Will's Reviews > God Created The Integers

God Created The Integers by Stephen Hawking
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's review
May 27, 2012

bookshelves: currently-reading, didn-t-finish

Tried to read this and threw in the towel. It's primarily a collection of the crucial mathematical writings from Euclid on. These old texts just aren't that readable.

Hawking's introductions are very interesting, and made me want to learn more about the history of math. But they're too rapid. Dim-witted readers of my ilk need to be coaxed through this stuff.

The stuff on the progression of ancient Greek mathematics is fascinating. The Pythagoreans had a philosophy wherein numbers, and relations between them, underlay all real phenomena. This theory yielded splendid results early on, with the surprising 3-4-5/Pythagorean-theorem thing being their most spectacular success. They let it go to their heads. Their theory fell apart because they couldn't find a way to express the square root of 2 in real numbers. The Babylonians had some tricks to come close: mainly, they had figured out that 7/5 was really, really close. Try it and see for yourself: 49/25 is so close 2 that it hurts! But the Pythagoreans needed to do better than that, because they had made these strong, absolute claims about reality being made up of ratios between real numbers. Attempts to derive a real solution led to contradictions, because the premise was flawed: the square root of 2 just isn't a real number. Euclid's work was an attempt to start anew after this failure.

There is also an interesting aside about Euclid. Hawking notes that the assumptions of Euclidian space -- straight, infinite lines that take up no space, and the like -- were treated for hundreds of years as literally true in the Aristotelian physics of the west. However, Euclid and the Greeks never imagined that they were literally true, because they had a cosmology where everything in the universe was spherical and contained. The post-Einstein understanding of space as curved and the universe as limited just happens to accord with the Greeks' view.

I caught tons of copy-editing errors in the short part I read. Stephen Hawking, I will copy-edit this for you! It's gonna cost, though.

This is an interesting subject and if there exists a more accessible work than this, I would love to read it. Does anybody have a recommendation?
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message 1: by OJ (new)

OJ Great review Will.

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