Beyond Reason: Eight Great Problems That Reveal the Limits of Science
Dewdney mixes layman's prose with mathematical abstractions, and the resulting book is like a girl who won't say yes or no. She's just interesting enough to make the frustration feel worth it at least for a while. I'm not a mathematical wizard. While I scored very highly in reading comprehension and language skills on the ACT, my math scores barely passed the threshold of acceptability think of an airplane chipping its undercarriage on the peak of a mountain.
I passed high school algebra and geometry with tears and travail, and never wanted to know anything about calculus or trigonometry beyond how to spell them. Dewdney makes me wish I'd worked harder at it. Not only because I might have a shot at fully grasping the nature of the problems he presents, but also because he's opened my eyes to the importance of mathematics in understanding our universe.
As he writes on page 2, "We still have to account for the amazing success of mathematics as a description of physical reality. The precision of so many theories of physical reality may hint at a deeper truth, that mathematics is a major structural foundation of our universe. Since we're on the topic of structure, the book is divided into two halves. Part One deals with the mathematical realities that tell us we will never 1 build a perpetual motion machine, 2 surpass the speed of light, 3 predict the behavior of quantum particles, or 4 predict the long-term behavior of dynamical systems e.
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Part Two deals with more abstract mathematical limits, telling us that we will never 5 square the circle, 6 prove every true mathematical theorem, 7 compute the answer to every yes or no question, or 8 compute every mathematical problem. This is the caveat hanging over the book like the Damoclean sword: will it still be relevant a century or two from now, or will we have uncovered deeper and broader mathematics that will reveal the key to passing through these barriers? I found the book's main fascination in the concept that mathematics describe the boundaries of the universe.
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In other words, the history of mathematical discovery has been like a man in an empty space slowly lighting candles to explore his surroundings. That is, until he lights a candle that reveals a doorless wall. Then he finds another, and another, and yet another. He realizes there is a profound structure surrounding him, but he can't see what the structure is.
As for what lies beyond the structure In summary, Beyond Reason is a tough slog unless you're mathematically sharp.
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However, it has given me a glimpse however unsatisfactory my vision of the boundaries on our existence, which is like getting to touch God's fingerprints. That alone is the worth the furrows left from scratching my head. September 27, - Published on Amazon. Dewdney's book is very interesting, challenging, and is, admittedly, a tough read. You might need ready access to Google to look up some of the terms he uses. But for the most part, anyone who took high school math and physics should be able to understand it.
I'd recommend it to college and graduate students, and math and physics instructors. It has its down points, but on the whole is a very intriguing look at some of the problems afflicting all our logic. October 15, - Published on Amazon.
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I have only glanced inside this book searching to see if there is a proper treatment of relativity. I was glad to see that no mention of relativistic mass is made, kudos for that. However, a few other sentences caught my eye.
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Ok, I have made simple math errors before though not after being reviewed by a publisher and the likes of M. Gardner et.
On page 56 it is said that for a particle at rest the inside of the square root is zero within the dilation factor when it must be one. Hopefully I was "lucky" and just happened to catch the only two glaring errors but it makes me wonder who proof reads such works.
Dewdney, A.K. 1941–
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