Free PDF The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us (MIT Press), by Noson S. Yanofsky
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The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us (MIT Press), by Noson S. Yanofsky
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Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.
Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.
Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
- Sales Rank: #44924 in Books
- Brand: Brand: The MIT Press
- Published on: 2013-08-23
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .88" w x 6.00" l, 1.65 pounds
- Binding: Hardcover
- 428 pages
Features
- Used Book in Good Condition
Review
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...
-Nature
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.
-Slate
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.
About the Author
Noson S. Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City University of New York. He is a coauthor of Quantum Computing for Computer Scientists.
Most helpful customer reviews
59 of 61 people found the following review helpful.
Good Book
By jerryb
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.
40 of 40 people found the following review helpful.
Fascinating exploration of the intersection of science and philosophy
By R. D Johnson
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. It shows you why intuition often fails, why the scientific dogma of one era is often debunked by the next, and explains how some knowledge of our universe will always remain forever beyond our grasp simply because we cannot 'step outside' our own self-referential existence. In some ways we're like the inhabitants of 2-D Flatland (another excellent book btw) trying to understand a wider 3-D world.
I do have one complaint with this book. There are copious footnotes in each chapter, some which are simple references, but many others which are additional explanatory material. These are all grouped together in a 'Notes' section in the back of the book. This required me to flip continually back and forth from each chapter to the 'Notes' section to read the additional material. It would have been better to present this material as true footnotes on each page; doing so would have eliminated a lot of tedious page-flipping.
14 of 16 people found the following review helpful.
A good overview of the limits of what math and logical reasoning can tell us
By A. Menon
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. The author considers the problems associated with figuring out the travelling salesman problem and then frames other problems relative to one another in terms of difficulty and shows how many are in fact equivalent. The author's goal is to show how some problems which are easy to state currently only have solutions which can be found in times that are longer than the age of the universe and that quantum computation would not be the answer to solving such problems. The author then moves onto basic computation theory and Turing's halting problem. He shows how there can be no program which knows whether a given input program with a given input will compute in finite time. He uses counting arguments from a previous argument to show how this works and as such starts to refer to earlier material. The author then discusses the hierarchy of larger and larger systems for which one cannot solve the halting problem even with the help of divine oracles. The author moves on to the limits of what can know physically. He discusses both chaos and quantum mechanics and discusses how the precision needed to know initial conditions is a fundamental constraint in being able to predict a clockwork universe and discusses how separately quantum mechanics makes particle dynamics fundamentally uncertain as a separate limitation. The author then discusses science and philosophy and how science has philosophical limits imposed on it. He discusses how induction is used as a principal to "prove" our scientific postulates which then form the bedrock of the emergent theory dependent on those postulates. We have no proof that at some point experiments might not repeat themselves as they have in the past. The author discusses the relationship between science and math and is very well measured about why and how there are relationships and what to make of them. He discusses the anthropic principle and its scientific worth. The author then focuses on some more purely mathematical ideas like the real numbers, rational, irrational and within that algebraic and transcendental numbers, he discusses group theory and goes back to computation and then covers some pure logic and arithmetical systems and some of Godel's ideas. The author goes into how mathematical systems cannot deduce whether all statements about a given system can be shown to be true or false and that there are limits to knowledge about any given system irrespective of how many assumptions/axioms are included.
There are a lot of different ideas the author discusses when familiarizing the reader with many of the limits of logic and reason we are fundamentally faced with. The author discusses grammar systems where terms are not all well defined, he discusses the problems associated with continuous space and motion on that space, he discusses chaos and quantum mechanics as well as the difficulty of computability of many easy to state problems- some due to time constraints others more fundamentally by the limits of what we can know. The author covers the limits of logic being able to answer all questions posed within any given mathematical system. A lot of information and thought has gone into this and one can learn a lot from this book. Each topic can be further researched and all are interesting overviews of where our knowledge fundamentally hits ceilings. I enjoyed reading much in this book.
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