Friday, April 15, 2016

Joseph Mazur's "Fluke: The Math and Myth of Coincidence"

Joseph Mazur is an emeritus professor of mathematics at Marlboro College, and the author of several popular mathematics books, including the highly acclaimed Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers and What's Luck Got to Do with It?: The History, Mathematics, and Psychology of the Gambler's Illusion.

Mazur applied the “Page 99 Test” to his new book, Fluke: The Math and Myth of Coincidence, and reported the following:
From page 99:
We are often deceived by the magnitude of our world. It is bigger than we think; it is smaller than we think. A hundred years ago we stayed close to our towns and villages. My great uncles and great aunts in Poland surely didn’t wander far from their shtetl. Today, because of our international mobility, we bump into friends and relatives without surprise. We don’t quite fathom the hugeness of the world when we can get from New York to Hong Kong in fifteen hours. If I ask you how many people in the world have committed suicide in the time it took you to read this paragraph, you might very well say zero. But to give you some sense of how large this world really is, let me tell you that, according to estimates from the World Health Organization, on average every forty seconds someone, someplace in the world, performs a successful suicide. That’s 2,160 people, every day, on average! The rate varies according to country. In India, where suicide is illegal, the rate is almost double the global average.

By definition, coincidences are events that happen without apparent cause. Apparent to whom? It does not mean there is no cause. The world generally works by cause and effect. I say generally, because there are acausal phenomena in physics, psychology, and religion. But the word apparent tells us that the moment we learn the cause of a coincidental phenomenon, its status diminishes to a simple time-space event. That must mean that coincidences are relative to the people affected by them. It also means that the unapparent cause is there, waiting to be discovered. If there is no cause at all, then it happens by chance.
The monkey problem brings up a century old question of whether or not a monkey could write a line of Shakespeare by randomly striking the keys of a typewriter. Yes, it’s not only possible, but also sure to happen. That’s because the prediction powers of mathematics differs from real life pragmatics. Given enough time, a well-fed and well-rested monkey will, not only type a single line of Shakespeare but also someday in her enduringly extensive life plunk out the entire contents of the British Museum.

For a simple explanation let’s not expect the British Museum, not the complete works of Shakespeare, and not even a sonnet, just the line shall I compare thee to a summer’s day? If our dear little golden monkey were to hit the letters s-h-a-l-l-I-c-o-m-p-a-r-e t-h-e-e-t-o-a-s-u-m-m-e-r-’-s-d-a-y in that order, we would surely consider it a grand coincidence.

She has a 25 to 1 chance of typing the first letter of shall, assuming the keyboard is limited to just lowercase English letters. And since one key hit is relatively independent of any others[1], her probability of typing the first five letters are just 26 × 26 × 26 × 26 × 26 = 11,881,376, or odds against hitting those letters as 11,881,375 to 1. Very slim odds, but not infinite to 1; and so, if she persists, she shall have a better than even chance of typing shall after twelve million more tries.

From page 99 of Fluke, and perhaps a few pages following, we learn how hard it is to randomly generate a Shakespeare sentence. We surmise that it would take an army of humans to sift through interminable sheaves of nonsense before recognizing anything of literary value. Readers understand that random monkey finger play cannot compete with human creativity. Readers deduce that words on a page live in the human spirit. They come from the collective intelligence of the human condition. The monkey problem feeds the mathematician’s curiosity, and perhaps the philosopher’s diggings of logical analysis, as well. The coldness of random letters on a page would not only be detected, but also scoffed as chilling emptiness. In other words, literature worthy of the true sense of authorship is a dynamical system of interplays between author, subject, and character, an autonomous cerebral collaboration that cannot be even approximated by simple random play.
[1] The keys hits are independent; however, some hits might be more likely than others, given their position on the keyboard.
Learn more about Fluke at Joseph Mazur's website and read about his five best books on gambling.

The Page 99 Test: What's Luck Got to Do with It?.

Writers Read: Joseph Mazur.

--Marshal Zeringue