Science and math can tell us everything there is to know about the universe, right? There must be people who believe that. If such people exist, they should definitely run out and read Noson Yanofsky’s new book, The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us. It’s informative, and it casts an amazingly wide net; it tells a rich story and tells it well.
But what about the rest of us? There are actually three sets of people whose knowledge and beliefs differentiate themselves in regard to the role of science and math. One set contains the people described above, the True Believers, who may or may not actually exist (perhaps they’re like unicorns); they will definitely profit from this book. To their right we see the Scientifically Unwashed, who know nothing about science, don’t want to know, and distrust all scientists and mathematicians (a distressingly large group in this country); they won’t profit from this book, since they never believed in math and science in the first place. To their left we see the Informed Citizens, whose range of scientific knowledge may vary from extremely shallow to very deep; they should definitely read this book, although it won’t tell them anything new if they are already well-informed on the wide range of topics Yanofsky discusses, especially if they have a healthy skepticism about exaggerated beliefs.
One exciting aspect of Yanovsky’s work is the way he builds bridges rather than walls — many bridges. Incorporating a healthy amount of philosophy and history, he discusses symmetry, tessellations, symbolic logic, Gödel, self-reference, the nonexistence of a quintic formula, the irrationality of the square root of 2, Turing, the halting problem, artificial intelligence, the idea of proving something impossible (such as covering a mutilated chessboard with dominos or trisecting a general angle), and paradoxes.
What do all these have to do with the thesis of the book? Well, you’ll have to read it to find out. Just don’t expect any graduate-level depth; Yanofsky is writing for the general public, not for experts. And just because he is writing about the limits of reason is not to say that he disrespects reason in any way. Here’s what he says to those who think he’s putting down logic and reason: