The mathamatics of foretelling the future
This is a step others would say to leaave out. But there is something very beautiful when you get down to what are called the “hard sciences” which first of all means physics. So a few words. Four equations, and you know all about electricity and magnetism. And, the most important part of hard sciences, you can predict the future. And if you do that you have learned something invaluable. So stay with me. First we jump ahead to what the great scientist Clerk Maxwell came up with in 1814, which are now called, appropriately Maxwell’s Equations. (Student electrical engineers wear T shirts with these equations printed on them.)
Why? I really, really, want you to see Science witha capital S. What does this mean? I am only going to exxplain the first equaltion. We are looking at “Integral Calculus.” The symbols, like the big S are "operators," or instructions what to do with the data. Like long division only more powerful. E is the electric field which creates force on an electron. A is the area of a volume around a bunch of charge q. The bit S says to add up all of the electric field around the volume and it will give you the amount of change in the volume. The big B, is the same thing for a magnetic field but it always comes out zero because every north pole magnet has a south pole magnet so they always add up to zero. The other two equations tell what happens when we change something. Now the little beautiful miracle.
When you solve these equations what pops out is one equation which is the wave equation of light and it tells you all about how the equation works. That is like fortelling the future. It happsn in all of science once you are able to write the equations. Then you can test the four equations by seeing if their prediction are right. Without them: no TV signals, no internet, no lenses and mirrors. Or at least none that work very well. And that is just a fraction. (More later.)