If someone separated the art of counting and measuring and weighing from all the other arts, what was left of each (of the others) would be, so to speak, insignificant.
Next you'd see a raft sliding by, away off yonder, and maybe a galoot on it chopping. . . you'd see the ax flash and come down-you don't hear nothing; you see the ax go up again, and by the time it's above the man's head then you hear the k'chunk!-it had took all that time to come over the water.
Mock on, mock on, Voltaire, Rousseau! Mock on, mock on: 'Tis all in vain! You throw the sand against the wind, And the wind blows it back again. And every sand becomes a gem Reflected in the beams divine; Blown back they blind the mocking eye, But still in Israel's paths they shine. The atoms of Democritus And Newton's particles of light Are sands upon the Red Sea shore, Where Israel's tents do shine so bright.
The lessons of science should be experimental also. The sight of a planet through a telescope is worth all the course on astronomy; the shock of the electric spark in the elbow outvalues all theories; the taste of the nitrous oxide, the firing of an artificial volcano, are better than volumes of chemistry.
Neither the naked hand nor the understanding left to itself can effect much. It is by instruments and helps that the work is done, which are as much wanted for the understanding as for the hand. And as the instruments of the hand either give motion or guide it, so the instruments of the mind supply either suggestions for the understanding or cautions.
Some persons have contended that mathematics ought to be taught by making the illustrations obvious to the senses. Nothing can be more absurd or injurious: it ought to be our never-ceasing effort to make people think, not feel.
But the whole vital process of the earth takes place so gradually and in periods of time which are so immense compared with the length of our life, that these changes are not observed, and before their course can be recorded from beginning to end whole nations perish and are destroyed.
Truth is compared in Scripture to a streaming fountain; if her waters flow not in perpetual progression, they sicken into a muddy pool of conformity and tradition.
Who are we? We find that we live on an insignificant planet of a humdrum star lost in a galaxy tucked away in some forgotten corner of a universe in which there are far more galaxies than people.
It is clear that there is some difference between ends: some ends are energeia [energy], while others are products which are additional to the energeia.
At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters.