The conclusion falls a bit flat, but Livio’s trip through mathematical history is thoroughly enjoyable and requires no...


Why does math describe reality so well? A scientist offers tentative answers.

Livio (The Equation that Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry, 2005, etc.), an astrophysicist at the Hubble Space Telescope Science Institute, frames his investigation with a history of math, beginning with the key question: Are mathematical truths discovered or invented? Pythagoras came down firmly on the side of discovery. His argument convinced Plato, and thus almost every ancient philosopher of note. The default assumption throughout most of history was that numbers, geometric figures and other mathematical truths are real. Galileo was the first to argue that scientific truth was necessarily expressed in mathematical terms. Newton’s highly accurate calculations of the gravitational force drove the point home, implying that math and physical reality were two sides of the same coin. Even probability and statistics, which seem fuzzier than the hard equations of physics, give useful answers in the world of quantum interactions. But then math began to explore realms of thought that had no obvious relation to the world as we experience it: non-Euclidean geometry, or the paradoxes of set theory and symbolic logic. The idea that math was a game invented by mathematicians rather than something inherent in reality became fashionable, perhaps even inescapable. Also, it became clear that certain undeniably useful scientific disciplines—Darwinian evolution, to name one salient example—resisted mathematical treatment. Even so, Livio shows that correspondences between mathematical discoveries and physical phenomena continued to crop up, often in abstract mathematics created without any idea of practical applications, such as Einstein’s use of non-Euclidean geometry. Knot topology, devised to explain a long-discredited model of the atom, turned out to have application to string theory. The author gives no final answer to the central question of math’s relationship to reality. There are physical phenomena that are modeled by math, he asserts, but we also understand reality with a brain wired to find mathematical relations all around it.

The conclusion falls a bit flat, but Livio’s trip through mathematical history is thoroughly enjoyable and requires no special training to follow it.

Pub Date: Jan. 6, 2009

ISBN: 978-0-7432-9405-8

Page Count: 320

Publisher: Simon & Schuster

Review Posted Online: May 20, 2010

Kirkus Reviews Issue: Nov. 1, 2008

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Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis...



Privately published by Strunk of Cornell in 1918 and revised by his student E. B. White in 1959, that "little book" is back again with more White updatings.

Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis (whoops — "A bankrupt expression") a unique guide (which means "without like or equal").

Pub Date: May 15, 1972

ISBN: 0205632645

Page Count: 105

Publisher: Macmillan

Review Posted Online: Oct. 28, 2011

Kirkus Reviews Issue: May 1, 1972

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Noted jazz and pop record producer Thiele offers a chatty autobiography. Aided by record-business colleague Golden, Thiele traces his career from his start as a ``pubescent, novice jazz record producer'' in the 1940s through the '50s, when he headed Coral, Dot, and Roulette Records, and the '60s, when he worked for ABC and ran the famous Impulse! jazz label. At Coral, Thiele championed the work of ``hillbilly'' singer Buddy Holly, although the only sessions he produced with Holly were marred by saccharine strings. The producer specialized in more mainstream popsters like the irrepressibly perky Teresa Brewer (who later became his fourth wife) and the bubble-machine muzak-meister Lawrence Welk. At Dot, Thiele was instrumental in recording Jack Kerouac's famous beat- generation ramblings to jazz accompaniment (recordings that Dot's president found ``pornographic''), while also overseeing a steady stream of pop hits. He then moved to the Mafia-controlled Roulette label, where he observed the ``silk-suited, pinky-ringed'' entourage who frequented the label's offices. Incredibly, however, Thiele remembers the famously hard-nosed Morris Levy, who ran the label and was eventually convicted of extortion, as ``one of the kindest, most warm-hearted, and classiest music men I have ever known.'' At ABC/Impulse!, Thiele oversaw the classic recordings of John Coltrane, although he is the first to admit that Coltrane essentially produced his own sessions. Like many producers of the day, Thiele participated in the ownership of publishing rights to some of the songs he recorded; he makes no apology for this practice, which he calls ``entirely appropriate and without any ethical conflicts.'' A pleasant, if not exactly riveting, memoir that will be of most interest to those with a thirst for cocktail-hour stories of the record biz. (25 halftones, not seen)

Pub Date: May 1, 1995

ISBN: 0-19-508629-4

Page Count: 224

Publisher: Oxford Univ.

Review Posted Online: May 20, 2010

Kirkus Reviews Issue: March 1, 1995

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