Probable Cause (Part 1)

I’m interested in probability. Not in how we calculate probability, because once you know how to do it, the whole thing can get pretty boring. But what probability is – that’s what I wonder about. Does it really exist? Or is it more like time, in the sense that it’s a way of measuring something we can’t quite put our finger on? And if it does exist, how does it work?

My introduction to the subject was likely similar to yours. My math teacher asked a question about colored marbles, and what would happen if you chose one at random.

“You have ten marbles in a box,” she said. “Two are red, three are green, and five are blue. If, without looking, you pull out a single marble, what is the probability that it will be green?”

Uninvited, my brain would immediately begin to ask questions of its own. “If I wanted a green marble, why would I take one without looking? Wouldn’t it save time if I just opened my eyes, so I could see what I was doing? And what is this situation involving marbles that’s so urgent that the first one has to be green?”

In an attempt to devise an explanation, I’d answer my own questions. Maybe I’m being held hostage. My kidnappers have blindfolded me, and, at gunpoint, are demanding that I reach into a box and select a green marble on the first try. I can feel their tension, and from there it’s easy to imagine the circumstances that would have driven them to such a desperate act. “They’re crying out for help,” I say to myself. “They must have a math test tomorrow.”

But my teacher wasn’t finished yet. “Suppose the first marble you choose is blue. Now what is the probability that the second marble will be green?”

Apparently, this crucial need for a green marble continued, yet we stubbornly refused to look into the box to find it. Then, just as I was growing tired of the teacher’s lack of critical thinking skills, she went on to a new lesson.

“Let’s say I flip this penny repeatedly, and it comes up heads ten times in a row. What is the probability that the next flip will be tails?”

Now she had my attention. Flipping coins had to be similar, at least in principle, to flipping cards. So, unlike the blind plucking of marbles from a box, here was a skill with real-life applications.

My friends and I all collected baseball cards. I use the word collected, but I don’t mean it in any organized, intelligent way. I mean we spent every nickel we had buying more and more packs of cards, hoarding them as though we were somehow enriched by their sheer number.

Baseball cards weren’t sold over the winter. The day they reappeared, usually in late March, we all ran like mad to the nearest store, moving as fast as possible while also keeping our legs as straight as we could, so the money jingling in our pockets wouldn’t spill onto the street. We were racing to see what this year’s cards would look like, and getting there ahead of everyone else meant you might have entire seconds to savor that discovery of vital information.

Minutes later, we’d stand on the sidewalk right outside the store and open pack after pack, rifling through each one to see which players we got, and how many. Like mindless machines, with each newly opened pack we’d shove another thin slab of brittle, powdered pink bubble gum into our already engorged mouths, all the while attempting to announce our latest acquisitions – at least the ones that would make the others insane with jealousy – and half-listening to their announcements, too.

Whenever I see the way stock market traders behave, screaming and biting and climbing over each other, it reminds me of those first days of baseball card season.

By summer, we’d each be walking around with a stack, sorted either by team or favorite players, with doubles and triples arranged together and ready for some high-pressure transaction. We’d show off our riches the way gangsters in movies would flaunt wads of money as they paid for a thirty-cent cup of coffee with a fifty-dollar bill. By the All-Star Break, we’d each have a shoebox filled with our most prized cards, which we stashed under a bed or hid in our closet behind the sweaters. The stack we carried around was for trading, or flipping.

The front of a baseball card had a picture of the player, his position on the field, and the name of his team. That was heads. On the back of the card were his career statistics, along with some useless trivia, such as “In the off-season, Hector trains pigeons.” That was tails. We’d hold the card by its opposite vertical edges. Then, with our hand down and to the side, we’d pull back, then forward, letting the card meet air resistance as it twirled to the ground. Heads beat tails, while two heads or two tails was a tie, and called for another flip. The winner picked up all the cards.

But was there a technique? Could we control the outcome of a flip, or was it just luck? Was probability influencing how much our stack of cards would grow or shrink by the end of the day? And if it all came down to just chance, why did some kids do so well, while others kept getting wiped out?

I eventually learned that, in the case of things like coins and cards, probability was a way to estimate how frequently a certain outcome would occur – not predict what would happen at any given moment. But it wasn’t really luck. It was that the object we were tossing was subject to so many competing forces, we couldn’t possibly measure them. In the case of a penny, there was the way we held it before the flip, the angle, how much energy we imparted with our thumb, air resistance, the surface it landed on, and other things. If we were flipping a manhole cover, we could easily forecast the result because the object is large and heavy, making those forces less significant. In other words, it would be simple to control whether it came up heads or tails. If we could shrink ourselves down, so a penny was like a manhole cover, we wouldn’t need probability.

Is that what’s going on with everything? We used to attribute almost all events to the decisions of the gods. Then science came along and showed us that some things we thought were mysterious and supernatural are open to understanding, if we’re willing to learn. But there’s still a lot that’s fuzzy. Think of those numbered ping-pong balls that used to determine the next lottery millionaire. Which numbers were drawn depended on thousands of tiny variations in motion, with each variation affecting the others around it, and with everything happening very quickly. No matter how sensitive or smart our instruments may become, things like that will remain unpredictable.

But what about the human element? Different people have different skills. We make decisions, sometimes for no discernible reason. Our ability to interact is unprecedented. Add randomness to the mix and almost any crazy thing can happen. You might even be kidnapped and forced at gunpoint to choose a marble from a box. Let’s just hope it’s green.

Tagged: baseball cards, coin toss, gangsters, kidnappers, lottery, luck, marbles, math, probability, randomness

Posted in: In Over My Head