Free Fall #7. Ive been teaching my Intro Geology class, which pays the bills so research can happen ... but all life is creativity if you play it right. Let me tell you how much fun it can be sometimes ... by showing you. The following is modified (mostly condensed) from todays class. Today I did not tell my students what the topic would be. Instead, I began with the old story of the philosopher who did an Eastern potentate a great favor, and was invited to the Treasury to name his own reward. Modestly, the philosopher requested that a chessboard be brought in, and that one grain of wheat be placed on the first square, two on the next, four on the one after that, then eight, doubling the number for every square until all 64 squares were done. The great ruler laughed and granted his wish, but soon came to regret it. The numbers doubled slowly at first -- 1, 2, 4, 8, 16, 32, 64, and 128 in the first rank of the chessboard, then 256, 528, 1046 and so on in the second rank. With the aid of a student holding a calculator, I wrote down all the rest of the numbers on the board, rounding them off as I passed one million -- and was not even halfway through. The numbers of wheat grains rose from a sparse meal that would fit in a cup, to enough to feed a country, to more grains of wheat, perhaps, than have ever existed, ending, on the 64th square, with no less than 8 quintillion grains. The king would have to forfeit his kingdom to the philosopher to grant this wish, and would still be forever in his debt. I passed from this to an ancestral chart online -- my own, as it happens -- to show how rapidly ancestors double as one builds a family tree. How long would it take for 64 generations of people to have children? I asked. It turned out that the number would be somewhere on the order of 2000 years -- a long time, but hardly beyond the realm of history: the time of Christ and the Emperor Augustus. I asked, were there 8 quintillion people alive in 1 AD? Obviously not. Where were all my ancestors, I asked. Where were yours? Every child has two biological parents; they must have existed. Finally someone offered that relatives must have married one another, and I said, Exactly right! Do you know who your tenth cousins are? Clearly not. No doubt, you will all be marrying cousins! One girl said eww to this, but other students nodded, and one remarked that we are all cousins. Exactly so, I said. Dont worry about it. In each generation, the genetic contribution of any one ancestor is cut in half. Since DNA is made of genes that are transmitted whole, not cut, and there are only so many genes in DNA, you must have many ancestors whose DNA has not been passed down to you. You are not very similar, genetically, to a distant cousin. And you have no choice but to marry a cousin. Two thousand years is a long time, but not long enough for peoples basic nature to change, I ventured. People were people two thousand years ago; they did not look very different and they thought the same way as they do now. No disagreement on this. Turn the numbers the other way, I said. Instead of imagining your ancestors doubling back into the back, think of your children and grandchildren. If they all have two children, in 64 generations, you could have 8 quintillion descendants. This raised eyebrows. That number of people could not survive on this planet, of course. We have doubts about 10 billion people being able to survive together in the coming century. Any species can produce more offspring than can survive. Consider the oak tree, producing perhaps a million acorns in its lifetime. A million oaks could not stand where one exists today. All species, human, animal, and plant, share this. And they are all different. We get half of our DNA from each parent, but our sisters and brothers do not get the same halves (except for identical twins). DNA is a very large molecule and, except for identical twins, probably no two people have ever been born who are exactly alike genetically. If a species offspring are all different, but can be too numerous for all of them to survive, then which ones actually do survive? The fittest, said one of the students (obviously one who had paid attention in a Biology class). After some discussion of this involving the gene for hemophilia in Queen Victorias family, an example that another student brought up, and a thought experiment concerning the mutation that created the first blue eyes in humans, the students had a better idea of what this might mean. I said, if the fittest survive, then the species is not quite the same as in previous generations. It has changed, maybe a lot, more likely only a little. Two thousand years is not enough for much change in people, but if the geologists are right and the Earth is billions of years old -- well, a lot can change in a few billion years. We call this evolution. Charles Darwin published this idea in 1859, and it is one of the major ideas in biology. Remember this. Class dismissed.
Posted on: Thu, 25 Sep 2014 00:02:58 +0000
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