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Customer Review

3 of 6 people found the following review helpful
3.0 out of 5 stars Pretty good, 31 Aug. 2007
This review is from: Galileo's Finger: The Ten Great Ideas of Science (Paperback)
On amazon.com this book scores very highly, with all the reviews (with the exception of one repeated review) being 4 or 5 stars. This makes me think, maybe Americans could care less about the "tone" of the prose. I mean, come on! Someone is writing about the laws of quantum mechanics, which may well be fundamental to every physical phenomenon, and all you care about is the prose?

Target audience is always a problem with popular science books and this is no exception. Not everything can be explained simply. The discussion of the interpretation of quantum mechanics is confused and confusing, but then, so is much of the relevant literature (I myself don't see what's wrong with "shut up and calculate").

The discussion of arithmetic is particularly confused, because it is never made clear (and I suspect the writer did not have it clear in his head either) exactly what is meant by "arithmetic". [In what follows I shall use the word Arithmetic to refer to common arithmetic, Peano arithmetic to refer to Peano arithmetic, and arithmetic to refer to Atkins' use of the word "arithmetic"].

Sometimes it seems like he means Arithmetic in the common sense, that is, the collection of statements about natural numbers that are true in the standard interpretation (a.k.a. number theory). But sometimes it seems like he means Peano arithmetic, which is a specific formal axiomatic system, a fragment of the former Arithmetic. These two things are not to be identified - there are number theoretical facts which are not a part of Peano arithmetic. This confusion doesn't really rear its head until the end of chapter 10, when Atkins concludes that the universe is made of arithmetic, so Godel's theorem applies to the universe, and the universe cannot prove itself consistent because arithmetic cannot prove itself consistent. If arithmetic here means Peano arithmetic, then it might make some sense. But there is no reason to think that all the mathematics that nature makes use of can be formalised in Peano arithmetic (this would exclude fairly elementary combinatorial statements, for one thing). If Atkins means by "arithmetic" the common Arithmetic, which I suspect he does, then what he wrote does not make sense. Godel's theorems do not apply to Arithmetic. In fact it is senseless to talk of the consistency of Arithmetic. One cannot define what Arithmetic is, so one cannot lay out a statement asserting the consistency of it.
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D. Thomas
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Location: England

Top Reviewer Ranking: 8,906,814