Reviews for Using and Understanding Mathematics 2001 A Quantitative Reasoning Approach

The average rating for Using and Understanding Mathematics 2001 A Quantitative Reasoning Approach based on 2 reviews is 3.5 stars.

Review # 1 was written on 2014-09-29 00:00:00 John Jolley Over fifty of my Goodreads friends have read Wittgenstein's Tractatus, a book which famously sets out to describe the limits of human understanding. None of them have read Weyl's Philosophy of Mathematics and Natural Science, which was written by another German-speaking author a few years later, with a related plan in mind. For the first chapter or so, I wondered why. The reason, alas, soon becomes all too apparent; Weyl's book is much more challenging. Wittgenstein does everything from first principles (notoriously, the book does not contain a single reference). If you have no background at all in formal philosophy, it is admittedly a bit hard to understand what on earth it's about. But as long as you possess a nodding acquaintance with logic and denotational semantics, the greater part of it is reasonably straightforward. It promises a great deal, but, as the author himself admitted later in his career, delivers surprisingly little. All the same, it does what it sets out to do in a pleasingly poetic way which give an impression of Delphic wisdom, and as such it has acquired a stable fan club which it will probably keep for at least for the next century. The nice thing about reading Wittgenstein - I admit it: I am one of those fans - is that it makes you feel that you, too, might be a great philosopher if only you could get your act together a tiny bit more. It's just a question of asking a few searching questions (what would it mean to say that it was two o'clock on the Sun?) and coming up with a striking metaphor or two (that ladder...) Weyl, alas, has the opposite effect. Dismayingly, he isn't even a member of the Philosopher's Union; when he presents his ID card for inspection, it says he's some kind of mathematician. Nevertheless, he turns out to have read all the classical Greek philosophers in Greek, all the medieval scholastics in Latin, and, needless to say, all the Germans. He has an intimate knowledge of Galileo, Newton, Descartes, Leibniz, Frege, Russell and more or less everyone else you can think of, all of whom he's also read in the original. The worst thing is that he doesn't even seem to be showing off; you get the impression that he moves in circles where people are simply expected to know this kind of stuff. When you complain, he gives you a puzzled look. In contrast to Wittgenstein, Weyl has specific issues to discuss. What is the nature of mathematical truth? His brief but rigorous discussion of Gödel's construction and its antecendents in self-referential paradoxes going back to the Socratics is startlingly thorough, as is his contrast of Brouwer's intuitionistic logic against Russell and Whitehead. He has an unusual but appealing approach to the relationship between symbols and objects, which he develops in terms of group theory rather than mainstream semantics. He illustrates with examples from relativity and quantum mechanics, both of which he takes for granted. He has interesting interludes on the nature of the chemical bond, the logical basis of evolution and the reason why there is an arrow of time. Modern knowledge sometimes shows he's wrong, but when he is it's generally due to facts he didn't have available; who would ever have believed in 1926 that nature might violate left/right symmetry? His guesses are generally pretty good: among other things, he calls the Big Bang and DNA correctly before there was any hard evidence for either. Looking around, I see a scattering of Nobel Prize winners, Fields medalists and similar people who hold the book in high regard. Weyl had an enormous influence on the development of twentieth century science and mathematics, but the things he did were so esoteric that it's hard to write popular books about them; the closest I've seen is Woit's Not Even Wrong, which one might briefly summarize as saying that that modern physics has screwed up by not paying enough attention to Weyl's ideas. Woit has also been largely dismissed as incomprehensible. Dammit, this book has completely bummed me out: I realize that it's in fact rather difficult to be a towering genius, and a great deal of study and hard work is evidently involved in getting there. I'm going to have to drown my sorrows. Bartender, give me a double Wittgenstein with a Feynman chaser. And keep 'em coming.

Review # 2 was written on 2016-09-17 00:00:00 Joseph Liberty One of my earliest memories is of hearing my great-grandma tell the story of how she met Frau Schrödinger at a rather wild party in Vienna in 1926. She asked her why she was carrying on with Weyl when she was, as she said herself, happily married. "Well," said Great-Grandma, "she told me that one of them had a better mind and the other one had a bigger dick, but I'd drunk so much champagne that I couldn't remember the next day who had what. And I never saw her again." I came out from under the table where I'd been hiding and asked what a couple of words meant, but was told it was past my bedtime.