Sunday 18 November 2011

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Graphic, above:  The set of all numbers, real and imaginary

JOHN BATCHELOR SHOW

Sunday  905PM Eastern (605P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 1 of 4

The insides of this book are as clever and compelling as the subtitle on the cover. Havil, a retired former master at Winchester College in England, where he taught math for decades, takes readers on a history of irrational numbers--numbers, like v2 or p, whose decimal expansion 'is neither finite nor recurring.' We start in ancient Greece with Pythagoras, whose thinking most likely helped to set the path toward the discovery of irrational numbers, and continue to the present day, pausing to ponder such questions as, 'Is the decimal expansion of an irrational number random?'

(Anna Kuchment Scientific American )

Sunday 920PM Eastern (620P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 2 of 4

Sunday 935PM Eastern (635P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 3 of 4

From its lively introduction straight through to a rousing finish this is a book which can be browsed for its collection of interesting facts or studied carefully by anyone with an interest in numbers and their history. . . . This is a wonderful book which should appeal to a broad audience. Its level of difficulty ranges nicely from ideas accessible to high school students to some very deep mathematics. Highly recommended

(Richard Wilders MAA Reviews )

Sunday 950PM Eastern (650P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 4 of 4

(Painting below)  The task of defining a number like pi is not as easy as it might seem, for as it was eventually proved, the ratio between the diameter and circumference of any circle is a number which is very close to the fraction 22/7 (in fact, this is a value which was very often attributed to pi in these early years), but which, as it turns out, is absolutely inexpressible by way of fraction or decimal. Most people are aware that the value of pi equals roughly 3.14, but the number doesn't end here; it continues on, without repetition, to infinity. This is what is meant by "irrational."

 

Sunday 1005PM EDT (705P Pacific): A Universe from Nothing: Why There Is Something Rather than Nothing by Lawrence M. Krauss and Richard Dawkins; 1 of 2

Theoretical physicist Krauss, author of several books about physics, including The Physics of Star Trek (1995), admits up front that he is not “sympathetic to the conviction that creation requires a creator.” The book isn’t exclusively an argument against divine creation, or intelligent design, but, rather, an exploration of a tantalizing question: How and why can something—the universe in which we live, for example—spring from nothing? It’s an evolutionary story, really, taking us back to the Big Bang and showing how the universe developed over billions of years into its present form. Sure to be controversial, for Krauss does not shy away from the atheistic implications of a scientifically explainable universe, the book is full of big ideas explained in simple, precise terms, making it accessible to all comers, from career physicists to the lay reader whose knowledge of the field begins and ends with a formula few understand, E=mc². --David Pitt

Sunday 1020PM EDT (720P Pacific): A Universe from Nothing: Why There Is Something Rather than Nothing by Lawrence M. Krauss and Richard Dawkins; 2 of 2

 

"With characteristic wit, eloquence and clarity Lawrence Krauss gives a wonderfully illuminating account of how science deals with one of the biggest questions of all: how the universe's existence could arise from nothing. It is a question that philosophy and theology get themselves into muddle over, but that science can offer real answers to, as Krauss's lucid explanation shows. Here is the triumph of physics over metaphysics, reason and enquiry over obfuscation and myth, made plain for all to see: Krauss gives us a treat as well as an education in fascinating style."--A. C. Grayling, author of The Good Book

Sunday 1035PM EDT (735P Pacific): The Book of Universes: Exploring the Limits of the Cosmos by John D. Barrow; 1 of 2

Einstein’s theory of general relativity opens the door for the study of other possible universes—and weird universes at that. The Book of Universes gives us a stunning tour of these potential universes, introducing us to the brilliant physicists and mathematicians who first revealed these startling possibilities. John D. Barrow then explains the latest insights that physics and astronomy have to offer about our own universe, showing how they lead to the concept of the “multiverse”—the universe of all possible universes. 112 illustrations

Sunday 1050PM EDT (750P Pacific): The Book of Universes: Exploring the Limits of the Cosmos by John D. Barrow; 2 of 2

 

Sunday 1105PM EDT (805P Pacific): Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose; 1 of 4

 

Dark matter was postulated by Fritz Zwicky in 1934 to account for evidence of "missing mass" in the orbital velocities of galaxies in clusters. Subsequently, other observations have indicated the presence of dark matter in the universe; these observations include the rotational speeds of galaxies, gravitational lensing of background objects by galaxy clusters such as the Bullet Cluster, and the temperature distribution of hot gas in galaxies and clusters of galaxies.

Sunday 1120PM EDT (820P Pacific): Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose; 2 of 4

Sunday 1135PM EDT (835P Pacific): Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose; 3 of 4

Sunday 1150PM EDT (850P Pacific): Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose; 4 of 4

 

Sunday/Mon 1205AM EDT (905 Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 1 of 4

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them.

Sunday/Mon 1220AM EDT (920 Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 2 of 4

Sunday/Mon 1235AM EDT (935P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 3 of 4

Sunday/Mon 1250AM EDT (950P Pacific): The Irrationals: A Story of the Numbers You Can't Count On by Julian Havil; 4 of 4

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