What does this mean? It's gibberish to me.

Consider this statement (8/15/2012): “Peach consumption in Catalonia is 5 times lower than in Italy.” The article said annual peach consumption in Italy is 22 kilos. What is it in Catalonia? Well 5 X 22 is 110, so the annual consumption in Catalonia must be -88 kilos. This is nonsense. So, what is it? No, I'm not going to give you the link. It's easy enough to look it up yourself, if you want. I want you to try to figure out what is meant by “5 times lower” and what is the annual peach consumption in Catalonia.

This type of expression became common a few years ago and I wondered then what the hell it meant. I figured that when something was reported as “5 times lower,” it meant 1/5 as much. But 1/5 as much is 80% lower, so it didn't make much sense.

Then, today, while looking through a magazine, I found this:

quote:

Letters from ScienceNews October 20th, 2012; Vol.182 #8 (p. 31)

Please excuse me for being pedantic, but ponder what information is conveyed by “observed lithium levels are three or four times lower than Big Bang physics predicts” "Black hole theory deepens lithium crisis" (SN: 9/8/12, p. 14) [4th paragraph, last sentence]. One time lower means zero. Three or four times lower mean negative quantities of lithium, which are nonsense. Fractions are best conveyed by terms indicating division, such as one-third. If all else fails, percent of works. Please join this old crank in efforts to run goofy number rendition out of fashion.
Brent G. Boving, Northville, Mich.

The reader is correct. Former Editor in Chief Tom Siegfried was known to stomp into a writer’s or editor’s office and demand a mathematical explanation (which of course could not be produced) upon catching a “times lower than” error. We regret letting one slip through. —Eds.

Then I found this online.

Five Times Lower / Less / Smaller

How can something be five times lower, or five times less, or five times smaller than something else?

Clearly, the people who write such expressions do not understand fractions, decimals, or percentages (although they might comprehend factors or orders of magnitude). Petroleum engineers, however, should exhibit ample evidence in their writing that they eat fractions, decimals, and percentages for breakfast. Therefore, they should never use these expressions, lest someone think the other numbers in the document equally fuzzy.

In the engineering world, five times larger means 5× or “multiply by 5.” If X is smaller than Y by a factor of five, then X = Y/5. That means X is one-fifth the size of Y, or 20% of the size, which translates to 80% smaller or a value that is 80% lower. Use those expressions instead to ensure clarity and give the impression that your number sense is 100%.

This message has been edited. Last edited by: tinman,

quote:

Originally posted by tinman:
“5 times lower,” it meant 1/5 as much.

That's what it means to me. If "5 times greater" means multiply by 5, then "5 times lower" means divide by 5.

It's about 50 years old?

This message has been edited. Last edited by: goofy,

I agree it doesn't sound logical but it's clearly meant to mean one fifth. The reasoning could go "if A is five times higher than B then B must be five times lower than A".

I think most people would interpret it as meaning one fifth. I certainly would. I try not to worry about whether language makes sense in terms of mathematics or formal logic because it rarely does.

This message has been edited. Last edited by: BobHale,

And while I thing about it, logically five times bigger should equate to six times as big, shouldn't it? If something is bigger by five times the amount than something that is a metre tall, then it is bigger by five metres and therefore is six metres in total.

As I said, it's useless trying to get mathematical or logical about it.

Language Log on Times more / less than.

quote:

Originally posted by BobHale:
... logically five times bigger should equate to six times as big, shouldn't it?

Yes, Bob, it should. And it bugs me that so often people use "five times bigger" in an argument that's meant to be persuasive but you're not sure what they mean. It shouldn't be ambiguous but it is because of the way it's so often misused. "Five times slower" is also an error to me. I understand that what is meant is 1/5 as fast, which is 80% slower. Why not say that?

quote:

Originally posted by tinman:
And it bugs me that so often people use "five times bigger" in an argument that's meant to be persuasive but you're not sure what they mean. It shouldn't be ambiguous but it is because of the way it's so often misused.

I don't understand at all how "five times bigger" is misused or ambiguous. It means "multiply by five" - what is clearer than that?

And tinman, you understand what is meant by "five times smaller", so what is the problem?

quote:

And tinman, you understand what is meant by "five times smaller", so what is the problem?

If something is 100 and another is "five time smaller," is the second 80 or 20? If you said "one-fifth smaller" people would know it was 80. No ambiguitiy. Or use a similar fraction to refer to 20 as a result.

quote:

Originally posted by Proofreader:
If something is 100 and another is "five time smaller," is the second 80 or 20?

20, obviously. Why would it be 80?

With hand on heart, can anybody here really claim that if your shirt was a hundred dollars and I said "my shirt was five times cheaper than yopur shirt" you would not understand that I mean my shirt cost twenty dollars?

Forget the mathematics, forget the logic, what would you actually believe I meant? Remember you are under oath.

quote:

Originally posted by goofy:


I don't understand at all how "five times bigger" is misused or ambiguous. It means "multiply by five" - what is clearer than that?

Bob just explained it. "Five times bigger" should mean 6 times as large.

quote:

Originally posted by tinman:

Bob just explained it. "Five times bigger" should mean 6 times as large.

Yes he explained it, but I didn't understand. What am I missing?

With regards to "times smaller" or "times shorter", is the trouble something to do with the fact that "times" can mean "multiplied by" and you can't multiply and get a smaller number?

This message has been edited. Last edited by: goofy,

quote:

Originally posted by goofy:
If one thing is 1 metre tall, and a second thing is 5 times taller, then the second thing is 5 metres tall.

No, the second thing is 6 meters tall. It's as tall as the first thing, plus 5 times as tall, for a total as 6 times as tall.

Let X = 1 meter. Y is 5 times larger than X. So Y = X + 5x = 6 X.

If Y was 5 times as large as X, then Y would = 5X.

The key is in the words "larger than" and "as large as." "Larger than" implies addition; "as large as" implies multiplication.

quote:

Originally posted by goofy:
And if a third thing is 5 times shorter than the first thing, then the third thing is 20 centimetres tall. What am I missing?

If something is 1 time shorter, it is 0.

If X = 1 meter and Y is 1 time shorter, Y = -X = 0. If Y is 5 times shorter, it is = to 5 X -(1) = -5.

If y = 1/5 of X, then Y = 1/5 X = .20 meters.

quote:

With regards to "times smaller" or "times shorter", is the trouble something to do with the fact that "times" can mean "multiplied by" and you can't multiply and get a smaller number?

Yes, if you multiply two positive numbers together, you get a larger positive number. To get a smaller number you must multiply by either a negative number (not applicable in this case) or a fraction.

quote:

Originally posted by tinman:

The key is in the words "larger than" and "as large as." "Larger than" implies addition; "as large as" implies multiplication.

Not to me. Thanks for explaining though.

quote:

Originally posted by tinman:
Yes, if you multiply two positive numbers together, you get a larger positive number. To get a smaller number you must multiply by either a negative number (not applicable in this case) or a fraction.

Well I finally understand what the trouble is. I'm with Bob though; we all understand what is meant.

I deplore the "five times smaller" style of referring to lesser quantities.

We have a system of numbers - cardinal, to show how many, and and ordinal to show position.

Trying to denote a lower position by using cardinal numbers is clumsy and, as others have pointed out, can be ambigious.

"Five times smaller" would far better be described as "A fifth the size".

quote:

cardinal, to show how many,

What does religion have to do with this?

I have just discovered that this is actually a venerable usage dispute. It has an entry in MWDEU. The argument is that since "times" has to do with multiplication, it can only be used to compare the greater to the smaller.

In reality, math and language are different things. This is what happens when we use one word to modify another: we change the meaning. MWDEU says

quote:

The question to be asked concerning such a construction as ten times less is not whether it makes sense mathematically, but whether it makes sense linguistically - that is, whether people understand what it means. The answer to that question is obviously yes. Times has now been used in such constructions for about 300 years, and there is no evidence to suggest that it has ever been misunderstood.

quote:

...but now I am resolved to drink ten times less than before - Jonathan Swift, 1711

quote:

Men who had ten or twenty times less to remember - W E Gladstone, 1879

MWDEU also talks about the objection to "times more", where "He has five times more money than you" could be misunderstood as "He has six times as much money as you." The fact is that "five times more" and "five times as much" are idiomatic phrases that mean the same thing. MWDEU concludes that the ambiguity here is "imaginary".

quote:

This might you reade, and ten times more
In the Bible - Robert Crowley, 1551

Arnie linked to Language Log on times more / less than. Everyone should read it, and the related post on the recency illusion.

This message has been edited. Last edited by: goofy,

goofy's post above is perfect. I sincerely do not believe that anyone would EVER construe "five times less" as meaning anything other than one fifth except when deliberately trying to claim an ambiguity that does not, in fact, exist.

Now, there is a genuinely potential for ambiguity in phrases like this but it does not lie in the grammar.

What, for example, does "five times bigger" mean? Does it mean five times the height or five times the volume?
But the potential for ambiguity lies in the undefined nature of the bigness not in the grammar of the phrase.

We cannot repeat enough that language is not mathematics and is not formal logic and should not be treated as if it is.

Just like those darned pesky double negatives we talked about at such length.
Not nohow.

(Incidentally, in goofy's last quote, I would probably read that as being eleven times as much, because of the "and" - this and ten times more being, in my view the same as this plus ten times more. It's a different construction altogether.)

Oh that was a fun read, goofy. The ability of folks to bloviate ex cathedra on matters linguistic never ceases to amuse me.

I've been reading this thread, but haven't commented on it yet. It is a very interesting discussion.

quote:

I sincerely do not believe that anyone would EVER construe "five times less" as meaning anything other than one fifth except when deliberately trying to claim an ambiguity that does not, in fact, exist.

I agree with you, Bob, and with Jim about the bloviating (one of my favorite words, BTW).

I don't believe there was any bloviating here. Just an attempt to give an opinion of the proper phrasing of a mathematical concept and an explanation for that opinion. I have never claimed to be an expert on anything. Thanks to all who responded in a constructive and civil manner.

Tinman, I am pretty sure z was not talking about bloviating here on Wordcraft. I thought he meant those prescriptivists who bloviate, ad infinitum, about things like this, thus the reference to goofy's "fun read."

I agree that this discussion has been civil.

I don't believe there was any bloviating here.

If by here, you mean in this thread, then no, I was not implying that any of us were the source of any bloviation. As Kalleh suggest, the bloviating I was referring takes place in the rants written by ill-informed normative grammarians.

Sorry, tinman, if I upset you inadvertently.

Then I misinterpreted your post, z. Please forgive me.