The Outer Limits of Reason

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A very readable and interesting book by Brooklyn College professor Noson Yanofsky. Although his page pegs him in the "Department of Computer and Information Science" there, the book shows that he's pretty good in physics, math, and logic too. Some of the chapters are based on lecture notes from a course he gives. The book's subtitle is: "What Science, Mathematics, and Logic Cannot Tell Us". You might suspect that what's upcoming is mystical handwaving, but no. Professor Yanofsky's musings are all pretty well grounded in real science, so good on him.

I don't remember why this went on my virtual to-be-read pile, but I had to wait until it came off the course reserve list at the Physics Library of the University Near Here. Someone else has a high opinion of it as well.

The book is a series of semi-independent topics, and each can be read by a bright teenager with a decent grounding in science and math. (I remember getting introduced to some of these ideas as a seventh-grader by the 1946 book, One Two Three … Infinity by George Gamow.) It is (therefore) somewhat of a hodgepodge, but a very entertaining one, romping through a host of counter-intuitive, paradoxical, mind-boggling areas. A random sampling: the two-slit interference experiment; the Monty Hall problem; the Travelling Salesman problem; the Halting problem; Gödel's Proof; Cantor's different types of infinity; Russel's Set Paradox.

And more, much more. I kept imagining that Yanofsky might be the type of guy who would punctuate each amazing revelation with a wide-eyed challenge to the reader: "Did I just blow your mind?"

Then on page 175, I see: "There are ideas and concepts here that are counterintuitive and will blow your mind!" Yeah, he probably is that type of guy.

I was slightly disappointed to not see any discussion of my late friend Ken Appel's proof of the Four-Color Theorem, which (at the time) was only achievable through a considerable number of computerized operations, unachievable by a human mind in finite time. Is that cheating?

Also absent (unless I missed it) is my standard sophomore dorm-room topic: what cosmic truths are beyond the reach of humans because we're simply not smart enough to see them? Dogs are pretty smart, but there's never been one that could solve even the simplest quadratic equation. What are the limits to our intelligence, and how could we tell if we were bumping up against them? Could we tell if we were bumping up against them? (Can a dog "get" the fact that mathematics is out of his intellectual ballpark?)


Last Modified 2024-01-27 5:36 AM EDT