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For some reason a lot of people have issues with theoretical models in science. Perhaps it's the impression that science is based on the evidence. That's a good impression to have, because it's accurate. We understand, develop, and test our understanding of nature through repeated observation and testing.

But evidence isn't the only game in town. There are other avenues for understanding nature available to the scientist. One of those is particularly powerful: the mathematical model.

Mathematics plays a key role in science. Actually, two roles. One is to provide compact, elegant descriptions for behaviors that we see in nature. It would be extremely difficult for me to give you an accurate picture of how a thrown ball behaves using the ambiguous words of a natural language. But Newton's laws can just sum it up perfectly without any waste.

The other role that mathematics plays is to enforce logical consistency. If we have some starting base or assumption, the rules of mathematics allow us to extend and broaden that base assumption to understand the full consequences of that assumption. With mathematics we can start at point A and end up at point C and know that we have an unbroken chain of logic connecting those two.

This means that if we have an assumption or hypothesis that has been tested, then we know with absolute mathematical certainty that anything flowing from that hypothesis must also be true (at least up to the level that the hypothesis has been tested against the real world). So if we know something is accurate, then we can use mathematical models to extend our understanding beyond what we can directly test and observe. This is used in every branch of science from biology to the big bang.

Sometimes we can only make a limited set of observations or a confined set of tests that only put some corner of the theory to the test. But the rigorous ironclad logic of mathematics allows us to extend from that tested corner to the rest of the room. So we can know in some cases without ever actually observing. Of course, nature is always capable of throwing curve balls and surprises, but that's true of even well-tested theories and ideas. In the end, the mathematical model allows scientists to extend our minds and our understanding beyond the normal confines of what has simply been tested. So if something is based on a model, you don't get to automatically disqualify it or discount it. It's in many cases just as powerful as what has been directly observed.


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