67 lines
3.5 KiB
Plaintext
67 lines
3.5 KiB
Plaintext
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15-Dec-84 23:20:47-EST,3587;000000000001
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Date: Saturday, 24 November 1984 16:46-EST
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Sender: John R. Kender <KENDER@COLUMBIA-20.ARPA>
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From: John R. Kender <KENDER@COLUMBIA-20.ARPA>
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Orig-To: BBOARD at COLUMBIA-20.ARPA
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Subject: The imperceptibility of Santa Claus
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ReSent-From: CARTER@RU-BLUE.ARPA
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ReSent-To: Info-Cobol@MC
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ReSent-Date: Sat 15 Dec 1984 23:12-EST
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"OK, Daddy, why has nobody SEEN Santa Claus on Christmas Eve?" Tough
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question. But, a few back-of-the-envelop calculations were enough to
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convince my doubting offspring that it was physically IMPOSSIBLE. To
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wit:
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Suppose that Santa starts at the International Date Line and travels
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westward, in order to maximize his time for delivering presents on or
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about midnight. Let's guess that there are 4 billion people, and so
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about 1 billion households worldwide. Just as we assume Santa has
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solved the travelling salesman problem (1 billion nodes!), so too we
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will assume that he can handle the unequal distribution of households
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over the land masses, too (Fiji Islanders, etc., probably don't have
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reason to doubt his presence). Roughly 1 billion / 24 hours gives 40
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million households / hour; and as there are 3600 seconds / hour, that
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gives us about 10000 households / second. Thus, Santa drops down the
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chimney and is gone, on average in .0001 second: FAR LESS time than
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the human eye (even dark-adapted!) needs to see--.01 second being
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about the lower limit established by tachistoscope studies.
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"OK, Daddy, then why has nobody HEARD Santa Claus on Christmas Eve?"
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Tougher question, and one that demands serious analysis. If Santa
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moves that quickly, of course, he is going to push a lot of air out of
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his way, and silent night would be more accurately be called the Night
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of the Sonic Booms. The envelop (last year's, once containing a
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Christmas card as yet unanswered) quickly fills up:
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Let's see: 1 billion households distributed on average equally over 4
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pi radius squared. That's about 12 times 4000 * 4000, but
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three-quarters of that is water (poor Fiji!): so about 3 times 16
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million, or about 50 million square miles. So, 1 billion / 50 million
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is 20 households / square mile, and if they were distributed in
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gridlike regularity, Santa has to travel (at LEAST, depending on the
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sophisication of his TSP solution) about 1/5 mile: 1000 feet in .0001
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second. Sound itself would take about 1.3 second; clearly, even if
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Santa were made of Kevlar and could withstand the accelerations
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necessary (poor toys!), Santa is not only booming about the Baby
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Boomers' babies, he is beginning to suffer from Fitzgerald
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contraction. (Let's see, here on the envelop flap: 1/5 mile in
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1/10000 of a second is 2000 miles / second, or about .01c, if c is
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rounded to 200000 miles / second.) Thus giving new meaning to
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"relative clause", he is approaching the danger of being misperceived
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as anorexic.
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Perhaps, then, the answer is as follows: you can't see Santa because
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he moves too fast; and, because he would look skinnier than you think,
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you wouldn't recognize him anyway. Further, any atmosphere
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overpressure generated by his rapid descent is canceled by the
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underpressure of his nearly instantaneous return: in contrast to most
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phenomena, the sonic boom cannot form!
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What remains to be explained, of course, in addition to the usual
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arrival of undamaged gifts (even on Fiji), is why the evening of his
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rapid transit is not marked by the spectacle of a multitide of gifts
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being sucked, nearly simultaneously, up through millions of chimneys
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throughout world, to trail happily in his wake.
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