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The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us Hardcover – August 23, 2013

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Editorial Reviews


Steering well clear of complex mathematics, Yanofsky canters though language paradoxes, infinity puzzles, computing impossibilities, the scope of fundamental physics and what he
believes to be the philosophical limitations of science. It is enjoyable ride...

This fascinating account describes the limitations of reasoning...Popular science readers will enjoy the well-written section explaining experiments in quantum theory... For centuries, humans' basic intuitions about the behavior of nature have been proven wrong, and now there is growing evidence in many fields showing that unavoidable limits exist to prevent people from eventually understanding it all. Researchers will appreciate the great selection of diagrams, complete bibliography and notes section, and useful index. Summing Up: Highly recommended.
  - Choice

Yanofsky makes problems and questions that should make your headache delightful to read and think about.

Phenomenal Book... Before picking up this book I'd not heard of "Noson Yanofsky," so I was astounded that this is the best, most lucidly-written volume for lay readers I've ever encountered on the underlying or foundational topics I most enjoy, related to mathematics; including issues that cross the boundaries of math, logic, philosophy, physics, and computer science.
  - Math Tango

Winner of  the 2013 PROSE Award in Popular Science & Mathematics, Association of American Publishers

Yanofsky has brought together insights about quantum mechanics, logic, and mathematics under one rubric. Very few others could pull that off. This book has the potential to be a classic.

(Prakash Panangaden, School of Computer Science, McGill University)

Yanofsky takes on this mindboggling subject with confidence and impressive clarity. He eases the reader into the subject matter, ending each chapter with further readings. His book is a fascinating resource for anyone who seeks a better understanding of the world through the strangeness of its own limitations and a must-read for anyone studying information science.

(Publishers Weekly, (starred review))

Yanofsky provides an entertaining and informative whirlwind trip through limits on reason in language, formal logic, mathematics -- and in science, the culmination of humankind's attempts to reason about the world.

(The New Scientist)

In my view, Outer Limits is an extraordinary, and extraordinarily interesting, book. It is a cornucopia of mind-bending ideas.

(Raymond S. Nickerson PsycCRITIQUES)

The scope of the material covered is so wide, and the writing so clear and intuitive, that all readers will learn something new and stimulating.

(Thomas Colin Leonardo Reviews)

From the Author

This is a popular science book that can be read by anyone interested in the limitations of science and mathematics. This book will also be of interest to people with a philosophical bent who are interested in how our universe works and what we can know about it.

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Product Details

  • Hardcover: 424 pages
  • Publisher: The MIT Press (August 23, 2013)
  • Language: English
  • ISBN-10: 0262019353
  • ISBN-13: 978-0262019354
  • Product Dimensions: 6 x 1.1 x 9 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (37 customer reviews)
  • Amazon Best Sellers Rank: #76,250 in Books (See Top 100 in Books)

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Customer Reviews

3.9 out of 5 stars

Most Helpful Customer Reviews

49 of 50 people found the following review helpful By jerryb on November 8, 2013
Format: Kindle Edition Verified Purchase
I really enjoyed this book; it made think about subjects I hadn't thought about in years. The bibliography is excellent and the author's comments and examples are often surprising but to the point. I think it could be better organized. Self reference keeps popping up, I wish it were all in one place. The book is organized into areas where reason presumably fails. I wish it were organized by types of failure. Also I think he casts too wide a net. I object to his inclusion of some mathematics examples. For instance the inclusion of the ancients' problems demonstrates as he points out later that their problems were not using the correct tools, not that reason was at fault. Similarly for solving quintic equations. It's as if we were out on a starry night and he said "look up. See those moons of Jupiter." I would say that it's not a fault of science or reason that I can't see them. I don't have the proper tool. Give me a telescope and I'll be able to see them. I have the same basic criticisms of including quantum theory. If there is not a final theory why say that there is a limit of science or reason to understand quantum phenomena? He may acknowledge that there are several theories or maybe a theory that no one has ever thought of which might finally be right. But that doesn't prove that there is a limit to what science might conclude in the future. Overall I think the author's best suit is logic and computing and I think it would have been a better book to have stuck to those subjects.

One shouldn't be dissuaded by my criticisms. Read the book, you'll enjoy it. I wouldn't have gone to the trouble of writing what I did write if I didn't like the book.
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34 of 34 people found the following review helpful By R. D Johnson on January 28, 2014
Format: Hardcover Verified Purchase
This is a book that is targeted to those who like to think. Although written for a general audience, it would be helpful to have some background in math and science beyond a few long-ago semesters in high school before diving in. You should have some comfort level with set theory, exponents, real and imaginary numbers, and the basic tenets of calculus and probability. The same is true for general physics, such as polarization, particle spin, and the like. Nothing deep, mind you, as the book isn't expecting you to solve equations or anything of the sort. However, the 'outer limits' involve travel beyond where science is now, so knowing something about where science currently is helps.

As an engineer whose math and science education hasn't totally faded away yet, I found this book fascinating. It explains the huge difference between 'countable infinity' and 'uncountable infinity' (something I had never been taught in school), and how the infinite number of solvable problems are dwarfed by an infinitely greater number of unsolvable ones. It goes over the P-NP and Halting problems in Computer Science with far more clarity than any CS textbook I've ever read. It covers chaos theory, the strange quantum world, and the equally curious world of general relativity and the mysteries therein that science has yet to (and in some cases never can) solve. It will also expose you to the philosophical debate about the curious relationship between math, science and consciousness, without having to plow through a course in philosophy. This book is a wonderful antidote to those (far-too-many) books that present science and math as always settled fact and incontrovertible truth.
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12 of 12 people found the following review helpful By A. Menon on February 25, 2014
Format: Hardcover Verified Purchase
Much of what science focuses on is reductionism and in particular the goal of reducing the world to the bare minimum of assumptions and postulates that can then be built up into all the complexity we see and feel. The outer limits of reason looks at the limits of what we can know and what we can reduce. It looks at lots of different ideas separately and analyzes lots of different forms of limitations that we must deal with. I'll give a quick overview of the subject matter.

The author starts out by looking at limits to logical consistency in our evolved language. He looks at some repurcussions of paradox's on self referencing sentences and shows how such systems can be looked at symbolically. The author then starts discussing how there are many ideas which do not have a platonic ideal and that their meaning is effectively subjective. The author discusses an eroding artifact that is refurbished and questions at one point is the original not considered the same as the remaining. There is no right answer to such a question. The author discusses Zeno and some of the issues we face when considering infinity. The author ends the chapter by considering logic methods that can accomodate that we humans dont define every object or word precisely before using, in particular systems like fuzzy logic. Where truth values can be indeterminate. The author then moves onto set theory and looks at Cantor's analysis of infinity. Countable infinity is considered as well as uncountable infinity and the ladders above infinity created by power sets. These treatments are self contained in the book though some outside knowledge wouldnt hurt. The author then moves onto the limits of computation in particular polynomial time problems as well as NP problems.
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