Why can mathematics and physics simulate natural phenomena so closely in thought experiments, calculations and computer programs?
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Math and physics are ways of reasoning about abstractions.
For example, 1+1=2 will be true for anything you can consider to be ‘one of a thing’.
One drop of water plus another makes two.
This kind of logic only works as well as the abstraction involved in calling something ‘one of a thing’, though. Does one wind plus one wind equal two winds? Where does a wind begin and end?
Even the water droplets are constantly losing and gaining molecules as they evaporate or condense from the surrounding air.
The logic of math applies unfailingly to abstractions, but abstractions only sometimes apply well to parts of reality.
When we shape our abstractions carefully to fit reality, the logic of math can carry us to accurate conclusions about the world. The accuracy of these conclusions will still be limited by the lossy compression of reality into the abstractions being considered, though.
For example, talking about the ‘pressure’ and ‘temperature’ of a group of ‘molecules’ can help you make a lot of predictions at that same level of abstraction, but it won’t give you any insight into the individual movements of atoms or the quantum level phenomena happening within/between them.
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