In contrast to the cynical mathematical "contradiction" to Santa, there is indeed proof of his existance.
Several key points are overlooked by this callous, amateurish "study."
1. Flying reindeer: As is widely known (due to the excellent historical documentary "Santa Claus is Coming to Town," the flying reindeer are not a previously unknown species of reindeer, but were in fact given the power of flight due to eating magic acorns. As is conclusively proven in "Rudolph the Red-Nosed Reindeer" (a no punches pulled look at life in Santa's village), this ability has bred true in subsequent generations of reindeer, obviously the magic acorns imprinted their power on a dominant gene sequence within the reindeer DNA strand.
2. Number of households: This figure overlooks two key facts. First of all, the first major schism in the Church split the Eastern Churches, centered in Byzantium, from the Western, which remained centered in Rome. This occurred prior to the Gregorian correction to the Julian calendar. The Eastern churches (currently called Orthodox Churches) do not recognize the Gregorian correction for liturgical events, and their Christmas is as a result several days after the Western Churches'. Santa gets two shots at delivering toys.
Secondly, the figure of 3.5 children per household is based on the gross demographic average, which includes households with no children at all. The number of children per household, when figured as an average for households with children, would therefore have to be adjusted upward. Also, the largest single Christian denomination is Roman Catholic, who, as we all know, breed like rabbits. If you don't believe me, ask my four brothers and two sisters, they'll back me up. Due to the predominance of Catholics within Christian households, the total number of households containing Christian children would have to be adjusted downward to reflect the overloading of Catholics beyond a standard deviation from the median.
Also, the assertion that each home would contain at least one good child would be reasonable enough if there were in fact an even 3.5 children per household. However, since the number of children per household is distributed integrally, there are a significant number (on the order of several million) of one child Christian households. Even though only children are notoriously spoiled and therefore disproportionately inclined towards being naughty, since it's the holidays we'll be generous and give them a fifty-fifty chance of being nice. This removes one half of the single child households from Santa's delivery schedule, which has already been reduced by the removal of the Orthodox households from the first delivery run.
3. Santa's delivery run (speed, payload, etc.): These all suffer from the dubious supposition that there is only one Santa Claus. The name "Santa" is obviously either Spanish or Italian, two ethnic groups which are both overwhelmingly Catholic. The last name Claus suggests a joint German/Italian background. His beginnings, battling the Burgermeister Meisterburger, suggest he grew up in Bavaria (also predominantly Catholic). The Kaiser style helmets of the Burgermeister's guards, coupled with the relative isolation of the village, suggest that his youth was at the very beginning of Prussian influence in Germany. Thus, Santa and Mrs. Claus have been together for well over one hundred years. If you think that after a hundred years of living at the North Pole with nights six months long that they remain childless, you either don't know Catholics or are unaware of the failure rate of the rhythm method. There have therefore been over five generations of Clauses, breeding like Catholics for over one hundred years. Since they are Catholic, their exponential population increase would obviously have a gain higher than the world population as a whole. There have therefore been more than enough new Santas to overcome the population increase of the world. So in fact, Santa has an easier time of it now than he did when he first started out.
Santa dead, indeed; some people will twist any statistic to "prove" their cynical theory.
Santa does exist
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