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Saturday, November 29, 2008

Gnome-o-gram: Tiling with Terabucks

Jonah Goldberg just published a column which begins with the sentence, “The costs of Washington's bailout fiesta are now so huge, you can see them from space.” Well, of course, I know Mr. Goldberg was being witty, but this is a literal-minded chronicle by a literal-minded chronicler, so let's work the numbers and see what a terabuck (T$, a trillion [10¹²] U.S. dollars would look like from space). The exercise may provide some perspective on the sums bandied about as ultimately futile attempts are made to ward off the grand deleveraging crisis.

To be specific, let's calculate the area covered by a trillion United States one-dollar Federal Reserve Notes. Each note is 6.14 inches wide, 2.61 inches tall, 0.0043 inches thick, and weighs about one gram. The area of one dollar bill is thus 16.0254 square inches—call it 16 exactly. The area of a trillion such bills is just 10¹² times this figure, 1.6×10¹³ in², or about 3986 square miles: a little less than the combined area of the U.S. states of Delaware and Rhode Island.

But the bailouts are a lot more than a terabuck, which seems more like the weekly tab as this thing snowballs. The current estimate for all of the bailouts, including the most recent of Citigroup. is 7.7 T$ (although, as Goldberg notes, some of this is in the form of loan guarantees and equity investments, which may ultimately be recovered [but if that were likely, why would private investors not put up the money?]). Let's assume here the taxpayer is, as they say in Texas hold 'em, “all in” and holding a losing hand, as is usually the case for taxpayers. Well, then we multiply the 3992 square miles per terabuck by 7.7, and get 30692 square miles of money, about the area of the state of South Carolina. If arranged in a square, it would be 175 miles on a side.

Definitely visible from space!

Now, instead of laying out the bills side by side, let's make a stack of them. With each bill 0.0043 inches thick, a terabuck stack works out to be about 67866 miles tall, almost exactly three times the distance of geosynchronous communication satellites above the surface of the Earth. Multiplying by the 7.7 T$ size of the bailout yields 522568 miles, more than twice the mean distance of the Moon.

What would a trillion dollars in ones weigh? With each bill about one gram, that's 1.1 million tons per terabuck, or 8.5 million tons for all of the bailouts so far. So you'd not only better bring a big wheelbarrow, but a sturdy one as well!

What if you used hundred dollar bills, the largest available denomination, instead of ones? Just divide the area, height of the stack, and weight figures by a hundred, yielding 307 square miles of tiled bills (a square 17.5 miles on a side), a stack 5226 miles high, and a total weight of 85000 tons—still easily visible from space.

Other gnome-o-grams

Posted at 20:01