Rosalyne and I were talking about how, when reading Dawkins’s books, you don’t want to read straight through, because you keep encountering Big Ideas that you want to think about more before going on.
The Ancestor’s Tale begins with a quote from Mark Twain: “History doesn’t repeat itself, but it rhymes.” I love that. Dawkins points out once again that — after the fact — it is very easy to look at a series of events and say how amazing it is that they worked out that way. If even one little thing had been different, you can say, this would never have happened. And, if you like the outcome — say, the existence of human beings — it is easy to decide that this outcome was the goal of all those little events. Unless there was someone writing things down at the beginning of the series, though, you are just like the pool player who never called a pocket and says “I meant to do that.”
This point, while hardly new, caught my attention yet again because I had just heard a lecture on the Doctrine of Providence. This is the idea that God governs the entire universe, in all things big and small, good and evil. Whatever bad things happen, happen only because God allows them. The enormous number of bad things that do not happen, do not happen because God prevents them. This doctrine is not prevalent in mainstream Protestant churches (where we generally believe in free will), but it is firmly held in the class I attend on Tuesday nights. I try hard to be open-minded in this class. It is probably the only time during the week that I talk with people who really completely disagree with me, so I think it is good for me to try to entertain their hypotheses, as it were.
But then Dawkins went on to a less familiar notion. That is, that the universe doesn’t really have a lot of options, not because God designed it, but because it is in the nature of universes to behave in certain ways. If you believe this, he says, then you would have to suppose that pi is always going to be three and a bit in all potential universes, because that is just how circles are, and no alternative is available. It seemed to me, on reading this, that it is a long way from pi to, say, the tendency toward symmetry among living things.
Then Sighkey posted her math question: why, when you multiply negative numbers, do you get a positive result? My initial reaction was “I don’t know and I don’t care, and this is why mathematicians don’t get invited to the really fun parties.” It reminded me of imaginary numbers, which I have always found really irritating. The question grew on me, however. (Particularly since our national honor seemed to be at stake.I mean, we all accept that our educational system is seriously flawed, and that Kiwi-a-go-go-land is famous for the splendor of theirs, but still…)
In the course of the day, I asked a bunch of people. The answers mostly ranged from “Our teachers don’t tell us that” to “That’s what’s in the book,” with a very strong undercurrent of “I don’t know and I don’t care.”
Now, I was asking teachers, for the most part. That Man, being an accountant, both knows and cares, and he said, “Because you’re going backwards.” The Empress said, with an unconscious echo of Dawkins, “It has to do with the nature of negative numbers.” Chanthaboune gave such a clear answer over at Sighkey’s xanga that I may ask her to do my taxes.
But are any of these answers really why negative numbers multiply to positives? Even Chanthaboune’s answer is only a clarification of the statement that two negative numbers multiplied together produce a positive answer. It is like the time I asked a math teacher why the ratio of a circle’s circumference to its diameter was always pi, and she opened her eyes very wide and said, “Because that’s how God made it.” Which is very like saying that it is the nature of negative numbers to multiply to positives.
In his sermon on Sunday morning, our pastor said that it was exciting to learn that the greenness of leaves is caused by chlorophyll, until you find that the definition of chlorophyll is “the stuff that makes leaves green.” And it may well be that many of the things that we treat as reasons are actually just descriptions.
Many thanks to all you kind people who went and welcomed Rosalyne01 to xanga. Here is Erin. I have done another row or two of the blue, and will welcome thumbs up and thumbs down votes on leaving it in versus pulling it out and redoing with something less contrast-y. And Kali Mama has tagged me. I will respond to that as soon as I can move on mentally from the Doctrine of Providence and the nature of negative numbers.