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The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity Paperback – September 1, 2001
"Theft by Finding: Diaries (1977-2002)" by David Sedaris
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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, labored 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 Shakespearean 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, 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 where science and religion meet. --Gregory McNamee --This text refers to an out of print or unavailable edition of this title.
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. --This text refers to an out of print or unavailable edition of this title.
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Top Customer Reviews
The book teases the reader with elements around the aleph and the kabbalah, and yet really never explores them in any detail - especially the assertion of Cantor's potentially Jewish heritage. The concepts of infinity take the reader to amazing places, and Aczel does a great job with examples - but fails to follow through when it comes to set theory and tying all the concepts together. The book slowly builds and the first 150 pages are great. The last 75 seemed hurried and disjointed as he tried to bring the elements together.
It was OK - and worth the read if only to ponder that which is infinite - and the mental challenges it invariably seems to cause. However, it's not on my top shelf.
Till I started to read this book from Amir Aczel. This is mathematics in another way. Not too much equations, formulas, integrals, etc. No, this is mathematics one may do by just sitting in a comfortable chair and playing with the thoughts bubbling up inside the brain.
This is almost about what Georg Cantor did. Besides describing many great scientist of his time, as Weierstrass, Riemann, Dedekind and others, the book describes thoroughly the life and work of Cantor. His successes and the serious problems he encountered. From what I read in the book I started really to admire Cantor. Most people would have given up with the severe opposition he faced during his life. But not Cantor, each time he went down, he stood up to fight for his ideas again.
Besides interesting mathematical topics, going back to the ancient Greeks, the book describes very well the atmosphere of the end of the nineteenth century. It also gives us an idea of life in the town of Halle in the eastern part of Germany, where Cantor lived and worked most of his life. I once had to stay a few days there. Taking the exit Halle I suddenly found myself in the middle of the nineteenth century. Rainy cobble stoned streets, apartment buildings from Cantor's time, it all was still there. That may change, lots of new roads and buildings are under construction.
The book not only describes the work done by Cantor on infinity, but it also continues with the scientists building further on the foundations laid by Cantor, as for instance, Kurt Gödel. So, the book provides the reader with a general and thorough view on all what was found, stated and developed on infinity up to the second half of the twentieth century.
Now I have read Aczel's book, do I know what infinity is? No, not really. But sometimes, when I sit in my comfortable chair, with Aczel's book close by, playing a little with this topic in my mind, I am sure I almost get it ...