Thursday, May 07, 2009

Not a drop in the bucket, not a few "pieces" of sand.

So, Obama's proposed some cuts in government spending. Because it's only $17 billion, and the 2010 proposed budget is $3.55 trillion, this is described as a "modest" cut. On NPR, it is described as "less than one-half of one percent." Which is slightly misleading ("less than" is pretty broad -- a lot less, or a little less?) NPR characterizes criticism "that his cuts were but a drop in a $3.4 trillion spending bucket". (The $3.55 trillion number comes from VOA News. I don't know why there's a disparity.)

Or, here's some actual criticism from NH Republican Judd Gregg:
"It is as if this was the Gobi Desert or the Sahara Desert, and you came along and took a few pieces of sand off the desert"

This innumeracy I cannot abide.

$17 billion out of $3.55 trillion is 0.479 %. If I used NPR's $3.4 trillion figure, it'd be exactly 0.5 % (not less). "Less than one-half of one percent" sounds small. Even the fraction - 1/200 - looks pretty small. (That's for 0.5%. The fraction for 0.479% is 17/3550, which looks, well, not obviously smaller than 1/200.)

A drop is one sixtieth of a teaspoon, and a typical bucket is 10 quarts, which is 320 fluid ounces. And there's six teaspoons in a fluid ounce. So "a drop in a bucket" is .00000868 %, or 1/115200. Which IS A WHOLE LOT SMALLER.

Yes, I KNOW it's just an expression. If NPR is using "just an expression" to REPORT NEWS, they must be using it to give people a concrete idea of the proportion between the ($17Bn) budget cut and the ($3.55Tn) budget. And they're giving them the WRONG CONCRETE IDEA.

And we haven't even gotten to the understandably biased but nonetheless unacceptably hyperbolic Gregg. Let's assume that Gregg's an idiot (because it makes him look BETTER) and that by "pieces of sand" he means handfuls (if he meant grains of sand, he's just lying. Or so thoughtless about what he says that he hasn't even considered whether it's remotely true or not, which is about the same thing.) So, what's the proportion of a few handfuls of sand to the Gobi Desert? Making some more assumptions about Gregg's inadequate understanding of deserts, suppose he thinks the Gobi desert is uniformly one handful of sand thick. The Gobi Desert is 500,000 square miles. If we round up a few handfuls to a square foot, a square mile is 27,878,400 square feet, so Gregg's proportion is 1/13939200000000, or .00000000000717 %.

You want to know what would be like a drop in the bucket? A cut of $31 million. With all the generous assumptions we gave Gregg's assessment, his comparison would accurately correspond to a cut of...25 cents.

Maybe Gregg can afford to overlook the difference between $17 billion and 25 cents. After all, he's only off by 10 orders of magnitude. That's one drop out of 579,437 buckets, by the way.

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Thalia said...

This analysis has made me ridiculously happy.

Thank you.

Terri said...

Thank you for that. :)

Sarah said...

AWESOME! If you haven't already submitted this as listener feedback to NPR, you must! And you should also send it to Senator Gregg. Your genius cannot be squandered on us mere blog readers.