Nietzsche foresaw a hundred years ago the plight of the cultivated mind, whom he embodied in the philosopher:

The spread of the towering sciences has grown enormous and with it the likelihood that the philosopher will grow tired, even as a learner, and will take refuge somewhere and specialize; so that he will no longer reach his proper height – his superspection, circumspection, and “despection”. Or he climbs aloft too late, when the best of his maturity and strength are gone, or when he is on the downgrade, coarsened and spoiled; so that his view of the world, his general estimate of things, is no longer of much importance. It is no doubt his intellectual conscience that makes him hesitate to be a dilettante, a centipede, a creature with a thousand antennas. 

No scheme lasts forever. There will arise a generation whose “general estimate of things” will regain importance, whose intellectual conscience will impel them in the other direction, toward sensing the world through a thousand antennas. For the bearers of culture continue to be born; the desire for is innate. To reincarnate Nietzsche’s philosopher, we need only look to the touching figure of the water boy who rowed Dr. Johnson and Boswell down the Thames to Greenwich. The friends were discussing the shaping influence of classical culture. Boswell thought people got on very well without it. Johnson partly agreed. “For instance,” he said, “this boy rows us as well without learning as if he could sing the song of Orpheus to the Argonauts, who were the first sailors.” Then he interrupted himself and called to the boy: “What would you give, my lad, to know about the Argonauts?” “Sir,” said the boy, “I would give what I have.”
pg. 22, The Culture We Deserve