Probabilities of Destruction

Several weeks ago, the news world was abuzz with the announcement that a 300-foot asteroid had been discovered with the highest recorded probability of hitting earth. If it hits us, it’ll happen right before Christmas in 2032.

The asteroid is 56 million miles away right now, so pause for a moment to consider how insane it is that tiny earthlings stuck on this planet are able to even calculate its trajectory. That’s akin to mapping out the path of a speck of dust on the moon using a magnifying glass in a park in Kansas.

The “probability” of this destructive event happening peaked at about 3% before NASA revised its estimate downward. Today, several space agencies have aligned around the chances being ~0.002%.

Now here’s my question for you: What on earth (pun intended) does a probability of 0.002% mean? Does it mean it won’t happen? Does it mean it definitely won’t happen? Does it mean that in some universe, it will happen, but we’re not in that universe? And if it does end up happening, will it mean our smartest scientists were wrong?

If anyone is left standing after the asteroid hits and is compelled to criticize the accuracy of such predictions, they might be reminded of the 2016 US presidential election, after which the world was aghast at the massive blunder made by alleged poll experts and statisticians. The polls had “predicted” that Hillary Clinton would win. She lost. The polls were “wrong”.

Yet all of that statistical analysis in the lead-up to the election gave Trump a nearly 30% chance of winning. To most people, then, a three-out-of-ten prediction is “wrong” if the event happens, but a slightly higher 50/50 prediction is “right” if the event happens. If the world was incapable of processing that 30% meant “still pretty darn probable”, how are we to make sense of a 0.002% chance?

Think about it this way: If I told you there was a 30% chance of rain tomorrow, and it rained tomorrow, would you be surprised? How about if I told you there was a 2% chance of rain, and it rained? How about if I told you there was a 0.002% chance of rain, and it rained? When does the prediction turn “wrong”?

The Two Types of Probability

I recently read the fantastic thought-provoking book Fluke, by Brian Klaas, in which he explores how randomness governs our lives. In one part of the book, he offers an insight I hadn’t before considered. And it’s changed the way I think about all of the above.

We often talk about the chances of something happening. And we use the same language (chance, odds, etc.) to describe two very different sets of possible events.

The first type of probability we humans like to cite is the measurable likelihood of something happening. A die has a one-in-six chance of landing on any given number. A coin has a one-in-two chance of landing on either side.

We know this because the Law of Large Numbers says so. We can rerun the experiment time and time again, and the more we do so, the more a given outcome will match these idealized probabilities. Flip a coin five times, and it may come up only heads. Flip it one million times, and the heads occurrences will make up about 50% of the outcomes.

These events are repeatable. And so another way of thinking of this type of probability is as the likelihood that a specific outcome will occur this time, out of the many other times the event has taken in the past and will take place in the future.

But what of events that are not repeatable, and that can only ever happen once? The 2016 election could only happen once. The path of the asteroid can only be traversed once. There is no replaying the simulation (at least, until AI can simulate any real world scenario accurately).

With non-repeatable events, our first definition of probability breaks down. “The likelihood that a specific outcome will occur this time, out of the many other times” is unmeasurable, because these events can only happen one time each.

That’s where the second type of probability comes in: It’s the confidence with which a statement about an uncertain event can be made.

Saying the asteroid only has a 0.002% chance of hitting us is the scientific community’s way of saying “Our models are sure it won’t hit us. But they’re not perfect. So that margin of error makes us only 99.998% sure we won’t get hit.”

As with the coin flip, there is a definitive answer to whether the asteroid will or will not hit us. We just don’t know what that answer is. But whereas the first type of probability purports to tell us, “Here is how this one event will fall into the history of every time this event was/will be/can be done,” the second one suggests, “Here is how this event will unfold, accounting for the fact that we really don’t know much about anything.”

That second type of probability is why weather forecasts are so wildly inaccurate. We only live in one universe, and our models of that universe are simply too basic to understand something as complex as weather.

Let’s hope asteroid trajectory models are more accurate than weather ones.

After all, there’s a big difference between what we know but can’t predict and what we don’t know. Let’s start talking about them differently.

Closing Words

Final words go to two quotes about probability.

The first is by George Boole, the mathematician who laid the foundation for pretty much all modern-day programming:

The second is by physicist Neil deGrasse Tyson: