Friday, October 17, 2008

The Ten Commandments and the Well Ordering Principle

When I was a kid (and all through my life, really,) my mother would periodically tell me to:

"remember the fourth commandment, the only commandment with a promise. --Honor your father and mother, that it will go well with you."

I was reminded of this last night while reading Sarah Vowell 'The Wordy Shipmates.' There is a part in this book where she's talking about how, for the puritans, this commandment applied not just literally to your parents but also to figures of authority (governments and such.) The only thing is that she calls it the fifth commandment.

So, excited at the chance to play scholar, I went to my bible and looked it up. And, sure enough, it was the fourth. So then I went and asked around the house, and somebody had another bible, and that one had it as the fourth too. The thing is, though, that nobody's bible enumerated the commandments. You have to count them yourself. --Since they are written in verse form, without numbers. And really, I wasn't sure if I was counting them right, because it seemed to me that there were really only nine commandments.

So this morning I looked it up on the internets. According to Wikipedia, there are several different traditions depending on your denomination. It just depends on how you split up the verses. Some people say that "you shall have no other gods before me," and "you shall not make yourself a false idol" are two different commandments. Whereas other people say that "you shall not covet your neighbors possessions" and "you shall not covet your neighbors wife" are two different commandments (when I had thought there only seemed like 9 commandments I was lumping both "don't covets" together as one commandment, and also lumping "don't make a false idol" and "have no other gods before me" as one commandment.)

The tradition of splitting up the "don't covets" but keeping the "don't make false idols" and "have no other gods before me" as a single commandment seems more reasonable to me but, honestly, it probably really doesn't matter a whole lot. This is the kind of thing that people probably got killed over in the 16th century. Hard core religious people would probably still get a little too worked up over it even today.

Anyway, all this thought about ordering reminded me of one of the first theorems that one learns in elementary number theory, The Well Ordering Principle. This theorem says that any collection of non-negative integers will always have a smallest integer. Think about this for a moment and you will see that what this theorem is really saying is that any collection of non-negative integers can be listed in order, or ranked (that's why it's called the Well-Ordering Principle.)

That theorem turns out to be an important building block in number theory, but what does it have to do with the Ten Commandments? I guess the point is that the numbering of the commandments matters only if it is also a ranking. i.e. commandment #1 is more important than commandment #2, commandment #5 is less important than commandment #4, etc.

I'm actually curious to know what religious traditions, if any, do consider the enumeration of the commandments to be a ranking. Maybe I'll give my dad a call and ask if he knows.

If she were ranking them, I'm pretty sure my mother, given here druthers, would have made "honor your father and mother" a little higher.

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