Queue (queue) wrote,

Infinity and the Mind

Rudy Rucker was mentioned in a meeting at work last week. It was also mentioned that my bosses know him, seeing as they published his book Infinity and the Mind. That title seemed familiar to me. I checked when I got home, and, lo, it was indeed the book that hrafn got me years ago that I never read. After pulling it off of the shelf, I set it on the table (I'm noticing lots of typos, which is understandable since it's almost 3 fucking o'clock in the morning and I'm still up, so all you Queue-Point types should pay attention). Tonight after dinner, I happened to mention in conversation a discussion I had with a college professor who was teaching a statistics and probability course that I was taking. This discussion had to do with his assertion that it was impossible for something to be exactly two inches long and my refusal to accept that assertion. Part of that discussion had to do with the claim that infinitely many zeros could actually add up to something. Anyway, I made a comment that maybe I should go home and read Infinity and the Mind to get some insight into this question. So when I got home, I started reading the book (after a phone conversation). I got sucked into reading the whole first chapter. It's a really interesting book, and absolutely accessible to lots of people, with no complicated numbers or calculations whatsoever. This is all a roundabout way (and I could make it more roundabout, since I remembered exactly how the conversation got around to me talking about my college class) of posing the following query. Let me just quote from the book (each chapter ends with some questions, and the answers are at the back of the book. What follows is the last question from the first chapter, followed by its answer).

Here is an example of an infinite regress. Suppose that some person wishes to prepare a text in which every appearance of the letters "man" is replaced by the letters "woman." If this is rigidly adhered to, then "man and woman" becomes "woman and wowoman," then "wowoman and wowowoman," and so on. What do you reach in the limit?
Full equality: "wowowowowo . . . and wowowowowo . . . ," with an infinite number of wo's in each case.
I understand the bit about how the number of wo's is going to be equal in each of them, how one more than infinity is really the same thing as infinity. What I don't understand is what the fuck happened to the man at the end. I mean, each instance of "man" is replaced with "woman," so it's always still there. I understand the difficulty, though. You can't say that it just appears after the last wo, since there is no last wo. Infinity is not a number that you can count to, so you will never reach the end to be able to say, "This is where we add the man." But, Jesus, it can't just disappear, can it? I mean, is it still there but we just have no way to express it? Or does it really disappear when you perform the infinite regression? And if it disappears, where the fuck does it go? This is really bothering me. Anyone have any insight?

For extra credit, rewrite my entry as if I were not only sleep-deprived but also high.

P.S. Seriously, why doesn't the LJ spellchecker recognize "blockquote" as a legitimate word? Every fucking time I quote something, it complains about that.
Tags: books, infinity, mathematics, reading
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