Thursday 1 October 2009

The Lottery Fallacy

While American novelist Anne Parrish was browsing bookstores in Paris in the 1920s, she came upon a book that was one of her childhood favorites - Jack Frost and Other Stories. She picked up the old book and showed it to her husband, telling him of the book she fondly remembered as a child. Her husband took the book, opened it, and on the flyleaf found the inscription: "Anne Parrish, 209 N. Weber Street, Colorado Springs." It was Anne's very own book. (Source: While Rome Burns, Alexander Wollcott)


I love stories like this. Here's another one:

When Norman Mailer began his novel Barbary Shore, there was no plan to have a Russian spy as a character. As he worked on it, he introduced a Russian spy in the U.S. as a minor character. As the work progressed, the spy became the dominant character in the novel. After the novel was completed, the U.S. Immigration Service arrested a man who lived just one floor above Mailer in the same apartment building. He was Colonel Rudolf Abel, alleged to be the top Russian spy working in the U.S. at that time. (Source: Science Digest)


These are what the layperson would describe as coincidences. Extraordinary coincidences, for sure, but coincidences all the same. They make for fascinating and surprising stories, and they always make me laugh and smile. On a very basic human level, they appeal to us. There's a feel of the supernatural to them, a spooky eeriness that gives us the feeling that these things couldn't possibly have happened by chance. It's magic, and the appearance of magic is a wonderful and heartwarming thing.

You can choose to stop there. You can choose to believe that, in the first story, fate somehow guided Anne Parrish to that bookshop thousands of miles from home to find the long lost book, or that Norman Mailer developed a kind of psychic connection with Rudolf Abel. There's nothing wrong with believing that (so long as you don't violently assert that it's true, and that anybody who disagrees is straight-out wrong), but if you enjoy a bit of thinking, there's something more you can get out of it.

"It must be a psychic connection," says the True Believer, "it's just too unlikely for it to be anything else!"
Well, OK... but let's look at it another way.
The UK lottery system uses 49 numbered balls, six of which are drawn at random to give the jackpot. The number of possible combinations puts me, with my lottery ticket, in with approximately a one in fourteen million chance of winning. In other words: very unlikely. Everyone playing the lottery each week faces the same odds. Yet somehow - miraculously - somebody wins! Wow! That person who won had a staggeringly low (one in fourteen million) chance of winning. That is overwhelmingly unlikely. And yet... they won!

If I were to tell that story to a True Believer and ask "how do you explain that?" they would probably look at me puzzled and say "But there's nothing to explain. Somebody, somewhere had to win!"

And BINGO! They've unwittingly refuted their own statement.

The simple fact is that coming across that book in Paris was not impossible. Neither was the possibility that Norman Mailer would unknowingly have written a story so similar to what was happening in the same building he lived in. These were just very unlikely events.

Let me give you another example of a very unlikely event that is not impossible. I'm thinking about somebody right now. A friend of mine, who knows my address, and could, in theory, call at my house at any time. They've never paid me a surprise visit before, and it would be especially unlikely in the middle of the night, but they could ring my doorbell right now. If I just think, really hard!
I won't hold my breath waiting for this to happen, but if it did, it would be staggering! This is because I predicted it.

"That a particular specified event or coincidence will occur is very unlikely. That some astonishing unspecified events will occur is certain. That is why remarkable coincidences are noted in hindsight, not predicted with foresight."--David G. Myers


Think about all of the times that you might have been thinking about somebody and just then, you get a phone call from them, or a text message. It can feel like a psychic bond. But imagine this... if it's a person who you happen to think about a lot anyway, and also somebody who texts you frequently, how much MORE amazing would it be if you never heard from them while you were thinking about them? Then think to yourself, "would I also be amazed if anybody who I'd recently thought about happened to call soon after I'd been thinking about them? You probably would! And when you think about how many people there are in your phonebook, it's bound to happen one day!

When you're dealing with large numbers of people and the events that they encounter, amazing things happen. You can't predict which of those amazing things will happen, or when, but you can bet that something extraordinarily unlikely will happen to you at some point in your life.

Some amazing coincidences have happened to me. Just consider, even, your very existence:

"The number of people who could be here, in my place, outnumber the sand grains of Sahara. If you think about all the different ways in which our genes could be permuted, you and I are quite grotesquely lucky to be here! The number of events that had to happen in order for you to exist, in order for me to exist. We are privileged to be alive and we should make the most of our time on this world." - Richard Dawkins


But I still love these stories. Why? Because I'm human. I'm susceptible to that momentary belief and the rush of feelings it causes. But then there comes a shift, from feeling to thought. And it's doing this that leads the True Believer to accuse skeptics of being joyless and soulless. I disagree.

"There are True Believers who refuse to, or cannot, make that move to detached thinking and find such an approach necessarily joyless. They miss that we can all feel that initial joy at such anecdotes and events, but only some of us get to experience another level of joy which is warmed by it's closer proximity to the truth. We need to live by our hearts as well as our brains to engage most wonderfully with this world: sadly there is often a proud refusal among True Believers to engage with the latter." - Derren Brown

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