The Mathematics Of ...

The Mathematics of Christmas

In the famous 1947 film classic Miracle on 34th Street, which was re-made in recent years, a man claiming to be Santa Claus is placed on trial. The judge is hoping to provide an answer for the age-old question, “Does Santa Claus really exist?” The judge comes to the conclusion that if you believe in something strongly enough then it becomes true. However, in reality just believing in something doesn’t make it true.

If you believe in the literal Santa Claus, you pretty much have to believe in miracles. Flying deer, an overweight Santa descending into your house through a narrow chimney, delivering millions of gifts all around the world in one night…all of this would take a great deal of faith to accept. According to a piece called The Mathematics of Christmas, here’s how it would have to work.

Let’s assume that Santa only visits those who are children in the eyes of the law, that is, those under the age of 18. There are roughly 2 billion such individuals in the world. However, Santa started his annual activities long before diversity and equal opportunity became issues, and as a result he doesn’t handle Muslim, Hindu, Jewish and Buddhist children. That reduces his workload significantly to a mere 15% of the total, namely 378 million. However, the crucial figure is not the number of children but the number of homes Santa has to visit. According to the most recent census data, the average size of a family in the world is 3.5 children per household. Thus, Santa has to visit 108,000,000 individual homes. (Of course, as everyone knows, Santa only visits good children, but we can surely assume that, on an average, at least one child of the 3.5 in each home meets that criterion.)

That’s quite a challenge. However, by traveling east to west, Santa can take advantage of the different time zones, and that gives him 24 hours. Santa can complete the job if he averages 1250 household visits per second. In other words, for each Christian household with at least one good child, Santa has 1/1250th of a second to park his sleigh, dismount, slide down the chimney, fill the stockings, distribute the remaining presents under the tree, consume the cookies and milk that have been left out for him, climb back up the chimney, get back onto the sleigh, and move on to the next house. To keep the math simple, let’s assume that these 108 million stops are evenly distributed around the earth. That means Santa is faced with a mean distance between households of around 0.75 miles, and the total distance Santa must travel is just over 75 million miles. Hence Santa’s sleigh must be moving at 650 miles per second -- 3,000 times the speed of sound. A typical reindeer can run at most 15 miles per hour. That’s quite a feat Santa performs each year.

What happens when we take into account the payload on the sleigh? Assuming that the average weight of presents Santa delivers to each child is 2 pounds, the sleigh is carrying 321,300 tons -- and that’s not counting Santa himself, who, judging by all those familiar pictures, is no lightweight. On land, a reindeer can pull no more than 300 pounds. Of course, Santa’s reindeer can fly. (True, no known species of reindeer can fly. However, biologists estimate that there are some 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, we cannot rule out flying reindeer.) Now, there is a dearth of reliable data on flying reindeer, but let’s assume that a good specimen can pull ten times as much as a normal reindeer. This means that Santa needs 214,200 reindeer. Thus, the total weight of this airborne transportation system is in excess of 350,000 tons, which is roughly four times the weight of the Queen Elizabeth.

Now, 350,000 tons traveling at 650 miles per second creates enormous air resistance, and this will heat the reindeer up in the same fashion as a spacecraft re-entering the earth’s atmosphere. The two reindeer in the lead pair will each absorb some 14.3 quintillion joules of energy per second. In the absence of a NASA-designed heat shield, this will cause them to burst into flames spontaneously, exposing the pair behind them. The result will be a rapid series of deafening sonic booms, as the entire reindeer team is vaporized within 4.26 thousandths of a second. Meanwhile, Santa himself will be subjected to centrifugal forces 17,500 times greater than gravity. That should do wonders for his waistline.

It’s a lot of fun to play along with the myth, but sane adults don’t accept the story as literally true. But the theme of Miracle on 34th Street is that it doesn’t matter if the story is fact or fiction. The important thing is that if you believe in Santa strongly enough, he becomes real for you.

The difference between what is actual truth and what is termed as “relative truth” is important for us to understand. For instance, if you think that you can run off the edge of a cliff and defy gravity like the Road Runner and Wiley Coyote, it doesn’t matter how strong your belief—it won’t hold you up. Gravity will take over every time, and you’ll get hurt. If you believe with all your heart that I’m only going to preach for just five minutes…well, I’ve got news for you…you’re living in Santa Claus land! Belief is of real value…but only if it is justified by fact.

The actual story of Christmas – the birth of our Lord – also involves a miracle, but this one happens on an unknown street in Nazareth some 2000 years ago. A young lady named Mary was told she was going to give birth to the Son of God. So what, you might say…births happen all the time. But this was slightly different, seeing that Mary was a virgin. Let me ask you, do you really believe in the miracle of the virgin birth or do you think that part was just made up? Is the miracle of the incarnation literally true or is it a myth that we have pretended to believe for so long that it has just seems real?…

Christian apologist Norm Geisler wrote, “God is not asking you to take a blind leap of faith into the darkness. He’s asking you to take a reasonable step of faith into the light.” To believe in the Miracle on 34th Street is more like a blind leap of faith. But to believe in the miracle of the virgin birth, the atoning death, and bodily resurrection is a reasonable step of faith into the light.

From a sermon by Michael Luke, Miracle on 34th Street, 12/12/2009