Computer Mathematics

Godel, Escher, Bach: An Eternal Golden Braid

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

This groundbreaking Pulitzer Prize-winning book sets the standard for interdisciplinary writing, exploring the patterns and symbols in the thinking of mathematician Kurt Godel, artist M.C. Escher, and composer Johann Sebastian Bach.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition (Springer Series in Statistics)

During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book.

This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for ``wide'' data (p bigger than n), including multiple testing and false discovery rates.

Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.

Pattern Recognition and Machine Learning (Information Science and Statistics)

The dramatic growth in practical applications for machine learning over the last ten years has been accompanied by many important developments in the underlying algorithms and techniques. For example, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic techniques. The practical applicability of Bayesian methods has been greatly enhanced by the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, while new models based on kernels have had a significant impact on both algorithms and applications.

This completely new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

The book is suitable for courses on machine learning, statistics, computer science, signal processing, computer vision, data mining, and bioinformatics. Extensive support is provided for course instructors, including more than 400 exercises, graded according to difficulty. Example solutions for a subset of the exercises are available from the book web site, while solutions for the remainder can be obtained by instructors from the publisher. The book is supported by a great deal of additional material, and the reader is encouraged to visit the book web site for the latest information.

Coming soon:

*For students, worked solutions to a subset of exercises available on a public web site (for exercises marked "www" in the text)

*For instructors, worked solutions to remaining exercises from the Springer web site

*Lecture slides to accompany each chapter

*Data sets available for download

On Intelligence

Jeff Hawkins, the high-tech success story behind PalmPilots and the Redwood Neuroscience Institute, does a lot of thinking about thinking. In On Intelligence Hawkins juxtaposes his two loves--computers and brains--to examine the real future of artificial intelligence. In doing so, he unites two fields of study that have been moving uneasily toward one another for at least two decades. Most people think that computers are getting smarter, and that maybe someday, they'll be as smart as we humans are. But Hawkins explains why the way we build computers today won't take us down that path. He shows, using nicely accessible examples, that our brains are memory-driven systems that use our five senses and our perception of time, space, and consciousness in a way that's totally unlike the relatively simple structures of even the most complex computer chip. Readers who gobbled up Ray Kurzweil's (The Age of Spiritual Machines and Steven Johnson's Mind Wide Open will find more intriguing food for thought here. Hawkins does a good job of outlining current brain research for a general audience, and his enthusiasm for brains is surprisingly contagious. --Therese Littleton

The Age of Spiritual Machines: When Computers Exceed Human Intelligence

How much do we humans enjoy our current status as the most intelligent beings on earth? Enough to try to stop our own inventions from surpassing us in smarts? If so, we'd better pull the plug right now, because if Ray Kurzweil is right we've only got until about 2020 before computers outpace the human brain in computational power. Kurzweil, artificial intelligence expert and author of The Age of Intelligent Machines, shows that technological evolution moves at an exponential pace. Further, he asserts, in a sort of swirling postulate, time speeds up as order increases, and vice versa. He calls this the "Law of Time and Chaos," and it means that although entropy is slowing the stream of time down for the universe overall, and thus vastly increasing the amount of time between major events, in the eddy of technological evolution the exact opposite is happening, and events will soon be coming faster and more furiously. This means that we'd better figure out how to deal with conscious machines as soon as possible--they'll soon not only be able to beat us at chess, but also likely demand civil rights, and might at last realize the very human dream of immortality.

The Age of Spiritual Machines is compelling and accessible, and not necessarily best read from front to back--it's less heavily historical if you jump around (Kurzweil encourages this). Much of the content of the book lays the groundwork to justify Kurzweil's timeline, providing an engaging primer on the philosophical and technological ideas behind the study of consciousness. Instead of being a gee-whiz futurist manifesto, Spiritual Machines reads like a history of the future, without too much science fiction dystopianism. Instead, Kurzweil shows us the logical outgrowths of current trends, with all their attendant possibilities. This is the book we'll turn to when our computers first say "hello." --Therese Littleton

The national bestseller by the "ultimate thinking machine" (Forbes) whose predictions for the future are startling, provocative--and closer to fruition than you think.

Ray Kurzweil is the inventor of the most innovative and compelling technology of our era, an international authority on artificial intelligence, and one of our greatest living visionaries. Now he offers a framework for envisioning the twenty-first century--an age in which the marriage of human sensitivity and artificial intelligence fundamentally alters and improves the way we live. Kurzweil's prophetic blueprint for the future takes us through the advances that inexorably result in computers exceeding the memory capacity and computational ability of the human brain by the year 2020 (with human-level capabilities not far behind); in relationships with automated personalities who will be our teachers, companions, and lovers; and in information fed straight into our brains along direct neural pathways. Optimistic and challenging, thought-provoking and engaging, The Age of Spiritual Machines is the ultimate guide on our road into the next century.

"The Age of Spiritual Machines will blow your mind. . . . Kurzweil lays out a scenario that might seem like science fiction if it weren't coming from a proven entrepreneur."-- San Francisco Chronicle
The Age of Spiritual Machines appeared on national bestseller lists, including the Boston Globe and the San Francisco Chronicle
Kurzweil's first book, The Age of Intelligent Machines, won the Association of American Publishers Award for the Most Outstanding Computer Science Book of 1990

Collective Intelligence in Action

There's a great deal of wisdom in a crowd, but how do you listen to a thousand people talking at once? Identifying the wants, needs, and knowledge of internet users can be like listening to a mob.

In the Web 2.0 era, leveraging the collective power of user contributions, interactions, and feedback is the key to market dominance. A new category of powerful programming techniques lets you discover the patterns, inter-relationships, and individual profiles-the collective intelligence--locked in the data people leave behind as they surf websites, post blogs, and interact with other users.

Collective Intelligence in Action is a hands-on guidebook for implementing collective intelligence concepts using Java. It is the first Java-based book to emphasize the underlying algorithms and technical implementation of vital data gathering and mining techniques like analyzing trends, discovering relationships, and making predictions. It provides a pragmatic approach to personalization by combining content-based analysis with collaborative approaches.

This book is for Java developers implementing Collective Intelligence in real, high-use applications. Following a running example in which you harvest and use information from blogs, you learn to develop software that you can embed in your own applications. The code examples are immediately reusable and give the Java developer a working collective intelligence toolkit.

Along the way, you work with, a number of APIs and open-source toolkits including text analysis and search using Lucene, web-crawling using Nutch, and applying machine learning algorithms using WEKA and the Java Data Mining (JDM) standard.

Python Scripting for Computational Science (Texts in Computational Science and Engineering)

The goal of this book is to teach computational scientists how to develop tailored, flexible, and human-efficient working environments built from small programs (scripts) written in the easy-to-learn, high-level language Python. The focus is on examples and applications of relevance to computational scientists: gluing existing applications and tools, e.g. for automating simulation, data analysis, and visualization; steering simulations and computational experiments; equipping old programs with graphical user interfaces; making computational Web applications; and creating interactive interfaces with a Maple/Matlab-like syntax to numerical applications in C/C++ or Fortran. In short, scripting with Python makes you much more productive, increases the reliability of your scientific work and lets you have more fun - on Unix, Windows and Macintosh. All the tools and examples in this book are open source codes. The third edition is compatible with the new NumPy implementation and features updated information, correction of errors, and improved associated software tools.

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science)

Some love it, some hate it, but The Emperor's New Mind, physicist Roger Penrose's 1989 treatise attacking the foundations of strong artificial intelligence, is crucial for anyone interested in the history of thinking about AI and consciousness. Part survey of modern physics, part exploration of the philosophy of mind, the book is not for casual readers--though it's not overly technical, it rarely pauses to let the reader catch a breath. The overview of relativity and quantum theory, written by a master, is priceless and uncontroversial. The exploration of consciousness and AI, though, is generally considered as resting on shakier ground.

Penrose claims that there is an intimate, perhaps unknowable relation between quantum effects and our thinking, and ultimately derives his anti-AI stance from his proposition that some, if not all, of our thinking is non-algorithmic. Of course, these days we believe that there are other avenues to AI than traditional algorithmic programming; while he has been accused of setting up straw robots to knock down, this accusation is unfair. Little was then known about the power of neural networks and behavior-based robotics to simulate (and, some would say, produce) intelligent problem-solving behavior. Whether these tools will lead to strong AI is ultimately a question of belief, not proof, and The Emperor's New Mind offers powerful arguments useful to believer and nonbeliever alike. --Rob Lightner

For decades, proponents of artificial intelligence have argued that computers will soon be doing everything that a human mind can do. Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his "little finger" told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

The Emotion Machine: Commonsense Thinking, Artificial Intelligence, and the Future of the Human Mind

In this mind-expanding book, scientific pioneer Marvin Minsky continues his groundbreaking research, offering a fascinating new model for how our minds work. He argues persuasively that emotions, intuitions, and feelings are not distinct things, but different ways of thinking.

By examining these different forms of mind activity, Minsky says, we can explain why our thought sometimes takes the form of carefully reasoned analysis and at other times turns to emotion. He shows how our minds progress from simple, instinctive kinds of thought to more complex forms, such as consciousness or self-awareness. And he argues that because we tend to see our thinking as fragmented, we fail to appreciate what powerful thinkers we really are. Indeed, says Minsky, if thinking can be understood as the step-by-step process that it is, then we can build machines -- artificial intelligences -- that not only can assist with our thinking by thinking as we do but have the potential to be as conscious as we are.

Eloquently written, The Emotion Machine is an intriguing look into a future where more powerful artificial intelligences await.

How We Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics

The title of this scholarly yet remarkably accessible slice of contemporary cultural history has a whiff of paradox about it: what can it mean, exactly, to say that we humans have become something other than human? The answer, Katherine Hayles explains, lies not in ourselves but in our tools. Ever since the invention of electronic computers five decades ago, these powerful new machines have inspired a shift in how we define ourselves both as individuals and as a species.

Hayles tracks this shift across the history of avant-garde computer theory, starting with Norbert Weiner and other early "cyberneticists," who were the first to systematically explore the similarities between living and computing systems. Hayles's study ends with artificial-life specialists, many of whom no longer even bother to distinguish between life forms and computers. Along the way she shows these thinkers struggling to reconcile their traditional, Western notions of human identity with the unsettling, cyborg directions in which their own work seems to be leading humanity.

This is more than just the story of a geek elite, however. Hayles looks at cybernetically inspired science fiction by the likes of Philip K. Dick, William Gibson, and Neal Stephenson to show how the larger culture grapples with the same issues that dog the technologists. She also draws lucidly on her own broad grasp of contemporary philosophy both to contextualize those issues and to contend with them herself. The result is a fascinating introduction--and a valuable addition--to one of the most important currents in recent intellectual history. --Julian Dibbell