Academic journal article et Cetera

One More Time

Academic journal article et Cetera

One More Time

Article excerpt

I DON'T KNOW how many times Marion Winik, a commentator on National Public Radio's "All Things Considered," has been married nor how many volumes of poetry she's published. Therefore, her stating early in her review of Erica Jong's Fears of Fifty: A Midlife Memoir that "Jong has been married three times more than I have [and] published 12 more volumes of poetry" got me to wondering. (1)

If Winik has been married once, then Jong must have been married four times (three times more than once). Unless, that is, Winik made the common overkill error of using "three times more" to mean only "three times as often as," in which case Jong may have been married just three times.

By mentioning the subject Winik suggests that she herself has been married more than once. If Winik has been married twice, then Jong must have been married eight times (three times more than twice). Unless, again, Winik indulged in overkill, in which case Jong may have been married just (if that's the right word here) six times (three times 'more' than twice, meaning "three times as often as twice"). But then, maybe Winik didn't use the word "times" in "three times more" in the sense of multiplication but only in the sense of occasions. This way, if Winik was married twice, Jong would have been married five times (three occasions more than twice).

Thus, depending on whether Winik had been married once or twice and on what she meant by "three times more," Jong could have been married three, four, five, six, or eight times.

Then, if Winik had been been married three times...but you get the idea. There's a puzzle here. And nothing in the rest of the review gave any further clue on the number of husbands netted by either Winik or Jong.

Whiffs of English-math indeterminacy begin to affect me like the potion quaffed by the curious Dr. Jekyll. The foaming brew of this Winik story transformed me in half a trice into the carousing Mathsemantic Monitor, who rushed forth to find and regale his own one-and-only with this latest example of innumerate folly.

"Who cares," she said with a raised eyebrow, "how many times Marion Winik or Erica Jong has been married? What does it matter?"

"That's not the point," said my bedeviled alter ego. "Here I've worked all these years to get past the words, to be extensional, and then a fancy writer, this Winik, seems to go out of her way to make her constructions impenetrable."

"Well," cooed my love with a smile, "she said she was a poet. Maybe she meant to be unclear."

And so I had to let Marion Winik off the hook. Maybe she meant to be unclear. If so, she succeeded marvelously.

She also put me on the lookout for similar examples not created by poets.

Question: do the constructions "four times as often as" and "four times more than" mean the same thing? Take a moment to think about it.

The answer, if we are to preserve both ordinary meaning and mathematical sense has to be no, they don't mean the same thing. Assuming they mean the same thing leads to an absurdity.

1. If four times as often as = four times more than, Then three times as often as = three times more than, And twice as often as = two times more than, And just as often as = one time more than.

This last is obviously absurd. The construction "times more than" falsely adds one more time. The correct line-up goes like this:

2. Four times as often as = three times more than, Three times as often as = two times more than, Twice as often as = one time more than, And just as often as = no times more than.

So we can say equivalent things two different ways, which are numerically just one apart. This leads to all kinds of complications.

For example, say your room is on the first floor of a three-story house. You go from the first to the second floor. You've gone up one floor, but you've been on two floors. Someone asks you at dinner how many floors you visited today. …

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