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Mystery Of The Aleph: Mathematics, The Kabbalah, And The Human Mind
 
 
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Mystery Of The Aleph: Mathematics, The Kabbalah, And The Human Mind [Hardcover]

Amir D. Aczel (Author)
3.7 out of 5 stars  See all reviews (51 customer reviews)

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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

From Publishers Weekly

Aczel's compact and fascinating work of mathematical popularization uses the life and work of the German mathematician Georg Cantor (1845-1918) to describe the history of infinityAof human thought about boundlessly large numbers, sequences and sets. Aczel begins with the ancient Greeks, who made infinite series a basis for famous puzzles, and Jewish medieval mystics' system of thought (Kabbalah), which used sophisticated ideas to describe the attributes of the one and infinite God. Moving to 19th-century Germany, mathematician Aczel (Fermat's Last Theorem) introduces a cast of supporting characters along with the problems on which they worked. He then brings in Cantor, whose branch of mathAcalled set theoryA"leads invariably to great paradoxes," especially when the sets in question are infinite. Are there as (infinitely) many points on a line as there are inside a square or within a cube? Bizarrely, Cantor discovered, the answer is yes. But (as he also showed) some infinities are bigger than others. To distinguish them, Cantor used the Hebrew letter aleph: the number of whole numbers is aleph-null; the number of irrational numbers, aleph-one. These "transfinite numbers" pose new problems. One, called the continuum hypothesis, vexed Cantor for the rest of his life, through a series of breakdowns and delusions: others who pursued it have also gone mad. This hypothesis turns out to be neither provable, nor disprovable, within the existing foundations of mathematics: Aczel spends his last chapters explaining why. His biographical armatures, his clean prose and his asides about Jewish mysticism keep his book reader friendly. It's a good introduction to an amazing and sometimes baffling set of problems, suited to readers interested in mathAeven, or especially, if they lack training. B&w illustrations not seen by PW. 5-city author tour; $30,000 ad/promo; 30,000 first printing.
Copyright 2000 Reed Business Information, Inc.
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First Sentence
On January 6, 1918, an emaciated and weary man died of heart failure at the Halle Nervenklinik, a university mental clinic in the German industrial city of Halle. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

51 Reviews
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3.7 out of 5 stars (51 customer reviews)
 
 
 
 
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4.0 out of 5 stars A worthwhile read...., Jun 18 2007
By 
Brad Camroux (Calgary, AB Canada) - See all my reviews
(REAL NAME)   
This review is from: The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (Paperback)
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.
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1.0 out of 5 stars Complete Nonsense, Jun 19 2004
By A Customer
This review is from: Mystery Of The Aleph: Mathematics, The Kabbalah, And The Human Mind (Hardcover)
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.
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4.0 out of 5 stars On the inifinity that comes next..., Jun 18 2004
By 
Gary C. Marfin (Sugar Land, Texas USA) - See all my reviews
(REAL NAME)   
This review is from: The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (Paperback)
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.

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