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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.

Grizzly
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    Is your problem with the fact that "Twice bigger" is an ungrammatical phrase, or with the difference in potential meaning between "twice as big" and "twice bigger"? – katatahito Jun 17 '19 at 02:54
  • my main problem is the example "b". However after seeing the usage of "long" I am completely confused about the example "a" as well. – Grizzly Jun 17 '19 at 02:56
  • So the grammer book is simply saying that "twice bigger" is not a phrase that we use in English, not commenting on a change in meaning if you replaces "twice as big as" with "twice bigger than" – katatahito Jun 17 '19 at 02:58
  • no explanation. Just these examples. If I think about the Earth in example B, "twice bigger than moon's Earth > "twice as big as the moon's Earth. Is that correct? – Grizzly Jun 17 '19 at 03:04
  • It should be as big as the* moon. It's missing the definite article. 2) Your analogy between the two sentences is wrong. It's four times bigger* versus *two* times bigger (which is fine). We would not say thrice bigger either—but three times bigger.
  • – Jason Bassford Jun 17 '19 at 04:02
  • Sorry I have missed "the". Edited. I know about once, twice and thrice but four times. Why "twice bigger" is not OK? – Grizzly Jun 17 '19 at 04:15