How Our Grandparents Perceive the World as Unchanging

Men can know a thing and yet know it quite ineffectively if it contradicts the general traditions and habits in which they live. [...] ONE of the most striking differences between the outlook of our grandparents and that of a modern intelligence today is the modification of time values that has occurred. By the measure of our knowledge their time-scale was extremely shallow. They had scarcely any historical perspective at all. They looked back to a past of a few thousand years and at the v...

 Public School Mathematics are Like Drills

“Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out—although it might seem that way from what you’ve been taught in courses called mathematics. Those integrals are to mathematics as weight training and calisthenics are to soccer. If you want to play soccer—I mean, really play, at a competitive level—you’ve got to do a lot of boring, repetitive, apparently pointless drills. Do professional players ever use those dril...

 Archimedes Discovers How to Measure Volume

Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the proble...