Comment Re:It is an issue throughout science (Score 1) 364
It is useful to note that some real things were discovered simply by applying mathematics with no direct physical evidence. That we revolve around the sun. That the earth is generally round. That the earth has a radius.
Then we begin to validate our experiences under controlled circumstances. We note that things do not fall dependent on weight, and things do not always slow down. We create the mathematical concepts of mass and force. We develop mathematical relations that say if we apply a force to a mass it will accelerate indefinitely. We also wrote an mathematical relations that said if we put a light bulb in a box it would produce enough energy to destroy the earth. This is classical physics, and it had problems, mostly that our experiences are limited.
So then two things happened. First the Earth was not destroyed by a light in a box, and some guy said this was because energy was quantized. It was a beautiful mathematical fix for a unreasonable mathematical prediction. Second, some other guy said that if a magnet was on a table and he walked by with another magnet, it was the same thing as he standing still with a magnet while the magnet on the table moved, and created a bunch of mathematical models that predicted a bunch of other previously unobserved phenomena. You see, the brilliance of starting with the math, developing something nice, then seeing if we can find stuff that is predicted in the those equations. It has lead us to think pretty equations are better, but that is because our observations have validated that more time than not, pretty equations are better.
Of course not everything we look for has been found, or can be said to even exist. Maxwel's equations would be much more pretty if we could find a magnetic monopole. Symmetry would be served it the graviton could be detected. On the other hand, the Higgs Boson does seem to actually exist, which aloows us to consider Newton as someone who simply did not just make a lucky guess, although it still does not explain why inertial and gravitational mass are the same.
Which is to say the job is not easy because the process one uses is going to depend on where you start and where you want to go. In modern physics, there is not always observations, or at least not observations based on our experience. It is true that if you lock a cat up in the trunk of a car all day, you will not know if the cat is alive or dead until you open the trunk and check. It is not true in our experience that the cat is both alive and dead. So pretty equations are another tool in our physics repitore. By investigating all implications of the equations, and if these implications represent reality, we prevent the unfortunate mistake of predicting that we can go as fast as we want.