The Need for Mathematics
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Science is a quantitative discipline. When we want to study some phenomenon we first make a model that represents the system we want to study. That model can be mechanical, such as a model of the solar system made of little balls (the planets, the sun, and maybe a few moons), and wires representing the paths taken by the planets as they whiz around the sun. To be accurate though, the sizes of the planets and moons, and their distances from the sun, must be made to scale, and this requires mathematics. When our models simulate more esoteric systems, mechanical models fail us (e.g. a model of subatomic interactions) and we rely completely on a mathematical model. The beauty is that the mathematical model accurately describes physical reality - the wonder is that it is able to do so. That we can use the simple mathematical recipe contained in Newton's law of gravity, discovered over three hundred years ago, to predict with high accuracy where Mercury will be in its orbit at the beginning of the third millennium (or the fourth, or fifth) is wonderful indeed. Even more wonderful perhaps, is the fact that if we very carefully checked Mercury's orbit against the predictions of Newton's mathematics we would find that they were not quite right, but the corrections provided by Einstein's mathematical theories just make up the difference. Mathematics, essentially games set up with strict sets of rules, need not have any connection with reality, but almost every mathematical structure seems to have a correlation with a physical process. We will see an elegant example of how pure geometry can describe pure physics shortly.