“Truly Large Numbing” (Coincidence and misuse of numbers)

IN SQUAREListening to 75 songs playing at random in my CD player, I wondered how many orders it could go in. Finding the answer would be easy. I needed merely to e-mail a mathematics Ph.D. that I knew.

I don’t know what the number was called, but recall that it was over 2.4 billion googol. That is a Truly Large Number, which is the best segue I can come up with for moving into the meat of this topic. We’ll look at the Law of Truly Large Numbers and see how it relates to the skeptic movement.

The Ph. D., who incidentally was also the best miniature golf player I’ve ever known (reckon he was using geometry), was a good professor, as he explained the answer. 75 tracks could be the first one played, 74 could be the second, 73 the third, and so on. So the answer was arrived at by multiplying 75 x 74 x 73 x 72, all the way to x 2. What had been an astronomical number shrouded in mystery and awe became an astronomical number that I understood.

I have plenty of company in my mathematics ignorance. If you’re in a room with 25 persons, many people think the chance of any two of them sharing the same birthday would be just one in 24, or about two percent. But it’s not just one person who has a one in 24 chance of having someone with the same birthday. There are 24 persons with that one-in-24 chance. That bumps the chance that at least two of them share the same birthday to just past 50 percent.

I am substantially out of my element when dealing with advanced mathematics, but I recognize when digits are being misused, and it’s a regular occurrence when it involves Truly Large Numbers. The most frequent abusers are mediums and fortune tellers, but conspiracy theorists and creationists also get in on the numerical chicanery.

How this can be exploited was shown by British illusionist and TV personality Derren Brown. He presented a system for winning horse racing bets. He had thousands of volunteers, then subsequently followed the winners. At the end, only the top performer was presented on TV, with the system seemingly vindicated.

The Law of Truly Large Numbers states with a large enough sample, many odd coincidences are likely to occur. More simply, with billions of people doing hundreds of things a day, it would be the most amazing thing ever if nothing amazing happened. This can be overlooked because people tend to seek meaning in life and prefer order over randomness.

But drawing supernatural conclusions relies on the Appeal to Ignorance. When making this appeal, the proponent, probably in all caps, will insist an occurrence is so unlikely that there can be other explanation. But mathematician and author John Allen Paulos clarifies that rarity isn’t evidence. Imagine someone (let’s make it Harpo Marx) shuffling and turning over 52 playing cards. Whatever order Harpo lays them in, there was about a one in a quarter-googol chance of that being the sequence when he began. Paulos notes it would be nonsense to conclude that Harpo could not have dealt them that way because the sequence was so improbable.

Anyone could see the absurdity of that conclusion. But it’s different when dealing with occurrences that have personal meaning. Then, the tendency is to ascribe genuine power to what the palm reader told you, what you prayed about, or what the telephone psychic predicted. In these instances, one holds tight to the subjective validation, and cognitive dissonance won’t let it go.

Uri Geller put down his bent spoons long enough to come up with a long list of “stunning coincidences” regarding the Sept. 11 attacks that added up to 11. One example: “September 11th is the 254th day of the year: 2+5+4 = 11.” Skeptic leader Robert Carroll countered with a list that contained many noncoincidences that added up to something other than 11.

A person may dream of an airplane crash the night before a wreck happens. With six billion people having multiple dreams each night, someone is going to have a dream about an airplane crash every day. I’ve had over 100 myself. At some point, someone will probably also hit on the place and airline. To call this proof of clairvoyance would require ignoring the many more dreams that don’t come true, or the things that happen without being dreamt about. Also, dreams are often vague or ambiguous, allowing many interpretations.

Highlighting an event’s rarity or unlikelihood is also a hallmark of the creationist. One difference from the others is that it usually also involves the misapplication of science principles. One example, from darwinsimrefuted.com: “For a 300-molecule-long protein to form by total random chance would be a one in 10 to the 390th power occurrence.” Throw in a straw man or two and the creationist instantly vanquishes evolution and biology. The misrepresentation here is that everything in the process is random. In actuality, evolution is a very slow process with many incremental steps, overseen by natural selection. As to the Truly Large Number correlation, I defer to to evolutionfaq.com: “In the prebiotic oceans of early Earth, there were billions of trials taking place simultaneously as the oceans, rich in amino acids, were continuously churned by the tidal forces of the moon and the harsh weather conditions of Earth. Considered in this more comprehensive and inclusive way, the true odds are revealed.”

This month, an Israeli soldier was shot, with the bullet hitting a grenade in his pocket. The bullet was blocked by the grenade, which failed to detonate. This made the social media rounds, with prayer cited as the reason. There was no mention of the thousands of persons slaughtered in the conflict in spite of all this prayer. The dud grenade was cited as proof of miracles, without reference to the millions of non-miracle working grenades over the past century.

Highly improbable does not mean impossible, as every winning lottery ticket demonstrates. It also doesn’t mean anything is at work beyond the Law of Truly Large Numbers.

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