Spectacular Improbabilities

In the past few days there were three stories of improbable events, two catastrophic and one that was potentially catastrophic. They were widely covered so you would almost certainly be familiar with them: plane crash, satellite collision, and submarine collision. While there is much of human interest in two of these stories, there is a common thread running through these separate events - probability - that always catches my interest.

First, there was the human tragedy near Buffalo. In the weeks and months ahead there will be painstaking work to reconstruct in excruciating detail the events leading up to the crash, and, importantly, to learn lessons to be applied in future. This should lead to increased air safety, which is already extraordinarily safe. It's gotten so safe in part through similar learning in past tragedies.

I can still remember a time when news of a plane crash would lead many people to a renewed fear of air travel despite the statistics of just how safe it was in comparison to alternatives. To me it seems novel that there is little of that today. It may be that the general population has finally understood this fact, that it is highly probable that when you get on an aircraft you will arrive at your destination safely and ready to complain about all the petty annoyances of modern air travel. The reaction is so muted that articles like this one in the Ottawa Citizen seem almost superfluous.

So, the likelihood of an air crash is low, especially in this part of the world. That's what makes it safe. However, there are many flights and passengers and so these tragedies happen with some regularity. Keep that thought in mind while I go through the next two events.

The second catastrophe involved no humans except for, perhaps, insurance underwriters, since it occurred in Earth orbit: the collision of an Iridium communications satellite with a decommissioned Russian military satellite. While this is a wildly improbable event, it is very probable that such an event was due. In the words of Douglas Adams, "space is big, really big," yet with the vast quantity of satellites and their detritus in orbit these collisions will occur.

Up until now the likelihood of a satellite collision in any span of time has been lower than for air crashes. This situation will continue for some time since air travel is getting safer, and for now at least traffic loads are down, even while the quantity of junk in orbit is increasing. I can imagine a time within a couple of decades when those lines of probability will cross and satellite (or debris) collisions will have the higher frequency. Luckily there are few humans in space right now, and they're in one location, so the chance of a human tragedy will remain low for some time. Some day this could change.

The third event, the near disaster, was that curious collision of submarines in the Atlantic Ocean. At first glance this has to be the most improbable of this set of events; there are few submarines and lots of water, and they're being steered by humans. This has even been part of the public relations from the navies involved:

“It's an absolute one in a million chance that the two submarines were in the same place at the same time,” said Lee Willett, head of the maritime studies program at the Royal United Services Institute, a London-based military think-tank. “There is no precedent of an incident like this — it's a freak accident,” he said.

Luckily there was no serious damage so it seems almost comical: two vessels with technology to evade detection manage to bump into each other.

Of course this last event is not quite as improbable as stated above since submarines are not randomly distributed over the surface (and depth) of the ocean. Indeed, this is not an isolated event, as Willett claims, and as is detailed in this New York Times article:

Military experts said there were a number of collisions between western and Soviet submarines during the cold war. In 1992, an American nuclear submarine, the Baton Rouge, was struck by a surfacing Russian submarine in the Barents Sea.

Unfortunately I don't have a suitable quote handy, but supposedly the reason why these collisions are not uncommon is that subs tend to closet themselves in the same areas, areas suitable to their covert or hidden activities, and which are far smaller in volume than the ocean.

The same is true of satellites. They are not randomly situated in space, but instead occupy similar orbits that are optimum for their intended applications. This is similar to the situation with the subs, and further explains why satellite collisions can happen. Unlike the situation with subs, and aircraft, the probability of disasters climbs after satellite collisions since the debris clouds occupy a greater volume than their original, intact, form, and even a single bolt at the high velocities involved can ruin someone's day.

We have made improbable events likely by making a multitude of "attempts". Just like with the lottery, it is very improbable that you will win but very likely that someone will win. So it goes with satellites and aircraft, and even it seems with subs.