Posted by Eugene Volokh:
"Times Less Than":
http://volokh.com/archives/archive_2009_09_20-2009_09_26.shtml#1253897118
An e-mail from a reader reminded me again of [1]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.
This prompted me to do some more searching, and discover not only a
usage of this phrase by [2]Jonathan Swift (via Merriam-Webster's
Dictionary of English Usage), but also by [3]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, [4]Robert Boyle, [5]John Locke, and more. Nor is this
some archaic usage; it remains routine today.
What's going on here? The correspondent whose message prompted me to
repost about this suggested that "A times less than B" might be a
[6]calque -- "a loan translation, esp. one resulting from bilingual
interference in which the internal structure of a borrowed word or
phrase is maintained but its morphemes are replaced by those of the
native language, as German halbinsel for peninsula" -- from my native
Russian, where "X raz men'she [or men'eye] chem" is routine. But that
hardly explains Newton and Herschel, I think.
Rather, I think what's going on in the critics' minds is itself a sort
of calque, though a calque from mathematics to human language. 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.
Nor can you somehow disprove my assertion by "logic" of the "but
'times' means multiplication!" sort. That is the logic of the calque,
and while calques sometimes do create usage (in Russian, for instance,
the word for "rhinoceros" is "nosorog," since "rhino-" translates as
"nos" [nose] and "-ceros" translates as "rog" [horn]), sometimes they
don't. If you want to know what is an acceptable form (though just one
of several acceptable forms) in English, including scientific English,
is, the actual usage of Newton and Herschel -- and, I suspect,
countless lesser lights of today -- tells us more than the abstract
logic of literal translation from mathematical symbols.
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 ...."
References
1. http://www.volokh.com/posts/1150829292.shtml
2.
http://books.google.com/books?id=2yJusP0vrdgC&pg=PA908&dq=%22times+less+than%22+%22dictionary+of+english+usage%22#v=onepage&q=&f=false
3.
http://books.google.com/books?id=zhM1t2fj4KcC&pg=PA66&lpg=PA66&dq=newton+%22three+times+less+than+before%22&source=bl&ots=KfcxGfbutB&sig=QjfWcPnEJEojKuVEXr3_xNCk-X0&hl=en&ei=_u-8SueEOYGwsgO64_DdAQ&sa=X&oi=book_result&ct=result&resnum=1
4.
http://books.google.com/books?id=BCAOAAAAQAAJ&pg=PA7&lpg=PA7&dq=%22had+they+been+ten+times+less+than%22&source=bl&ots=C5tt_maq1u&sig=horRd_Eq1loq_CXjqc_7EM4zkxw&hl=en&ei=WO-8SrT1KJKqtgPzm5W7BA&sa=X&oi=book_result&ct=result&resnum=1#v=onepage&q=%22had%20they%20been%20ten%20times%20less%20than%22&f=false
5.
http://books.google.com/books?id=-uSzdaXce5gC&pg=PA297&dq=%22times+less+than%22&lr=&as_drrb_is=b&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=1800&num=100&as_brr=0#v=onepage&q=%22times%20less%20than%22&f=false
6. http://dictionary.reference.com/browse/calque
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