» Why Beauty Is Truth: A History of Symmetry

Why Beauty Is Truth: A History of Symmetry Reviews

Customer Rating:
Summary: Nice Overview
Comment: Professor Stewart is to be commended for a nice "walking tour" (to quote another reviewer) of mathematic history. He makes the topic accessible for the non-mathematician, and combined with an obvious passion for the topic maintains the reader's attention. The book starts off well, but stumbles here and there before Prof Steward hits his stride in the 18th and 19th centuries. His account of this period is fascinating and well-written. When he arrived at quantum theory, however, I believe Prof Stewart could have been a little more even-handed about the prospects of string theory.
I would not pretend to have the grasp of mathematics and physics of Prof Stewart, but I have read Greene's elegant universe books (bought the DVDs--excellent production, even if over-hyped) and other works extolling string theory. Most of these works are for a non-math person with interest in the sciences, and almost all of the books I've read provide history/background on "how we got here". Just about all of the authors (Prof Stewart included) observe how some theorists of the past clung to an idea without a proof or experiential evidence to support their hypothesis, but that's exactly what many advocates of string theory are doing today. If they're right, good for them, if they're wrong, in a hundred years someone will write a book wondering how in the world anyone could have bought into such ideas based on so little evidence! Sincerely, I admire the passion of these incredibly bright folks, but when one writes a book and softly criticizes a dead person for clinging to an idea without evidence, and then does the same thing on a different topic/different time---I'm suggesting only a little more perspective.
This was a fun read and recommended for anyone wanting a nice diversion into the field of mathematics, with a smidgen of physics thrown in for good measure.
One last thing: given the format, the illustrations for this book are top-drawer and accessible---a great aid to those of us non-mathematician types.

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Customer Rating:
Summary: Nearly gets the balance of history and math right
Comment: This book tries to pull off a difficult trick: being both a history of mathematics and mathematicians, and also a primer on group theory and symmetry. Glossing over the real technical details, Stewart does a good job explaining the math, but a good deal of it still went over my head--although he tries to keep things simple, he expects you to actually *remember* some key parts of high-school math.

Math sections alternate with passages about the lives of the discoverers of various theoretical advances. As much as the math gets simplified, so does the history. Facts, people, and context go whipping by at points, reducing some important information down to single lonely sentences.

And amazingly, for a book titled "Why Beauty is Truth", there's no single clear definition of what (mathematical) "beauty" is. There are plenty of references to "elegant" equations, or even beautiful ones, but no statement about why mathematicians might find them so, even though I think such a definition is quite simple. David Gelernter's wonderful definition from Machine Beauty would be ideal: "simplicity plus power equals beauty." That is, an equation which is simpler, and which gives useful leverage or has predictive abilities, is elegant and beautiful. A long equation tailored to a specific problem is merely functional.

The most compelling idea in the book, which appears a few times, is that the structure of mathematics is not merely an analogy or functional metaphor for "the real world" but is an actual, literal description of it and can even make testable predictions about it. The terrific book Strange Matters: Undiscovered Ideas at the Frontiers of Space and Time looks at that predictive power in more depth, specifically in the field of cosmology.

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Customer Rating:
Summary: You can't trisect an angle with a compass and straightedge
Comment: Why Beauty Is Truth: A History of Symmetry
S. Marsh statement "you can trisect an angle" is not true in its historical context.

Historical context: It is not possible to trisect all angles using only a compass and a straightedge (unmarked ruler).

In his book, Stewart says that it is possible to compute values to great precision,(which includes using iteration) but not by compass and ruler. He does mention that it is possible to trisect some angles, specifically mentioning 180 which trisects to 60 which can be constructed by making a regular hexagon. But trisecting 60 degrees by compass and ruler to produce 20 degrees is impossible, Note that 20 is the exact value of a trisected 60 degree angle but you cannot construct that angle, with a straightedge and compass.

As Stewart makes clear in this book, the important thing is not that you can't, but why you can't. And the why leads to group theory and other advances.

I found this book to be extremely interesting. Group theory is new to me. I found this book is an introduction as to why it was important to Einstein and to modern physics.

I recommend this book.

I found the following on-line tutorial on Galois theory useful:
http://nrich.maths.org/public/viewer.php?obj_id=1422

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Customer Rating:
Summary: I liked it, but, you can trisect an angle
Comment: Not only can Achilles catch a tortise, he can also trisect an angle.

It just takes infinite iterations.

As iterations -> infinity, angle -> trisection

I figured it out in eighth grade, and later was glad to see that the theory of limits wasn't something I'd made up.

But for a book that is a combination of light history and fun explorations, it makes for a good holiday read.

Other than repeating the old saw that you can't tri-sect an angle one too many times.

You just have to be very patient. ;)

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Customer Rating:
Summary: let's judge this book by its cover!
Comment: It would take most people just a few milliseconds to recognize that the butterfly on the book's cover is asymmetric. Indeed, the claim that nature is symmetric, made in this book (and so often elsewhere - e.g., by Weyl) is manifestly false. (BTW: check the dimensions of Leonardo's so-called Vitruvian Man to discover - perhaps - the real Da Vinci code!) The apotheosis of symmetry is to be found in the architecture of Albert Speer. The apotheosis of asymmetry is to be found in the architecture of the universe -- or,just as well, in any of those extraordinary formations photographed by the Hubble telescope.

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