[.ca] The Mystery of the Aleph: Mathematics, the Kabbalah, and ... (ISBN 0743422996)

From Amazon.co.uk:
The search for infinity, that sublime and barely comprehensible mystery, has exercised both mathematicians and theologians over many generations: Jewish mystics in particular laboured with elaborate numerological schema to imagine the pure nothingness of infinity, while scientists such as Galileo, the great astronomer, and Georg Cantor, the inventor of modern set theory (as well as a gifted Shakespeare scholar), brought their training to bear on the unimaginable infinitude of numbers and of space, seeking the key to the universe. In this sometimes technical but always accessible narrative, Amir Aczel, the author of the spirited study Fermat's Last Theorem, contemplates such matters as the Greek philosopher Zeno's several paradoxes; the curious careers of defrocked priests, (literal) mad scientists, and sober scholars whose work helped untangle some of those paradoxes; and the conundrums that modern mathematics has substituted for the puzzles of yore. To negotiate some of those enigmas requires a belief not unlike faith, Aczel hints, noting, "We may find it hard to believe that an elegant and seemingly very simple system of numbers and operations such as addition and multiplication--elements so intuitive that children learn them in school--should be fraught with holes and logical hurdles." Hard to believe, indeed. Aczel's book makes for a fine and fun exercise in brain stretching while providing a learned survey of the regions at which science and religion meet. --Gregory McNamee

Where's the beef ?:
A very wordy, but interesting book. The author intertwines the subject matter around a very well developed background, in fact a little too well developed. The main story is about the human mind's inability to contemplate infinity . The author points out that there are warnings in the Kabbalah, the Jewish book of mysticism, about peering into this aspect of mathematics. The famous mathematician Georg Cantor is credited with discovering and pioneering this area of mathematics. Mysteriously every time Cantor attempted to seriously delve into infinity theory he experienced a mental breakdown. Kurt Goebel another famous mathematician was also mentally affected by working in this area. The very basics of what they were considering was performing mathematical operations on magnitudes of infinities. Infinities of different sizes. It is a strange concept but something akin to asking, "what set has more members, a set of all the integers or the set of odd integers "? Once infinities are ordered then they may be ranked and considered eligible for mathematical operations. This is the second book I have read by Mr. Aczel. I believe the title of this book should have lead to the "meat" of the story, but the background history and the biography of Georg Cantor is given the same weight as the "mystery of the Aleph". The same was true of another book by Mr.Aczel, "God's Equation" the background material overshadowed the story. I would prefer a little more in-depth text about the heart of the matter.

On the inifinity that comes next...:
I would never have imagined that a quest this abstract could entail a story so human. Yet, that is exactly what Amir Aczel provides in this smooth tale of the many humbling encounters with the realm of infinity. There are two lessons from this compact survey on the effort expended and the toll imposed on those bold enough to go where no person can go. First, the urge to comprehend infinity is an ancient quest and inextricably tied to the effort to ascertain the nature of God. Second, getting to know infinity can be massively bad for one's mental health. Mr. Aczel manages an almost impossible task (infinity tends to do that) in this text. He is (a) attempting to survey an enormous amount of the history mathematics and, to some extent, religion, and (b) providing a glimpse into the lives of those mathematicians that have ventured into this field. At the heart of this book is Georg Cantor, founder of modern set theory. Cantor sought to transcent an intuitive understanding of infinity. He sought an ordered system; specifically he sought to prove what became known as the continuim hypothesis: basically, that the lowest order of infinity (some cardinal numbere) was followed by the cardinal number, c (thus permitting Cantor to give ordere to his transfinite numbers). Against this hypothesis stood the possibility, urged by any number of Cantor's opponents, of infininty somewhere before one reached c. The search to prove what Godel later demonstrated to be an undecidable hypothesis may well have led Cantor (and Godel for that matter) to madness. At minimum it may have activated any underlying predisposition to mental illness in both men. They were not, as Aczels's discussion of the Kabbalists shows, inifinity's first victims. Aczel has provided a balanced and very human exploration into a topic that draws its victims as a moth to the flames.

Interesting book, but not necessary:
Aczel wrote this book in layman terms and he did a good job explaining the concept of transfinite numbers. However, the association of the concept of infinity with another concept, God, is totally nonsense. (Same with the application of the Incompleteness Theorem to god.)

Complete Nonsense:
Although the book's content about mathematics is informative, its association of abstract mathematics with Judaism is completely ridiculous. The author tries hard to establish a link between the ponderings of some ancient Rabbis and Cantor's astonishing accomplishments and between some religious concepts and mathematical infinity. Please do not read this book if you are in any way serious about mathematics or science. Over and over again, the author promotes god and the Jewish religion whereas I was just interested in the exciting mathematics of the period. I consider this book propaganda for Judaism and mysticism. It is one of those instances where a religious zealot tries to cast his absurd views into science.

A worthwhile read....:
Though it's been some time since I read this book, I recall that I was (and still am) fascinated with its subject matter. The mathematics of the continuum is fascinating enough on its own, even if it may be somewhat incomprehensible to many. But when the philosophy of the continuum is brought into the picture, all kinds of interesting things happen. Another reviewer said that connections between the mathematics of the continuum and Jewish mysticism are without basis. I disagree. I feel that Mr Aczel has provided a very sound, logical basis for his statements. Additionally, if you're looking for a thorough treatment of the mathematics of the continuum, you need only look at the title of this book to realize that it will not be found within its pages. Titles with the words "Mystery" and "Kabbalah" must be given the benefit of an open mind. Any mathematician should understand that.