2

A real-world example from a computer book that I've been reading recently:

Bitmaps do not use any compression and can be three or four times the size of the same image in other file types such as JPEG, TIFF or PNG.

When we use this construction, do we ALWAYS mean that something is a certain number of times BIGGER than something else? So, if I say something like this:

Now the size of the original file is five times the compressed file.

The only way this can be understood is the size of the original file is five times bigger than the size of the file that we got after compression? Correct?

Or maybe it's possible to denote whether the thing in question is bigger or smaller than other thing we're comparing it with by simply adding the words bigger and smaller? Like this:

Now the size of the file is five times smaller the size of the original file.

Am I making any sense?

  • The age of the universe is three times [that of] the earth. The age of the earth is three times less than [that of] the universe. Nothing particularly significant about size as opposed to age, length, weight or any other "scalar" attribute. – FumbleFingers Feb 18 '15 at 18:26
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    In the case of the smaller file size, it may be more accurate to say The file is now one-fifth the size of the original file. This makes it clear that, if it was 100 MB, it's now only 20 MBs... five times smaller may be a bit ambiguous. – Catija Feb 18 '15 at 23:27
1

The form, X is [number] times the size of Y always means X is [number] times bigger than Y.

The form, [number] times smaller is perfectly acceptable, clear (not ambiguous in any way), and is often more popular or even the only idiomatic form in common usage. I'll call this the Times Smaller Form. The preference (aka "popularity") for this usage (instead of the Fraction Form) grows as [number] gets bigger. This is demonstrated in the following Google Ngrams.

Google Ngram Three, Four (three times smaller + one third the size),(four times smaller + one fourth the size)
In these Ngrams, positive values means the Times Smaller Form is more popular and negative values means the Fraction Form is more popular. (See footnote #1 for an explanation of the Ngram equations.1) Note above that the only instance (in this Answer) where the Fraction Form is more popular than the Times Smaller Form is "one third the size". In all other cases (in this answer), the Times Smaller form is more popular.

Google Ngram Five, Ten (five times smaller - one fifth the size)/(five times smaller + one fifth the size),(ten times smaller - one tenth the size)/(ten times smaller + one tenth the size) Note that these are at about 50%, which is higher than three and four.

Google Ngram One Hundred, One Thousand (one hundred times smaller - one hundredth the size)/(one hundred times smaller + one hundredth the size),(one thousand times smaller - one thousandth the size)/(one thousand times smaller + one thousandth the size) Again, these are higher than the prior ngrams. +100% here means all instances are in the Times Smaller Form. The Fraction Form is non-idiomatic in this case.

Google Ngrams for Ten Thousand and One Million also show +100% of usage is in the Times Smaller Form indicating this is virtually an idiomatic form. On the other hand, it's grammatically correct to say "ABC is one ten-thousandth the size of XYZ". Interestingly, the Fraction Form doesn't strike me as odd or wrong in any way, but the searches in Google Ngram (and various corpora at http://corpus.byu.edu/) suggests this usage is rare.

Also note that the Times Smaller Form has even more usage than shown here since it has two variants for large numbers: a hundred times smaller, one hundred times smaller, a thousand times smaller, one thousand times smaller, etc. For example, it's natural to say "This is a thousand times smaller than that." See Google Ngram Variants


FOOTNOTE 1: Normalizing Google Ngram results.

In these Google Ngrams (A - B)/(A + B) shows a normalized difference from -1 to 1 (shown by Google Ngram as -100% to 100%).

  • In all Ngrams, A = Times Smaller Form, B = Fraction Form
  • 0% means "no difference" in popularity between the two terms.
  • Positive values mean the first term (A, the Times Smaller Form) is more popular.
    (A value of +100% means there are only instances of A.)
  • Negative values mean the second term (B, the Fraction Form) is more popular.
    (A value of -100% means there are only instances of B.).

This method allows us to compare widely different result-counts on a common scale.

  • Pair #1 is A=15, B=5.
  • (15 - 5) / (15 + 5) = 10 / 20 = 50%.
  • The difference 10 is 50% of the total 20.

  • Pair #2 is A=3000, B=1000

  • `(3000 - 1000)/(3000 + 1000) = 2000 / 4000 = 50%
  • The difference 2000 is 50% of the total 4000.

Even though Pair #2 is far more common than Pair #1, they both demonstrate that A is more popular than B, and in the same relative ratio. A potential weakness is that smaller result counts are less accurate. For example, A=3, B=1, also results in 50%, but this would be too small to be reliable.

2

(The size of) A is five times (the size of) B. In this case, A is indeed always bigger than B. You can read the "five times" as follows:

The size of A is the size of B, plus the size of B, plus the size of B, plus the size of B, plus the size of B.

The sentence is showing that something is equal to something else:

(The size of) A is **equal to* five times (the size of) B.

If you want to use bigger or smaller, you need to use than:

(The size of) A is five times bigger than (the size of) B.
(The size of) A is five times smaller than (the size of) B.

Note that these expressions are ambiguous: not everybody will understand the same thing, especially not in the case of x times smaller: how big is 4 times smaller than 100? If it is really important to not be misunderstood, use unambiguous formulations like:

A is one fifth the size of B.
A is five times as big as B.

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    I strongly urge that people avoid any "X times smaller/shorter/lighter/etc." form and use the reciprocal as shown above ("1/X the size/height/weight/etc."). – Hellion Feb 18 '15 at 22:07
  • @Hellion I think that using fractional statements is better than using the reciprocal... sometimes you really want to make the smaller thing the emphasized subject of the statement. – Catija Feb 18 '15 at 23:29
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    @Hellion - I completely agree. Egregious example: The urinals at my work have a little sign over them "These urinals save 88% more water than conventional urinals." I think they probably mean "These urinals use 12% of the water that conventional urinals use" - but maybe not. Either way, "these urinals" are the emphasized subject, but only one way means something mathematically. – Adam Feb 19 '15 at 17:05
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    @Adam, I'd be tempted to flush such a urinal 7 or 8 times, just so I could save 600-700% more water. :-) – Hellion Feb 19 '15 at 17:19

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