We have written the equations of water flow. From experiment, we find a set of concepts and approximations to use to discuss the solution–vortex streets, turbulent wakes, boundary layers. When we have similar equations in a less familiar situation, and one for which we cannot yet experiment, we try to solve the equations in a primitive, halting, and confused way to try to determine what new qualitatitive features may come out, or what new qualitative forms are a consequence of the equations. Our equations for the sun, for example, as a ball of hydrogen gas, describe a sun without sunspots, without the rice-grain structure of the surface, without prominences, without coronas. Yet, all of these are really in the equations; we just haven’t found the way to get them out. …The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colourful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets–those eight or ten balls, each agglomerated from the same dust clouds and each obeying exactly the same laws of physics. The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrodinger’s equation contains frogs, musical composers, or morality–or whether it does not. We cannot say whether something beyond it like God is needed, or not. And so we can all hold strong opinions either way.
We have written the equations of water flow. From experiment, we find a set of concepts and approximations to use to discuss the solution–vortex streets, turbulent wakes, boundary layers. When we have similar equations in a less familiar situation, and one for which we cannot yet experiment, we try to solve the equations in a primitive, halting, and confused way to try to determine what new qualitatitive features may come out, or what new qualitative forms are a consequence of the equations. Our equations for the sun, for example, as a ball of hydrogen gas, describe a sun without sunspots, without the rice-grain structure of the surface, without prominences, without coronas. Yet, all of these are really in the equations; we just haven’t found the way to get them out. …The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colourful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets–those eight or ten balls, each agglomerated from the same dust clouds and each obeying exactly the same laws of physics. The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrodinger’s equation contains frogs, musical composers, or morality–or whether it does not. We cannot say whether something beyond it like God is needed, or not. And so we can all hold strong opinions either way.
