April 12, 2002 (Ira Pilgrim)
Apparently there is nothing that cannot happen today.
Some things happen very rarely; say once in a million or billion or trillion trials or even more infrequently. They are not impossible because they do happen. Whether a rare event will happen while you are looking, or whether it will affect you, is another matter.
What is the probability of my winning the California state lottery? It is zero, zip. It is impossible. Why? Because I wouldn't ever play the lottery, nor would I ever gamble against those odds. That's a game for suckers.
I have had some highly improbable experiences. For example, my wife and I were having lunch in a restaurant in Amsterdam, with a view of the street below. I spied an old friend of ours walking along. I yelled at him and he joined us. What is the probability of that happening? It is "1," or 100% or certainty. It is certain because it did happen. What would the odds be of such an event happening if you calculated it before the event happened? It is extremely improbable. Many people, including some professional statisticians, seem to believe that the laws of probability make things happen. They don't; they merely describe what does happen and how often.
A weirder incident happened during the year that I was teaching in Nigeria. My wife was joining me for a two week vacation. I picked her up at Lagos airport and we were driving back to Ibadan. As often happens in Lagos, we were stuck in a go slow (traffic jam). A black man in a car that was also stuck, but going in the opposite direction looked at me and said "Hi, Ira," and started moving. he indicated that he would turn around and join us. I said to my wife, "Who was that?" She replied, "That's Eric." "Who the hell is Eric?" I said. "Eric Opia," she replied; "I met him at my cousin Rachel's house in San Jose." We got together with Eric and I asked him how he knew who I was. He said that he had seen my picture on the jacket of my book that my wife had showed him. How about that for an improbable event?
I sat in on the first few weeks of a course in probability given by the mathematician Jerszy Neyman. He spent the entire time on the subject of randomness. That was because this simple concept seems to be very difficult for people to really understand. And it is the basis of all of statistics. I didn't realize that, while I could manipulate the numbers and do a good job of it, I really didn't have a grasp of it until now. What brought me to this understanding is a computer game called poker squares. It consists of dealt cards arranged at random with 5 cards across and five cards down, making a total of 25 out of a deck of 52 cards. You then re-arrange the cards into various poker hands which are scored, with a royal flush being 100, a straight flush 75, a full house 25 etc. The objective is to score over 200 points. I have been using it as an escape. It frees my mind of any disturbing or worthwhile thoughts. In the process, I sometimes saw unusual distributions of cards in different suits. I wondered if the game was "fixed." It wasn't. What I was observing was what can be expected with a random deal of the cards. If you played the game for a long time, you might see a 10, jack, queen, king, ace, all spades in an orderly row on the top. The same would be true of any other combination in any other place on the grid.
I had a lot of fun when I taught an introduction to statistics. I would ask the class: "Suppose you were tossing a fair coin. You toss it four times and get heads every time. On the fifth toss, would the chances of getting a fifth head be greater then 50:50 or less?" Most people believed that it would be different. Some said that your chance would be less because you have already gotten 4 heads. Some said that it would be greater because you are on a streak of heads. There is only one correct answer: that what you got on the first four tosses has no effect on the next toss and the chance of getting a head is still 50:50. How could one or two or more coin tosses possibly affect the next toss? However, if you believe in magic, anything is possible.
Some people believe that the laws of chance make things happen. They don't. What they do is describe what will probably happen in a large number of events. Similarly, the Law of Gravity describes what gravity does; it doesn't make anything happen. The Laws of Chance can tell you what the odds are that something will or won't happen. If someone plays a lot of poker, he will probably see one or more royal flushes in his lifetime despite the fact that the odds of getting a royal flush are one in 649,739(in 5 card stud poker).
What I am saying is that no matter how improbable an event is, once it happens it is a certainty. Also that a highly improbable event will inevitably happen. Whether you will see it happen, or if it happens to you is another matter.
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