Author:
Wade A. Tisthammer
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Date Posted: 02/12/04 10:29am
In reply to:
Duane
's message, "Guess who's back (guess who's back (guess who's back))" on 02/11/04 9:39am
>Wade, Ben, Dam, Don, Jorge:
>
>(well, maybe not Jorge) (Whatever happened to him,
>anyways?) ;)
>
>First, my apologies to any of Ben's Forum regulars
>I've left out. It's been a while, and its nice to see
>that the diehards are still live and kicking.
>
>On to Wade's paradox.
>
>There is no paradox.
>
>Let's review the argument:
>1) Tristam requires one year to record a day's worth
>of events
>
>2) The past is an infinite amount of time.
>
>3) If the past is an infinite amount of time, there is
>a 1:1 correspondence of days to years.
>
>4) Therefore, Tristam can complete his biography.
>
>#4 is clearly an inappropriate deduction because of
>the additional axiom you stated:
>
>1) a) Tristam cannot write about a day before he has
>lived it
>
>which implies that Tristam's experience of and
>existence in time is directional. #3 clearly follows
>from #2, but they are both unrelated to our hero's
>plight. Tristam experiences time in a linear fashion,
>and therefore exists within time, as you've defined it
>in this argument. It follows, therefore, that Tristam
>can never complete his autobiography, since his rate
>of completion is less than his rate of accumulation of
>new experiences to write about.
>
>(Incidentally, I can't say I'd be very interested in
>reading the chapters about "The Writing Years": "I was
>writing and writing and writing and writing and
>writing and writing...")
>
>There is technically no paradox in this argument. It
>appears to be paradoxical due to the fact that axiom
>#2 and inference #3 are lexically similar to the
>situation in axiom #1, but, clearly, deduction #4 is
>inappropriate given corollary 1.a).
>
>Comments? Complaints? Dissent? Please let me know.
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.
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).
So we have a dilemma on our hands. Either Shandy finishes his autobiography at some point or he is infinitely far behind. Which one do you choose? And what day did Shandy write about last year?
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