2) There are 2 billion children (persons under 18) in the world. BUT since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total - 378 million according to Population Reference Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes. One presumes there's at least one good child in each.

3) Santa has 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 822.6 visits per second. This is to say that for each Christian household with good children, Santa has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house. Assuming that each of these 91.8 million stops are evenly distributed around the earth (which, of course, we know to be false but for the purposes of our calculations we will accept), we are now talking about .78 miles per household, a total trip of 75-1/2 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding and etc. This means that Santa's sleigh is moving at 650 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle on earth, the Ulysses space probe, moves at a mere 27.4 miles per second - a conventional reindeer can run, tops, 15 miles per hour.

4) The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized Lego set (2 pounds), the sleigh is carrying 321,300 tons, not counting Santa himself, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300 pounds. Even granting that "flying reindeer" (see point #1) could pull TEN TIMES the normal amount, we cannot do the job with eight, or even nine. We need 214,200 reindeer. This increases the payload - not even counting the weight of the sleigh - to 353,430 tons. Again, for comparison - this is four times the weight of the Queen Elizabeth (the ship, not the monarch).

5) 353,000 tons traveling at 650 miles per second creates enormous air resistance - this will heat the reindeer up in the same fashion as spacecrafts re-entering the earth's atmosphere. The lead pair of reindeer will absorb 14.3 QUINTILLION joules of energy. Per second. Each. In short, they will burst into flame almost instantaneously, exposing the reindeer behind them, and create deafening sonic booms in their wake. The entire reindeer team will be vaporized within 4.26 thousandths of a second. Santa, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 4,315,015 pounds of force, reducing him to a pink blob of goo.

In conclusion:

If Santa ever DID deliver presents on Christmas Eve, he's dead now.

If Santa ever DID deliver presents on Christmas Eve, he's dead now.

**~~~~~**

# More Notes on The Imperceptibility of Santa Claus

"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, 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.

"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 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.

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