Monday, December 17, 2018
Sunday, December 16, 2018
The Imperceptibility of Santa Claus
"Okay, Daddy, why has nobody SEEN Santa Claus on Christmas Eve?"
Tough question. But, a few back-of-the-envelop calculations were enough to convince my doubting offspring that it was physically IMPOSSIBLE. To wit:
Suppose that Santa starts at the International Date Line and travels westward, in order to maximize his time for delivering presents on or about midnight. Let's guess that there are 4 billion people, and so about 1 billion households worldwide. Just as we assume Santa has solved the travelling salesman problem (1 billion nodes!), so too we will assume that he can handle the unequal distribution of households over the land masses, as well (Fiji Islanders, etc., probably don't have reason to doubt his presence). Roughly 1 billion / 24 hours gives 40 million households / hour; and as there are 3600 seconds / hour, that gives us about 10000 households / second. Thus, Santa drops down the chimney and is gone, on average in .0001 second: FAR LESS time than the human eye (even dark-adapted!) needs to see--.01 second being about the lower limit established by tachistoscope studies.
"Okay, Daddy, then why has nobody HEARD Santa Claus on Christmas Eve?"
Tougher question, and one that demands serious analysis. If Santa moves that quickly, of course, he is going to push a lot of air out of his way, and silent night would be more accurately be called the Night of the Sonic Booms. The envelope (last year's, once containing a Christmas card as yet unanswered) quickly fills up:
Let's see: 1 billion households distributed on average equally over 4-pi radius squared. That's about 12 times 4000 * 4000, but three-quarters of that is water (poor Fiji!): so about 3 times 16 million, or about 50 million square miles. So, 1 billion / 50 million is 20 households / square mile, and if they were distributed in gridlike regularity, Santa has to travel (at LEAST, depending on the sophistication of his TSP solution) about 1/5 mile: 1000 feet in .0001 second. Sound itself would take about 1.3 second; clearly, even if Santa were made of Kevlar and could withstand the accelerations necessary (poor toys!), Santa is not only booming about the Baby Boomers' babies, he is beginning to suffer from Fitzgerald contraction. (Let's see, here on the envelop flap: 1/5 mile in 1/10000 of a second is 2000 miles / second, or about .01c, if c is rounded to 200000 miles / second.) Thus giving new meaning to "relative clause", he is approaching the danger of being misperceived as anorexic.
Perhaps, then, the answer is as follows: you can't see Santa because he moves too fast; and, because he would look skinnier than you think, you wouldn't recognize him anyway. Further, any atmosphere overpressure generated by his rapid descent is canceled by the underpressure of his nearly instantaneous return: in contrast to most phenomena, the sonic boom cannot form!
What remains to be explained, of course, in addition to the usual arrival of undamaged gifts (even on Fiji), is why the evening of his rapid transit is not marked by the spectacle of a multitude of gifts being sucked, nearly simultaneously, up through millions of chimneys throughout world, to trail happily in his wake.