Under the Times

A Facebook comment reminded me again of this debate — some people argue that “A times less than B” is “mathematically incorrect,” “simply wrong,” and so on. The theory is that “times” refers to multiplication, so “5 times less than B” to mean “B/5” is mistaken, though “5 times more than” to mean “5xB” (or possibly “6xB”) would be fine.

But somehow this logic was lost on, say, Isaac Newton (“If the Diameters of the Circles … be made three times less than before, the Mixture will be also three times less; if ten times less, the Mixture will be ten times less”), Sir William Herschel (“remember that the sun on Saturn appears to be a hundred time less than on the earth”), Erasmus Darwin, Robert Boyle, John Locke, and more. Nor is this some archaic usage; it remains routine today.

What’s going on here? My sense is that many people’s objections rest on an assumption that English is, or ought to be, like math. It’s true that if you view “times” as “x” and “less” as “-” then “A times less than B” is either literally meaningless, or corresponds to “B-AxB.” But of course in English, including the English used by scientists of the highest caliber, “times” doesn’t always mean “x” and “less” doesn’t always mean “-.” We see that from the very examples I just gave, as well as from observed common usage.

This having been said, it may well be that “A times less than B” is suboptimal usage, precisely because it annoys enough people. (I am skeptical that it genuinely confuses a considerable number of people.) But to say that the usage is “simply wrong” or “mathematically incorrect” is to misunderstand the connection between mathematics and English, including the English used by people who are masters of mathematics.

Finally, a request for people who want to argue the contrary: Please preface your comments with “Isaac Newton was wrong about how to talk in English about mathematics, and I am right, because ….”