A reader writes, apropos my Slate piece,
Canada cannot have crime rate ten times lower than the crime rate in the U.S. It can have crime rate of one tenth the crime rate of the U.S.
I've heard this objection before, but I'm just not sure I understand its foundation. Indeed, if "X times lower" meant "lower by X times the original amount," "ten times lower" would make little sense (except if for some reason you said that -9 was ten times lower than 1). Or if you somehow just defined "times lower" as an error, it would be, by definition, an error.
What I don't grasp is what justification, besides the objector's own view of what the language should be, there is for this. This is, to my knowledge, a common part of normal English usage. It's not confusing. It's not illogical unless one defines "lower" in a pretty strange way.
Even if one is a prescriptivist, who argues that a statement is bad English if it doesn't conform with The Authorities, what Authorities actually condemn this? There might be some, and please let me know if there are, but I just don't know of any, and my quick and dirty search didn't come up with any.
Naturally, if you think that this usage is ugly or annoying, I can't really argue with that. And if enough people think that, one might want to avoid the usage simply to avoid annoying one's readers. But I took the "cannot" to mean "cannot, without violating the rules" rather than "cannot, without annoying me." Where are those rules set down?
Related Posts (on one page):
- "Times Less Than":
- Ten Times Lower:
10 times lower = divide by 10 = one-tenth
If someone has a problem with such language, it's likely that this person has far more serious problems than the language.
Likewise, a logician will avoid the ambiguous "All men are not wimps," since it can mean either "No man is a wimp" or "Not all men are wimps."
Americans are verbally confused and something needs to be done about it. Nowadays you will almost never hear anyone on TV or radio answer a question with a simple "yes." It's always "absolutely." And the real brain-fart is the ubiquitous solecism "the problem is, is that ...."
But, then, I have trouble figuring out what people really mean when they use expressions like "twice as light," or, in ARP's example, "two times lower (or smaller)." I'd just say Person A's weight was half that of Person B... assuming of course that this is the meaning intended.
But the difference between two times smaller and three times smaller (as they've been defined here) is not the same as the difference between three times smaller and four times smaller, and neither one of them is equal to "one time," the original number.
That is why I think this usage is problematic.
You're right that it's only wrong if it's defined as wrong, but that's true of any language rule, isn't it?
X is 10 times higher than Y -> X = 10*Y
X is 10 times lower than Y -> 10*X = Y
The main construction is
X is 10 times Y
which clearly indicates that X=10*Y. Higher than is a null modifier which does not change the sentence, though possibly clarifies it. Lower than inverts the sentence. I don't find the sentence at all ambiguous, though it seems that many people here do. My best guess is that most of those who find it ambiguous don't speak about ratios too often.
This essentially answers Eugene's question. The meaning is unclear to enough people that its probably best to avoid this locution, even if it is not objectionable in an objective sense.
"times less, times more: Writers who speak of three times more or three times faster often mean 'multiplied by 3,' but precise readers are likely to understand the meaning as 'multiplied by 4': the original quantity or speed, plus three more times. For clarity, avoid times more, times faster, times bigger, etc. Write four times as much (or as fast, etc.) And do not write times less or times smaller (or things like times as thin or times as short). A quantity can decrease only one time before disappearing, and then there is nothing left to decrease further. Make it one-third as much (or as tall, or as fast.)"
--The New York Times Manual of Style and Usage
Indeed, I'd argue that this is even the preferred usage, because the 10 stays the same and is therefore easier on the brain. Say object X is 50% larger than Y - the 50% is not interchangeable (object Y is 2/3 as large as X).
Seems to me that this is just further evidence that, on the internet, there will always be someone to criticize something, no matter how silly that criticism is.
The problem for those of us who tend to nitpick is simply that, while such a misusage is perfectly decipherable (as a result of it being so common), it is still a misusage because "times" doesn't mean "divided by" any more than "plus" means "subtracted by." If there's a rule at play, it is that words mean what the dictionary defines them to mean. tp://www.bartleby.com/61/4/T0220400.html
If I were to tell you that the fire alarm is going off, would you burn to a crisp as you posted a comment about how my thinking isn't clear, as the alarm is really "going on?"
Vague speech or writing is bad. Commonly used idiomatic speech that isn't literally true is not a problem.
I don't think the usage is "mathematically incorrect." Language isn't math. There's a reason that mathematicians use specialized symbols to describe mathematical concepts and relationships; they're far more compact and precise than everyday language. As others have pointed out, there's often a lot of ambiguity in our attempts to describe mathematical relationships using everyday language, instead of the symbols that mathematicians have developed for that purpose. But I don't think that's true in this case. I think the typical writer/speaker who uses "ten times lower" means "one tenth," and I think the typical reader/listener understands it to mean that. As long as that's true, I see nothing "mathematically incorrect" about it.
1) "ten times greater" and "ten times lower" are generally used in the sense that Volokh used them, or at least that is how I have always heard them used. I wouldn't say - as some commenters have - that Volokh is misusing them because you can't misuse a colloquial phrase by definition - it means what it means.
2) Like many colloquial phrases, it means something different when translated technically. The problem appears to be that many people haven't actually heard it used that way, and if they attempt to discover its meaning by pure thought it may mean something different.
3) Since many people apparantly have never heard this phrase, it may be best to avoid it as some commenters suggest.
4) Bear in mind that this is true of all colloquial phrases and this is really all we're talking about. I was a math major in college but I have never before now thought it odd to use "ten times greater" or "ten times lower". You don't think about the inherant logic of colloquial phrases until you run into someone who isn't familiar with it.
5)Mahlon said "Such usage indicates an inability to think clearly." I sometimes disagree with Mr. Volokh, but having read him for several years, I can safely say that if your premise leads you to the conclusion that he can't think clearly, you should check your premise.
"One times larger" = "100% larger" = "Two times as much."
"Two times larger" = "200% larger" = "Three times as much."
...
"Ten times larger" = "1000% larger" = "Eleven times as much."
If a reader has to guess what a writer means by "ten times larger," how can a reader possibly interpret "ten times smaller" with any confidence?
I think JGR has answered that question quite nicely: The only readers who have to guess what a writer means by 'ten times larger' are readers who aren't familiar with colloquial English, and readers who insist on parsing colloquial English using pure logic. I'm willing to consider the possibility that writers should try to accommodate the former group. I have no time for the latter group. Language is a grown order. Get over it.
Exactly. Which is why no one would ever read the phrase the way you are. Did any of you really think that the original source could have possibly meant this? Of course not.
As I've noted elsewhere, attitudes like that displayed in your comment,are fine if you're
- childish
- impatient
- indebted to no-one.
However, writers who write to persuade can't afford to
- piss off intelligent readers
- mislead
- fail to make their case.
Professors, and to an even greater extent lawyers, really ought to have a clue when they write. If a locution draws attention away from the point, and towards the (stupid, meaningless, obscure and misleading) words themselves, then why use it?
Oh yes. "You have no time" for people who will fail to read your point as a result. They should "get over it."
Noted, but not persuasive.
Oh - and why didn't you write "I could care less" about such people? It'd be just as annoying and literally wrong.
Let's say the sentences read "In Canada, 10 people are murdered each year. There are ten times more murders in the US than there are in Canada."
How many murders are there then in the US? 100 or 110? I have no idea. Ten times more is 100 more, therefore I would think 110. But most everyone here seems to think that 100 would be what the author intended.
The answer is 100. Not because you can parse it logically and arrive at that unequivocal answer, but because that's what the usage means in colloquial English. Perhaps you weren't previously familiar with the usage. That's OK. Now you are.
I don't know if you have a beef with Matt from another thread I'm not familiar with, but I thought his comment was common-sensical and not remotely childish. When I was in seventh grade our advanced class learned geometry. After that, whenever a teacher would make reference to a line that they drew on a chalk board, some student would say "Mr. Smith, that's not actually a line. It doesn't go on forever and it has width". Har-har. What is forgivable immaturity in a seventh grader is simply annoying in an adult, and that's all I took Matt to be saying.
What do you mean by "would cut it?" I argue that this is unclear. The fact that I make this argument means that you didn't communicate clearly.
Sorry, not buying it. "Ten times as many people are killed" = 100, but "Ten times more murders" = 110. And since I was able to quote an Authority, at least I know I have the NYT on my side.
Wrong on both counts, I'd say.
Repeat as needed.
I'm with Eugene on this one.
"Ten times higher" and "Ten times lower" are multiplying a difference between two objects to describe a third object.
If you say that the A is "ten times higher" than B, what you are saying is that A is "ten times higher" than B is higher than zero. The fact that one is usually operating from a base of zero makes this a common expression.
When you start talking about "ten times lower" though, you run into a problem in that there is no base referent.
Frank is two times shorter than John is....
.... shorter than what?
If Frank is two feet tall, and John is four feet tall, and Susan is six feet tall, then Frank is two times shorter than John is than Susan, but John is twice as tall as Frank (is than the ground).
These sort of comparisons require a referent, and when you don't have one, it's sloppy and imprecise language. Often, the referent will be implied, but if it isn't then it's breaking the rules of logical sentence construction -- rules that, like the serial comma rule -- don't really mean much until something major gets screwed up because people are being imprecise.
-Michael
The problem is that in colloquial English in other locations, it means 110. Perhaps you weren't previously familiar with the usage. That's OK. Now you are.
It rather demands the question of which colloquial usage one should rely upon — and this discussion lends itself to the answer, "None, of course." There's a reason why colloquialisms are frowned upon in formal writing.
However, as it relates to the original question, I don't think an issue of confusion exists. It's hard to tell with colloquialisms, of course, but I don't know of any place where "x times smaller" leads to a similarly ambiguous, but still plausible result.
It's certainly an awkward construct that should probably be avoided, but it's not as bad as in the other direction.
Thanks for the advice. Let me rephrase that comment:
"Language is a grown order; therefore, it doesn't adhere perfectly to the rules of logic, or to any other set of prescribed rules. It makes its own rules as it goes. Whether you like it or not, this is simply the nature of language. The fact that you may not be able to parse the phrase 'ten times lower' using ruthless logic, and arrive at a certain understanding of what it means, doesn't invalidate the usage. Meaning proceeds from usage, not from the rules of logic. Thus the relevant question isn't what you think 'ten times lower' should mean, logically. The relevant question is what it does in fact mean. And what it means is 'one tenth.'"
There you have it. But that took a lot longer than the original comment, and I very much doubt it's going to persuade anyone who isn't already persuaded by the time they've read down the page far enough to reach this comment. Furthermore, I don't think there's anything in that much longer version that a reasonably intelligent person (there are many here) wouldn't have deduced from my original observation that "language is a grown order." So what have I gained through all those extra words, and all the time I spent typing them?
Now...I will say that it never occurred to me that "four times bigger" means (or should mean) 5 times that size, but now that my attention is drawn to it I'll wonder every time I see it. And (extrapolating) that means that nobody should ever use it; because a listener like me will be forced to wonder whether the writer meant the hyper-correct thing or the common (technical) error.
In general, I suggest that the people willing to use "ten times less" should apply the principle of charity, and understand that those of us who oppose it are not being deliberately obtuse; we find it genuinely jarring. It is, all other things being equal, the writer's job to make things easy for the reader, rather than to insist (when there's a known controversy around something) that the readers should figure out the writer's meaning and to hell with them if they get tripped up.
The answer is 1/10th, as many people have said above. The fact that we are haggling could equally mean that some people are simply obsessed with problems of clarity that don't really exist. If I say I put my money in the bank and you respond that you have no idea whether my money is kept at a financial institution or buried in the mud beside a river, then I'm not failing to communicate clearly, you're simply being obtuse.
And, to hit it from another angle, "mathematical logic" vs "formal logic" is a valid distinction, but not so much when you're making a mathematical statement.
Also, I'm very disappointed that my screen name hasn't elicited any comments, as I thought it quite clever. It's a comment on my politics (libertarian tinged coservatism) as well as a mildly offensive allusion to Snoop Dogg/rapper expression. Quite an unusual amalgamation, no?
Which locations? Could you give me an example? (A link would be ideal.) I just Googled the phrase "ten times more." Several of the links on the first results page don't give enough information to let me determine whether, in context, the phrase means (x+10x) or 10x. But among those that do provide enough information, in all cases it appears that "ten times more" means 10x. Again, that's just the first page of a Google search; it's hardly conclusive evidence. But it is evidence. (I could keep going, but the search retrieved 1,030,000 results and there's a limit to how much time I'm willing to devote to this little project.)
As I said in my first comment, I prefer to avoid the "times lower than" construction because it strikes me as sloppy and imprecise. But really, I think people are making far too much of it. I think its meaning is fairly clear. And on further reflection, I'd add that it really doesn't matter whether the author of the original Slate piece to which Eugene referred meant (x+10x), or 10x. For purposes of a publication like Slate -- which is not a formal academic publication -- whether the American crime rate is 1000% or 1100% is just a technical detail; the important point is that the American crime rate is (or rather was alleged to be) much higher than Canada's. Presumably there are very few readers who'd say, "oh, well, 10x would be fine, but by golly, 11x is just out of control!"
What other locations? I have never encountered misunderstanding over what "10 times more" than a starting point of 10 means. I highly doubt that you, or Forest Girl, either naturally assume the phrase means 110, or would spend several minutes paralyzed with confusion at what the speaker meant, before throwing up your arms and deciding to go with an average of 105.
Just my 2 cents.
I like it. But at first glance I thought it was a somewhat unflattering allusion to the rest of us.
Who is this "we" you speak of? I don't wish to apply prescriptivism as opposed to descriptivism in this case. Why should I?
"Writers who speak of three times more or three times faster often mean 'multiplied by 3,' but precise readers are likely to understand the meaning as 'multiplied by 4'
If I always hear the phrase used in the first manner, and then I read this in the New York Times, I'm going to translate that sentence into this: "Almost everyone uses three times faster to mean times three, but technically it can also mean multiplied by 4". What I'm going to flatly insist on is that their statement "are likely to understand the meaning as 'multiplied by 4' is flatly wrong. If almost everyone uses the phrase in one way, they ARE NOT going to assume it is used in a different way; At most, they will say that they are not sure how it is being used. Several commenters here seem to suggest that if a colloquial phrase is almost always used one way, but the New York Times says something different, that somehow CHANGES the fact that the phrase is almost always used one way and not another.
If the New York times were to write "Precise readers are likely to understand the phrase 'the blind leading the blind' as someone who is physically unable to see leading someone who is physically unable to see" the fact that it was written in the New York Times wouldn't make it so.
I have a ton of trouble seeing how this could possible be incorect. Whatever your disagreement here, the math isn't wrong. This disagreement is about how precisely one should undertstanding the meaning of an English sentence mathematically.
On the other hand, even in that mode I'm enough of a descriptivist that the line of questioning in much of this thread, that of "but is anyone at all really confused by these usages?" seems to me to be on target. If nobody's confused, that's relevant information. And yet, if something's a shibboleth that marks one's usage as "not formal", that's also a raw fact -- at a particular moment in the evolution of the language, at least.
DRWN,
"Obdurate" may not be exactly the word you're looking for, but one of its meanings ("resistant to persuasion or softening influences") is fairly close.
What does "One Times More" mean?
A) One Times X = 1*X = X (i.e. you have colloquially negated the More)
B) One Times X More of/than X = 1*X + X = (1+1)X
Depending on the reader's dialect, either definition could be valid, and B) is actually mathematically accurate. Because of the potential confusion, the above is bad grammar and should be avoided. (And if A was what you intended, than the More is superfluous and thus twice bad grammar.)
Although I do like the comments that think A) is obvious and proper (e.g. logicnazi - if only you lived up to your name, doubly embarassing coming from someone with a technical background) intensely humorous, because we entirely negate or ignore words (the more) in proper english all the time, right?
What does "One Times More" mean?
A) One Times X = 1*X = X (i.e. you have colloquially ignored the More)
B) One Times X More of/than X = 1*X + X = (1+1)X
Depending on the reader's dialect, either definition could be valid, and B) is actually mathematically accurate. Because of the potential confusion, the above is bad grammar and should be avoided. (And if A was what you intended, than the More is superfluous and thus twice bad grammar.)
Although I do like the comments that think A) is obvious and proper (e.g. logicnazi - if only you lived up to your name, doubly embarassing coming from someone with a technical background) intensely humorous, because we entirely negate or ignore words (the more) in proper english all the time, right?
If I say that the crime rate in the US is 15% higher than the crime rate in Canada, we all know that I mean that the difference is 15% of the crime rate in Canada, so we can get the crime rate in the US by multiplying Canada's rate by 0.15 and adding the result to Canada's rate. That's because the lower/higher formulation is an additive differential comparison, not a multiplicative one. That is, the 15% is the relative difference.
To clearly imply what the author meant, we should say any of "10% of", "one tenth of", "one tenth as large as" — all multiplicative comparisons — or "90% less than", "90% lower than", or "90% smaller than" — all additive differential comparisons.
The first three of these are preferred, since comparisons of two numbers are best stated as relative differences when the ratio of the larger of two numbers to the smaller is less than two, and as ratios otherwise. Thus, one should say "15% larger/smaller” or "50% greater/smaller than", and "2.5 times" or "one third of", but not "150% more than" or – by far the worst – "3 times smaller than."
It doesn't matter that one can figure out what the author meant; it stops your flow of thought to do so, and hence is not the best style.
ForestGirl and the New York Times style manual have it right. Take it from an Engineer/Mathematician.
Eugene Volokh: A writer writes, appropos my article, "Eugene Volokh writes that a policy consists of "the blind leading the blind", but this isn't true because they're not physically unable to see" (Explanation follows not really incorrect)
guest: "blind leading blind" = clueless leading clueless
russ: "The usage is simply linguistically incorrect. I first heard this usage when I met my (formerly Russian) wife and it just sounded wrong. I was 40 at the time and I'm fairly well read and I've just never seen it before. Guess that makes me weird or something.
Mahlon: "The word "blind" refers to being physically unable to see. Your usage is simply wrong. Your meaning therefore is vague and the sentence plainly ridiculous. It cannot be. Such usage indicates an inability to think clearly. You are wrong.
logicnazi: "blind leading blind just MEANS clueless leading clueless"
Dean Kimball: "I agree with the Russ and the original criticism. "the blind leading the blind" is simply inaccurate. Yes, we could all agree to a meaningful definition of this phrase and move on. However, I believe language matters. If we make the small effort required to remove any ambiguity (say "the clueless leading the clueless" instead of "the blind leading the blind"), we are being accurate wihtout sacrificing clarity and consistency of language.
SeanF: "the difference between being blind and being clueless is the difference between not being able to physically see and not knowing what is going on.
That is why I think this usage is problematic.
You're right that it's only wrong if it's defined as wrong, but that's true of any language rule, isn't it?
Forestgirl: "Not sure whether you would consider this an Authority, but it explains what I don't understand about that formulation:
"Precise readers are likely to understand the phrase 'the blind leading the blind' as someone who is physically unable to see leading someone who is physically unable to see"
guest: "I'm confused as to how the wording is in any way ambiguous. Is it reasonable to infer that physically blind people are leading physically blind people?
Seems to me that this is just further evidence that, on the internet, there will always be someone to criticize something, no matter how silly that criticism is.
PAC: "It's not really plausible to claim, as some commenters have, that the phrase "the blind leading the blind" is unclear and leads to confusion. Everyone understands the person who uses that formulation to mean "the clueless leading the clueless"
The problem for those of us who tend to nitpick is simply that, while such a misusage is perfectly decipherable (as a result of it being so common), it is still a misusage because "blind" doesn't mean "clueless"
jgr: I believe I can summarize the main points.
1) "the blind leading the blind is generally used in the sense that Volokh used it, or at least that is how I have always heard it used. I wouldn't say - as some commenters have - that Volokh is misusing them because you can't misuse a colloquial phrase by definition - it means what it means.
2) Like many colloquial phrases, it means something different when translated technically. The problem appears to be that many people haven't actually heard it used that way, and if they attempt to discover its meaning by pure thought it may mean something different.
3) Since many people apparantly have never heard this phrase, it may be best to avoid it as some commenters suggest.
4) Bear in mind that this is true of all colloquial phrases and this is really all we're talking about. I was an English major in college but I have never before now thought it odd to use "the blind leading the blind". You don't think about the inherant logic of colloquial phrases until you run into someone who isn't familiar with it.
5)Mahlon said "Such usage indicates an inability to think clearly." I sometimes disagree with Mr. Volokh, but having read him for several years, I can safely say that if your premise leads you to the conclusion that he can't think clearly, you should check your premise.
hedberg:
The comments in this thread indicate quite well the confusion that can result from these imprecise usages and justify the rule quoted by ForestGirl:
blind = blind
clueless=clueless
If a reader has to guess what a writer means by "the blind leading the blind," how can a reader possibly interpret anything else they say with any confidence?
Deezrightwingnutz: I don't know why people complain about the usage colloquial phrases that don't make sense when analyzed technically. I could care less.
Matt22191: [explains jgr right]
forestgirl: Matt, I'm not buying it. blind means physically unable to see
Okay, I'm gonna stop since this took a ridiculous amount of time. It reminds me of that recent story where the guy dug a 60 foot hole in his yard and said "he just got carried away". I only meant to do a few spoofs, and just got carried away.
People are defending the phrase because it is colloquial. That's fine, for speech and for casual writing (personal letters and blogs). It's fine if the actual numbers aren't important and if what you're trying to get across to your readers is that "it's a really big difference." But I wouldn't want to see it in a newpaper or magazine article, a demographic study, a medical journal or a legal brief--anywhere that precision and clarity matters.
It is no harder to write "one tenth" or "10 percent" than "10 times less"--in fact it is easier, since they take up both fewer characters and fewer words. And the first two have the added benefit of being logically accurate (they mean the same thing mathematically and logically as they do colloquially), whereas someone trying to logically or mathematically figure out "10 times less" might take that to mean 9 percent (roughly) or something less than zero.
So if the difference in crime rates is tangential to your point, it is a BIG difference, you're speaking or you're writing in a relatively casual forum or publication, and all you're really trying to show is that there is a big difference (and people are unlikely to want to figure out the exact numbers), then "10 times less" is perfectly acceptable. If you're writing in a forum where precision matters, or this is just one of several comparisons you're making (e.g., "the crime rate in Canada is 10 times less than in the US and 14 times less than in Mexico") you're better off using more precise terms.
And by the way, I'm not sure that "x times lower than" is as informal as you suggest. I just ran a law review search in Westlaw's LAWREV-PRO database. The phrase "ten times lower" appears 26 times in law reviews and journals dating back to 1995. That's not a lot, but remember that those results are for law reviews and journals, which are considerably more formal than Slate. ("Ten times more" appears 796 times. The oldest result is a 1953 note in the Stanford Law Review.) Perhaps someone else feels like searching the NYT's archives.
here, we read that "three times less" is OK with IBM, and according to the N.Y. Times here, "the rate of infection with misoprostol was 12 times lower,", and here the Times reports that Dr. harvey Sugerman says "extremely obese patients had death rates as much as five times lower".
A search of the N.Y. Times turned up many examples of "times less" or "times lower". It is commonly used.
I've never tried to avoid "x times higher" because it makes perfect sense to me... but judging from this discussion, more people don't know what I mean when I say that (x times higher than y is x*y; I've never considered it as "(x+1)*y") than when I saw "x times lower".
I'll probably continue to be uncomfortable with the former, irregardless.
Suppose that the standard height for the top of a door is 72", and I have a 70" door -- the top of my door is 2" lower. The top of your 52" door is ten times lower. Under common construction, the top of your door would only be 7".
If you and I both start with $1M in a bank account, I burn through $10K and you burn through $100K, then yours is ten times lower than mine is.
If a $20 book is on sale for $19 and then is marked down 10 times lower, it ends up at $10, not $1.90.
I agree that this construction is commonly used, even among academics. But, that's hard indicative of correct usage. I'm sure that we can all point to common gramatical errors -- my pet peeve being the variety of ways in which people misuse the word "myself."
If "ten times lower" means dividing by ten, then "one time lower" would, indeed, mean dividing by one; in other words, not changing the original number. "One time lower" proves that the "times lower" usage is incoherent.
I may eventually work it out from context that they mean what you claim they mean -- but language that is confusing enough that it needs to be worked out from context is (to use a technical linguistics term) crappy. In particular, oral use of such language is horrid, because while the listener stops to puzzle out what the speaker is saying, he misses the next words said by the speaker.
For those who are anal about precise grammar, "times" does not mean addition, it means multiplication. You want to claim the need to be precise, but then you throw addition in there for no reason.
I've never heard it, but, by the Prof's logic, "one time lower" would still work as a sentence. It's an incoherent idea expressed correctly, according to Eugene's line of thinking.
For those who are anal about precise grammar, "times" does not mean addition, it means multiplication.
But "times lower" means multiplying by a fraction, or division. So why not just be clear to everyone and use the language of division in the first place?
The reason you've never heard it is that it's stupid to say, because it's assumed that "one time lower" means dividing by one. If "one time higher" means what the 10x+x=11 folks think it means, then you would have heard "one time higher". That's the test for Volokh's question, and it demonstrates that "ten times larger" means 10x. Otherwise, you would have heard it.
As far as language, the important discrimination is times/division versus addition/subtraction. Multiplication and division are essentially the same thing.
Count me as one who finds both usages confusing and wrong. What's driving me batty, though, are some on the other side who say, "Everyone knows what that means," or "no one would be confused by that," or "no one would interpret that phrase that way" -- despite dozens of comments by people who DON'T know what it means, ARE confused by that, and WOULD interpret the phrase that way. Feel free to argue that your usage is more correct, but when you claim that no one can possibly disagree with you in the face of dozens of people who do, you just look like a moron.
For the record, when I hear that something is "three times AS LARGE AS," I multiply by 3. When I hear "three times LARGER THAN," I multiply by 4.
I haven't the vaguest notion what "three times smaller than" would mean.
The crime rate of X is 4.6 times lower than the crime rate of Y.
The crime rate of X is one 4.6th the crime rate of Y.
I mean, get real people.
The crime rate of X is 4.6 times lower than the crime rate of Y.
The crime rate of X is one 4.6th the crime rate of Y.
I mean, get real people.
Bite me, you ignorant slut.
I am a native English speaker, and I would not be certain what was meant by "10 times lower."
I don't believe you. You are smarter than that. Give yourself more credit.
("Bite me, you ignorant slut"--is that a humorously intended quotation from a famous film?)
Well, anyway, my two cents: the intuitive understanding is that when something is 10 times lower than X, it is equal to X/10. So put me in that camp I guess... I just don't see how you can understand the expression to mean anything other than what I just described, imprecise and awkward as it may sound.
But then again, I'm a Russkie, and "v desyat raz menshe" is both grammatically correct and translates as "10 times less/lower." (Ditto Markusha).
One tenth: It's the American Way.
/OR NOT?
I believe it's from an old SNL news segment with Jane Curtin and Dan Aykroyd in which the latter would lose control in an argument and say, "Jane, you ignorant slut." But I was but a wee one for the early years of SNL so my memory is fuzzy about the exact context. I will say that SNL these days is TEN TIMES LESS GOOD than it was then. Sorry!
Paul Brian is an American professor. He asks, in his prefatory notes to Common Errors in English, "Does it oppress immigrants [my emphasis] and subjugated minorities to insist on the use of standard English?"
Shangui: You rattle my memory and I do recall the SNL routine, vaguely. It was much more amusing then than it is now, indeed. I doubt that I am every going to commit to a specific quantity of more or less than -ness again.
Saying "x times lower" isn't a cardinal sin; saying "1/x" is plainly clearer.
I'm embarrassed that I keep checking the comments to this post.
However, it takes willful parsing of the statement to turn it into something else. If the original sentiment had been expressed by a mathemetician, yes then there could be valid criticism for sloppy expression, but the author has clearly and plainly conveyed to the readers what his thoughts were.
That's not a valid argument for usage, even when true. If you gave Americans a spelling test, greater than 50 percent would probably spell "harass" as "harrass", or "minuscule" as "miniscule". No one will ever misunderstand either way, but that doesn't make it correct, or OK, or colloquial. It's still just wrong.
My opinion is that this also applies to using the word "times" correctly. I don't mean that as snarkily as it sounds, but I do think that's why there's so much defensiveness in this thread.
"I don't know what 5 times colder than 20 degrees Celsius means."
-214.4 degrees.
http://tinyurl.com/r2659
The first rule of any language is to say what you mean clearly. The phrase "ten times lower" for a number which has to be positive flunks that.
The SNL skit was a takeoff of a 60 Minutes feature in the 1970s called Point and Counterpoint, which featured a prominent male conservative (James Kilpatrick) and prominent female liberal commentator (Shannon? Alexander) debating current affairs. SNL's version was much more entertaining. One correction: Dan would frequently begin his response to Jane with "Jane you ignorant slut" and launch into his mock conservative diatribe.
Regardless of how you feel about "10 times less," I think we can all agree that if you want to use this construction, best not to recast it as "1000 percent less."
But the fact is that most of the comments seem directed at the "I'm right because most people understand" or "I'm right because most people don't understand" argument.
I'll say it one last time: THERE'S A MISSING PREPOSITION.
It actually reminds me of the single most useful T.V. SciFi quote ever:
Lyta: Damnit, I have earned some respect!
Kosh II: Respect? From whom?
It's exactly like "ten times lower" -- than what?
"A is ten times lower than B."
Guess what? B isn't "lower" than anything in that sentence. Ah... I'm not going to get into this again. Go up and read my first post.
It's a really useful thing to always fill out your implied prepositions, or at the very least, be aware of what you're implying in case there is confusion.
You made two false statements. Why would you make statements that are false? It's bad form.
That depends what your definition of 'is' is.
Seriously, words have meanings, and I find it astounding that a professor of law, of all things, is defending imprecise language. After all, the common man's perception is that lawyers must be paid per word.
Several commenters have attempted to defend this faulty usage, but none have offered a mathematically literate defense.
If our language is not precise and clear, then we have Orwell's Newspeak.
I don't like such usages, and I think they're better replaced with the perfectly good and clear constuctions English already has for such things ("a third" rather than "three times less") ... even though they're understandable in common use.
Michael: If B is a rate of 100 per 10,000, then if A is "ten times lower than" (1/10), the rate is 10 per 10,000.
The lower and higher here are not height relative to some unstated measure, but rates, relative to zero. (The problem, such as it is, being that English common use uses lower and higher to mean a smaller number and a higher number. This isn't much of a problem, if we don't let the coincidental relationship to their use for physical size confuse us.)
Jeez.
It's like saying black is white. What you end up with is nothing but gray - a world where language is useless in making distinctions of meaning. Next, we will abolish subject-verb agreement, pronoun references and punctuation. We might as well go straight back to grunts and whistles.
As lawyers, which I assume most commenters here are, we should be especially senstive to imprecise use of language. Who here can honestly say that he has never read ambiguous statutory language. Think of the amount of time and money wasted in arguing the intent behind a legislative enactment.
The linguistic sin committed in the quoted passage is relatively minor. If most people believe that they understand what the author meant (and if, in fact, they do) the author was at least mostly successful. If you are satisfied with "good enough," however, then you should drop out of this conversation. There is a bigger issue at play which should not be brushed aside.
Americans are becoming increasingly illiterate. I have taught Masters candidates who cannot write a simple sentence. My children's elementary school teachers cannot spell. Acceptance of this abuse of the language perpetuates that abuse. My family, communityand nation are being infected with this disease.
But who am I to lecture all of you? Take some time to read the writings of Richard Mitchell, the Underground Grammarian.
http://www.sourcetext.com/grammarian/
First, I must admit with embarrassment that I read all these 122 comments.
Second, I think that if all of us here were to put our collective time, talents, and energy together, we could solve some much more important problems than this.
And this comes from a professional wordsmith (who actually cares about stuff like this)!
I'd also like to announce that after the time I have wasted on this thread, I am ten times less likely to delve into such a comment-flurry again... ;)
I can live with "five times more" and "five times less". For the former: "He has more than you. By how much? By a factor of five is how much more he has than you."
An SUV weights more than a motorcycle. A motorcycle weighs less than an SUV. A simple reversal. So if an SUV weighs ten times more than a motorcycle, then expressing it the reverse direction we say that a motorcycle weighs ten times less than an SUV.
There are some sticklers who grimace at "I'm with you 110%" on the basis that more than 100% is impossible. They are incorrect, even by the strictest mathematical interpretation. More than 100% is certainly possible, even of the same thing. (Obviously the cargo capacity of this truck can be 150% of the cargo capacity of this other truck.) But if I put 1100 pounds of stuff in the first truck, and it is only rated for 1000 pounds of stuff, then I will be operating it at 110% of capacity. Setting aside the built-in safety margins, if I make a habit of doing this the truck will wear out too fast, and it won't handle as well, but at the moment it's giving 110%. Of course, if by "I'm with you 110%" you think I mean "I'm with you at 110% of the maximum amount I could be with anybody", then the complaint is valid, and you are probably the type of person that when I say "Oh, I thought your house was smaller than it is" says "Nonsense, how could anything be smaller than it is?"
If there was a 12% difference in the unemployment between last quarter and this, does that mean last quarter's rate was 88% of this quarter's rate, or that this quarter's rate is 112% of last quarter's? (Difference implies directionality of the comparison less than "than".)
95 is lower than 100. 50 is ten times lower than 95 (relative to 100).
Eleven. Exactly. One-tenth times louder.
When numbers are involved, if you don't sound like you know what you're talking about, there's little point in saying it at all.