Synopses & Reviews
In Probably Approximately Correct
, computer scientist Leslie Valiant proposes a revolutionary algorithm-based theory to describe how life evolves and learns. He begins by describing two, seemingly different, kinds of algorithms for handling and storing information about the world. One is the algorithm we call evolution by natural selection, which extracts and stores information that enables an organisms descendants to survive. The other is what we call learning, which enables us to extract and store information so that we can survive. While they may appear distinct, Valiant argues that they are notrather, they are both manifestations of the same algorithm, which he calls probably approximately correct.” The goal of life and of learning, he says, is not perfection, but just enough to get by. And when we apply that insight to our own algorithmsthose we develop to run on computerswe get a new and more powerful way to think about one of computer sciences hottest trends: machine learning, evolutionary computing, or genetic algorithms, to use three terms that more or less describe the same thing. Valiant argues that the three decades effort to recapitulate lifes evolution on a computer has failed because those designing the algorithms have neglected to take proper account of the probably approximately correct” model of how evolution works. Valiant offers here both a powerful take-down of the present state of evolutionary computing and a new, better path to powerful learning machines.
A startlingly original synthesis by one of computer sciences greatest minds, Probably Approximately Correct has profound implications for how we think about behavior, cognition, and ultimately the two most important questions of all: the possibilities and limits of human intelligence and of biological evolution.
The quest for machines (and codes) that never make mistakes was only a first step toward machines (and codes) that learn from them. Leslie Valiants Probably Approximately Correct
is a detailed, much-needed guide to how nature brought us here, and where technology is taking us next.”George Dyson, author of Turings Cathedral and Darwin among the Machines
Insightful.... This is science at its best, driven not by dogma and blind belief, but by the desire to understand, intellectual integrity and reliance on facts.... The book is written in a lively, accessible style and is surprisingly entertaining. Its funny how your perception of even mundane tasks can change after reading ityou start thinking algorithmically, confirming Dr. Valiants maxim that computer science is more about humans than about computers.”
New York Times
[A]n engaging meditation on complexity and on how living things often unwittingly use math to navigate it.”
Computer scientist Leslie Valiant celebrates Alan Turing as the progenitor of a third scientific revolution, potentially as profound as Newtons and Einsteins in transforming our understanding of the world. Why not a fourth revolutionwhy omit Darwin? Because, Valiant dares to say, Darwins theory is radically incomplete, and until it is equipped to make quantitative, verifiable predictions, evolution by natural selection cannot account for the complexity of living things and is not more than a metaphor. But Valiant offers no drop of succor to creationists. Rather, he seeks to arm neo-Darwinian theory against their onslaughts by elucidating the mechanistic, quantitative basis it must have in a world without a designer. The algorithms of computational learning theory, he posits, will be keyin particular, a special kind he calls ecorithms, which incorporate information gathered from the environment to improve an organisms performance. Turings heirs have only just begun to plot its equation.”
[Probably Approximately Correct] really shines as an introduction to computer science theory to the general public, providing a compact and accessible description of basic, important results
. This is a book that should be on every computer scientists shelf so that when someone asks, Why is computer science theory important? the three word response can be, Read this book.”
A scholar at the intersection of computing and evolutionary neuroscience, Valiant explores ecorithms: algorithms that learn by interacting with their environment, not from their designerand so are fundamental to the process of evolution. His text is clear and approachable, with some work; the argument is sweeping.”
[Valiants] major point is that Darwin introduced evolution by natural selection, but the detailed mechanism is still sketchy. A hundred years of genetics has filled in some details, but Valiant sees the computational details as essential and still missing. The goal of this book is to encourage further research and to set a paradigm for such work. As Erwin Schrödingers What Is Life? inspired those who built molecular biology, Valiant hopes to inspire those who will build a future computational biology. Highly recommended.”
This remarkable book is carefully constructed to give the lay person a sense of subtle problems in mathematics and artificial intelligence, and offers a framework for biologists and computer scientists to use in jointly investigating the most fascinating and enigmatic biological questions.”
Marc Kirschner, Chair, Department of Systems Biology, Harvard Medical School, and coauthor of The Plausibility of Life: Resolving Darwins Dilemma
This book contains a lot of fresh thinking and elegant, nuanced ideas. It is more than probably approximately brilliant. I am amazed by how much insight has been packed into relatively few pages. Anyone interested in computation, learning, evolution, or human nature should find these pages extraordinarily stimulating and informative.”
Stephen M. Kosslyn, Founding Dean, Minerva University, and former director, Center for Advanced Study in the Behavioral Sciences, Stanford University
Ecorithms are algorithms that learn from interaction with their environment. This book provides a theoretical framework for understanding the power and limits of ecorithms and applies it to human cognition, biological evolution and artificial intelligence. It is elegantly written and will be accessible to a wide circle of readers.”
Richard Karp, Turing Award winner and director, Simons Institute for the Theory of Computing, University of California, Berkeley
This little book is hugely ambitious. It takes on the task of creating a quantitative, mathematical theory to explain all essential mechanisms governing the behavior of all living organisms: survival, learning, adaptation, evolution, cognition and intelligence. The suggested theory has all the characteristics of a great one. It is simple, general, and falsifiable, and moreover seems probably, approximately, correct!”
Avi Wigderson, Nevanlinna Prize winner and Professor of Mathematics, Institute for Advanced Study, Princeton
The quest for machines (and codes) that never make mistakes was only a first step toward machines (and codes) that learn from them. Leslie Valiants Probably Approximately Correct is a detailed, much-needed guide to how nature brought us here, and where technology is taking us next.”
George Dyson, author of Turings Cathedral and Darwin among the Machines
Probably Approximately Correct is a great book. It was eye-opening to me, as a mathematician, to learn how we think and reason, and as a grandfather, to understand better the development and learning of my four-month-old grandson. Valiants book offers deep insights, both for young and old.”
Shing-Tung Yau, Professor of Mathematics, Harvard University, and coauthor of The Shape of Inner Space
[Valiant] grounds his hypotheses in solid computational theory, drawing on Alan Turings pioneering work on robust problem-solving and algorithm design, and in successive chapters he demonstrates how ecorithms can depict evolution as a search for optimized performance, as well as help computer scientists create machine intelligence.... His book offers a broad look at how ecorithms may be applied successfully to a variety of challenging problems.”Publishers Weekly
We have effective theories for very few things. Gravity is one, electromagnetism another. But for most thingswhether as basic as finding a mate or as complex as managing an economyour theories are weak or nonexistent. Fortunately, we dont need them, any more than a fish needs a theory of water to swim; we muddle through. But how do we do it? In Probably Approximately Correct
, computer scientist Leslie Valiant presents a theory of the theoryless. The key is probably approximately correct” learning, Valiants model of how effective behavior can be learned even in a world as complex as our own. This model reveals the shared computational nature of evolution and learning, shows how computers might possess authentic intelligence, and sheds some light on human nature, shaped as it has been by evolution and adaptation. Valiant also shows why pragmatically coping with a problem can provide a satisfactory solution in the absence of any theoryafter all, finding a mate is a lot more satisfying than finding a theory of mating.
Offering an elegant, powerful model that encompasses all of lifes complexity, Probably Approximately Correct will revolutionize the way we look at the universes greatest mysteries.
From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns.
How does life prosper in a complex and erratic world? While we know that nature follows patternssuch as the law of gravityour everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?
In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiants theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.
Offering a powerful and elegant model that encompasses lifes complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.
About the Author
is the T. Jefferson Coolidge Professor of Computer Science and Applied Mathematics at Harvard University. He is a Fellow of the Royal Society and a member of the National Academy of Sciences. He is a winner of the Nevanlinna Prize from the International Mathematical Union, and the Turing Award, known as the Nobel of computing.
Table of Contents
2. Prediction and Adaptation
3. The Computable
4. Mechanistic Explanations of Nature
5. The Learnable
6. The Evolvable
7. The Deducible
8. Humans as Ecorithms
9. Machines as Ecorithms