I think one of the things they mean is: Motives matter. The way that one reaches a conclusion has an importance all its own.

There is another way that a clock gone awry exemplifies an aspect of human behavior. Yesterday, I spoke with someone—I'll call this person "J."—who told me that everyone who held a certain belief—one near to my own heart—was "off." Not entirely crazy, J. said, but "off."

As J. spoke, I looked beyond to the clock on the wall of the diner where we sat, with its neon sign reading, "TIME TO EAT". It made me think of Lewis Carroll's brainteaser about which is more accurate—a stopped clock, or a clock that loses a minute every day. The answer is the stopped clock; the other one is right only once every two years.

I thought about what it meant to be "off" compared to J. If J. were set to the right time, and I were off by just one minute, such a seemingly small difference would gradually pull us farther and farther apart.

It wasn't until the next day, when I reread Carroll's brainteaser, that I realized just how much it chimed true. Perhaps I'm reading too much into it, but it strikes me as a painfully brilliant satire of all manner of apologetics:

THE TWO CLOCKS

WHICH is better, a clock that is right only once a year, or a clock that is right twice every day? `The latter,' you reply, `unquestionably.' Very good, now attend.

I have two clocks: one doesn't go at all, and the other loses a minute a day: which would you prefer? `The losing one,' you answer, `without a doubt.' Now observe: the one which loses a minute a day has to lose twelve hours, or seven hundred and twenty minutes before it is right again, consequently it is only right once in two years, whereas the other is evidently right as often as the time it points to comes round, which happens twice a day.

So you've contradicted yourself once.

'Ah, but,' you say, `what's the use of its being right twice a day, if I ca'n't tell when the time comes?'

Why, suppose the clock points to eight o'clock, don't you see that the clock is right at eight o'clock? Consequently, when eight o'clock comes round your clock is right.

`Yes, I see that,' you reply.

Very good, then you've contradicted yourself twice: now get out of the difficulty as best you can, and don't contradict yourself again if you can help it.

You might go on to ask, 'How am I to know when eight o'clock does come? My clock will not tell me.' Be patient: you know that when eight o'clock comes your clock is right, very good; then your rule is this: keep your eye fixed on your clock, and the very moment it is right it will be eight o'clock. 'But—,' you say. There, that'll do; the more you argue the farther you get from the point, so it will be as well to stop.