Fantasy and Reality

Is there a link between fantasy, imagination and Platonism (irrelevant of whether one believes Platonism to be true)?

For instance, if we imagine a 'perfect' circle that is not absolutely feasible in reality, does this compare to a musical idea that is similarly 'difficult' (with or without performance?). Is, in this sense, a score in reality a fantasy?  And then what about other aspects of our imaginations?  How does all this compare with fantasy?  Do we really wish our fantasies to become reality?  And if they become reality, do they subsequently remain 'fantastic'?

Similarly, if there's a link between, say, an artistic fantasy and any other sort, are there links between the type or nature of these fantasies? 

Another thing about fantasies is, of course, that they are in general, private matters.  When they relate to the fantasies of others then between those people there may exist a particular bond or affection, at least in relationship to the fantasies that they share - most obviously, perhaps, seen between two newly acquainted lovers.  However, it is quite evident that these fantasies do not necessarily remain synchronised - visions may bifurcate and individuals find that a once shared fantasy is now little more than an embarrassment.  At these points it is likely that our fantasies may separate us from the rest of the world.  If no one is there to share them, what else can happen?  More acutely, there are many who fantasise about things which are directly or indirectly condemned by society.  There are many instances of individuals who have to find their way through this loneliness and rejection.  

Can these, often unhealthy fantasies in any way relate to the lofty visions of mathematicians or musicians?

Equally extraordinary is the recent case of 'Benjamin Bilkomirsky(?)' whose book 'Fragments' concerning his experiences as a child survivor of the Nazi Concentration camps has been questioned by Daniel Ganzfried.  Within the last few weeks the German publisher of the book has withdrawn it in response to this possible fraud.  The question is, if the fraud is true, whether Bilkomirsky(?) is mad or bad.