Author:
Wade A. Tisthammer
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Date Posted: 02/13/04 12:02pm
In reply to:
Damoclese
's message, "Infinity interrupted" on 02/12/04 12:14pm
>>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.
That is the paradox, or at least a part of it. The fact that it implies an absurdity/absurdities is the whole point.
>>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?
Remember we’re counting backwards. Day 365 is 1 year ago. Day 1461 is 4 years ago. So if 4 years ago he finished writing about the day that existed 4 years ago, at that point his autobiography is finished because he has written all the days of his life so far at that point.
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