"OK, 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, too (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.
"OK, 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 envelop (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 sophisication 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 multitide of gifts being sucked, nearly simultaneously, up through millions of chimneys throughout world, to trail happily in his wake.