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It's all a bit symbiotic isn't it? Observation leads us to theories and the theories point us in different directions for observation. These either confirm or refute the theories. Which then get modified and sent back for observation...so both happen together. However, I am always amazed at how intricately mathematics is a part of how things work. And how well it predicts what is later observed.
I think the main thing with any body of knowledge is to keep an open mind. Use what tools we have, but always be open to other possibilities.
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