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Thursday, January 15, 2004
On Exponential Growth
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November 30, 2005
I received a message from Mr. Coffee pointing out that my criticism was, in fact, wrong. While I stand by my assertion that the term "exponential" is frequently abused, such was not the case in the eWEEK article:
On your old blog site, you purport to correct my use of the term "exponential" (as opposed to "geometric" growth).
My use is consistent with this passage:
Exponential Growth
The continuous-time analogue of geometric growth is what is known as exponential growth...
In the case of the exponential process, t can assume any real value. However, if t takes an integer value, then equation (7) can be identified with equation (1) of geometric growth...
which you'll find at http://www.qmw.ac.uk/~ugte133/courses/elomath/lectures/06intrst.pdf
I take some pains to use terms correctly. If you're going to leave your criticism on line indefinitely, I'd appreciate the opportunity to add a comment to that (now static) page.
- Peter Coffee, eWEEK
I have apologized to Mr. Coffee and posted a follow-up article. His comments were added to this post at his request.
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I can't stand it any more.
People, please: I am okay with English as a living language. I don't complain about "fast" being used as an adverb anymore, and I have accepted the use of third-person plural pronouns for third-person singular of indeterminate gender. And it doesn't bother me a bit to defiantly split infinitives or to begin a sentence with a conjunction. I may be a few centuries behind the curve with all of this, but I have conceded what is already lost.
But if you're going to use mathematical terms, precision is imperative. As Peter Coffee pointed out,"exponential" does not mean "fast". Nor does it mean whatever it was he was trying to describe. I think he, like most of the media, really should have used "geometric." For the layman, and for the record, here's the scoop:
- arithmetic growth: Numbers are added. Let's say you have three dollars, and each day you get two dollars more. After four days, you'll have 11 dollars: 3 + 2 + 2 + 2 + 2.
- geometric growth: Numbers are multiplied. Let's start with that same three dollars, but each day, it will double, i.e., be multiplied by two. After four days, you'll have 48 dollars: 3 x 2 x 2 x 2 x 2.
- exponential growth: Numbers are raised to a power. We'll start you out with three dollars again, but each day, it will raise to the power of two (multiply by itself), or square. After four days, you'll have 43,046,721 dollars: 3 ^ 2 ^ 2 ^ 2 ^ 2.
Exponential growth is way beyond fast. It also just doesn't happen in the sort of contexts to which it's usually applied in the media: populations, deficits, market growth, and the like.
Maybe I shouldn't get upset about what may be simple hyperbole. Or even hyperbola. Let's make a deal: if you'll get this one thing right, I'll stop fussing about how English is transitioning to a language in which verbing nouns is acceptable. I wouldn't mind at all, though, if you'd also stop abusing the apostrophe.
Posted 01/15/2004 13:50 by Fritz | Comments (1) | TrackBack