I've always gone after seemingly impossible goals. And it's not entirely an irrational pursuit. Joseph Agassi, in “Science and society: studies in the sociology of science," says:
"...one chief reason for pursuing the seemingly unattainable may be that we do not know whether in principle it is attainable or not. We can even say, we do not know what our goals are--whether individually...or collectively..."
He says further that "...though endless search can be frustrating, and though peace of mind can be achieved with little or no search, we do have empirical testimony of lives devoted fruitfully and happily to tasks not yet attained and perhaps unattainable. Kepler's search for the harmony of the spheres and Einstein's search for a unified field theory are such instances, and by no means the only ones."
Harold Bloom in his study of Dante Alighieri also sheds considerable light on the subject, thus:
"...Dante invokes the miser to explain what the seeker after knowledge is not; the miser is doomed to failure, since, by pursuing the unattainable, he desires always to desire.
'e in questo errore cade l'avaro maladetto, e non s'accorge che desidera se sempre desiderare, andando dietro al numero impossible a giugnere'
'and into this error falls the accursed miser, and he does not realize that he desires himself always to desire, going after a number impossible to reach.'