Tag Archives: Randomness

31 Days – Ratcheting

We have only 3 days left in this month’s 31 Days of Wonder, and I’ve saved a good one for you. I call it the ratcheting effect, and we owe our existence to it.

First let’s play cards.

If you were to shuffle a deck of cards perfectly (completely randomizing it) over and over again, how long do you think it would take until, by chance, it fell into order? (“Order” in this case means Ace through King of Spades, followed by Ace through King of Hearts, and so on — one specific order.)

Well, there are about 8 * 1067 possible ways to arrange 52 cards. By comparison, the universe is only about 4 * 1017 seconds old.  If you were to shuffle once every 5 seconds, you would have to shuffle for incalculably many lifetimes of the universe before you’d expect even one perfect ordering.

Now suppose we change the game. This time, each card has the unusual property that if it happens to get shuffled next to its correct neighbor, then the two will ride together for all the remaining shuffles.

How long do you think it will take before the deck is in order?

Last night, I wrote a little computer program to perform this experiment. On average, it took only 55 shuffles to put the deck in order. You could do that in less than 5 minutes — a lot less than even one age of the universe.

When something that’s “right” sticks, the situation can ratchet toward a desired outcome very quickly.

So what does this have to do with us? How do we owe our existence to the ratcheting effect?

Some people think the chance formation of even a single cell is wildly improbable. And so it would be if it had to form in one step, but that’s not the way it happened. Just as the cards in our second deck stuck together to form sub-units, which then coalesced further until the deck was ordered, life ratcheted up in steps, each of which was naturally preserved.

In fact, the more experiments we do in this area, and the more Earth-like planets we discover, the more likely it seems that we are not alone in the universe. Now that’s something to wonder about!