Mark Spahn writes:

## Numerical comparisons: "three times ~er than" versus "three times as ~ as"

"Arab isolation has exacted a heavy economic cost. Algeria was only very slightly poorer than Portugal in 1960; today Portugal isthree times richerthan Algeria. Syria was a substantially wealthier country than South Korea in 1960; today, South Korea is more thanfive times richer."(

This quotation makes a numerical comparison between pairs of numbers that measure the richness of countries, such as their average per-capita annual income.An End to Evil: How to Win the War on Terror,by David Frum and Richard Perle, page 170)

To say that "Portugal is three times as rich as Algeria" means numerically thatP= 3 ×A, wherePandAare the average per-capita annual income of Portugal and Algeria, respectively.

To say that "Portugal is 300 percent richer than Algeria" means thatP=A+ (300% ofA) =A+ (3.00 ×A) = 4 ×A. ButP= 4 ×A, translated back into non-mathematical wording, means that "Portugal is four times as rich as Algeria."

What does it mean to say that "Portugal is three times richer than Algeria"? There are two possibilities:

(1)Which interpretation of "three times richer" is right? Logically, interpretation (1) is correct, but in practice, a Google search of "P=A+ (3 ×A) = 4 ×A. Since "three times" means the same as "300 percent," "three times richer" should mean "300 percent richer," and, by the above argument, "300 percent richer" means the same as "four times as rich."

(2)P= 3 ×A. By this interpretation, "three times richer" means the same as "three times as rich."

Ntimes ~er than" would find that interpretation (2) is adopted by almost all of the examples that include enough information to resolve the numerical relationship between the two compared quantities.

(June 4, 2004)