MATHEMATICS AND THE SCIENCES — LASLEY 193 



and Maxwell and verified by Hertz. He Las heard of the more recent 

 prediction by Einstein of the shift toward the red end of the spec- 

 trum, caused by the deflection of light in a gravitational field, verified 

 in the solar eclipse of 1919. These and many others, such as Men- 

 delejeff's prophecy as to the discovery of gallium, scandium, and 

 germanium, and such as Hamilton's prediction of conical refraction, 

 have cast science in the role of one of the major prophets. Even 

 Pearson concedes science the ability to predict, as well as to describe. 

 Mathematics provides in its differential laws a pattern for these 

 predictions. "A differential law," says Einstein, "tells us how the 

 state of motion of a system gives rise to that which follows it in 

 time." "If we know how the velocities and accelerations depend 

 on position, we can trace out the past and future of our universe," 

 says Pearson. This is done by means of differential equations with 

 proper boundary value conditions. The chemist does it when he 

 predicts the position of the electron in its orbit. The astronomer 

 does it when he predicts the position of the planet in its orbit around 

 the sun. Despite Heisenberg's uncertainty as to our ability to 

 measure both position and velocity, the schedules of the planets are 

 much better known than are those of the crack Chicago to New 

 York trains. 



INVENTION 



Science is known to many only for its inventions. Much of its 

 popularity with the masses is due to the added comforts and en- 

 joyments with which it supplies them. Their eye is open for the 

 so-called practical things of science. The auto, the radio, and the 

 thousands of gadgets which give us our arm-chair civilization, endear 

 science to the heart of the multitude. 



But this has not been the path of scientific progress. These things 

 have usually been but byproducts. Hertz little thought when he 

 verified Maxwell's electromagnetic waves that he was laying the 

 foundation for radio. Perhaps as often the practical leads back 

 into the fundamental principles, as do the principles lead to inven- 

 tion. Again, when the scientist thinks himself most theoretical, he 

 may be near a very useful practicality. "Indeed," says Kichards, 

 "the developments of the wave mechanics now in progress may be 

 fraught with graver practical consequences for humanity than the 

 approaching commercialism of television or rapid transoceanic pas- 

 senger flying." 



It is an old story to the mathematician, whom the cry of "prac- 

 ticality" fails to arouse. Archimedes, tracing his conies in the 

 sand when Marcellus' soldiers snuffed out his genius, had no thought 

 of a Kepler using them to describe the paths of the planets. Argand, 

 Gauss, Wessel in their abstract imaginings about the complex num- 



