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Is it grammatically correct to say:

  • This book is twice as expensive as that one.

  • That book is twice as cheap as this one.

  • This rope is twice as long as that one.

  • That rope is twice as short as this one.


I was studying comparatives and on some forum I found a discussion about expressions like "twice as few" and "twice as little". On that forum native English speakers all have agreed that such expressions sounded weird to them, and made no sense, because "twice" means multiplication and is opposite in meaning to being smaller. For example, it is incorrect to say: "I have twice as few books as he." And so I was wondering if "twice" is also opposite to being shorter, cheaper and slower, etc. Could anybody please elaborate on how "twice as few" is incorrect while "twice as short" is correct?

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I agree with Sam K's answer — the sentences using "twice as cheap" and "twice as short" are correct, but unusual compared to the sentences using "twice as expensive" and "twice as long". I also agree pretty much with the reasons in that answer, that the two sentences have different implications because of something that's different about the adjectives. I want to clarify a little bit in the details, though.

When you say "X is twice as Y as Z" (for example "Texas is twice as big as Montana"), there's an implication that Z already has some quality of Y, but X has it twice as much. That is, Montana is big, but Texas is twice as big. With some adjectives (the ones Sam K calls "strong"), this implication is weakened because they're the ordinary adjectives used to describe the extent of something. If you want to know the size of something, you can ask "how big is it?" If you want to know the length, "how long is it?" If you want to know the cost, "how expensive is it?". So you can say "twice as big as an ant" without implying that an ant is very big at all. It's already understood that a thing has some size, some length, some cost.

But when it comes to adjectives like "small", "short", or "cheap" (what Sam K calls the "weak" adjectives), something can only be small, short, or cheap in comparison to something else. If there's no obvious target for comparison, then it's compared to something that would be considered normal or average in the context of the conversation. So, "these apples are twice as cheap as those ones" usually implies that those apples are cheaper than usual (for apples, or for fruits), but these ones are even cheaper. It's impossible to have the same kind of mathematical precision you do with "twice as expensive"; there's too much inferred and unstated.

If you want that effect, great! If you don't, then you might want to use "half as long" instead of "twice as short", "half as expensive" instead of "twice as cheap", etc. They're more neutral, more precise, and more common.

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Your phrase

twice as adjective
twice as slow

is used as an intensifier in the same way as

much adjective+er
much slower

very adjective
very expensive

extremely adjective
extremely expensive

but gives a more specific magnitude for comparison

three times slower
ten times slower
an order of magnitude slower

when the comparison is made of a value which is greater, using "twice as adjective" is obvious. However, when used with a value which is less, one might expect "half" to be used, as in

That book is half as expensive as this one.
That rope is half as long as this one.

I have heard "twice as cheap" be used, but never "twice as short", although both are grammatically correct in structure.

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Are they grammatically correct?  Perhaps.  Are they sensible?  Not really. 
 

Expense and length are directly measurable attributes.  Cheapness and shortness only make sense in contrast to some other expense or length.  Allow me to offer two examples:

First, let's assume we find something that costs $10.  A ten dollar pack of chewing gum is fairly expensive, while a ten dollar three-piece suit is quite cheap.  Regardless, if another item is twice as expensive, we immediately know that it costs (around) twenty dollars.  Also, an item that's exactly half as expensive costs $5.  Only one number is needed to express expense, and it's easy to do the math to that number.

Second, let's assume we find another store selling the same item for $8.  Compared to the $10 price, sure, that's cheap.  If we're looking for an item that's twice as cheap, what price do we want?  Do we want a $6 item because that's twice the two-dollar discount from $10?  Do we want a $4 item because that's half the $8 price?  Cheapness can't be represented by only one number, and I have no idea what math that phrasing is meant to indicate.

 
In my dialect, I am aware of one obvious exception to this pattern.  In the absolute sense, heat is a directly measurable attribute, but cold only makes sense in comparison to some other amount of heat.  However, if the current weather happens to include a sub-zero temperature (which, locally, implies the Fahrenheit scale), I might say "tomorrow will be twice as cold" as shorthand for "tomorrow will be twice as far below zero."

Other exceptions also exist, but those exceptions involve an easily-reached absolute zero.  For instance, I understand that "twice as dark" and "half as bright" are directly equivalent.  As far as my naked eye can tell, zero brightness is as easy to find as a windowless room or an artist-quality charcoal pencil.

 

Above all else, please remember that "grammatically correct" and "sensible" are two completely different ideas. 

This colorless green idea sleeps successfully.

The grammar of the above sentence is impeccable and beyond reproach.  However, it was designed (within the constraints of good grammar) to make no sense.  There exists an entire class of sentences like it, all designed to be examples of "when good English goes bad".

The questions "Is it good English grammar?" and "Is it good English?" can have completely different answers.  Phrases like "twice as cheap" or "twice as short" are grammatically sound and easy to produce, but they are difficult to parse and practically impossible to understand.

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They are technically all correct. However, their true meaning varies from sentence to sentence. I'm going to address them in order, starting with:

This book is twice as expensive as that one.

This sentence is usually interpreted in two ways. The first (and I believe the most common), is that if the price of Book 1 ("that one") is $10, then Book 2 ("this book") is $20. The other method of interpretation would be that, for example, Book 1 ("that one") is $20, Book 2 is ("this book") is $30, and Book 3 (a hypothetical book to which you are comparing the others) is $10. Book 1 is $10 more expensive than Book 3, and Book 2 has a price difference between itself and Book 3 of twice that as Book 1, so it is twice as expensive.

That book is twice as cheap as this one.

This sentence is usually only translated using the second method from the previous sentence, which I will call the "comparative" method. All that you need to do is make Book 2 the hypothetical comparison book, and have Book 3 be the book that has a difference twice that of Book 1 compared to Book 2.

I'm not going to go through the other two sentences as they follow the same methods of interpretation as the others. If the adjective used is "strong" (expensive, long, etc.), then there will be the two interpretations. If the adjective is "weak" (cheap, short), then generally there is only the "comparative" method. These interpretations come from colloquial English, and although it is still correct, using "twice as < weak adjective >" is much less common, replaced instead with "half as < strong adjective >."

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Twice as cheap means free. Twice as short means zero length. Twice as slow means stopped.

"Twice as cheap" (meaning 100% cheaper, which means free) and variants are commonly misused in marketing which, if you have a knowledge of maths and law, can cause them to be legally obligated to give you the item for free, or even pay you to take it (for such lines as, "three times cheaper," which would mean 200% cheaper, or the negative value of the original price).

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  • As much as I agree to the math, I'd like to see a source for your claims of legal or contractual obligations created. – I'm with Monica Aug 18 at 15:04

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