"n times greater"

[alice]

OK, here's a few questions prompted by phrases which turn up a lot in news reports. What number is three times greater than 10? Is "twice greater than" meaningful at all? And, in general, is "n times greater than" the same as "n times as large as"?

According to my 1976 copy of The Complete Plain Words, the answers are respectively 40, "probably not", and "no". But dissenting opinions, justifications thereof, and the ensuing debate, are encouraged here. Go for it.

[Pthagnar]

given the only other answers are "30", "maybe yes" and "yes", i don't see much room for discussion

[Kai_DaiGoji]

I ran into this with the phrase - "five times hotter than." I was trying to think about this to determine how hot the 500 C oven we used at work was. At first I thought "it's five times as hot as 100 C, therefore 5 times boiling temp, therefore, 1060 F." But it's not. It's 932 Fahrenheit. 1060 F would also be, on paper "five times hotter than boiling" - but these two temps aren't the same, and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't: cannot be.

[Pthagnar]

that's because you fucked up and didn't use absolute degrees. it works in kelvin.

or rankine, if you absolutely insist

[Pthagnar]

ie.

10 rankine = 5.5556 kelvin
100 rankine = 55.556 kelvin

[WeepingElf]

I ran into this with the phrase - "five times hotter than." I was trying to think about this to determine how hot the 500 C oven we used at work was. At first I thought "it's five times as hot as 100 C, therefore 5 times boiling temp, therefore, 1060 F." But it's not. It's 932 Fahrenheit. 1060 F would also be, on paper "five times hotter than boiling" - but these two temps aren't the same, and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't: cannot be.

The only meaningful use of expressions such as "5 times hotter than" is IMHO by means of an absolute scale such as the Kelvin scale. 100 °C is 373.16 K, so 5 times as hot as 100°C is 1865.80 K = 1592.64 °C, which is much hotter than 500 °C - hot enough, indeed, to melt steel.

But I feel that "5 times more" is the same as "6 times as much as", to answer the initial question.

[Sir Rei]

I ran into this with the phrase - "five times hotter than." I was trying to think about this to determine how hot the 500 C oven we used at work was. At first I thought "it's five times as hot as 100 C, therefore 5 times boiling temp, therefore, 1060 F." But it's not. It's 932 Fahrenheit. 1060 F would also be, on paper "five times hotter than boiling" - but these two temps aren't the same, and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't: cannot be.

They rounded up.
Companies tend to do that.
Mine does.

[Yiuel Raumbesrairc]

OK, here's a few questions prompted by phrases which turn up a lot in news reports. What number is three times greater than 10? Is "twice greater than" meaningful at all? And, in general, is "n times greater than" the same as "n times as large as"?

According to my 1976 copy of The Complete Plain Words, the answers are respectively 40, "probably not", and "no". But dissenting opinions, justifications thereof, and the ensuing debate, are encouraged here. Go for it.

Would I translate the expressions in French, my impression would be :

(trois fois plus gros que dix) = 30
(deux fois plus gros que x) = yes (and would equal 2x)
(n fois plus gros x = n fois aussi gros que x) = probably yes

[finlay]

I ran into this with the phrase - "five times hotter than." I was trying to think about this to determine how hot the 500 C oven we used at work was. At first I thought "it's five times as hot as 100 C, therefore 5 times boiling temp, therefore, 1060 F." But it's not. It's 932 Fahrenheit. 1060 F would also be, on paper "five times hotter than boiling" - but these two temps aren't the same, and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't: cannot be.

The only meaningful use of expressions such as "5 times hotter than" is IMHO by means of an absolute scale such as the Kelvin scale. 100 °C is 373.16 K, so 5 times as hot as 100°C is 1865.80 K = 1592.64 °C, which is much hotter than 500 °C - hot enough, indeed, to melt steel.

But I feel that "5 times more" is the same as "6 times as much as", to answer the initial question.

I've also read that the heat scale should maybe be thought of as logarithmic, at least in terms of how we perceive it.

Same with sound – five times the frequency is not five times the pitch, because the pitch is the auditory percept and is logarithmic...

[maıráí]

OK, here's a few questions prompted by phrases which turn up a lot in news reports. What number is three times greater than 10? Is "twice greater than" meaningful at all? And, in general, is "n times greater than" the same as "n times as large as"?

3 times greater than ten should be 30, 'twice greater than' would be double, and 'n times greater than' is synonymous with 'n times as large as', unless you mean great as in good, mighty, etc.

[alice]

So what would "once greater than 10" be, other than a little barmy?

[finlay]

"not greater than 10 any more"

[alice]

Ouch, my ribs.

[Terra]

and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't

Well, they can be meaningful if they're included in sentences like: "It's five times hotter than the kettle is.", which would mean it's: (KettleTemp * 5), as opposed to the (KettleTemp * 5 + KettleTemp) which the first makes me think of. But yeah, it's still a clunky sentence and should be avoided in favor of: "It's five times as hot as the kettle.", with the sentence altered accordingly to get the desired result.

[Kai_DaiGoji]

and the only conclusion I can draw is that phrases like "five times hotter than" sound meaningful, but aren't

Well, they can be meaningful if they're included in sentences like: "It's five times hotter than the kettle is.", which would mean it's: (KettleTemp * 5), as opposed to the (KettleTemp * 5 + KettleTemp) which the first makes me think of. But yeah, it's still a clunky sentence and should be avoided in favor of: "It's five times as hot as the kettle.", with the sentence altered accordingly to get the desired result.

Except the meaning of 5 times hotter than the kettle depends entirely on the temperature system being used. You can get several different answers that are all mathematically correct.

[su_liam]

But only using the absolute scale do you get an answer that's physically correct.

And that will always come out to the same actual temperature. So... mathematically correct.

[Travis B.]

But only using the absolute scale do you get an answer that's physically correct.

And that will always come out to the same actual temperature. So... mathematically correct.

And this actually does matter in contexts like materials science, where one gets things like how the temperature at which creep becomes significant in a material is generally a rather predictable fraction of the melting point of that material, that is, on an absolute scale.

[zompist]

What number is three times greater than 10? ... the answers are respectively 40

Wow, that sounds very wrong to me. Here's a fairly random test: Google for "three times greater", skipping cases where the phrase is used without giving the actual numbers:

x3
x3
x2.5
x3
x3

And so on. Perhaps someone uses it for x4, but it can't be too common.

FWIW I can see saying 40 is "300% greater than 10". After all, "5% greater" means x1.05, so "300% greater" should mean x4.

[alice]

It gets even sillier if you go the other way: what is "three times smaller than" 120?

[faiuwle]

It gets even sillier if you go the other way: what is "three times smaller than" 120?

40? It seems pretty intuitive that if someone said it was "ten times smaller than 120" they would mean 12, and likewise, ten times larger would be 1200.

[finlay]

But only using the absolute scale do you get an answer that's physically correct.

And that will always come out to the same actual temperature. So... mathematically correct.

But note that this hasn't much relevance in terms of our perception of heat, which is more logarithmic, like our perception of pitch.

[Chargone]

It gets even sillier if you go the other way: what is "three times smaller than" 120?

Indeed. this particular construction bugs me no end because it doesn't mean anything.

'times' is inherently Not Smaller Than if you're using whole numbers!

seriously, three times smaller? what does that even Mean?

now, 'one third of' makes sense. for numbers that aren't silly in base ten, one can even say 'what's 0.xxxx times five?' or some such...

but 'x times smaller than' runs face first into logic fail.

mind you, one could make the case that it's related to double negatives... (of course, for Those, it depends, among other things, on exactly what negatives you're talking about...)

[Richard W]

Times is clearly an adverb meaning 'multiplicatively rather than additively'.

[alice]

Times is clearly an adverb meaning 'multiplicatively rather than additively'.

Actually, it's a newspaper The point is:

- does "three times greater" mean the same as "three times as much"?
- is "twice greater" meaningful at all?
- is "three times less than" the same as "one third of"?

My opinion is "no" to all three, but you know what is said about opinions.

[Richard W]

Times is clearly an adverb meaning 'multiplicatively rather than additively'.

Actually, it's a newspaper

Your thinking of the Times.

The point is:

- does "three times greater" mean the same as "three times as much"?
- is "twice greater" meaningful at all?
- is "three times less than" the same as "one third of"?

My opinion is "no" to all three, but you know what is said about opinions.

Empirical study says yes to the first two. I haven't researched the last one.

The normal expression is 'two times greater' rather than 'twice greater', which accords with times being an adverb, by a rough ratio of 4 million raw Google hits to 10,000. "Twice greater" looks like a hypercorrection for "two times greater".