Poetry of the Universe: A Mathematical Exploration of the Cosmos (英語) ペーパーバック – 1996/1/15
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In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores the leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.
It is a great book on its subject and a must read, though challenging, (the unreferenced footnotes at the back of the book- which are a great addition- does not help in reading this book), the effort is well worth it.
One of the most important ideas contained in this book is on p. 192, which is a footnote to p. 104 in the main text. It is too long quote in full but the jest is:
"Taken together with other efforts throughout the 1920's, both observational and theoretical, to try to establish first the reality and second the meaning of de Sitter's 1917 prediction of a redshift-distance relation, they constitute a body of work that makes all the more mysterious the myth of Hubble's sudden discovery of the relation in 1929."
Having said that Osserman does not go where Morris Kline goes re: "Non-Euclidean Geometries and Their Significance," which is found in Kline's "Mathematics for the Nonmathematician" and "Mathematics- The Loss of Certainty," et. al., both are recommended.
From the front cover piece of "Mathematics- The Loss of Certainty ... refutes the myth that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible," regarding the significance of the development of Non-Euclidean geometries in the 1800's. "For two thousand years the entire intellectual world accepted the Greek doctrine that the axioms of Euclidean geometry and of mathematics in general, were truths about the physical world, truths so clear and so evident that no one in his (or her) right mind could question them." ("Nonmathematician" p. 452-453).
Kline also says: "Gauss had the intellectual courage to create non-Euclidean geometry but not the moral courage to face the mobs, for the scientists of the early nineteenth century lived in the shadow of Kant whose pronouncement that there could be no geometry other than Euclidean geometry ruled the intellectual world. Gauss's work on non-Euclidean geometry was found among his papers after his death." See also: Lobachevski; Bolyai and Riemann.
Finally Kline again: "The implication of non-Euclidean geometry, namely, that man may not be able to acquire truths, affects all thought." ("Nonmathematician" p. 476).
The point is, Osserman's book is a great exposition on the development non-Euclidean geometry.
John Wheeler's sentence should also be included: "Matter and energy tell space how to curve and space tells them how to move," is in a lot of books on Gravity.
During the great period of global exploration the Europeans placed rigorous demands on maps, demands that stretched the capabilities of mathematicians. Robert Osserman offers a striking parallel between that endeavor and our modern efforts to unravel the form and structure of the universe.
Osserman's description of the evolution of abstract geometries is fascinating. We learn about the remarkable contributions of the combined genius of Euler, Gauss, Lobachevsky, Bolyai, Riemann, Minkowski, and Einstein to our new understanding of cosmology. Gradually, Osserman brings us full circle from the problem of representing a spherical (or elliptical) earth on a Euclidian flat map to the more difficult problem of representing an expanding universe characterized as a hypersphere.
This is a good little book and I can recommend it to a wide audience. Osserman conveys the beauty and excitement of mathematics without delving into equations. In parallel, he provides expanded footnotes in an appendix for the mathematically inclined. I suggest reading the appendix after completing each chapter, mathematically inclined or not.
In keeping with his title, he offers pertinent, often poetic quotes in each chapter such as: Euclid alone has looked on Beauty bare. Pure mathematics is, in its way, the poetry of logical ideas. The most distinct and beautiful statement of any truth must take at last the mathematical form. (By Edna St. Vincent Millay, Albert Einstein, and Henry David Thoreau.)
I should here confess that as a math major I took a course from Professor Osserman on linear algebra about 30 years ago. His teaching style then mirrored his writing style in this book--calm, understated, confident.
Additionally, I probably never thanked him at the time for giving me a great math experience during that course. (For non-mathematicians who haven't had such an experience, let me assure you that there is exhilaration in struggling with an initially complicated mathematical idea that suddenly becomes crystal clear.)
So, belatedly, if you're reading this review, Professor, THANK YOU!
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