I am three times dumber than you not to know this already
June 17, 2010 9:54 AM Subscribe
Saying "it's three times less" seems nonsensical to me. Please enlighten me.
I am always seeing writers saying things like, "It's 20 times smaller," or "3 times less calories!" or, just now, an actual physicist describing distances as "many billions of times smaller."
Now, back when I learned math, I learned that a quantity was one times itself, right? And you could say, "It's three times as much," and that meant to multiply that quantity by 3.
But if something is, say, 1/3 as much, you have to say "a third as much" or "one-twentieth the size" or something similar.
It makes to sense to me to say that something is "three times smaller," because if it were ONE time smaller (that is, its own size smaller) it would be zero.
So people saying things like that always seems innumerate to me. Am I wrong about that? Is there a way in which this formulation makes mathematical sense?
Alternately, I see this so much that I've pretty much decided it's an idiom--that we say "three times smaller" and mean "one-third the size" and the writer and all her readers all just take it that way, and even though it's not literally true, it's how we say it in our kind of English. So, that is, it is innumerate but the usage is so accepted that, outside of your pedantic math prof's class, it's nonetheless a correct usage.
So, which is it:
1. It's innumerate, and its usage makes the user look dumb. It's an error, in other words.
2. It's innumerate, but its usage is idiomatic and therefore correct.
3. It's not innumerate, and here's why.
4. ?
I am always seeing writers saying things like, "It's 20 times smaller," or "3 times less calories!" or, just now, an actual physicist describing distances as "many billions of times smaller."
Now, back when I learned math, I learned that a quantity was one times itself, right? And you could say, "It's three times as much," and that meant to multiply that quantity by 3.
But if something is, say, 1/3 as much, you have to say "a third as much" or "one-twentieth the size" or something similar.
It makes to sense to me to say that something is "three times smaller," because if it were ONE time smaller (that is, its own size smaller) it would be zero.
So people saying things like that always seems innumerate to me. Am I wrong about that? Is there a way in which this formulation makes mathematical sense?
Alternately, I see this so much that I've pretty much decided it's an idiom--that we say "three times smaller" and mean "one-third the size" and the writer and all her readers all just take it that way, and even though it's not literally true, it's how we say it in our kind of English. So, that is, it is innumerate but the usage is so accepted that, outside of your pedantic math prof's class, it's nonetheless a correct usage.
So, which is it:
1. It's innumerate, and its usage makes the user look dumb. It's an error, in other words.
2. It's innumerate, but its usage is idiomatic and therefore correct.
3. It's not innumerate, and here's why.
4. ?
It's three times smaller = if you multiplied the thing by three, it would be original size. It is 1/3 the size of the other thing.
It depends on your frame of reference. If you are talking about the new, smaller thing, it seems fine.
posted by Meatbomb at 10:03 AM on June 17, 2010
It depends on your frame of reference. If you are talking about the new, smaller thing, it seems fine.
posted by Meatbomb at 10:03 AM on June 17, 2010
"But if something is, say, 1/3 as much, you have to say "a third as much" or "one-twentieth the size" or something similar."
Yup, it's an idiom. I don't think people have very deep knowledge of the difference between 1/3 as much vs. 3x as much.
posted by amethysts at 10:05 AM on June 17, 2010
Yup, it's an idiom. I don't think people have very deep knowledge of the difference between 1/3 as much vs. 3x as much.
posted by amethysts at 10:05 AM on June 17, 2010
It makes [no] sense to me to say that something is "three times smaller," because if it were ONE time smaller (that is, its own size smaller) it would be zero.
See, that is what sounds innumerate to me because 'one times [anything]' is the identify function, so 'one time smaller/larger' means no change.
Why does it not make sense for 'larger' to mean multiply and 'smaller' to mean divide? Is it because they both use 'times'? Division can be 'times' too, just as subtraction is a form of addition.
posted by Rhomboid at 10:07 AM on June 17, 2010 [2 favorites]
See, that is what sounds innumerate to me because 'one times [anything]' is the identify function, so 'one time smaller/larger' means no change.
Why does it not make sense for 'larger' to mean multiply and 'smaller' to mean divide? Is it because they both use 'times'? Division can be 'times' too, just as subtraction is a form of addition.
posted by Rhomboid at 10:07 AM on June 17, 2010 [2 favorites]
Or if you want to think of it from a non-mathematical way, then "A is 3 times larger than B" means if you take three Bs and line them up end to end you'd get one A, and "A is 3 times smaller than B" means if you take three As and line them up end to end you'd get one B.
posted by Rhomboid at 10:12 AM on June 17, 2010
posted by Rhomboid at 10:12 AM on June 17, 2010
One third as large = three times as small.
posted by abc123xyzinfinity at 10:12 AM on June 17, 2010
posted by abc123xyzinfinity at 10:12 AM on June 17, 2010
You are treating language as if it were math or logic. It is not. (If it were, "slow up" and "slow down" wouldn't mean the same thing.) Try to focus on how phrases are actually used rather than what you think they "should" mean. (Cf. all the idiots who claim that "anti-Semitic" doesn't/shouldn't/can't mean "anti-Jewish" because Jews are not the only Semites and/or Jews are not actually Semites.)
In other words, the correct answer is 3: it's not innumerate, because language is not math.
posted by languagehat at 10:13 AM on June 17, 2010 [2 favorites]
In other words, the correct answer is 3: it's not innumerate, because language is not math.
posted by languagehat at 10:13 AM on June 17, 2010 [2 favorites]
Also I think you have an odd definition of "innumerate". If Person A knows what mathematical concept they're trying to express, and uses language to express it to Person B that Person B understands with no room for ambiguity or error, nobody in this transaction can be called innumerate.
posted by game warden to the events rhino at 10:18 AM on June 17, 2010 [2 favorites]
posted by game warden to the events rhino at 10:18 AM on June 17, 2010 [2 favorites]
Response by poster: In other words, the correct answer is 3: it's not innumerate, because language is not math.
I take your point, but when it's language about math, or describing quantities, or measurements, then it seems to me the language has to make sense in terms of the math.
That said, I really am comfortable saying, "That's what it means, and everybody knows it, so it's working just fine." If I could just get over noticing it because I remember what I learned in math class, life would be perfect.
posted by not that girl at 10:18 AM on June 17, 2010
I take your point, but when it's language about math, or describing quantities, or measurements, then it seems to me the language has to make sense in terms of the math.
That said, I really am comfortable saying, "That's what it means, and everybody knows it, so it's working just fine." If I could just get over noticing it because I remember what I learned in math class, life would be perfect.
posted by not that girl at 10:18 AM on June 17, 2010
So people saying things like that always seems innumerate to me. Am I wrong about that? Is there a way in which this formulation makes mathematical sense?
Yes, you're wrong about that, and there is a way in which the formulation makes mathematical sense in casual language.
Take "A is three times smaller than B!"
Mathematically, this just means A is one-third the size of B.
What the usage is telling you is what the normative quality of the object is, and what they're emphasizing. Saying "B is three times bigger than A!" gives the same information but carries the connotation that B is in some normative sense large. Saying "A is three times smaller than B!" connotes that A is small, and it tells you that the speaker is emphasizing the smallness of A rather than the largeness of B.
Or, if you'd rather, while it's not something you can measure with a ruler, objects can have qualities of largeness and of smallness. Call it smallth. "A is three times smaller!" means A has three times the smallth of B.
posted by ROU_Xenophobe at 10:19 AM on June 17, 2010 [1 favorite]
Yes, you're wrong about that, and there is a way in which the formulation makes mathematical sense in casual language.
Take "A is three times smaller than B!"
Mathematically, this just means A is one-third the size of B.
What the usage is telling you is what the normative quality of the object is, and what they're emphasizing. Saying "B is three times bigger than A!" gives the same information but carries the connotation that B is in some normative sense large. Saying "A is three times smaller than B!" connotes that A is small, and it tells you that the speaker is emphasizing the smallness of A rather than the largeness of B.
Or, if you'd rather, while it's not something you can measure with a ruler, objects can have qualities of largeness and of smallness. Call it smallth. "A is three times smaller!" means A has three times the smallth of B.
posted by ROU_Xenophobe at 10:19 AM on June 17, 2010 [1 favorite]
Best answer: It's idiomatic, and I personally would try to avoid phrases like "three times smaller", where there is both an exact relationship and a small enough value that people should have an intuitive feel for it. However, in defense of the Physicist, some things are much easier to construct in this way; as you can see by trying to create the equivalent "correct" form of "many billions of times smaller."
posted by ecurtz at 10:24 AM on June 17, 2010
posted by ecurtz at 10:24 AM on June 17, 2010
Sorry, but since no-one else is sticking up for the OP here, I agree with her. I think it's innumerate and makes the user at least sound like he/she isn't thinking about what he/she is saying. I know perfectly well that language is often illogical, but there is no reason to be illogical when a perfectly satisfactory and idiomatic alternative is available.
posted by Logophiliac at 10:25 AM on June 17, 2010 [1 favorite]
posted by Logophiliac at 10:25 AM on June 17, 2010 [1 favorite]
Is it because they both use 'times'? Division can be 'times' too, just as subtraction is a form of addition.
But no one says "You found a hundred dollar bill on the ground?! I've enver found more than a twenty. That's negative 80 dollars more than you found!"
The issue here, as pointed out by languagehat is one of language, not math. The phrase "n times less" is accepted to mean "1/n less" or "times 1/n". Even though it refers to a mathematical comparison, the language does not translate literally to an equation.
For what it's worth, it bugs me, too, but it's not worth fighting against. My pet battle is electrocute vs. shock.
posted by owtytrof at 10:40 AM on June 17, 2010
But no one says "You found a hundred dollar bill on the ground?! I've enver found more than a twenty. That's negative 80 dollars more than you found!"
The issue here, as pointed out by languagehat is one of language, not math. The phrase "n times less" is accepted to mean "1/n less" or "times 1/n". Even though it refers to a mathematical comparison, the language does not translate literally to an equation.
For what it's worth, it bugs me, too, but it's not worth fighting against. My pet battle is electrocute vs. shock.
posted by owtytrof at 10:40 AM on June 17, 2010
A is n times larger than B: A = nB
A is n times smaller than B: nA = B
If it helps you can think of the words "larger" and "smaller" as an operator that tells you which of the terms is being multiplied by n.
posted by PercussivePaul at 10:47 AM on June 17, 2010
A is n times smaller than B: nA = B
If it helps you can think of the words "larger" and "smaller" as an operator that tells you which of the terms is being multiplied by n.
posted by PercussivePaul at 10:47 AM on June 17, 2010
I think it makes sense if you think of it the following way:
1 times larger: the same size
1 times smaller: the same size
2 times larger: doubled in size
2 times smaller: half the size
When someone says "X times smaller" instead of "X times larger", just mentally take the reciprocal of X before multiplying. That's what the "smaller" means. I don't think that saying something is 1 times smaller would mean that it has zero size; I think instead that kind of meaning is conveyed by expressions like:
100% larger: doubled in size
100% smaller: zero size
The consistent usage is as follows:
A is X times larger than B means that the size of A is the size of B times X.
A is X times smaller than B means that the size of A is the size of B divided by X.
A is X% larger than B means that the size of A is the size of B plus X*B/100.
A is X% smaller than B means that the size of A is the size of B minus X*B/100.
I don't understand how, if a consistent mapping exists between mathematical expressions and language used, it could be considered "innumerate".
posted by a snickering nuthatch at 10:47 AM on June 17, 2010 [2 favorites]
1 times larger: the same size
1 times smaller: the same size
2 times larger: doubled in size
2 times smaller: half the size
When someone says "X times smaller" instead of "X times larger", just mentally take the reciprocal of X before multiplying. That's what the "smaller" means. I don't think that saying something is 1 times smaller would mean that it has zero size; I think instead that kind of meaning is conveyed by expressions like:
100% larger: doubled in size
100% smaller: zero size
The consistent usage is as follows:
A is X times larger than B means that the size of A is the size of B times X.
A is X times smaller than B means that the size of A is the size of B divided by X.
A is X% larger than B means that the size of A is the size of B plus X*B/100.
A is X% smaller than B means that the size of A is the size of B minus X*B/100.
I don't understand how, if a consistent mapping exists between mathematical expressions and language used, it could be considered "innumerate".
posted by a snickering nuthatch at 10:47 AM on June 17, 2010 [2 favorites]
I don't think it's innumerate. Not understanding the underlying mathematical relationship would be and indication of innumeracy; expressing it somewhat imprecisely is, though regrettable, not innumerate.
I think this whole issue is overly pedantic (and trust me, as someone who teaches calculus to a lot of engineering students, I have no problem being pedantic about math).
posted by MidsizeBlowfish at 10:48 AM on June 17, 2010
I think this whole issue is overly pedantic (and trust me, as someone who teaches calculus to a lot of engineering students, I have no problem being pedantic about math).
posted by MidsizeBlowfish at 10:48 AM on June 17, 2010
Sometimes there's confusion when there's a mix of X% larger and X% the size of. So if you have Laundry Detergent that's "Now 533% More!" it's 633% the size of the original.
posted by yeti at 10:56 AM on June 17, 2010
posted by yeti at 10:56 AM on June 17, 2010
By the there is a phrase in programming called "syntactic sugar" which describes a type of construction that is provided by the language as a convenience to the programmer, e.g. i++ instead of i=i+1; for whatever reason the programmer may find the "sugar" easier to use, even though they're functionally equivalent.
I've always understood is construction, "A is n times smaller than B", to be syntactic sugar for "A is 1/n times larger than B". I think everyone else is saying the same thing. It's a convenient form because it's easier for humans to parse the meaning when n is greater than 1. But you don't have to give up and call it an idiom of language, nor is the usage imprecise or innumerate, if you think about this way (which most people seem to implicitly).
posted by PercussivePaul at 10:58 AM on June 17, 2010
I've always understood is construction, "A is n times smaller than B", to be syntactic sugar for "A is 1/n times larger than B". I think everyone else is saying the same thing. It's a convenient form because it's easier for humans to parse the meaning when n is greater than 1. But you don't have to give up and call it an idiom of language, nor is the usage imprecise or innumerate, if you think about this way (which most people seem to implicitly).
posted by PercussivePaul at 10:58 AM on June 17, 2010
I could understand the issue if it was used in an academic context. It's imprecise language. But that very imprecision is what makes it perfect for ordinary casual conversation and simply conveying the feeling of a size to someone, especially someone whose understanding of maths is rudimentary.
posted by Magnakai at 11:35 AM on June 17, 2010
posted by Magnakai at 11:35 AM on June 17, 2010
There's too much chance for confusion when using fractions. If I said:
A is 1/3 smaller than B, then you would know that A is 2/3 of B (0.66). But if I said A is 1/3 as small as B, then I would mean that A is 1/3 of B (0.33).
posted by blue_beetle at 12:08 PM on June 17, 2010
A is 1/3 smaller than B, then you would know that A is 2/3 of B (0.66). But if I said A is 1/3 as small as B, then I would mean that A is 1/3 of B (0.33).
posted by blue_beetle at 12:08 PM on June 17, 2010
There is some room for confusion, if you say something has three times more. That could mean itself, plus three times that. I know that's not the case here, just a related usage that can be vague.
posted by StickyCarpet at 12:13 PM on June 17, 2010
posted by StickyCarpet at 12:13 PM on June 17, 2010
A lot of this usage is found in product marketing. In consumers' illogical minds, a bigger number always means better. If you sell a widget with 25% the failure rate of your competitor, then you advertise "4 times fewer problems," not "1/4 the problems." Enumerating any quantifiable attribute of your product as less or lower than your competitor's is bad, even if it's a negative attribute.
A "light" version of a product might have "three times less fat" which implies that you can consume three times as much. That implication isn't as strong if something has "1/3 the fat."
posted by bgrebs at 1:20 PM on June 17, 2010 [1 favorite]
A "light" version of a product might have "three times less fat" which implies that you can consume three times as much. That implication isn't as strong if something has "1/3 the fat."
posted by bgrebs at 1:20 PM on June 17, 2010 [1 favorite]
It makes to sense to me to say that something is "three times smaller," because if it were ONE time smaller (that is, its own size smaller) it would be zero.
But by this logic, "three times bigger" would be equivalent to multiplying something by four, as "one time bigger" would mean doubled. Basically, if you take "one time smaller" to mean '-100%' you have to also take "one time bigger" to mean '+100%'...
posted by Dysk at 1:24 PM on June 17, 2010
But by this logic, "three times bigger" would be equivalent to multiplying something by four, as "one time bigger" would mean doubled. Basically, if you take "one time smaller" to mean '-100%' you have to also take "one time bigger" to mean '+100%'...
posted by Dysk at 1:24 PM on June 17, 2010
I can see where the physicist is coming from though. The smallness of what he's describing is its key attribute. Which sounds better, "A is billions of times smaller than B" or "the size of A is less than a billionth of that of B." How about "the smallness of A is many billion times that of B?"
posted by bgrebs at 1:29 PM on June 17, 2010
posted by bgrebs at 1:29 PM on June 17, 2010
Math aside, no professional copyeditor/proof reader would let this stand in any publication. Check CE-L, the professional copyediting listserv -- this is a common question.
It's confusing terminology that's easy to avoid, so why not avoid it?
posted by coolguymichael at 2:02 PM on June 17, 2010
It's confusing terminology that's easy to avoid, so why not avoid it?
posted by coolguymichael at 2:02 PM on June 17, 2010
Sometimes it's completely wrong. It's never appropriate to use this in temperature scales. Neither "twice as cold" nor "twice as hot" mean a damn thing since the zero point for temperature is arbitrary.*
* Unless you use absolute zero, which we don't in day to day communications.
posted by chairface at 4:36 PM on June 17, 2010
* Unless you use absolute zero, which we don't in day to day communications.
posted by chairface at 4:36 PM on June 17, 2010
As a young lad who stocked sheetrock occasionally, I'd often wonder if saying that carrying one sheet of 5/8" waterboard was twice as light as two sheets of 5/8" or if it was only half as heavy. It seems equivalent but strange.
posted by Barry B. Palindromer at 1:45 PM on June 18, 2010
posted by Barry B. Palindromer at 1:45 PM on June 18, 2010
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