connotationmeaningusage
As far as I know, “intellectual gymnastics” is used in a negative sense. For example, the discipline of philosophy can be belittled as “intellectual gymnastics”.
However, a university in Japan seems to be advertising one of their new academic programs by using the term in a positive sense as follows:
Advanced Education in the Liberal Arts — Intellectual Gymnastics
Is this simply an incorrect use because of connotation? Or is there maybe some other connotation of the term that is positive?
Doesn't seem so. First of all it has another meaning
To agree with or be in harmony with
(TheFreeDictionary, near the end of page)
This meaning is obviously not negative
Returning to the meaning you had in mind. I didn't find any indication as to whether it is supposed to be always negative or not. It's nothing more than
To associate or begin to associate with
here or
Associate with, become acquainted with (especially by chance)
here From this definition fall in with implies accidental rather than negative nature of acquaintance.
No. Effusive is not negative, it has a positive connotation to it. 'He was very effusive in his praise of the features.' is fine.
effusive
adjective demonstrative, enthusiastic, lavish, extravagant, overflowing, gushing, exuberant, expansive, ebullient, free-flowing, unrestrained, talkative, fulsome, profuse, unreserved
He was effusive in his praise of the General.
Also,
This ngram for effusive in his praise and effusive praise shows the expressions are on well-trodden territory:
Best Answer
The negative version of the phrase is similar to "jumping through hoops"; in other words, performing a physically demanding or tiring task for a small or shallow reward. In this case, it's referring to the act of wasting your mental strength thinking about something that doesn't deserve the time and effort.
The positive version takes into account the positive connotation behind exercising: the brain is a muscle, and giving it a "work out" strengthens it. In this case, doing "unnecessary work" is still of benefit.
I believe the first version is, as you said, far more common, but both seem to make sense in their own contexts.