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Title: PI in the Sky : Counting, Thinking, and Being by John D. Barrow ISBN: 0-316-08259-7 Publisher: Back Bay Books Pub. Date: 20 October, 1993 Format: Paperback Volumes: 1 List Price(USD): $19.99 |
Average Customer Rating: 3.83 (6 reviews)
Rating: 4
Summary: hey mr. wanton arborcide from iceland
Comment: doesn't the mathematical concept of greater than
come from a human mind? sure, some birds can count and distinguish between object sizes but can they creatively abstract and apply the concept to solve other physical problems?
nope. and if you think the whole book is based
on a false premise, it still has some interesting views, facts and features.
does it warrant a 1 star?
i mean you can learn from everything.
even mistakes.
i mean i learned from you just now.
Rating: 1
Summary: wanton arboricide
Comment: The author's leading claim in this book is that "the only mathematics we know is human mind and brain based mathematics." This claim can be understood in either of two ways, which the author does not distinguish from one another. On one hand, by "mathematics" he might mean the practice or family of practices that go by that name (the sort of thing that a math teacher gets paid to teach). In this sense, it is just trivial that the only mathematics we know depends on humans, just as the only civil engineering or basketball we know depends on humans. But let's be charitable, and try to construe the author's claim in a way that does not reduce it to a mere triviality. Let's suppose that by "mathematics" he means not the practice of investigating mathematical fact, but the body of fact thus investigated. But if that is what he means, then his claim is clearly false. It is clearly false, for example, that the fact that 1 is less than a million depends on humans, their minds, or their brains.
Thus, the whole book is premised on a fallacy that can be spotted by a second year philosophy major.
Rating: 4
Summary: Will There Be Pi in The Sky By and By When You Die?
Comment: Barrow, an astronomer at the University of Sussex when this book was published, provides an entertaining and informative account of the foundations and philosophy of mathematics. Do mathematicians invent or discover mathematics? What 'reality' do mathematical entities like pi have? What accounts for what physicist Eugene Wigner has called, in a now-famous paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (299)? After an interesting account of the history of counting and numbers, Barrow discusses in succeeding chapters the philosophies of formalism, inventionism, intuitionism, and platonism, a sophisticated version of which he seems to favor. Perhaps most mathematical workers follow what Alfred Korzybski called "the 'christian science' school of mathematics, which proceeds by faith and disregards entirely any problems of the epistemological foundations of its supposed `scientific' activities" (Science and Sanity 748). I commend Barrow because he considers these epistemological questions important and writes about them so engagingly. Barrow's discussions of theories and personalities provide useful background for understanding mathematical foundations. As for Barrow's conclusions, from a non-aristotelian view, the appeal of platonism seems understandable as an example of identification, the confusion of orders of abstracting. Barrow doesn't seem to consider that mathematicians may both invent and discover mathematics. He seems so taken with the effectiveness of mathematics in the natural sciences that the notion of mathematical entities existing solely as high-order abstractions in human nervous systems seems insufficient to him. As Korzybski pointed out, we live in a world of multi-dimensional, ordered structures or relations. It does not seem unreasonable, then, that we can map this world with an exact language of relations, i.e., mathematics. But as Korzybski also pointed out many times, "the map is not the territory."
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Title: The Artful Universe : The Cosmic Source of Human Creativity by John D. Barrow ISBN: 0316082422 Publisher: Back Bay Books Pub. Date: 01 September, 1996 List Price(USD): $19.99 |
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Title: Impossibility: The Limits of Science and the Science of Limits by John D. Barrow ISBN: 0195130820 Publisher: Oxford Univ Pr on Demand Pub. Date: December, 1999 List Price(USD): $18.95 |
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Title: The Book of Nothing : Vacuums, Voids, and the Latest Ideas about the Origins of the Universe by John Barrow ISBN: 0375726098 Publisher: Vintage Pub. Date: 13 August, 2002 List Price(USD): $15.00 |
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Title: The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by MARIO LIVIO ISBN: 0767908163 Publisher: Broadway Pub. Date: 23 September, 2003 List Price(USD): $14.95 |
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Title: The Constants of Nature : From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe by JOHN BARROW ISBN: 0375422218 Publisher: Pantheon Books Pub. Date: 14 January, 2003 List Price(USD): $26.00 |
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