Walking recently past a lottery machine with a friend I found myself randomly proclaiming that I would play for this week’s jackpot. Being unable to pick good numbers to use, I decided that I’d simply use the winning numbers from last week’s drawing.
“That’s stupid,” my friend declared.
“I know, I know,” I replied. “The lottery is a tax on people who are bad at math.”
“Well, yeah. But that’s not what I meant. I meant that it’s stupid to play last week’s numbers because the odds are worse that the same numbers will be drawn twice in a row.”
At that point my eyes lit up in that dickish way they do when I realize that I’ve caught someone being wrong. My desire for a sense of intellectual superiority was artificially bolstered by the fact that this friend had just wholloped me at several consecutive games of Scrabble and I was looking to heal some wounds.
“No,” I replied. “The odds are the same regardless of what numbers I play.”
He protested some more, so I set him straight with an example:
“Say I have a hat filled with 100 slips of paper numbered 1 through 100 and I ask you to stick your hand in and draw one at random. What are the odds you draw a five?”
“One-in-one hundred,” he answered.
“Yep. Now say I have the same hat; You’re going to draw out a single number, put that number back in, mix it up & draw again at random. What are the odds that you’ll draw five twice?”
“I dunno. A lot worse.”
“Yep,” I said again. “Simple probabilities like that are calculated by multiplying the odds across trials. It was 1-in-one hundred for the first draw, and the same for the second. 1/100 times 1/100 is 1/10,000, so yes, quite a lot worse.” He thinks I’m making his point for him, so I continue: “Now imagine that you’ve already done the first drawing and chose a five. You’ve put it back in, mixed the numbers up and are about to draw again. What are the odds you’ll draw the five again?” There was an awkward pause as he realized my point. “It’s one-in-one hundred, of course, because after the fact, the probability of you drawing that first five is 100% since it’s already happened. The only statistic I need to be worried about is the one for the future draw… The one that hasn’t happened yet.”
The point settled in for him and he asked if I was just going to buy the damned ticket, then. I told him no; that it was stupid because the lottery is a tax on people who are bad at math (glad I talked myself out of that!). As we walked out of the store, I felt compelled to use his new understanding of probabilities as a teachable moment. You see, this friend is also a creationist (I know a lot of them, I don’t know how I befriend so many, I just seem to be a magnet for young-Earthers) and he had recently regaled me with proclamations about how wildly improbable it is that we exist at all and that the world is so perfectly suited for us. At the time I had simply offered the pithy story of the puddle marveling at how perfectly designed to fit its form the pothole it lived in was. Now I had something far better.
“You know,” I started meekly, “I think that kind of misunderstanding of probability is really common. It’s easy to consider the unlikeliness of events from the perspective of before they happened.
“I’m thinking of your comments the other day about how unlikely it is that humans exist and what a strange and improbable turn of events it took to lead to your and my births. But really, the massive improbabilities are only massive when viewed as a whole, as though you and I walking here now is the best possible scenario for the universe and ‘isn’t it so amazing that that’s what happened?’ I’ll grant that it’s a great scenario for the two of us, but small changes in the recent past could easily have lead to two other people standing here talking about probabilities, or two people talking about baseball, or no people at all because of some nuclear catastrophe. We just happen to be here as the beneficiaries of the fact that something had to happen, and that something happened to be us.”
I went on to explain that the incremental progressions brought by chance and natural selection are what make evolution such a compelling and explanatory theory. I told him that in denying evolution he denies himself the ability to understand the world in its complexity: to understand heart failure, or appendicitis, to make sense of the tragedy of disease and famine. He needn’t attempt to rectify the belief in an omnipotent and loving God with the reality of the imperfections of human form and the wasteful loss of life in natural disasters. There’s no point in trying to find God’s reason for taking a life via cancer, or drowning, or age and decrepitude. We know why these things happen already, and the answers are strewn across a field of time 4.5 billion years wide.
I tell this story here on this blog not because I ‘m trying to proselytize as an atheist. It’s really not all that important to me whether or not you believe in God. It is important to me, however, that you choose to think critically and integrate new data and new ideas into your understanding of the world. Failure to do so is what leads to poor science curricula in school, and ultimately hurts us as individuals, as a nation and as a world. If you simply choose to discard inconvenient data when it suits you or conflicts with your preconceived beliefs, then you can fully expect others to do the same. In due time, we find ourselves defending the most basic sciences from attack by those who are simply too lazy or too scared to think and we raise a generation of children who are forced into ignorance by intellectual cowards.
My friend was silent for a while after I gave him my perspective. Sadly, the next words from his mouth were, “I still think you’re less likely to win using last week’s numbers.”