>And why art could be a core subject in school, equal with math, literature
To what are we referring when we speak of "art"? Quite often for some reason it is used to denote only the static visual arts such as painting and sculpture. N. distinguishes between art and literature here. Despite this distinction it often refers also to the various arts in general. My use of the term reflects a comprehensive definition.
>It is not fluff or dessert, but a serious training of neural
>networks to behave in a flexible, more complex and nonlinear pattern (the
>most famous well-known example is "Mozart for Math").
A few recent posts expressed this perspective by saying that we should be able to discern the function of art through evolutionary psychology. Of course art has served such purposes throughout our history and it may ultimately be motivated by issues concerning sexual selectivity. But I have long had a suspicion that part of what N. says above is the case and is probably the best line of research on art: learning---not entertainment, distraction, communication of historical, moral, et cetera notions, means of navigating interpersonal conflict, and so on---could be the primary effect or function of art. Learning in the sense that she mentions here: something at a relatively low level, like neural network training. Does anyone know of any studies in which we have before-and-after neural activity data (say, from an fMRI or PET) on people engaging in reading, viewing, or listening to various types of artworks? (I would also ask the same for the playing of video games.) Such studies may now point to rather tenuous or broad correlations or may lack them entirely. There may be a way to pursue this before nanotech, though.
I am not exactly sure what you mean by "nonlinear" here. Art can possess many different attributes; not all art follows or promotes very unusual chains of association, if this is what you mean by "nonlinear". (Sorry if I'm making a big deal about it but that is one of the buzzwords that get quite recklessly thrown around nowadays.)