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Genesis of a Historical Novel

Saturday, January 21, 2006

identity, infinity, etc.

Dang. I just lost this post after writing about three paragraphs. I zipped over to look something up on Wikipedia, and got the dreaded "fatal error" message box: Firefox had made a fatal error. I was forced to close Firefox and lose my post. I had not copied each paragraph and pasted it in Word, as I used to with Netscape because of its proneness to crashing in this way. So I am disappointed with my new browser.

I was saying something like this. I woke up with a desire to resume the chase for the meaning of identity. I believe in following my mind where it wants to go: it's good to follow your passion, moment to moment, if possible. I started by keying some material from Communitarianism and Individualism, the fourth essay entitled "Membership" by Michael Walzer (excellent, as were the previous three; the book so far is first-rate). Countries, like clubs, have admission policies: rules for admitting new members. These rules reflect the members' idea of who they are, their identity.

This got me thinking about the mathematics of set theory. I prowled the livingroom bookshelf to find Infinity and the Mind by Rudy Rucker, a worn mass-market paperback that I bought in 1984. In it he quotes a definition of set made by the main inventor of set theory, Georg Cantor:

A set is a Many which allows itself to be thought of as a One.

Hm, I thought, what is this but a description of Arthur Koestler's holon from The Ghost in the Machine? Here is an extract:

A "part" generally means something fragmentary and incomplete, which by itself would have no legitimate existence. On the other hand, a "whole" is considered as complete in itself. But "wholes" and "parts" in this absolute sense just do not exist anywhere. What we find are intermediary structures on a series of levels in an ascending order of complexity: subwholes which display, according to the way you look at them, some of the characteristics commonly attributed to wholes and some of the characteristics commonly attributed to parts.

The term I propose is "holon," from the Greek holos = whole, with the suffix on which, as in proton or neutron, suggests a particle or part.

I had fetched down The Ghost in the Machine from the coffeetable to set up a document for it in Word.

Rucker started his discussion of sets with a reference to the ancient problem of the One and the Many: Is the world fundamentally One, or Many? Is it made out of one basic thing or substance, or a plurality of these? Plato spent much of his career pondering this topic, without a conclusive result. His final writing on it was a wry observation that the topic was one that young thinkers liked to believe they had understood, and liked furthermore to talk endlessly about. Rucker himself admits he does not have the answer--only his own (very penetrating and persuasive) ideas on the topic.

I'm intrigued by set theory and what is called transfinite mathematics--the mathematics of infinity (for which set theory is the strongest mathematical toolkit). I suspect that transfinite mathematics is the mathematical branch of theology, for if the Absolute Infinite (symbolized in mathematics by uppercase omega) is in any way existent, it would have to be what we refer to as God. The study of the lesser infinities below the Absolute Infinite (and there are, well, infinitely many of those) would be a kind of theological undertaking.

But the Many and the One flagged something else: de Santillana's The Origins of Scientific Thought, in which he examines how early Greek thinking led toward what we now call science. The problem of the Many and the One was a scientific question, with responses that included the atomism of Democritus--the atomism with which we "moderns" still view the world today. For the idea of little indivisible bits of blind matter flying through the vacuum of space, interacting, was due to Democritus, hundreds of years before Christ.

This merely sketches some of my thoughts from this morning. Kimmie and I went downtown to buy fabric at the store Dressew on Hastings--a lovely old-time store, crammed with excellent things. A good time. I'm late for tea!

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