Under the Microscope/Prof William Reville:This week I will mark the season by taking a scientific meander very loosely held together by the theme of Christmas and I will finish up with a few seasonal jokes. First of all we must ponder the gargantuan task faced by Santa Claus, as outlined by Roger Highfield in an article on Santa's Science on www.firstscience.com/site/articles/christmas.asp.
Santa's market is huge. There are 2,106 million children under 18 in the world. Assuming 2.5 children per house, Santa has to make 842 million stops on Xmas Eve. The populated land-area of the planet is 150,000,000sq km, and, assuming each home occupies the same sized plot, the distance between each home is 0.42km.
Each Xmas Eve Santa has to travel 842 million multiplied by 0.42km which equals 356 million km to get down all the chimneys. If Santa travels against the direction of rotation of the earth he has nearly 48 hours to deliver his presents to everyone everywhere on Xmas Eve. This means Santa has just over two ten-thousandths of a second to travel between each of 842 million houses. To cover 356 million km in this time means his sleigh travels at a speed of 2,060km per second. The speed of sound is 0.33km per second, so Santa is travelling at 6,240 times the speed of sound.
When an object exceeds the speed of sound a sonic boom will ensue when the object catches up with the pressure waves it generates when moving. But, we don't hear any sonic booms on Christmas Eve, so obviously Santa has found a way to suppress these booms. By the way, in case you thought that Santa exceeds the speed of light, which would be forbidden by the laws of physics, rest assured. He travels at 2,060km per second and the speed of light is 300,000km per second.
Santa stops at each house, which means he has to travel at double the speed already calculated (which assumed no time for stopping) - 4,120km/sec - and, going from house to house he must accelerate from 0km/sec to 4,120km/sec in two ten-thousandths of a second - an acceleration of 20.5 million km per second per second. Acceleration due to gravity is 9.8m per second per second so Santa's acceleration is about two billion times greater. Fighter pilots find it difficult to cope with accelerations more than a few times gravity. Santa must therefore somehow create an artificial world in his sleigh whereby the accelerating force is cancelled out.
So, let us leave Santa be for the time being and move on to consider the subject of fractals and Christmas. A fractal is an object that looks the same regardless of the scale at which it is examined. An irregular coastline is an example of a fractal, clouds are another. Christmas offers several examples of fractals. Consider the Christmas fir tree. Each branch resembles the whole tree as do the sub-branches off each branch and the branches off them even down to the needles on the tiniest branches. The whole tree is a nest of patterns that repeat at various scales.
Other fractals you will encounter at Christmas include the snowflake (probably the most commonly cited fractal in nature), ice crystals and crumpled wrapping paper. Even the relationships among the notes and voices in a Bach Christmas Cantata can be described by fractal relationships. The "regular roughness" of fractal patterns are seen throughout nature - clouds, broccoli floret, fern leaf, mountain, highway and street patterns, river basins, clusters of galaxies, etc. Our blood vessels branch out in a fractal pattern ensuring oxygen gets to all parts of the body evenly.
And now a few Christmas jokes.
- The three wise men arrived to visit the child lying in the manger. One of the wise men was exceptionally tall, and bumped his head on the low doorway as he entered the stable. "Jesus Christ!" he shouted. Joseph said, "Write that down, Mary; it's better than Clyde!"
- Why the Little Angel is at the top of the Christmas Tree.
On Christmas Eve as Santa pulled his favourite pair of red pants on, they ripped. So, he had to put on another pair, which was a bit too tight. He then went to check on the rest of the preparations. The elves were sick. The reindeers had shin-splints. Santa went into the kitchen to take a calming drink, and the bottle was empty. Now he was really mad. All of a sudden, there was a knock at the door. Santa, in his angry state, ignored it. There was another knock. Santa was in no mood for this. When the knock came again, Santa - filled with rage - threw open the door. Standing there was a little angel who said, "Hi Santa! What do you want me to do with this Christmas Tree?"
- How Jesus Escaped. Soon after Christmas, the teacher told her students about an angel appearing to Joseph in a dream, warning him about danger to the baby Jesus and telling him how to escape from it. The students were asked to draw a picture about the story.
Larry's picture had an odd element in it. "Larry, I see Joseph and Mary with the baby Jesus on a donkey, but what is that following the donkey?"
"It's the flea, teacher."
"Flea? What flea?" asked the teacher.
To which Larry repeated the Bible verse, "Take Mary and Jesus and flea to Egypt ."
- William Reville is associate professor of biochemistry and public awareness of science officer at UCC - http://understandingscience.ucc.ie.