Words and Numbers

I've picked up American Psycho again, and this time intend to finish it. The story concerns a man, Patrick Bateman, with a double life of super-rich super-shallow businessman, and sadistic serial sex-killer - or someone who fantasises that he is.

The technique of the novel is to alternate between painfully long scenes of yuppie banality, and revolting (but detatched) scenes of brutal torture and murder, both becoming more intense and surreal as the story progresses and Bateman slides further into insanity and delusion.

The reader has no way of knowing which episodes (if any) are real, except that some are implausible (eg. a TV documentary about a boy who fell in love with a box of soap powder), some are impossible (a park bench following the killer home), and some make better sense as "slips" in a fantasy (the cleaning women never notices the bloodstains on the carpet, and it's unclear how Bateman disposes of the corpses).

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I only mention it because I can't remember the last time I finished a novel.

In my 20s I read 10 pages of Finnigans Wake, 30 pages of The Satanic Verses, and three quarters of Dune. In my teens I read everything I could find by James Baldwin, Samuel Beckett and William Burroughs, and in childhood it was the fantasy of Piers Anthony, Alan Dean Foster and David Eddings. At around 30 I read most of John Le Carre's spy stories, so one of those might be the last fiction book I completed.

Aside from short stories by JG Ballard and Philip K Dick, it's mainly been books by British philosophers of the Empiricist school, articles by Stephen Jay Gould, Noam Chomsky, Geroge Orwell and a dozen trotskyist thinkers, plus textbooks on music theory, the sciences and linguistics.

Actually, I do remember the last novel I read - "Winter Frost", a police procedural by RD Wingfield.

So I've no idea whether to call myself well-read or not.

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I found a fascinating article (well I think it is) on Wikipedia about why "0.999~" (zero, point, and then an infinite number of nines) equals "1". 0.999~ doesn't just very very nearly equal 1 for practical purposes, it doesn't eventually get to 1 when the final 9 is reached, it actually is exactly equal to 1.

I've been bothered by infinity and infinitessimals for years, but now I think I'm a bit less confused about them. We say the row of nines "terminates at infinity", as though infinity were an unimaginably huge but finite number, and there were some immensely distant final 9 at the infinity-th digit. But what it means is, the row does not terminate - it is in-finite, that is, not finite, or, without a final digit, without end.

But the row of 9s can be summed - though it would take an infinite amount of time to do so manually. And at the end of this endless process, the sum has converged to 1, but only because the process is endless. And this paragraph shows just how misleading it is to talk about mathematics in ordinary language, because if read literally, it's utter gibberish.

However, it doesn't come out as gibberish to put it another way. 0.999~ isn't a process of summation at all - it's an unchanging value, as is 1.000~ and 3.000~. 0.999~ has an infinite number of nines, and 3.000~ has an infinite number of zeros, both of which would take an infinite amount of time to add up if you tried. But you've go no difficulty in accepting that 3.000~ is a value not a process, and it's just a quirk of human cognition that 0.999~ "feels" like you don't get to the complete value until you've read the final digit - even when there isn't one.

So, if 0.999~ equals 1, what does 0.333~ equal? Not 0.333~4, because that's to fall back into the notion that there's a final digit at infinity, in this case with another one after it. Not 0.4, because that would make 0.333~ greater than 0.334.

The answer is that 0.999~ and 1 are two different ways of writing the same value, but there's only one way of writing 0.333~ as a decimal.

Incidentally, 0.333~ multiplied by 3 equals 0.999~, which equals one. In other words, one third, multiplied by three, equals one. Neat, isn't it?

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Right. My good intentions to get a good night's sleep at night resulted in a half hour doze at midnight, an hour of insomnia, and five hours wide awake in front of the computer. So it looks like I'll go to sleep in late morning again.

Good morning.