Customer Reviews

Mystery Of The Aleph: Mathematics, The Kabbalah, And The Human Mind

5 star:		(20)
4 star:		(12)
3 star:		(7)
2 star:		(6)
1 star:		(6)

 

 

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.

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.

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.

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.

This book was, for me, a fascinating introduction, both to the theory of infinite sets and to the remarkable tradition of Jewish mysticism. With my limited mathematical training, I knew I was in over my head before I started the book. Nevertheless, the author shows that those ancient Kabbalists were really on to something.

Aczel writes in a way that is utterly profound, expounding on the mysteries of the maker of all infinity, the Blessed Ein Sof (the true essence of which can never be known to humans), at the same time delving into the mysteries of transfinite theory, and its creator, Georg Cantor, who went mad trying to concieve of that which can never be fully understood. Of all of the books that I have read, this is by far one of the most profound. You don't have to a Kabbalist or lover of mathematics to enjoy this book, Aczel writes in a way that makes the macrocosm of infinity easily understandable by the avearge reader. However, love of Kabbalah and math is a plus in understanding the profundity of the message the book conveys.

Aczel has gotten a lot of press, so I read two of his books to evaluate whether to recommend them to my students. I do not recommend his work to anyone. His topics are interesting and important, but his treatment is very disappointing. Light and fluffy writing can help ease laypeople into reading science, if it is organized and accurate. Aczel's is not. He wanders among ideas without developing them in enough depth to appreciate. He poses interesting questions as if he intends to answer them, but does not.

Read Simon Singh or Timothy Ferris instead. Just as easy to read, and far more coherent and satisfying.

This delightful little book is a Cook's Tour of some very important personalities in mathematics and their work on the concept of Infinity (actually various magnitudes of infinities, I guess), the Continuum Hypothesis, and the Axiom of Choice. While the author takes us back to the ancient Pythagoreans and their determination to keep irrational numbers secret knowledge, the story really centers around Georg Cantor and his struggles in founding the study of mathematics in this field. Cantor was a mystic as well and there is also more than one appearance of the Kabbalah.

Certainly, you can't learn the subject from this book. However, like visiting some vast architectural wonder that you can only take in as a big view, this book places lots of Post It notes on important points if you want to begin reading more deeply about these profound ideas. And if you don't, it is certainly a fund way to spend a few hours.

The author provides four pages of references for further reading, but if, like me, you don't know the field you will likely have to do preliminary studies to just get to the foothills of really taking on the subjects studied in this book. If you already understand the math then this book is likely too light for you unless you somehow missed out on the history of your field.

I enjoyed the book and if you are interested in how serious thinkers learned to think about Infinity and what it actually means, then this book is a fine initial guide.

I really expected to like this book. God, infinity, Kabbalah -- how could you _miss_?

It was okay, I guess.

So what happened? Well, frankly, although the biographical information on Georg Cantor and Kurt Goedel is pretty good and the mathematical history is reliable, there's no real meat in the discussions of either infinity or the Kabbalah. Every time I thought Aczel was really going to get rolling and make a profound connection, he sort of petered out and changed the subject.

It's too bad, because Aczel really does have an important point lurking in here: the mathematics of infinity really does provide a window into the Ein Sof, and there probably is a connection (both historical and deeper) between the Kabbalistic and the Cantorian uses of the Hebrew letter alef. I'd have enjoyed some more thorough exposition, even at an elementary level, of both sides of this equation.

But for that, the reader will have to look (for infinity) to Rudy Rucker's _Infinity and the Mind_ or (slightly more elementary) Eli Maor's _To Infinity and Beyond_, or (for the rest) to any of numerous sources on Kabbalah. This book is only about a quarter-inch deep.

On the plus side, though, I will say that this isn't a bad book for somebody who has never encountered the subject(s) before. Just don't expect a lot of specificity; Aczel usually doesn't offer much more than vague allusions.

Aczel has a way of making the most mundane really interesting. He wrote one of the best non-fiction books I have ever read in Fermat's Last Theorem. With this book, he continues his combination of a math book with the movement, clarity, and pace of a novel. The unfortunate part about this book is that no matter how good Aczel tries, the subject of infinity is not as interesting.

This is a chronicle with some mathematicians' obsession with, and the history of, the concept of infinity. First, he goes into the ancient origins of infinity, from Pythagoras to the discovery of irrational numbers, to the Jewish sect that dealt with infinity. Then he explains Galileo, Bolzano, and others' perspectives and expansion of infinity, including set theory.

The most important part deals with George Cantor, a man who expanded upon, and ultimately went insane trying to figure out infinity. He details his steps towards madness, and his views on set theory, it's axioms, and the concept of order of infinity.

Unfortunately, though told brilliantly told, doesn't capture the interest that Fermat's Last Theorem elicited. The concept of infinity, and it's order, is not that interesting a subject, as it lacks a practical purpose, and is not a problem that many have dealt with, educational or otherwise.

Overall though, it's a very good book, and I highly recommend it.