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pattern where none exists than by failure to identify an existing pattern. Thus, the evolutionary tendency to identify patterns also results in identifying ostensible patterns, including patterns that do not exist. We can take the Bible code as an instance of incorrect identification. By constructing sentences consisting of only every n th word of the text in the Bible, it can apparently be shown that many of the events in modern life were allegedly foreseen in the Old Testament. Careful statistical tests proved that these patterns have no scientific reality. From the outset, however, the tendency to find patterns overcame scientific caution. In later sections we will come across other mental errors deriving from discovering patterns where they do not exist.
    Much of mathematics, both in research and in the various stages of learning mathematics, focuses on the identification of patterns in sequences. Here are a few simple exercises. Continue the sequence:
    2, 4, 6, 8, 10,…
    At a relatively early age, children will recognize the sequence of even numbers and will correctly give the next numbers in the sequence, 12 and 14. More knowledge is required to recognize the following sequence:
    1, 4, 9, 16, 25, 36,…,
    but it is not difficult to see that the numbers in the sequence are the squares of the numbers 1, 2, 3, 4, 5, 6, so that the following numbers will be 49 and 64. We should point out and emphasize that these sequences do not necessarily continue as we have suggested. In other words, these extensions of the sequences do not derive from a logical necessity. Moreover, theanswers are culture dependent. Here is an exercise attributed to the mathematician and historian Morris Kline. Continue the sequence:
    4, 14, 23, 34, 42, 50, 59,…
    The answer? 72. The numbers in the sequence are the numbers of the streets at which the Manhattan Subway C stops, and the next station is at 72nd Street. I would guess that if regular travelers on the New York subway were given this exercise, many would have given the answer 72. I have deliberately avoided saying that they would have given the right answer, because this is not a matter of right and wrong. The answer is right if that is what the questioner intended. It is easy to see, however, that the human race has the inborn intuition to continue series such as the above in a reasonable manner, and to understand what the questioner wants. (We will discuss again this exercise in the last chapter of this book.)
    Clearly one must not exaggerate, and the story of the four-engine airplane flying from New York to London comes to mind. About an hour after takeoff, the pilot announces that one of the four engines has failed, but there is nothing to worry about. The other three are working as they should, and the flight would just take nine hours instead of the originally scheduled six. A short while later the pilot announces that a second engine had ceased functioning, but not to worry, the only effect was that the flight would now take twelve hours. A while later comes the third announcement, that the third engine is now out of action, so the flight time is now fifteen hours. At this point a passenger jumps up and asks, “Is there enough food and drink on board in case the fourth engine fails and the flight takes eighteen hours?” (It would be interesting to ask mathematics students to complete the sequence in the event that the fourth engine stopped working.)
    Some continuations of sequences, even if there is no logical necessity, are directly connected with natural phenomena. Let us take, for example, the following sequence:
    1, 1, 2, 3, 5, 8, 13, 21,…

    Each number (from the third) in the sequence is the sum of the previous two numbers, so that the next two in the sequence would be 34 and 55, and so on. This is the Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci, or Leonardo of Pisa (1170–1250), whose book Liber Abaci (1202) included extensive development of