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Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level.
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For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has even attempted to answer it until now.
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In this illuminating and provocative book, Gregory Chaitin argues that we can’t be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.
- Sales Rank: #1511985 in Books
- Brand: Brand: Vintage
- Published on: 2012-05-08
- Released on: 2012-05-08
- Original language: English
- Number of items: 1
- Dimensions: 8.37" h x .62" w x 5.30" l, .59 pounds
- Binding: Hardcover
- 144 pages
- Great product!
Review
Praise for Gregory Chaitin’s Meta Math!
�“A startling vision of the future of mathematics. . . . The Chaitinesque intellectual future will be eternally youthful and anarchic.”
—American Scientist
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“Math’s dark secret is out . . . Chaitin explains why Omega, a number he discovered thirty years ago, has him convinced that math is based on randomness.”
—Time
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“Is our universe computable? Is mathematics inevitable? Chaitin and I have been discussing these kinds of questions for a very long time, and it’s great to see him explain his point of view on them so passionately here.”
—Stephen Wolfram, creator of Mathematica and author of A New Kind of Science
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“A clearly written and witty look at a difficult subject. . . . Chaitin explains with infectious enthusiasm how mathematics doesn’t equal certainty.”
—Science News
"Captivating . . . With extraordinary skill and a gentle humor, Chaitin shares his profound insights."
—Paul Davies, author of How to Build a Time Machine
About the Author
Gregory Chaitin is widely known for his work on metamathematics and for his discovery of the celebrated Omega number, which proved the fundamental unknowability of math. He is the author of many books on mathematics, including Meta Math! The Quest for Omega. This is his first book on biology. Chaitin was for many years at the IBM Watson Research Center in New York. The research described in this book was carried out at the Federal University of Rio de Janeiro in Brazil, where Chaitin is now a professor. An Argentine-American, he is an honorary professor at the University of Buenos Aires and has an honorary doctorate from the National University of Cordoba, the oldest university in Argentina.
Excerpt. � Reprinted by permission. All rights reserved.
One
Introduction: Overview of Proving Darwin
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Like many pure mathematicians, I like giving “chalk” talks: improvised talks given on a blackboard or white- board using a minimum of technological assistance. Another strategy is for me to fill the board with what I want to cover just before I start to lecture, while people are still coming in, so that they can take in all the key ideas at a glance. In a large auditorium, however, a projector is necessary, or nobody will see anything.
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On the facing page you can see me giving an overview of this book in a large auditorium at the Federal University of Rio Grande do Sul in southern Brazil. The four slides I prepared are on pages 5 and 6. They summarize Chapters 2 to 4, which outline my strategy for making biology mathematical. After you finish reading these chapters, you should review the slides. Then they will make more sense.
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You’ve heard people refer to DNA as a computer program? Well, that’s the whole idea: to make this metaphor into a mathematical theory of evolution. In fact, it turns out that the mathematical tools for doing this were already available in the 1970s. More precisely, we will treat evolution as a random walk in software space. Random walks are an idea that mathematicians feel comfortable with, although the space we are walking around in at random is bigger than usual.
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I call this proposed new field “metabiology” because it is a highly simplified version of real biology—otherwise I wouldn’t be able to prove any theorems. These theorems are presented in Chapter 5, which is the climax of the book, and was a talk that I gave at the Santa Fe Institute. Chapters 6 to 8 discuss the broader significance of metabiology, theological, political and epistemological. And then there are two appendices.
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In the first appendix you can read the crucial section on self-reproducing automata in John von Neumann’s far-seeing “DNA = Software” paper that influenced Sydney Brenner, who in turn influenced Francis Crick—a remarkable fact that I only discovered while working on this book. And the second appendix gives some additional mathematical details that may be of interest to experts.
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Finally, I give a short list of suggested further reading, some books and a few articles that are important if you want to really understand metabiology. These are the books and articles that helped me the most to come up with a strategy for making biology mathematical, plus a few more related items that I threw in just for the fun of it. Enjoy them all!
Most helpful customer reviews
38 of 47 people found the following review helpful.
Interesting ideas but short on actual content/results
By J. Andrew Howe
This book promised so much, and yet delivered so little. To be sure, the author has some very interesting ideas that are worth being exposed to but that does not save this book. The first problem is in delivery - almost the entire book seems to be taken verbatim from class lectures. Certain content is duplicated often enough, that the book could have been cut in half with no loss. The second issue lies in the content itself. The author claims to have developed a working toy model of Darwinian evolution. But there's one fundamental problem here - his model relies on algorithmic mutation to introduce diversity, whereas real organisms generally undergo bitwise mutation. Hence, his model allows for a much more sophisticated search of the genotype space than is allowed in nature. In the same vein, by his own admission, the model can not actually be simulated, because it relies on a fitness function that can not be guaranteed to produce a result.
Not as important, but still misleading, is that his result claims to model Darwinian evolution. This is not true, as Darwinism posits that all existing life forms came into being from nothing (or from a primordial soup, if you wish) solely through natural selection acting on genetic crossover & mutation. What his model actually demonstrates (or would, if it could be simulated) is non-Darwinian adaptation & evolution. His evolution is only capable of tiny incremental changes that can not possibly create entirely new structures - they can only rearrange existing structures.
In summary, the fundamental ideas relating biology-mathematics-creativity are very interesting, as is the goal of developing a mathematical model for evolution. However, all this is worth a 30-60 minute lecture; not this book.
14 of 17 people found the following review helpful.
Thought-provoking.....
By Michael Jandrok
Mathematician Gregory Chaitin attempts to provide a mathematical model of evolution in this short book based on a university course given in the Spring of 2011 at the Federal University of Rio de Janeiro, where the author is a professor. It also adapts material given at one of his lectures at the Santa Fe Institute. It is a quick read and an outline at best of his work, but it does give the reader a general idea of the concepts behind what the author calls "metabiology", an attempt to model evolutionary adaptation through computer software rather than natural software, otherwise known as DNA.
The central premise of this book is that by utilizing algorithmic information theory and the flexible and creative nature of postmodern mathematics, one can construct a working mathematical toy model of evolution, creating a piece of randomly mutating software that selects for a fitness trait. The main idea here is that DNA is a naturally occurring piece of software, our internal programming language as it were. This is not an original concept, but it is one that Chaitin expands upon greatly in the text.
I'll admit that it's an absolutely compelling idea. Evolution, after all, is the backbone of modern biology, but its main concepts are often misunderstood or outright rejected by a significant portion of the population. If one can really take a mathematical model and "prove" that the basic mechanisms of evolution (random mutations and natural selection) work as advertised, then it could go a long way towards advancing scientific literacy.
Keep in mind that the author's model is simplistic at best, selecting for only one trait and having none of the environmental pressures that truly drive adaptation. That said, it DOES work, and it provides a foundation for more complex models that will more thoroughly mimic life processes in the future, especially as biotechnology advances into computer science.
There ARE mathematical formulas presented in the text, but they don't overshadow the main ideas. You'll probably understand most of the general ideas if you have a basic proficiency in high school level algebra and/or logic. The appendices go into additional technical detail, but they can be skipped unless you have the educational foundation to fully understand the concepts presented.
I'd recommend this book to anyone with an interest in the subject matter, though I would like to see an expanded and more accessible revision of this work at some point in the future.
6 of 7 people found the following review helpful.
The Motivation to Look Deeper
By T. H. Ray
I feel compelled to weigh in here, if only to help balance the negative reviews. It's true that one who is not familiar with Gregory Chaitin's broader research program will probably not fully comprehend important points of his lecture series on which *Proving Darwin* is based. As one who has listened to Dr. Chaitin hold forth to an enchanted audience for a 20 minute stretch without benefit of notes or visual aids, however, I expect that if you give him a chance to influence your thinking on how life and mathematics intersect and evolve together -- you'll be enchanted, too. More, you might be motivated to look into the rich tapestry of results that Chaitin has woven from his Algorithmic Information Theory and Omega Number.
It's well worth the effort.
~ T.H. Ray
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