1) The mathematical invention of the number zero '0' which furthered many advanced branches of Math, even though (it would seem) the Torah does not recognize it. [The closest thing would seem to be the word אין , but that still does not encompass the full effect of the mathematical zero]
2) (Part of) the mathematical concept of limits, essentially a matter of saying "I know this can never be but let's pretend it is and build upon that".
3) Once, during a difficult period of life, there was a girl I had a few exchanges with and became smitten with. Because the exchanges were few and far between my mind mentally projected alot of idealisms about her and who she was, 'till the thought of her became more like a vision of some utopian beauty to strive for, carrying me through alot of difficult times and hardship. [Similar to Viktor Frankl's account of his wife's vision in the book Man's Search For Meaning]. Some time thereafter, I got something of a "closer look" of who the girl was and 'click', like someone had just flipped a light switch my vision of her totally disintegrated-- it was all a fantasy, and yet it carried me through and helped me.
4) I personally was able to throw myself wholeheartedly in my studies in yeshiva because of the paradigmatic vision I had of the yeshiva's hashkafa and it's staff. Had I seen them then with the-less-than-impressed perspective I have of them now-- I never would have grown as I did those years...
[Many years later I heard a speech by one of the faculty being given in a community shul. It was horrible. Riddled with inconsistencies, misquoting Gemaras and showing a general impression of narrow-minded ignorance. If not for the speakers being held in high esteem in many circles I probably would have felt little compunction in telling him he was a moron]
So with all that said, if in fact this concept is true, it behooves us to know where we see it in the Torah.... I have my doubts as to whether it's the perfect answer but what comes to mind is what i've heard is a Rambam in the Moreh who says that in a sense all of עבודת בית המקדש is a בדיעבד insofar as it's a physically oriented activity trying to engage with a non-physical Being. The Rambam continues to explain that although it's a "false fantasy" we have no other choice being that we're physical beings and we naturally think in physical terms... not a perfect fit but it's related I think....
[Heard related (and deeper) concepts from my Rebbe, Rav Matis Weinberg, in discussions of Pr' B'Shalach and Metaphor http://www.thelivingtree.org/indexArchiveShemot.htm ]
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