It is the Late city that first defies the land, contradicts Nature in the lines of its silhouette, denies all Nature. It wants to be something different from and higher than Nature. These high-pitched gables, these Baroque cupolas, spires, and pinnacles, neither are, nor desire to be, related with anything in Nature. And then begins the gigantic megalopolis, the city-as-world, which suffers nothing beside itself and sets about annihilating the country picture.

The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.

One day the last portrait of Rembrandt and the last bar of Mozart will have ceased to be — though possibly a colored canvas and a sheet of notes will remain — because the last eye and the last ear accessible to their message will have gone.

And the National Socialists believe that they can afford to ignore the world or oppose it, and build their castles-in-the-air without creating a possibly silent, but very palpable reaction from abroad.

At last, in the gray dawn of Civilization the fire in the Soul dies down. The dwindling powers rise to one more, half-successful, effort of creation, and produce the Classicism that is common to all dying Cultures. The soul thinks once again, and in Romanticism looks back piteously to its childhood; then finally, weary, reluctant, cold, it loses its desire to be, and, as in Imperial Rome, wishes itself out of the overlong daylight and back in the darkness of protomysticism in the womb of the mother in the grave.

Optimism is cowardice.

To-day we live so cowed under the bombardment of this intellectual artillery that hardly anyone can attain to the inward detachment that is required for a clear view of the monstrous drama. The will-to-power operating under a pure democratic disguise has finished off its masterpiece so well that the object's sense of freedom is actually flattered by the most thorough-going enslavement that has ever existed.