whatever their dimensionality.
The Armchair Universe
(The Armchair Universe, W. H. Freeman, New York, 1988)
A collection of lightly edited columns from Scientific American, including the Mandelbrot Set, wallpaper for the mind, analog computers, hypercubes, the conversational program Racter, a checkers-playing program, three dimensional Life, the sharks and fish of Wa-Tor, core War, and many others. Readers with a modicum of programming skill can bring most of these recreations to life.
The (New) Turing Omnibus
(The New Turing Omnibus, Computer Science Press/Freeman, New York, 1993.)
The new edition of The Turing Omnibus, a favorite reference for the most significant and interesting developments in computer science and computing mathematics. Although many of the topics covered are normally part of the senior undergraduate and graduate curricula, they have been made readable for those with only a slight acquaintance with mathematics and computing. Topics include: artificial intelligence (eg. Waltz's vision system and game trees), theory of computing (eg. Turing machines, the Chomsky hierarchy, and computability), complexity theory (eg. Cook's theorem), mathematical programs (eg. the Mandelbrot Set), data structures (eg. search trees, hashing), 66 topics in all.
The Magic Machine
(The Magic Machine, W. H. Freeman, New York, 1990)
The second collection of lightly edited columns from Scientific American. Topics include the Julia and Mandelbrot sets, chaotic systems, Braitenberg vehicles, a computer made entirely out of ropes and pulleys, computers in nanotechnology, fractal images, the Banach-Tarski paradox, people puzzles, core war, and many other topics.
Two Hundred Percent of Nothing
(Two Hundred Percent of Nothing, John Wiley & Sons, New York, 1993)
A review of current patterns of math abuse and innumeracy in the modern world. It's not getting better, but worse! Examples of misapplied statistics, advertising math, chart abuse, how special interest groups of all stripes bend math to their liking, government figures, and much more. All examples are from real life, sent in by hundreds of math abuse detectives. The final section is a must read: math education is declining, even though (as the book demonstrates) we all have an inborn ability to do mathematics, as evidenced by the complexity of social calculations.
The Tinkertoy Computer
(The Tinkertoy Computer and Other Machinations , W. H. Freeman, New York, 1993)
A collection of lightly edited columns from Scientific American, including Designer Fractals, programming Space War, wringing computer music from chaos, creating mechanical computers, face space, scanning the cat, Mark V. Shaney, drawing latticeworks by hand, and many others. Readers with a modicum of programming skill can bring most of these recreations to life.
Introductory Computer Science
(Introductory Computer Science , Computer Science Press, New York, 1996)
The most user-friendly introduction to computer science ever written. Although suitable for undergraduate majors, this book was written for non-majors. It introduces the neophyte student to the twin arts of programming and logical thought needed to understand how computers work, how programs run and how programmers think. The sub-title, Bits of Theory, Bytes of Practice, says it all.
Yes, We Have No Neutrons
(Yes, We Have No Neutrons, John Wiley & Sons, New York, 1997)
The title, suggested by the marketing geniuses at Wiley, replaces the author's title: The Sorcerer's Apprentice. The introduction explains how science works when investigators follow the scientific method. (See Science and Technology) The eight examples of "bad science" (a term we are forced to adopt in place of "non-science") span the twentieth century: N-rays, IQ, Freud, SETI, neural nets, Biosphere 2, and cold fusion. There are some fascinating stories of how pride and ambition prevent scientists (sorcerers) and would-be scientists (apprentices) from realizing the dreadful mistakes they are making. Some problems are subtle, as in SETI, the search for extra-terrestrial intelligence. If aliens are sending us messages, fine! But if aliens are not sending us messages, there is no way for Drake's search program to discover this since there is no stopping rule. The hypothesis is non-falsifiable. At best, the SETI program amounts to only half an experiment.
( Hungry Hollow, Copernicus, New York, 1998)
The most complete explanation of natural environments outside of a textbook, yet an easy and engaging read. The book uses seven scales or dimensions to frame seven worlds, like nested Russian dolls, to explain the effect of size on organisms and to bring home a central message: most of the real action in natural environments is invisible! Yet there is Lotor the raccoon and Dianne the biologist, as well as several other characters among the three thousand species that inhabit the Hollow, to take the reader on a trip of discovery from the very small to the very large. In the end, Hungry Hollow is threatened by developers. How can it be saved by a native grave?
Mathematical Mystery Tour
(Mathematical Mystery Tour, John Wiley and Sons, New York, 1999)
From the Temple of Apollo to the Arabian desert, and from the winding canals of Venice to the medieval halls of Oxford, a search through highlights in the history of mathematics for an answer to the timeless questions: Why is it that the cosmos -- from the tiny world of atoms to the shape of the universe itself -- is so miraculously governed by mathematical laws? Could it be that our world is in some sense made of mathematics, as Pyhagoras famously proposed? Or is it we (or the mathematicians among us) who make mathematics? Are the remarkable theorems and equations that describe the world around us discovered, or are they created? Is mathematics the very fabric of the cosmos, or does it exist only in the human mind?
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