C. S. Lewis says (in “Of Other Worlds”): “[The fairy tale] stirs and troubles him (to his life-long enrichment) with the dim sense of something beyond his reach and, far from dulling or emptying the actual world, gives it a new dimension of depth. He does not despise real woods because he has read of enchanted woods: The reading makes all real woods a little enchanted.”
So the question is: what makes the world around us look a little more than it appears? I wonder why such a seemingly important question is not asked that often anymore. In a recent philosophy of science lecture (on the importance of questions in physics), the lecturer was stressing which was the major difference between Einstein and Bohr’s points of view, in their life-long debate: Einstein critiqued quantum physics theory, as it did not provide an explanation of what the universe is, but it worked only as an instrument for predicting certain small-scale events. In contrast to Bohr, for him it was important to ask this question: what it is the true essence of the thing that I am studying? Even though Bohr did not find it a useful question, he was too performing a kind of looking beyond the thing that we study, that scientists usually do: generating an abstract interpretation (through formulas). What such a method does is not helping to understand better the essence of It (whatever that it is), but to quote G. Vattimo, to transcend the single phenomenon by placing it in a wider sphere, in an artificial network of relationships, to try and see how it works and how it relates to the things around.
Both ways (stories and science pieces) are ways of looking beyond. Like any good story teaches us, some things can only take you so far, and from there on you will need to find your own answer to the riddle. What it may come down to is to employ the proper language, the one that will make it possible to be used in order to continue the adventure: if it is the mathematics’, the rules of poetry, the brush strokes of the artists or the abductive reasoning remains to be seen.
For now, what we can do is to follow some reasonable guidance, as the one provided by Lewis Carroll:
“Don’t enter the water
Till to swim you are able.
[…]Believe in fairies.
If you are able,”
Bodies and academia 
Nice post—thanks for sharing these thoughts. They push me to reflection, particularly as they strike a chord with something I recently read (by English author Walter de la Mare): “A man must either believe what he sees, or see what he believes; I know no other course”—which expresses, I believe, both sides of a sight/belief dynamic. Sight and belief mutually determine one another. (I take “belief” here to refer to the ways we make sense of something, the assumptions that fill in the gaps and underlie our understanding of something. In this sense, belief can be, as you say, the language of math, poetry, etc.) The maxim “Seeing is believing” attests to the general acknowledgement that sight informs belief (which seems to uphold conventional conceptions of science). But equally so does belief inform sight. How we see (the “wider sphere” in which we see) determines what we (can) see (cf. Stanley Fish). Or more specifically—as the C.S. Lewis quote suggests, believing in stories can open our eyes to new (one might say beautiful) aspects of the “actual world.”
Thank you for your comment! I do think it enriches my post, by elaborating on the seeing-belief pair of concepts (which I merely hinted at). And I am glad if they make one reflect, as that was my intention- your comment has the same effect.