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The Non-Euclidean Revolution, by Richard J. Trudeau
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Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
- Sales Rank: #2304660 in Books
- Brand: Brand: Birkhäuser Boston
- Published on: 1999-05-11
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 6.25" w x .75" l, .0 pounds
- Binding: Hardcover
- 270 pages
- Used Book in Good Condition
Review
From the reviews:
"Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library."--Choice, February 1988
"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text."--Mathematical Reviews
"In The Non-Euclidean Revolution, we have a mathematically rigorous explanation of … sea change in mathematics which is at the same time suitable for any educated reader. … I have found that this book achieves my goal of bringing some serious mathematics into our honors program and Trudeau’s goal of bringing his readers through the 19th century revolution brought about by an alternative to Euclid’s geometry. … Trudeau’s book shines as a guide to that revolution." (Mark Bollman, MathDL, May, 2008)
From the Back Cover
How unique and definitive is Euclidean geometry in describing the "real" space in which we live?
Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.
Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
"Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library."--Choice (review of 1st edition)
"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text."--Mathematical Reviews
Most helpful customer reviews
5 of 12 people found the following review helpful.
Propaganda history
By Viktor Blasjo
This is on the whole a standard semi-historical text on non-Euclidan geometry. What sets this text apart from the others in this genre is Trudeau's candidness regarding conclusions and interpretation of this story. Trudeau's conclusions and interpretations are precisely those of the blue-eyed research mathematician of today, not realising that he is distorting history for the purpose of propaganda. His propaganda goal is simple: intuition is bad, formalism is good. The history of non-Euclidean geometry does not support this conclusion, so Trudeau has to fake it. He does this in the form of fictitious dialogues with a student, whose stupid "intuitions" are always set straight. For example, this alleged student has the alleged "intuition" that Playfair's axiom is necessarily true. His feeble struggle with Trudeau's iron intellect even needs to be condensed by this statement:
"Time goes by. More proofs are suggested. Trudeau, with obvious pleasure, demonstrates how each proposal turns on some assertion logically equivalent to Postulate 5. Finally the other lapses into exasperated silence." (p. 161).
The conclusion sanctioned by Trudeau is that intuition should be given up in favour of formalism. But this is complete bogus-history. The whole point of the debate concerning Postulate 5 was precisely that it was *not* intuitively obvious. Which is why Trudeau is reduced to fighting, "with obvious pleasure," a fictitious opponent. While the result was not intuitive, the nature of the formal system suggested that it could be proved. Thus *it was the formal system that fooled us,* not our intuitions about geometry. Therefore, if any lessons are to be learned from the history of non-Euclidean geometry it is the exact opposite of that sanctioned by Trudeau.
Among the many other things which Trudeau gets backwards because of his doctrinal blindness are the relation of logic to mathematics (p. 14) and why Kant was wrong (p. 250). But I do not have the patience to detail these things.
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