Monday, September 20, 2010

Taking Numbers Too Seriously

Numbers are deceiving, as the author of Proofiness [think "truthiness"] explains below. Much like us, the ancient Indians had loose terminology for numbers. What do we mean by a zillion or a kajillion, a lot, or a long ways? Answer: It's context-dependent. Whereas a zillion haircuts means a couple of hundred, a zillion stars means "more than we can count."

Similarly people have long asked, How long is a great kalpa (aeon)? It is, of course, four sub-aeons long. One can hardly say exactly. But exactly is what British and German translators demanded, and they got it: 4.32 billion years. (The Buddha instead defined astronomical numbers using staggering similes, but the commentarial Path of Purification is very specific about different types of kalpas).

How many is a lot? That would be precisely 500. When Buddhist sutras use 500, they only really mean "a lot." How long is country mile (yojana)? It is the distance an ox can plough before needing to be unhitched and rested. But more precision was needed, so its true vague meaning was replaced with a proofier sounding "seven miles." Similarly, when the redactors of the sutras went from an oral to a written tradition, things conveniently got sorted by number.

The Numerical Discourses of the Buddha (Anguttara Nikaya) is a great example of how this easy (and potentially misleading) classification system came to look. Anguttara literally means "increased by one." Instead of going by subject matter, any loose sutra that said four of these or five of those made it into the Book of Fours or Book of Fives.

We like 10 and 100, but the ancient Indian preferred 8 and 108. The flexibility of numbers as secondary to the Truth is perhaps never made more clear than with the question, "How many precepts are there?" Five, 8, 10, take your choice since they more or less refer to the same set of items divided up in different ways. In short, numbers are a convenience not to be taken too seriously.

The Dark Arts of Mathematical Deception
Proofiness by Charles Seife (NPR interview)
...But trusting a number too much can be dangerous, the author says. It’s a phenomenon he calls ‘disestimation,’ and it happens when people take a number far too seriously.

Seife recalls the story of a docent at the American Museum of Natural History in New York, who gave the age of a dinosaur as 65 million and 38 years.

“The guide says, well, when I started at this museum 38 years ago, a scientist told me it was 65 million years old. Therefore, now, it’s 65 million and 38.” Seife says the docent was placing far too much value on the 65 million figure, “when in fact, the error involved in measuring the dinosaur was plus or minus a hundred thousand years. The 38 years is nothing.”

And speaking of error, Seife has some choice words about opinion polls and the way they’re reported. “When journalists report polls, they just don’t know better that they shouldn’t take these results literally,” he explains.

Seife says the margin of error you see attached to a poll is only measuring one specific kind of error: taking too small of a statistical sample. “But in fact, when polls go wrong,” he says, “it’s due to a completely different type of error, called a systematic error.”

That means the poll hasn’t been set up correctly or the questions are misleading, or simply that people answering the poll are lying — which Seife says happens quite frequently. “So when journalists report polls, most of which aren’t worth the paper they’re written on, I think they’re kind of innocently performing an act of proofiness.” More>>

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