Usage of twice and two times with "size"

Question

Below are taken from a grammar book.

a) The Earth is about **four times as big as** the moon. 
   = The Earth is about **four times  bigger than** the moon.



b) The Earth is about twice as big as Mars. 
   ≠ twice bigger than.

If (a) is correct, then how come I cannot use twice in the same way in the example (b)?

I have taken a look at

Has the illogical "three times bigger" replaced "three times as big" in common usage?

and

"X times as many as" or "X times more than" .

Especially on the second link I can totally understand the logic and I agree. But in these examples, it is size and I cannot really figure out why. The last example being;

c) That cable is only **half as long as** this one. 
   ≠ half longer than.

On this last example, I can totally understand why it is not equal. But when it comes to (b), I simply cannot explain. Aren't twice and two times are same things?

While searching I also found this; Does this ‘twice’ mean two times, or double in quantity?

There is a difference between something being "two times longer than...."
 and "two times as long as... " Say something is 10 ft.

If above statement is true then how come (a) is correct? A clarification would be great as I am having a terrible headache because of this.

Answer 1

The reason you can't use "twice bigger than" is simply because this is a phrase we do not use. I am not sure exactly why, maybe someone else has a better reason than that, but I do not. The information presented by your grammar book is just about the grammatical correctness of each substitution, as opposed to making a sentence with a similar unambiguous meaning.

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For the other pages you have linked, the question isn't of grammar, but in exactness and level of ambiguity.

Referring to your last question about "two times loner than ... " vs. "two times as long ..." This will confuse native speakers too. They are saying that the difference in the usage is that in the first, "two times" describes how much longer and in the second, "two times" describes the actual length.

I tend to disagree, and think that the first usage is ambiguous enough for most people that it shouldn't really be used.

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As other posters in the answers you have linked point out (and is reinforced by the difference in answers), using "times more than" form is pretty ambiguous, or difficult to ensure your meaning is accurately understood.
if X and Y are numbers

"Y is two times as big as X" --> Y is 2*X (Y: 4, X: 2)

"Y is 200% of X" --> Y is 2*X (Y: 4, X: 2)

"X has increased by 200% to become Y" --> Y is X+2*X (Y: 6, X: 2)

"Y is two times bigger than X" could be referring to both of the situations above (Y being 4 or Y being 6.) Some may argue one way or the other, but the fact that it is unclear is definitely apparent.

Answer 2

When there are two expressions that logically mean the same thing, but only one of them is used, this simply means that one expression has gained currency, and the other one has not. In the case of twice as big as/bigger than, there's no logical reason that one dominates over the other, but a quick look at a usage graph shows that as big as is pretty much used to the exclusion of bigger than after twice.

Google Ngram

The practical reason for using the preferred form over the unpreferred one is simply not to look like an outsider or to appear not to have a strong grasp on colloquial English. In simple terms, you want to sound normal.

In any case, I'd recommend the as (adjective) as in all cases, even when the other version is allowed, as it seems to me to impart greater clarity.