| Subject: Infinity interrupted |
Author:
Damoclese
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Date Posted: 02/12/04 12:14pm
In reply to:
Wade A. Tisthammer
's message, "What day did he write about last year?" on 02/12/04 10:29am
>What day did Shandy write about last year? I think
>that, if this man existed and had been writing from
>eternity past, he would be infinitely far behind. But
>this generates an absurdity of its own. Let's call
>the day he wrote about last year point B and
>the present point A. If Shandy is infinitely
>far behind, point B in the past is infinitely far away
>from point A. But then would point A ever be reached?
> It can't, because it's an infinite distance away, and
>an actual infinite cannot be formed by successive
>addition. For instance, Let’s count. Suppose you
>start with 1 and successively add one every second. 1,
>2, 3, 4… and so on. Will you ever reach a point where
>you can honestly say, “I’m done. I’ve reached
>infinity”? No, the number will just get progressively
>larger and larger without limit. There is no greatest
>possible integer. Same thing when you’re counting
>with days. Day 1, 2, 3, 4... you can’t reach a point
>of day “infinity,” because the numbers will just get
>larger and larger without limit. The present would
>never be reached.
That is the main problem I have with this seeming paradox.
>
>Why can’t point B be some finite distance from point
>A? Can’t point B be, say, 1458 days ago without
>generating an absurdity? As it turns out, no. The
>numbering scheme we’ll use will be to count backwards.
>For instance, yesterday is day 1, two days ago is day
>2 etc.; last year is year 1, two years ago is year 2
>etc. Suppose he had just finished writing about day
>1458. Remember, Shandy cannot write about days he
>hasn’t lived yet, and he never skips ahead. Suppose he
>had just finished writing about day 1458. But if last
>year (year 1) he wrote about day 1458, what day did he
>write about 4 years ago (year 4)? Well, in year 4 he
>wrote about day 1461. But day 1461 is 4 years ago
>(year 4), so if last year he wrote about day 1458,
>then 4 years ago he finished his autobiography.
>And we get the same paradox all over again. We can
>see that this goes for being finitely behind for all
>D, where D is the day he wrote about last year (point
>B). In the formula Y = 4*(D ? 1)/1457 where Y
>is the year he finished (rounding up).
How is it that by being on day 1461 and then being on day 1458 implies that he finished his autobiography? It seems to me that you're only moving backwards along arbitrary points on an infite line. 1461 is no more the cap to his novel than 12987654 is.
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