Posted by Eugene Volokh:
Careful With Those Scientific Allusions:
http://volokh.com/archives/archive_2007_12_30-2008_01_05.shtml#1199559637
I just noticed this item from Andrew Sullivan in [1]The Atlantic:
Consider this hypothetical. It�s November 2008. A young Pakistani
Muslim is watching television and sees that this man -- Barack
Hussein Obama -- is the new face of America. In one simple image,
America�s soft power has been ratcheted up not a notch, but a
logarithm.
Now I've been trying hard to stifle my natural temptation towards
mathematico-linguistic pedantry. Really, I have. "A number of" to mean
"many" still annoys me -- zero is a number; so is one -- as does "to
the nth degree" (depends on the n, no?). But I have to acknowledge
that these are established English idioms, governed by the rules of
English idiom, not of mathematics. I don't like 'em, but that's my
problem, not the speaker's.
Still, if you're going to try to come up with new figurative usages,
it seems to me that the figure of speech should fit rhetorically. "A
number of" at least sounds large, but "a logarithm" doesn't.
Logarithms, I think, generally seem small. In all the commonly used
bases, they are smaller than the original number, often much smaller.
A million is a big number; comparatively, the base-ten logarithm of a
million (six) is much smaller.
A logarithmic scale does have the property that small steps can
correspond to large increases, which is what I take it Sullivan is
referring to. But "ratcheted up ... a logarithm" doesn't quite capture
that, I think. "Exponential increases" does communicate "large
increases," in a way I have to grudgingly accept (down, math pedant
self, down!). But logarithm is the opposite of exponential, not a
synonym. And when new terms are coined, the correspondence to the
original referent does matter, especially given that most people who
even know what a logarithmic scale is will likely think of the
original referent.
My sense is that scientific allusions, like classical allusions, tempt
people into error -- they sound cool, and people use them because of
that rather than because they're apt. So think twice before you
ratchet things up a logarithm.
References
1. http://www.theatlantic.com/doc/200712/obama/3
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