Sunday, January 30, 2011

The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind


Author: Amir Aczel
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind
New York: Basic Books, 2000.

Amazon.com Book Review
by Gregory McNamee



"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 George 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 at 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."

One and Many


Title: The One and The Many

Author: Richard Hooker



"All human cultures in some way have to deal with accounting for the myriad of objects and phenomena surrounding them. We live in a world of infinite objects that are constantly changing, yet even in this imposing world of objects and change, there seems to be an underlying unity and stability.

For instance, every human being begins as an infant and then grows into an adult. Every adult is a different object than they were as an infant -- in fact, they are unrecognizable as being the same object. Yet we recognize that they are the same object, that something has remained the same even though the infant has changed into an object that is nowhere close to its original state.

Likewise a corpse is nothing like the original living human being, but we still recognize that something has remained constant.

We can see the same stability and constancy even across objects. While the world is full of trees, there is still some constancy and stability to "treeness" which never seems to change.

This observation of the world of phenomena leads many cultures to believe that the infinity of things and their changes can ultimately be related back to a single object, material, or idea. The problem of finding the one thing that lies behind all things in the universe is called the problem of the one and the many.

Basically stated, the problem of the one and the many begins from the assumption that the universe is one thing. Because it is one thing, there must be one, unifying aspect behind everything. This aspect could be material, such as water, or air, or atoms. It could be an idea, such as a number or "mind." It could be divine, such as the Christian concept of God or the Chinese concept of Shang-ti, the "Lord on High."

The problem, of course, is figuring out what that one, unifying idea is.

Philosophy in the Western world begins with this question; the earliest Greek philosophers mainly concerned themselves with this question.

As a result, the problem of the one and the many still dominates Western concepts of the universe, including modern physics, which has set for itself the goal of finding the theory that will "unify" (unify means "make into one thing") the laws of physics.

In China, the one thing that unifies the universe is the tai chi, or Great Ultimate. The Great Ultimate is divided into two opposite forces (yang and yin) and five material agents. Beyond this, the Great Ultimate is undefined. In Taoism, the "way" or Tao contitutes this Great Ultimate; it is equally undefined."