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Hi Kooyeen,

Heh, that's pretty difficult. I'm afraid there's no real connection, LOL. I think you are trying to improve the same way I used to. You are the only one who could improve the way you think, or used to think. Laughing out loud and thinking out loud are dangerous acts on forums like this. I needed a lot of rules of thumb, Many learners living in non-English speaking lands surely will agree with you and feel the same. so that I could understand by myself what was good and what was not. The problem is that I found out English is actually a little bit too complicated, and I ended up asking a lot of questions (I still ask anyway, LOL). One of the latest complications I've come across is the fact that I realized there are too many different kinds of English. There are big differences between the ways people speak. So when you get an answer here, it's just one opinion, from one person. There are maybe thousands of people who would disagree, This phenomenon occurs even in English environments, perhaps more so, and so it's not unique to your situation. The reality is, we need to choose a source which we can trust and go with it. I rely on education and informative TV programs. but they don't post here, maybe then don't post anywhere, actually. One little example... if you ask here about "anyways", maybe you'll get an answer like "It's odd, some people might say it but it's incorrect and I cringe everytime I hear it". But I remember one time I was browsing through Youtube... I heard a lot of teenagers say "anyways" It's wrong and I heard from time to time from natives  as well.

Consider:

The US dollars used to be much stronger than Canadian's. = The Canadian dollars were much weaker than US dollars before.

The Canadian dollar is nearly as strong as the US dollar = The value of one Canadian dollar is barely less than that of US.

It's just a matter of how we want to convey the idea rather than the rule of thumb in my not-so-native mind.

Consider the basic idea of equality.

Jack was assigned to clean out the stables, but he was not [equal to / up to] the task.

Note the measurement 'upward' from an assumed 'low' starting point of 'no ability to do the task'.  And how 'equal' is synonymous, in some sense, to 'up'.  There is no possibility whatsoever that this sentence could mean that Jack cleaned the stables even better than expected.

Likewise, as strong as = equal to the strength of = up to the strength of; not as strong as = not equal to the strength of = not up to the strength of (where equal has its ordinary language meaning -- not its mathmatical meaning).

All gradable adjectives are treated in the same way.  not as X indicates "not reaching as high on a scale starting from zero X-ness".  The metaphor is always of movement upward from a zero point and negation means the failure to reach a certain value along this upward movement.  The existence of an adjective with an opposite meaning is irrelevant, because that adjective is measured on its own scale from the zero-degree point of that adjective.

The fact that a joke results when the words are taken mathematically is proof that mathematical equality is not intended within the meaning of such expressions.  No one is ever admitting the possibility of his inferiority when he says, "You're not as smart as me"!  The response "No.  I'm smarter" is simply sophomoric. 

CJ