If the consistency between the two is so absolute, why can we not investigate the physical nature of the universe through analysis of pure number? Particularly at the quantum scale?
closed as off topic by Qmechanic♦, Manishearth♦, dmckee♦ Dec 4 '12 at 19:13
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The ancient greeks did physics qualitatively & philosophically. Pythagoras asserted mystically that all was pure number. It wasn't until renaissance Italy that Galileo put these two together to create the impetus for a new physics.
So the answer to your question, thinking historically, is yes.
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Duh. Because not all of mathematics is physical. I can always make up some mathematical model that says I should float upwards instead of being pulled downwards by gravitation, but experimentation proves otherwise. Of course there is much to mathematical physics, but that is hardly all of physics.
It also seems related that Quantum physics uses many 'tricks' up its sleeve that don't seem mathematically rigorous too.
Clarification. What is physics? Physics is the fundamental science. Science is based on the scientific method, which relies on experiment to test the validity of hypothesis. Thus in physics mathematics is only a tool to model the universe, not the main subject. In physics, mathematics, if to become or become accepted by physics, must make predictions, explain phenomena, and be consistent with experimentation. Thus pure mathematics investigation is NOT physics.
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