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The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us.

THE OUTER LIMITS OF REASON: What Science, Mathematics, and Logic Cannot Tell Us by Noson S. Yanofsky. Cambridge, MA: MIT Press, 2013. 424 pages. Hardcover; $29.95. ISBN: 9780262019354.

"Who knows the mind of the LORD? Who is able to give him advice?" (1 Corinthians 2:16).

This is a popular-level science book in the publishing niche of classics such as Hofstadter's Godel, Escher, Bach, or Penrose's The Emperor's New Mind. It is an exploration of the limits of reason. What can reason tell us about the limits of reason? A fascinating read that goes against the grain in choosing to explore what science, mathematics, and reason tell us cannot be revealed, rather than what they have or have not yet fully explained. As the author (a computer scientist from Brooklyn College) advocates, in many ways that which we cannot reach is more intriguing; why are there limits to what we can know? Why cannot reason take us beyond those limits? Essentially the book is a gathering together of recent (~ the last 100 years) results in physics, mathematics, and computing science that shed light on the scientific limitations of reason: if you will, an updating of traditional philosophical thinking on epistemology.

Firstly, the book is well written and thoughtfully put together. Explanations are accessible to the non-expert; this shines through particularly in the discussions on quantum mechanics, which were the best I have read. It's an engaging read, covering subjects in depth, while remaining lighthearted and often witty. Diagrams and figures are used effectively to aid understanding. Mathematical equations are virtually absent as the author confesses to following the publishing adage that "every equation reduces the readership by half." Each chapter ends with further reading suggestions; footnotes are used effectively pointing to references, deeper explanations, and interesting side comments.

Individual chapters are essentially self-contained, addressing the central issue from different points of view, so we have nine chapters covering such diverse topics as language, philosophy, physics, mathematics, computing science, and metaphysics. Each of the chapters contains a treasure chest of known paradoxes and limitations. Examples include the liar paradox, Zeno's paradoxes, the travelling salesman problem, Turing's halting problem, Godel's incompleteness theorem, and Schrodinger's cat. Usually these types of puzzles put my head in a spin, leaving me unsatisfied by the resulting intractability. However, I did not find that to be the case in this book; the author adeptly steers the reader on a route through many of these limitations without diminishing one's appreciation of the world we inhabit. Yanofsky unpacks these limitations, putting them in context and helping to uncover why these boundaries of reason arise.

The tenth and final chapter seeks to gather these separate chapters together to build a collective picture. Certain themes emerge. Of utmost importance is that of the common occurrence of self-referential systems: for example, "I am lying," the set that contains all sets that don't contain themselves, and even the universe that observes itself. Another theme is distinguishing between what is describable and what is indescribable. The author explains that by "... the very nature of language, what can be described is countably infinite. In contrast, what actually exists 'out there' is uncountably infinite" (p. 345). Yanofsky further adds:

This is stated without proof because I cannot quantify all phenomena. To quantify them, I would have to describe them and I cannot do that without language. So there might be an uncountably infinite number of phenomena and only a small, countably infinite subset describable by science. This is the ultimate, nonscientific (science must stay within the bounds of language) limitation on science's ability. (p. 175)

What we know is a drop, what we don't know is an ocean. (Isaac Newton, quoted by Yanofsky, p. 345)

The book does not advocate any particular religious (or nonreligious) perspective; however, it does address many topics that arise in science-faith discussions, such as the anthropic principle, interpretations of quantum mechanics, the unreasonable effectiveness of mathematics in natural sciences, chaos theory, philosophy of science, et cetera. At many conjunctions, a deity is posited as a possible solution among others to mysteries arising from these topics.

Let us seek to fathom those things that are fathomable and reserve those things which are unfathomable for reverence in quietude. (Goethe, quoted by Yanofsky, p. 354 n11)

The modern scientific revolution has resulted in an explosion of human knowledge and understanding of the workings of the universe. We have gained immense predictive capacities and developed remarkable technological innovation. And yet the methods of science and mathematics now see their own limits. This may seem humbling, and it is, but as the author concludes, as humans we typically live beyond reason. We make decisions not purely on logic and reason, but by feelings and intuitions. We value beauty, ethics, and wonder that defy rational explanation but provide life with real meaning. I would add that the transcendental conditions of our experience are not sensible unless we say that they are grounded in Jesus the author of life.

Overall, an enjoyable book that I am sure I will return to in the future.

Reviewed by Sam Pimentel, Assistant Professor of Mathematical Sciences, Trinity Western University, Langley, BC V2Y 1Y1.
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Author:Pimentel, Sam
Publication:Perspectives on Science and Christian Faith
Article Type:Book review
Date:Sep 1, 2014
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