I’ve flown north for the winter, leaving behind this crummy weather:
for this:
Much better. Along with leaving that damnable squint-inducing sun, I thought I’d also left behind the world of grammar curmudgeons when I got back to Pittsburgh. After all, this is the sort of town where many people add an r to wash and half the people find nothing the slightest bit odd about saying “My grammar doesn’t need corrected.” But as always, I was mistaken.
Last month, I argued that “five times bigger” is obviously grammatical. Unfortunately, James Kilpatrick didn’t read that post. Today I looked at Literal-Minded, who directed me to The Language Guy, who directed me to an old Kilpatrick column, which directed me to an older Kilpatrick column, in which he opines that “statistically speaking, there is no such thing as ‘six times lower.'” I am not a statistician. That much I will freely admit. However, I’m willing to bet that neither Kilpatrick nor Lewis Guignard of Crouse, N.C., to whom Kilpatrick turns to buttress his claim, are statisticians either. And the reason I am willing to make that bet is that, statistically speaking, there is such a thing as “six times lower”.
In fact, if Google is to be trusted, there are on the order of 16,000 such things as “six times lower” on the Internet. And it’s not just a bunch of idiots using “six times lower”. The phrase is attested in an Irish newspaper, an Australian newspaper, and an Indian government press release. Furthermore, there are a lot of hits for times lower in Google Scholar, including 10 or so in books and journals with the word “statistics” in their titles, suggesting that people who actually are statisticians are fine with the construction as well. So, statistically speaking, Kilpatrick is completely wrong.
As it turns out, the construction is over 200 years old. David Hume, he of the famous philosophical development that I forgot as soon as I turned in the AP European History test, wrote in his History of England:
“Yet the middling price of cattle, so late as the reign of king Richard, we find to be above eight, near ten times lower than the present.”
Given that Hume died in 1776, I am pretty comfortable in claiming that the construction X times lower predates Kilpatrick. Heck, it predates the United States of America.
Now the only remaining objection to the eminently reasonable X times lower construction is that its meaning isn’t immediately clear. But that’s rubbish. It means exactly what it sounds like it ought to mean. The Brie was six times cheaper than the cave-aged Gruyere means that if the Brie cost $4, then the Gruyere cost $24. But don’t just trust me on that one. Trust the press release for the Nobel Prize awarded to Claude Cohen-Tannoudji, William D. Phillips, and Secretary of Energy nominee Steven Chu:
“It was found that the temperature was about 240 µK. This … agreed very well with a theoretically calculated temperature – the Doppler limit … Phillips found in 1988 that a temperature as low as 40µK could be attained. This value was six times lower than the theoretically calculated Doppler limit!”
So, just as with five times bigger, if you continue to object to six times lower, you are, statistically speaking, dumb.
Summary: “Six times lower” is no less intelligible and no less grammatical than “five times bigger”. Which, of course, is both intelligible and grammatical.
24 comments
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December 21, 2008 at 7:51 pm
Neal
I wrote about a similar issue last year: how it makes no sense to say something is X% hotter OR colder if you’re measuring in Fahrenheit or Celsius. The post links to an earlier one on locutions such as half less, and a Jan Freeman column on the issue you’re discussing here.
December 21, 2008 at 7:52 pm
Matt
How about halfway more up?
December 22, 2008 at 10:05 am
Watch Yer Language - Your Monday reading list
[…] Gabe at Motivated Grammar defends the “X times lower” construction. We’ve been around this one a couple of times […]
December 29, 2008 at 8:24 am
Daniel
Neal, I feel compelled to dispute your claim that “it makes no sense to say something is X% hotter OR colder if you’re measuring in Fahrenheit or Celsius.” Of course it makes sense. If the high today is 68 degrees Fahrenheit and someone says it’s going to be only half as warm tomorrow, then it’s obvious that the person means it’s going to be 34 degrees Fahrenheit tomorrow. And the same holds true if we’re dealing with Celsius (although I feel sorry for anyone living in a place where the high ever hits 68 degrees Celsius!). Is it technically accurate from a physics perspective? No, but it’s casual conversation, not physics class. You might as well argue that it makes no sense for a musician to say that third plus a third equals a fifth because that’s not how mathematics works.
January 23, 2009 at 3:21 pm
Gabe
Matt: The Jelly Belly factory is a place where logic fears to tread.
Neal/Daniel: These are both good points. I am much more reluctant to say that “half as hot” (based on Fahrenheit/Celsius scales) makes sense than I am to say “six times lower” makes sense. I don’t feel like I would object to someone else saying it, but I doubt I would use it myself. I feel like it is completely comprehensible, but still notably awkward.
October 2, 2009 at 6:05 am
Lewis Guignard
Citing a misuing authority, perhaps Nobel Prize winners, does not make their grammar and math correct.
What they have actually described is 6 times larger in a negative direction.
The best way to determine the way to say it is to ask a question: what is 6 times lower than 25?
Well?? What is the answer?
What is six times larger than 25?
If you want an answer that is 1/6th of 25 then say so.
You, sir, are wrong and as Aldous Huxley said (paraphrased) ‘ignoring facts doesn’t make them go away.’
Neither do appeals to Nobel Prize winners whose grammar is wrong. Further the contributor above – Daniel – converts the multiplier to make his point, making his point wrong. Twice is not 1/2.
Lewis Guignard
October 2, 2009 at 10:42 am
Gabe
Lewis: I’m sorry, but I have next to no idea what you mean by “six times larger in a negative direction”. The only possible parsing I have for it is multiplying by negative six. So -24 is six times larger than 4 in a negative direction, if I were forced to assign a meaning to the phrase. (I think it’s worth noting that there are absolutely zero hits for “times larger in a negative direction” on Google.)
As for your questions, in my mind four-and-one-sixth is “six times lower than 25” and 150 is “six times larger than 25”. To me, those answers are pretty obvious, although I take it you do not find them so.
Lastly, I agree with your citation of the Huxley sentiment; we must strive to be empiricists in all matters. But I don’t exactly see how I’m the one ignoring the facts. We have historical usage (Hume), common contemporary usage (Google), unambiguous usage by the intelligent (Chu). Claiming that these are all just misuses and can therefore be ignored is exactly the definition of ignoring the facts. Now, if you have an argument based on something more than the incredulous assertion that no one could possibly understand “X times lower”, I’d be interested to hear it, but so far all you have done is sweep away facts and add a lot of question marks.
March 3, 2010 at 4:47 am
Lewis Guignard
So write 6 times less as a math equation. What exactly is the symbol for times less?
I believe it will be (x 1/6) which, in American would be ‘times one sixth’ or paraphrased ‘one sixth of’.
TImes less – sloppy, although often used as you are proud to point out.
March 3, 2010 at 9:30 am
Gabe
Lewis: It seems you’ve answered your own question. You seem to think there is a one-to-one correspondence between mathematical expressions and English language expressions, but there isn’t. For instance, how would you say “x .43”? “Times point-four-three”, “times point-forty-three”, and “forty-three percent of” (among others) are all valid. You even say that you’re paraphrasing the math equation with “one-sixth of”. Why then is “six times lower” not a valid paraphrase?
As for my seeming pride, I don’t have a horse in this race. I’m proud to point out that “X times less” is common usage, and commonly understood, in the same way that I am proud to point out any fact to anyone who insists that fact isn’t true.
March 5, 2010 at 3:41 pm
Lewis Guignard
Agreed. Times less would appear to be a colloquialism. These are sloppy usage, to which I defer to your judgement as to when to use them.
But, as Galileo and others would attest, common knowledge and belief do not make truth.
As an aside, I have been arguing with myself about this since I first read the disagreement. I didn’t even know James K. had used my note until months after the occurence. After having read all the posts, I still don’t like times less, but…
In my defense, arguing that many others believe something is not an arguement which has ever carried any meaning to me. Facts are important. Sloppy English is not accurate.
March 6, 2010 at 12:00 pm
Gabe
Lewis: There’s a crucial difference between physics and language: unlike physics, language is a human construct with no objective reality underlying it. There is no logical imperative for English to have Subject-Verb-Object order; it is just what most everyone who speaks English has implicitly agreed to do. A language is what we make it, and what we have made it. The relevant facts are therefore the distributional patterns of language as used (spoken and written) by its speakers. Thus, what people believe IS the language. It’s not at all like saying that black holes don’t exist because we don’t believe in them.
You keep on declaring things sloppy English. What makes them sloppy? Do you mean that it’s ambiguous? I will certainly grant that there is some ambiguity, although I don’t think there’s very much. And ambiguity alone is not sufficient reason to throw something out of language — otherwise, how would singular and plural “you” have stuck around so long?
And you keep on saying that “facts are important”, but I’ve only seen three facts in your argument. 1) You find the phrase “times less” not to jibe with mathematical symbols in a simple manner. 2) You think that it is sloppy English, presumably for that reason. 3) It is often used. Other than that you’re tossing out vague pronouncements that it’s a grammatical error, that it’s sloppy, and that I’m ignoring facts.
October 8, 2010 at 3:46 am
Lewis Guignard
Are you still here?
Language, as you seem aware, is a tool used to communicate. Sloppy is when it can easily be misunderstood, which is the reason Mr. James K. asked the question to start with. You know the one, the one you are so busy defending. If it was clear and easily understood, he would have never asked the question nor I have responded as I did. This is because it was sloppy and its point not easily discerned.
Your facts are ones of how many people use the sloppy construct. I agree, that is a fact. It is still sloppy else, see paragraph above. I defer to Mr. K’s concern and made my response and, as I considered him an expert in the field of communication, will defer to his opinion, not yours. Accuracy in communication is the goal.
October 8, 2010 at 1:02 pm
Gabe
Lewis: I think we’re approaching a consensus. Sloppiness is in the eye of the beholder. You seem to find X times lower much harder to understand than I do. But then, I find certain sentences you’ve used, e.g. It is still sloppy else, see paragraph above. to be quite difficult to understand. I assume you don’t find them tricky, or else you wouldn’t have used them.
So my point is that the fact that one of us finds a construction easily misunderstood may not be indicative that most speakers of English do too, and so the strength of one’s opposition to a construction needs to be tempered by how much it is used and understood by everyone else.
November 11, 2010 at 1:36 pm
Drew
I think this is absurd. Usage by others doesn’t make something correct. How many well-meaning people use the words “its” and it’s” incorrectly, for instance?
The fact is, 6 times less isn’t just sloppy, it’s wrong. If you have ten, six times ten is 60. Sixty less than ten is 10 – 60 = -50. If you mean -50 to be six times less than 10, then I suppose it’s correct. But you usually assume the person means “one-sixth”. That isn’t because it’s correct, it’s just the most reasonable interpretation because the correct meaning doesn’t make any sense.
“5 times more” is even more problematic, because a misinterpreted result is usually still reasonable. 5 times 10 is 50. Five times more than 10 is 10 + 50 = 60…or did you mean to say 50? “5 times as much” is much more appropriate because it’s unambiguous.
You say it is clear to you, but to those of us who are more mathematically rigorous see a serious problem with both phrases.
Drew
November 11, 2010 at 2:19 pm
Daniel
Drew: If usage by others doesn’t make something correct, what does?
As I mentioned before, complaining that casual conversation lacks mathematical precision makes about as much sense as arguing that it makes no sense for a musician to say that third plus a third equals a fifth because that’s not how mathematics works. The purpose of language is not precision: it’s communication. You yourself said that if someone says “six times less”, then “you usually assume the person means ‘one-sixth'”. We can argue about why we do this, but the fact is most people do this without a moment’s hesitation. (I can not prove, but strongly suspect, that the only people who don’t do this without a moment’s hesitation are people who have consciously or subconsciously trained themselves to hesitate so as to satisfy their pedantic impulses.) If most people do this without a moment’s hesitation, then communication has been achieved. That means that from a linguistic point of view, the phrase is correct. That it is not correct from a mathematical point of view is irrelevant if you’re not in a mathematics classroom.
November 11, 2010 at 3:02 pm
Drew
The difference is that those of us who use mathematics regularly have developed an intuition of mathematical concepts. When I read “six times”, without a moment’s hesitation, my mind thinks multiply. When it sees ‘less’, without a moment’s hesitation, it thinks ‘subtract’. If I say 6% less, you would multiply and then subtract, and that is never misunderstood. When I see ‘6 times less’, I likewise multiply then subtract. I only assume otherwise because the result is unreasonable, then I usually lament how ignorant the writer was to have expressed it that way.
Your premise about where someone else’s mind goes “without a moment’s hesitation” is presumptuous, to say the least. And when there’s an alternative as simple as “one sixth” that’s completely unambiguous, using the wrong phrase is doubly inappropriate.
Additionally, when you’re communicating numbers, mathematical precision is of utmost importance, isn’t it? Otherwise, what’s the point of saying “6 times” to begin with? You could just say “much less” if you’re not trying to be precise.
And in music, ‘third’ and a ‘fifth’ are ordinal numbers (first, second, third), referring to the 3rd and 5th notes of the scale, not fractions. You wouldn’t say you were the 1/3 name on a list. It is just as inappropriate to refer to the intervals as 1/3 or 1/5. The fact that you brought that up only demonstrates a misunderstanding of their meaning. When you add them, you’re not adding fractions, you’re adding the intervals (and to be precise, you need to add a major 3rd and a minor 3rd to get a 5th). From a mathematically rigorous perspective, it makes perfect sense.
December 1, 2010 at 2:24 pm
Gabe
Drew: You claim that Daniel is being presumptuous in saying that most people read “X times less” without hesitation, but I find you to be much more presumptuous with your suggestion that Daniel, me, and others are not in your special class of people “who use mathematics regularly”. I’m not interested in turning this into a pissing contest of who has the greatest mathematical qualifications, as I’m sure you have fine credentials as well, but you’re off base here. I majored in mathematics as an undergrad, and my job is creating mathematical models of language. I use mathematics regularly, and have a strong intuition of mathematical concepts. But there’s a reason why math is done with symbols and variables. Math doesn’t translate well in words, and mathematical logic certainly doesn’t survive the transition.
The trouble with your argument is that you are breaking down an idiom, and then acting appalled when its semantics aren’t compositional. You could as well complain that no farms are bought when someone “buys the farm”. After all, when I read “buys”, I think of purchasing, and when I read “the farm”, I think of agriculture. If I lamented the ignorance of those who wrote “bought the farm” idiomatically, I imagine they’d lament my ignorance of the English language. “Six times less” is an idiom with a well-known and agreed-upon meaning of “one-sixth”. Period. There is no other interpretation that reasonable people apply to this idiom unless they’re actively trying to misinterpret it.
As for there being an alternative in “one sixth”, of course there are alternatives. There are (there’re) alternatives for (to) pretty much anything (almost everything) in English (our language). There isn’t, however, a single “right” alternative. And in different situations, different alternatives can be better or worse. Notice, for instance, the Nobel Prize example I put in the original post; “six times less” is good there, because they’re excited to have gone beyond the theoretical lower limit. If it were “one sixth the limit”, it doesn’t sound like the limit’s been breached.
March 3, 2012 at 9:06 pm
Tom Walinski
My son, the aspiring linguist, points out that if enough people misuse a word it becomes an acceptable usage. This must be one such case. I have seen commercials that advertise ‘Use three times less’ of a product. Obviously, one times less of anything is zero. I will never be convinced that it is correct to say X times less, regardless of how public officials may misuse it.
February 12, 2013 at 10:05 am
Rick Mark
“X times less” is clearly wrong, no matter how many citations can be found in common usage. “1 time less” would equal zero. More “times less” must be less than zero. Using “times less” to refer to a fractional amount is imprecise, unclear, misleading, and uncommunicative. So it’s wrong.
You can find a clear argument for this here: timesless.com
Writers and editors have a responsibility to use language correctly and to defend against its misuse. There may be no doubt that the definition of “correct usage” is always changing; but if you’re going to accept any and all usage, even if it makes no sense, why have grammar guides at all?
Correct usage helps people understand each other; incorrect usage causes people to misunderstand each other.
March 20, 2013 at 1:25 am
Gregory Scott
Gabe, it might be worth checking out how recent “six times less” is as a usage. I’m in my sixties, and I really can’t recall hearing this usage twenty years ago. And the meaning of “one-sixth” is not at all obvious to me, so I find the phrase annoying. Nor does it show up often enough to have sunk in, really, as an idiom. It is possible, however, that younger folks, including yourself, are more accustomed to that definition. Remember, though, there are a lot of people about who are over forty. You want to communicate to them too, and it’s no use just blowing them off as ignorant.
March 20, 2013 at 1:29 am
Gregory Scott
P.S.–I’d actually note that while I have for some time suspected that “six times less” meant 1/6, this blog post is the FIRST TIME I have ever seen that identity expressed explicitly. And I read a lot.
August 26, 2013 at 8:06 pm
Mark Conn
Thanks Rick Mark! I’ve read this thread and a few others, and you are the only one who got it right!
I came looking because of a recent bathroom tissue ad that claims one can use “four times less” of their product. Once a person is down to “one times less”, that person is down to not using any tissue, at which point there would be serious hygiene issues and an absence of friends.
August 26, 2013 at 8:08 pm
Mark Conn
Oops. Kudos also to Tom Walinski and his son!
June 24, 2015 at 7:37 pm
Noel Victor Comley
I am about to run out of the room screaming