Mathematics is the most commonly used tool for describing nature, the most accurate way of doing so, and often the method of knowing it. In...
Mathematics is the most commonly used tool for describing nature, the most accurate way of doing so, and often the method of knowing it. In exploring nature, we often infer new, previously unrecognized behavior of physical reality by manipulating a mathematical formula already considered valid to describe nature.
And the method works in general. If we start from a mathematical relationship that is valid for nature and manipulate the formulae according to the strict rules of mathematics, the new relationship we eventually arrive at is certain to remain valid for our world.
However, the thought arises: if the initial state of mathematical relationships and the final state of the newly derived mathematical conclusion are valuable because they carry valid knowledge about our world, any intermediate form of mathematical manipulation should and must also have a physical meaning that is valid for nature.
Certainly, we could gain countless new insights if, in manipulating physical formulas, we not only interpreted the initial context and the conclusion to our physical reality, but also tried to interpret each intermediate form of mathematical formulas as a concrete physical state and understand what it might claim about the way the world works.
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