The Case of the Incomprehensibly Big Super Volcano

The Yellowstone Super Volcano is every American's favorite geological Apocalypse-in-waiting.* Every 700,000 years, give or take a few hundred thousand, this buries a significant portion of the western US in various astounding superlatives. But this article on the recent 4.8 earthquake at Yellowstone has the biggest (and silliest) superlative I've come across in a while. The article states that,

"Late last year a new study into the enormous super volcano found the underground magma chamber to be 2.5 times larger than previously thought — a cavern spanning some 90km by 30km and capable of holding 300 billion cubic kilometers of molten rock." 

Now, 90*30=2700, and 300 billion over 2700 is 111,111,111.1111, or a bit more than 110 million. So for the volume of the cavern to be 300 billion cubic kilometers, the cavern would have to be 110 million km deep, or roughly 8700 times the diameter of the earth, about 2/3 of the distance to the sun. That is one deep hole. With the utmost respect to the Ragnarokian prowess of the great and powerful Super Volcano, I question whether its magma chamber is roughly one third of the entire Earth. Rather, I suspect that this is another case of innumeracy (or at least i-unitacy) on the part of a reporter. 300 billion cubic kilometers of molten rock is not likely, but 300 billion cubic meters of molten rock is quite plausible. A cubic kilometer is a billion cubic meters, so 300 billion cubic meters is 300 cubic kilometers, which is about how big you would expect a 90*30 km cavern to be. Still figuratively, but not literally, astronomical.

The fact that reporters often don't understand units and don't do the basic arithmetic to check numbers is nothing new, but it has only just occurred to me that there is a systematic bias in this. As when NPR casually mentioned the "240 mile deep water" off Alexandria, or when I heard on the radio that a local bank was receiving a bailout in the hundreds of trillions of dollars, reporters always seem to get the numbers wrong in a way that grossly exaggerates the claim. If the magma cavern was stated to be 300 billion cubic millimeters (equal to 300 cubic meters) instead of 300 billion cubic kilometers, a reporter or editor probably would have found that unsatisfying and therefore caught the mistake. If it was instead 300 Sextillion cubic meters, it would look sexy and nobody would likely question it. But there is probably another bias at work. Once a number is really big, substituting another really big number generally doesn't change the impression much, and if one doesn't understand what the numbers mean, it is therefore equivalent. Incomprehensibly Big = Incomprehensibly Big. So overstating your case by a factor of a billion isn't go to raise nearly as many alarms as understating it and thereby eliminating the hugitude.


*You only think you prefer that tired old tectonic fault.