An e-mail from a reader 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.
This prompted me to do some more searching, and discover not only a usage of this phrase by Jonathan Swift (via Merriam-Webster's Dictionary of English Usage), but also by 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? The correspondent whose message prompted me to repost about this suggested that "A times less than B" might be a 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 ...."
UPDATE: A comment, which regrettably failed to follow the eminently reasonable request in the preceding paragraph:
It's disappointing to see Mr. Volokh make this argument. The formulation is confusing. It could reasonably be argued that while 3X10 equals 30 then 3Xless than 10 would be a minus 20. People who use math in their work would never use the subject formulation. I thought it was limited to journalists.
First, it could reasonably be argued that "three times less than ten would be a minus twenty" -- if one has no idea about how actual humans talk. Of course no-one would use "three times less than ten" to mean that. Perhaps it's distracting or annoying, but it would take a lot to persuade me that anyone would actually think "'"If the Diameters of the Circles ... be made three times less than before'; does that mean 1/3 of the original, or negative two times the original?." Maybe Data, but then again he seems to have had some troubles with contractions, too.
Second, "people who use math in their work would never use the subject formulation"? Really? Might there be some evidence against this assertion available, I don't know, somewhere? I'm not sure, but I could have sworn I saw some ....
Related Posts (on one page):
- "Times Less Than":
- Ten Times Lower:
A x < B
Or put another way, A x X, where X < B.
Which is not a very helpful formula.
And I reject your argument from authority. Just because presidents of both parties have said nucular doesn't make it a correct pronunciation. Or to mix metaphors, if Sir Isaac Newton told you to jump off a bridge, would you do it? ;-)
"A times less than B" means (1/A) * B
People who get upset by this are, I think, largely people who struggle with mathematics in the first place. :-) ..bruce..
Thread has already been won.
You seem to be saying that "correctness" is defined by mathematical logic. But we're not talking about the rules of mathematics, or of gravity plus medicine (the subject of the bridge jumping hypothetical), which may follow such logic. We're talking about the rules of English; where's your support for the proposition that English is defined by mathematical logic? Isaac Newton didn't adopt such a proposition; why should we.
As to "one time less," no-one would say "X is one time less than Y," just as no-one would say "X is one time more than Y." But that just reflects the fact that English idioms, being idioms, can't always be stretched to all possible applications -- again, English is not mathematics.
If people understand, effective communication happens.
It would probably work with "we have one-tenth times fewer murders," although that feels a little clunky. People would understand what that means.
I wouldn't use this in a computer program on either input or output, but for talking with human beings it's just fine.
English is shot through with imprecision, which is why we talk in mathematics in the first place. If you want to pick nits, pick 'em. Just don't drag a whole field you have only the haziest conception of into the matter.
Genuinely curious whether Newton was considered a particularly gifted explainer of scientific ideas in English. Haven't read Principia, but was it highly rated on this count, as opposed to being comprehensive and pathbreaking?
real English is American English, his good math stuff was written in Latin, and his beta-version English has some weird letter "s" that looks like an "f", goofy pronouns that sound like bible talk and distinct meaning for the words will and shall.
Doesn't 'one tenth times fewer' == 'ten times more' :-)
It sounds like a great way for the mayor to spin a massive
crime wave.
The Principia, or Philosophiæ Naturalis Principia Mathematica, was written/published in Latin. And I don't remember it being highlighted as a particularly well written work in Latin.
I don't like applying the word "correct" or "incorrect" to the "three times less" phrasing; I'd prefer something like "imprecise".
What I think [i]is[/i] incorrect is your use of argument by authority; my reading of your post is that you were the one arguing that the "three times less" phrasing is somehow correct because of Sir Isaac's use of it.
Dan Weber wrote:
True, but it would be more precise, and less open to misinterpretation in the general sense to say that murder is down by 90%. :-)
No, it's not. You're a pedant with a lingering lust for your prescriptivist 7th grade English teacher.
Mary's beaker is 3 degrees
Jill's beaker is 1 degrees
Joe's beaker is -9 degrees
Jack's beaker is -15 degrees
The temperature of Mary's beaker is 6 degrees less than the temperature of Paul's beaker.
Which of the following is true?
A. The temperature of Jill's beaker is three times less than that. [i.e., 1/3 of Mary's]
B. The temperature of Joe's beaker is three times less than that. [i.e the difference between Paul and Joe's beaker (-18 degrees) is three times the difference between Paul and Mary's beaker (-6 degrees)]
C. The temperature of Jack's beaker is three times less than that. [i.e. 3x the delta between Paul and Mary, but starting from the temperature of Mary's beaker]
P.S. Isaac Newton was wrong about how to talk in English about mathematics, and I am right, because Newton stole the calculus.
Fedya's argument is ____ times less likely to convince folks that Eugene's.
Scientific notation is allowed.
I think Isaac Newton used some math in his work.
The answer to your question is that I originally started with a second number that was "three times less" than the first number. If you start out at 1/3, the second and third interpretations (3x the 2/3 delta, with different starting points) are always a negative number. I then realized that there was no need for the first number to be "three times less" than the first, but didn't change the numbers.
The reason I chose degrees rather than apples was that it would be better to say "fewer" rather than "less than" if it were apples.
None of them are correct. Unless you're using the Kelvin scale (which you obviously aren't, since you've got negative values), temperature data is interval data. When using interval data it doesn't make sense to use statements like "twice as much" or "three times less". In order for these sorts of statements to be meaningful, they need to be applied to ratio data: data that does not depend on a scale with an arbitrary zero point, like numbers of things, size, mass, etc.
Paul: 50 degrees
Mary: 48 degrees
Mary is 2 degrees less than Paul.
Which is three times less than that?
A. Jill, 16 degrees (48/3)
B. Joe, 44 degrees (50 - 3*2)
C. Jack, 42 degrees (48 - 3*2)
The mathematical claim (10 times less means something other than 1/10th in mathematics therefore it must mean that in plain English) would require that rules of English usaga be based on mathematics. While you may believe that is desirable, that doesn't mean it is how language actually works.
Perhaps that stronger claim is, "X times less means something else (or means nothing) if used in mathematics. Therefore, if it is used in English, it will be ambiguous which meaning is being employed." This, of course, is a simple claim of ambiguity. The problem with this is that it makes the common mistake of confusing potential ambiguity (this sentence can be understood in more than one way) with actual ambiguity (people are likely to understand this sentence in a way other than that which is intended, or in extreme cases, this meaning of this sentence is actually indeterminable). THe problem is, if you are attacking this for potential ambiguity, then nearly every sentence is going to be subject to criticism. The English language, and probably every language, has a great deal of built in potential ambiguity. This is eliminated through context and common usage (and other ways, like punctuation).
I would argue that X times less than is only potentially ambiguous. I would doubt that there are many native speakers who read that and actually think, "I don't know what this sentence means." I would argue that even those who are annoyed by it are able to immediately recognize the meaning, even if they find the usage disagreeable.
It is true that some people have argued against this usage (at least in the last fifty years), but this has been in use for at least ~300 years and is understood by virtually all native speakers. I think that places a heavy burden on the prescriptivists who claim it is not correct English.
If what you mean is that W= Y/X, then why not say that expressly (e.g., W is one half of Y instead of W is two times less than Y)? The W=Y/X formulation is clearer and shorter, something that writers should generally strive for.
It really gets me when X is not a whole number (e.g., W is .70 times less than Y). No, Bruce, I don't have any problem understanding actual math, but this one always gets me. (Do they mean that W is 70% of Y? 70% less than Y?) Gets me every time.
If it is changed to gallons, I agree, your use of "that" is ambiguous. I would no more know that "correct" answer if you phrased it in the "acceptable" form, "which is one third as much as that?"
Rubbish. Your quote is from Newton's Opticks, and in case you haven't heard, Newton didn't even get the physics right, much less the English (or the spelling!). He advocated a "corpuscular" theory of light, which we now know to be a woefully insufficient theory, albeit useful in limited circumstances. For an accessible treatment of the modern theory of light, I recommend "QED: The Strange Theory of Light and Matter" by Richard Feynman.
So, if Newton couldn't even get the physics right, why should we trust his English?
Looking at the page you linked, one finds the gem, "But in the Figure pt composed of the less Circles, the three less Circles ag, bh, ci, which answer to those three greater, do not extend into one another, nor are there any where mingled so much as any two of the three sorts of Rays by which those Circles are illuminated, and which in the Figure PT are all of them intermingled at BH." Dust thou thinkst it would be just fine for schoolchildren to learn to say "less Circles" instead of "smaller circles" -- because Sir Isaac did? Is it fine for them to learn punctuation and grammar from Sir Isaac, so that we may all capitalize important Nouns, and perhaps elide the terminal "and" in a sequence such as "ag, bh, ci"? Rubbish.
So: "Isaac Newton was wrong about how to talk in English about mathematics, and I am right, because ..."
(1) I was born in America in the 20th century,
(b) I got a "5" on my English AP exam, and
(iii) I was on the U.S. Mathematical Olympiad Team,
(IV) I have a doctorate in theoretical physics from MIT...
none of which Sir Isaac could claim, and none of which matters one whit to this argument!
So much for the Argument from Authority.
If you're comfortable with "3 times less", are you equally comfortable with "twice as less"? Eleanor Wilson Orr wrote a book with that title about a decade ago, explaining in great detail how defective grammar leads to defective mathematical understanding.
BBB
We would now like to express the opposite relation (by which I don't mean the negation, but the relation going the other way). Since the opposite to "X is larger than Y" is "Y is smaller than X", it is natural to say that "Y is ten times smaller than X" if and only if "X is ten times larger than Y".
Now the two statements are mathematically equivalent, but they are not equivalent rhetorically -- we usually perceive them as statements about the first among the two quantities mentioned. Similarly, "X is ten times less than Y" and "X is one-tenth of Y" are mathematically equivalent yet are not the same rhetorically.
If, however, it had been a common usage for the past three hundred years, and everyone used and understood it, I probably wouldn't care. The book you point to identifies exactly the problem with the argument though. The statement that "defective grammar leads to..." begs the question. Maybe the book makes a better argument, but this seems to say "twice as less cannot be understood in mathematics, therefore using it in English will detract from your understanding of math, therefore it is ungrammatical in English." It may be ungrammatical, and using it may detract from understanding of math, but the two are in no way related.
I always dismissed it as a contemptible solecism created by and copied by ignorant writers. And, since "10 times less than" can't sensibly mean anything other than "one tenth as much," why not just say that?
"times" is part of the terminology of "increase"; "less" is part of "decrease." Putting them together is at best sloppy.
Must admit I knew nothing of this usage by pre-eminent scientists.
IF it was theirs. Maybe it must be credited to the translators.
Paul: 50 gallons
Mary: 48 gallons
Mary has 2 gallons less than Paul.
Who has three times less than Mary?
A. Ann, 16 gallons (48/3)
B. Bob, 44 gallons (50 - 3*2)
C. Cal, 42 gallons (48 - 3*2)
This is why you would never say "twice as less" to mean "half." Because one would rightly be confused as to what one was meant to double.
The English language is full of idioms that don't correspond to the literal meanings of the individual words. My favorite example is "ice cream," which literally refers to iced cream, not cream made out of ice. That doesn't make the idioms wrong; it just means that you can't import the rules of a foreign means of communication -- Latin, mathematics, computer programming, and so on -- to understand them, and especially the rules of a means of communication that generally doesn't include idioms.
I think "twice as less" is rare, since "half" has been with us before written language. "One tenth" is a far more sophisticated concept and does not have such a long history.
Newton, Schnewton. Gimme a break. Spend some time reading how folks wrote about math at the time, and then look me in the eyes and tell me you honestly want to see everyone write that way today. Their writing style was often imprecise, confusing, and/or hard to read. I'd hardly point to that archaic style as the best model to follow today.
The reason I don't like it, though, is this:
The difference between "three times more" and "four times more" is the same as the difference between "four times more" and "five times more."
However, the difference between "three times less" and "four times less" is not the same as the difference between "four times less" and "five times less".
That seems to suggest that "times" somehow means something different with "less", that one "time" is not the same as another "time" - and one "time" is never the same as the original number, which it always is when used with "more".
"Twice As Less" is a book, as it happens:
http://tinyurl.com/ya6vdap
I've read it, and the author has a little trouble parsing the meaning. IIRC, I was somewhat frustrated that she didn't talk to some of the students who used it to find out what they meant.
Anyway, this thread is all the evidence necessary to suggest it's a confusing usage.
Is essentially correct, but what is interesting is the origin of this usage, which is common to other languages than English. It arises from an era when most people were acquainted with multiplication, but not with division, and unfamiliar with the notion of "reciprocal". Most people today find that difficult to imagine, but just listen to the talk of children after they learn multiplication and before they learn division.
Incidentally, among mathematicians one does occasionally get the usage that translates into
A * [-∞, B)
where * == multiplication operator and
[ ...) == half-open interval, that includes the lower endpoint but not the upper. The above expression =
[-∞, A*B)
Oh snap!
But here's a counterexample for anyone who's interested. "Orders of magnitude less" An order of magnitude is a ten-base exponential multiplyer, so shifting orders of magnitude is effectively a timesing operation.
So is it wrong to say 'orders of magnitude less?' Cause if it's wrong, I don't wanna be right.
As I'm sure you know, "order of magnitude less" means "the order of magnitude is less", as "order of magnitude" is the exponent of 10 in the scientific notation. It's the same as "ten times less". We allow it, but I think it's a colloquialism.
None of these things are as confusing or likely to be wrong as expressions including the word "percent."
X *= 10^-n
which is computer notation for "X is replaced by its value multiplied by 10 to the -n power".
Hope that is clear. :)
I disagree.
Dealing with fractions ("1/3 as much as before...") is less intuitive for many people than dealing with whole numbers ("3 times less than before...").
It's also much harder to say if you're dealing with a larger number, e.g., "three hundred fifty one times less than before..." versus "one three hundred fifty first as much as before..."
However, "twice as few" gets 2,740,000 hits.
Finally, on our language, in general.
Wittgenstein, Philosophical Investigations, para. 18.
One clear way to think about the expression is that "times" in the phrase "times less" is a unit modifier.
You have five less soldiers less than a full brigade (i.e. 1495)
You have five score soldiers less than a full brigade (i.e. 1400)
You have five hundred soldiers less than a brigade (i.e. 1000)
You have five fold soldiers less than a full brigade (i.e. 300)
You have five times soldiers less than a full brigade (i.e. 300).
I also like the notion that "times" used without modification is really an abbreviation of "times more than". There is never a circumstance when "times" unmodified means something different than "times more" unmodified. And, this makes "times more than" and "times less than" inverse operations of each other.
In the same vein, without the "times" part the phrases "more than" and "less than" can be understood as inverse operations of each other rather than simply different operations than each other.
The historical dating is also interesting. The authorities cited and the way that the phrase is used suggest that the useage predates widespread use of the concept of negative numbers.
It doesn't work the same way with "three times less." If I give you 9 marbles one time, it's not possible to give someone else 9 marbles "three times less." Giving someone else "three times less" doesn't make any sense because I only have you marbles one time.
But if I gave you one marble 9 times, and gave someone else one marble 3 times less, then the second person gets six marbles, not 3.
I went to the water fountain three times today.
You would have me say that I went to the fountain three times more. More than what?
All modern mathematician carry out calculus using the notion methods of his co-inventer of calculus Gottfried Wilhelm Leibniz. Leibniz introduced several notations used to this day, for instance the integral sign ∫ representing an elongated S, from the Latin word summa and the d used for differentials, from the Latin word differentia. This ingenious and suggestive notation for the calculus is probably Leibniz's most enduring mathematical legacy.
Let's complain about improper uses of "quantum", "organic", and "parameter" instead. Oh, and since I'm OT already, how about "hone in on" instead of "home in on". And "factoid" to mean "little fact" instead of "something that looks like a fact, but isn't".
And back on topic: Since (as SeanF pointed out) one of the items being poorly communicated with this idiom is proportion, I want to register a complaint about journalists who seem to instinctively choose the least-informative representation whenever given a choice between an absolute number or increment, vs. a percentage or proportion.
It's Friday after lunch and I'm off my meds...who can focus on work?
Generally, the Argument from Authority is not a logical basis for scientific proof. But, language is more like law than science. Sometimes "authority" is what makes a linguistic useage right. Useage dictionaries have used this principle for centuries.
The reason that most people in the world speak languages that are mutually intelligble by millions of people is that the general public has had an intuitive preference for dialects used by those in positions of authority. A dialect can be correct, while another can be incorrect, in a social context, precisely because of the relative authority of the speakers.
The speakers of Sanscrit has so much authority that their linguistic practices had a great deal of influence on which dialects of Dravidian were viewed as most correct, even though Dravidian languages aren't even derived from Sanscrit. Most modern languages arose from the dialect favored in royal courts. These days, television and radio personalities have supplanted to role of genuine power holders to some extent. One of the most influential style guides today, a book making calls on what is "correct," is published by the Associated Press.
As an exception that proves the rule, some of the distinctive elements of the upper class New England American dialects of English, like its non-pronunciation of the letter "h" at the beginning of a word, were specifically adopted after the American Revolution in defiance favored pronunciation in the English court at the time.
If Mars has a diameter of 10,000 miles and you make it 3 times less it is clearly impossible that the diameter is now -20,000 miles and so he must mean reduce to 1/3 the original value.
However, where it tends to annoy me is in a formulation like this: "This year's drop in violent crime was three times less than last year's drop of 3%." I honestly could not say whether they mean crime had dropped 1% or 9% (let alone the discounted possibility they actually mean it rose 6%).
Plus there's the fact that I can't begin to predict whether the speaker is a pedant on this issue. So while I don't get worked up about it unless personally I try to keep it a phrasing that has minimal ambiguity (and won't run me afoul of usage nags).
So I'd say "If the Diameters of the Circles ... be made one-third that they were before" or "If the Diameters of the Circles ... be made 66% less than before" and "this year's drop in violent crime was 9% while last year's drop was 3%."
And if I heard Newton saying any of this, I'd try to touch his wig and giggle like a schoolgirl and not care at all about his phrasing. Then I'd tease him about all that alchemy stuff.
And, if I tried to make sense, it would be multiplying A by some number that is less than B, or, probably more accurately, the set of numbers less than B (which, presumably, if both A\>0 and B\>0, and we are talking real numbers, means all the numbers less than A*B).
My thoughts are that if you want to do reciprocals, then call them that, and if you want to divide A by B, then call it that.
p.s. Interestingly, this blogger interface has real problems with less than signs in comments, as they are the start of a HTML command.
ohwilleke has nailed the argument why referring to Newton is unconvincing.
Because Isaac Newton was a journalist, not a mathematician....
All of your statements about temperature are meaningless unless using a true temperature scale like Kelvin ;-)
Every single linguistic textbook which I have ever read (and I read as many of them for fun as I do court opinions, and I read enough court opinions for fun to hang out here....) starts off with the basic statement that natural languages are defined by use.
Technically a widespread construction cannot possibly incorrect in a natural language!
Zero, of course. :-)
"Ten times less" is nonsensical, even if people compensate for the failure and recognize the speaker is trying to say B is only 10% of A.
Noam Chomsky is a linguist, and one of the stupidest people I have ever read. He really thinks Marx wsa onto something, and has never changed his views despite the manifest failure of marxism as a political or economic system to provide the "liberation" or "abundance" or "justice" it promises. When an idea or set of them have a 100% failure rate...that would be, er...I dunno...but usually if one can think, one decides to stop trying it.
Progressives enamoured of marx are regressives, trying to sell bad failed ideas from the past as if they will work, this time.
Stepping back onto the thread, the linguistic books can cram it. Ten times less than something doesn't make sense mathematically, and so the comment is misleading, wrong or foolish.
No wonder kids can't do math, they have adults throwing foolish comparisons like this at them.
I think that "x times less" is a useful and understandable phrase to use when you're saying that less is actually more.
'x times less' is good language when you're expressing the factor by which the small is better than the large.
Fedya: "Zero, of course. :-)"
I frown upon arguments that divide by zero.
Here's a picture of Fedya
If the savings are small, I will usually say "the optimized file is now one-sixth the size of the original, and will download six times faster."
If the savings are larger (which is very common), though, that "seems wrong"; it seems clunky and likely to require multiple readings. So I use the "times smaller" phrasing; I'll say "the optimized file is now 80 times smaller than the original, and will download 80 times faster."
Isaac Newton was right about how to talk in English about mathematics, because... he agrees with me.
What does that have to do with linguistics principles which have remain largely unchanged for over a hundred years.
If you don't like Chomsky, try reading George Steiner (he can't stand Chomsky's linguistics and falls more in the Whorf/Sapir camp).
A) -10
B) -90
C) something else?
If you say "times more than" or "times less than," your audience is less likely to understand you, and more likely to have to struggle to understand you, than if you'd used some other formulation.
I think it's no accident that all your citations are from a very long time ago. I've been hanging out in technically-minded circles most of my life, and I can't remember ever hearing someone use "times more than" or "times less than." (Although, when a subject is implicit, "... times more" seems occasionally felicitous.)
Radical descriptivism, combined with a willingness to comb through centuries of English written by smart people, will lead you to some strange linguistic beliefs. If I added every Humean or Lockean formulation to my stock of English, my writing would look ridiculous. I have a responsibility to my listeners and readers, and that responsibility is incompatible with my helping myself to any locution any smart English user ever published.
P.S. — Of ~course~ I know some things that Newton didn't know about how to write scientific English... in 2009. How could Newton have known what English would be in 2009?
'Times' is the preferred word to represent factor or scale. Its acceptability to express comparison is much better than percentages, and I think better than fractions on those occasions where 'less is more'- where you're expressing the smaller number as the better number.
So a thing is smaller, and better... by what factor? It's 'X times less than.'
It may be a bit cumbersome, but it's a bottom-line point-making phrase, not a math-handy calculation phrase.
I think "three times more than" and "three times less than" are perfectly understandable in their normal usages.
Next, I await the great debate over whether the following sentence is incorrect in English:
"Who did you meet yesterday?"
(Gotta love cases like these, pun intended)
I might be quite wrong about whether the phrase is felicitous. It struck me as very odd, but it can be hard to retain a sense of usage when you know you're reading a blog post about usage.
As smart and reasonable as Prof. Volokh is, I just don't think extreme descriptivism is tenable. (David Foster Wallace's "Authority and American Usage" is excellent on this subject.) If "times more than" is acceptable, that is because the phrase is a part of correct contemporary English, not because Newton used it.
Extreme descriptivism is a practical necessity in fields like historical linguistics. The reason is that language usage changes over time and drifts relative to its roots. It is also important in comparative linguistics because various dialects may have different rules (see the habitual tense in African American Vernacular English for example).
I think that what you are arguing is "effective style" rather than "correct usage." This has to be separated or else we would all be reprimanded every time we say "So, who did you meet yesterday?" This is because the prescriptive approach would be to use the "objective" (merged dative and accusative) instead and say "So, whom did you meet yesterday?" But that just sounds wrong. Interestingly Edward Sapir in 1912 predicted the imminent death of "whom" in informal communications.
"Effective style" is prescriptive. This is what we REALLY want our schools to teach. However it is not the same thing as "correct usage" which is descriptive. IMO we should separate these issues.
Thanks for responding so helpfully.
I'm not sure I exactly see your point. Language definitely changes. Languages and dialects definitely have different rules. I don't see how any of that decides the question whether, given a language at a time, correct usage is to be determined descriptively or not. One can be a prescriptivist and hold that 2009 English uses "who" in the accusative/objective.
Using English and using English well are certainly two different things, but nothing you say shows that correct usage is descriptive. If I use Hume's English, I might fail not only to use English well but to use English--contemporary American English--at all.
So, do you begin business letters with "To who it may concern?" If we accept an objective (i.e. accusative/dative) "who" as a prescriptionist, then that should be the correct, accepted form. However it is not. The phrase we accept has "whom" in it.
Once again, I think this is a matter of effective style rather than correct usage. If I try to avoid the problem above by addressing my letter "To whoever it may concern" that certainly doesn't sound jarring but it isn't effective style either.
Similarly dialects which use double and triple negatives aren't necessarily wrong in their usage. We don't use them in formal communications because they don't sound very educated so once again it is a stylistic rather than a syntactic rule. On the other hand, "My aunt said he wanted to have us over for dinner" where "he" in context refers clearly to "my aunt" IS incorrect because it violated deeply held and pervasive gender checks built into the language, and it is not an accepted use of "he."
I think George Steiner ("After Babel") said it best, that language is fundamentally a simplified model of the world and that it necessarilly contains some ambiguity. I would add to that the notion that natural language is usually autochthonous and as such one doesn't have the same strictness in syntactic rules that one has with a computer language.
Why does this matter?
Consider the Ebonics debate. The debate centers largely around whether AAVE is "bad or lazy English" or whether it is an interesting dialect which is hence a part of our national heritage. To a prescriptionist, the former seems most appealing and to the descriptionist the latter seems most appealing. I certainly hold with the latter.
However, this doesn't mean that the concerns about what we teach our kids magically goes away just because we say "It's an interesting and important dialect." The worry (which is well justified by the way multiculturalism is handled elsewhere in our education system) that this will undermine rather than support critical education is a valid one if we continue with a prescriptionist framework exclusively.
However, a solution can be found in being more honest about what we want kids to learn in English class. Instead of teaching "correct English" we want kids to learn how to be able to write and speak in a certain dialect and style which we believe best prepares kids for economic success later in life.
Now, one other point relative to this forum. Legalese is a little different. It is far more prescriptive than modern English simply because of its hyperdefined nature and the effect of error. Similarly invented languages or dead languages are more prescriptive simply because they are tied to a specific static authority separate from the speakers.
As someone who thinks that "three times more" means "three times as many," I guess the answer is: because with "percent more" expressions, by convention, no change or difference is 0% more, but with "times more" expressions, by convention, no change or difference is 1 time more; also by convention, these expressions are used only when there is non-zero change or difference, so one doesn't actually say "0% more" or "1 time more" to express no change or difference.
But, for the reason that "three times more" is inconsistent in meaning with "300% more," I think expressions of the form "three times more" should be avoided, and a fortiori, expressions of the form "three times less" should be avoided.
Also, "one-third as many" and "one-third less" mean very different things. If I hear that city A has one-third as many murders as city B, and city C has one-third less murders than city B, then I calculate the murder ratio of city A : city B : city C = 1 : 3 : 2. I assume that "three times less" is intended to mean "one-third as many" (or "one-third as much") and not "one-third less."
Thanks again for the response. You say a lot that's worth responding to, but quickly first: there's absolutely no reason that a non-descriptivist would have to hold that Ebonics is "bad or lazy English." She probably would have to hold that AAVE is different from some other English dialect.
For myself, I think it's very difficult to hold that AAVE is "bad English." AAVE is no less rule-governed than [pick another form of English], and dismissing it as "bad English" leaves one unable to account for AAVE mistakes as mistakes.
It's quite common for people to saddle prescriptivism (which might not be the best term for all anti-descriptivist views) with all sorts of crazy views that are no part of it. If prescriptivism committed me to the view that AAVE is bad English, I'd run away screaming from it [that is: from prescriptivism, not from AAVE].
I hate to break it to the engineers and mathmaticians, but there are people in the world that do not see math in their heads when reading something. The general scale is all that is being referenced in saying things that way, not the exact to-the-decimal-point number.
My bet is that if you asked people who find reading engineering or math articles boring as hell would find absolutly nothing wrong with "times less than".
The ones that dont like it are the ones that read a sentence and automatically figure out the word problem in mathmatical form. In this case "times less than" does not conform to the basic word problem form and this is what bothers them about its usage.
If you realize that the usual phrase is not "A times B equals C" (using "times" as an operator in an expression of the relationship of A and B to C) but that "times" refers to iterations or instances, you'll be fine.
So that "if I multiply B A times" would be an older form of our more compact expression, and "if I divide B A times" would also be quite sane. These yield the mathematical expressiong (A * B) and (B / A) which we gloss "A times B" and "B divided by A"; note the asymmetry of the translation, with division retaining its term, but multiplication losing its.
Hence the confusion of those who forget that "I can go to the store three times" is perfectly intelligible without any algebra in play.
And after a bit of thought, I find 'times less than' to be awkward and confusing.
People's posts on the internet actually caused me to change my mind. I apologize- it'll never happen again.
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