Mathematics and Physics

There have indeed been civilizations upon your planet that understood as well as you, and without your kind of technology, the workings of the planets, the positioning of the stars -- people who even foresaw "later" global changes. They used a mental physics. There were men before you who brought back data quite as "scientific" and pertinent. There were those who understood the "origin" of your solar system far better than you. Some of these civilizations did not need spaceships. Instead, highly trained men combining the abilities of dream-art scientists and mental physicists cooperated at journeys not only through time but through space.

Physics and philosophy are at most a few thousand years old, but probably have lives of thousands of millions of years stretching away in front of them. They are only just beginning to get under way.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases... mental power... Probably nothing in the modern world would have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility.