Infinity and the absurd

From your school days, do you remember Zeno’s Paradox? You learn about it, struggle through the explanations, and then dismiss it as total nonsense. Which in sense it is.

It goes like this. Achilles and the Tortoise agree to a running race. Achilles, the great warrior, magnanimously allows the poor old Tortoise a head start. Big mistake, because this now means he will never be able to pass him. For every time he reaches the place where the Tortoise was, that creature, slow as he may be, will have advanced just a bit further, and so the process repeats itself. The fractions may get smaller and smaller, but the sequence of them is infinite.

How is it, then, that despite an infinite number of steps, Achilles is unable to overtake the Tortoise? Another version of the paradox goes like this. Suppose I want to walk across this room, from one side to the other. First (of course) I must walk half the distance. Then, I must walk half the remaining distance. Then I must walk half the remaining distance ... and so on. In other words, I can never reach the other side of the room, for the sequence of distances (of a half, a quarter, an eighth, a sixteenth, a thirty-second, and so on), being infinite, never ends.

For those of us who are not mathematicians, it is the sort of exercise best left behind in the Sixth Form. Except that it does offer a vivid picture of absurdity, and a striking parable of the futility of fractions.

No better picture sums up the recent publication, GS Misc 1033. Taking nearly 7,000 words it outlines possible revisions or rewordings of Clause 5.1.c, proposed by the House of Bishops and thrown out by General Synod in July. We are here at the level of sixty-fourths, a-hundred-and-twenty-eighths, or worse.

The whole process of the women bishops’ legislation is moving forward ever more slowly in smaller and smaller increments. Surely, this infinite sequence of ever more detailed modifications is getting us nowhere. Once more we are reminded of the words of Jesus, ‘That thou doest, do quickly.’ Or in modern terms, ‘Just get on with it.’

Anthony Saville

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