Much remains to be explained about the remarkable encounter between two nuclear ballistic missile submarines in the Atlantic in early February. The whole affair really puts the Foxtrot* in “WTF”:http://en.wiktionary.org/wiki/whiskey_tango_foxtrot.

One angle probably not worth fixating on is the idea, mooted in the “comments at ACW”:http://www.armscontrolwonk.com/2188/when-ssbns-collide, that this was no coincidence. There’s just no plausible reason to operate SSBNs intentionally in proximity to one another.

But meant another way, perhaps it was no coincidence. It’s easy to “underestimate”:http://www.totalwonkerr.net/1849/whats-the-chance “probabilities”:http://www.totalwonkerr.net/1855/whats-the-chance-ctd for at least a couple of reasons.

First, the “role of iteration”:http://www.totalwonkerr.net/1849/whats-the-chance. If the chance of a bad event per patrol is one umpteenth, the chance of a bad event per umpty-ump patrols may be a good bit higher. (It’s the complement of the chance-of-no-bad-event-per-single-instance raised to the power of the number of instances.) We tend to overlook this.

The implications of this point for the chance of general nuclear war are left as an exercise for the reader. Happy spreadsheeting, and sleep well.

Second, the “assumption of independence”:http://www.totalwonkerr.net/1855/whats-the-chance-ctd. It’s simplicity itself to do calculations such as the one above, but it assumes that each instance is not influenced by any other instance. They’re all mutually independent. But whether it’s satellites or sous-marins, there routinely seem to be reasons — physical, technical, geographic, etc. — to operate in similar or overlapping patterns. In short, there are dependencies between events. This, too, is easy to overlook. Among other things, it makes the math a great deal harder.

The implications of this point for credit default swaps are left as an exercise for the reader should be lost on no one by now.

All of which is a way of saying that the “shut-mouthedness of the French and British navies”:http://www.nytimes.com/2009/02/17/world/europe/17submarine.html about this event is no indication of anything more sinister than the wholly reasonable desire to preserve secrecy about their SSBN patrol areas. Based on what’s been published so far, you can already make some educated guesses about the general vicinity of this event, which ought to be enough to make anybody a little uneasy.

It helps to recall why the boat goes under the water in the first place: so you can’t see where it goes.

*Yes, I realize that neither of these boats has much in common with a “Foxtrot”:http://www.russiansublongbeach.com/Scorpionfacts.html except that they all go under the water.