Is it not the purpose of math to tell us "how" to connect things? At the bottom, there are some axioms that we accept as basis of the model, and using another formal model we can infer what to expect from anything whose behavior matches our axioms.
Math makes it very hard to reason about models incorrectly. That's why it's good.
Even parts of math that seem particularly outlandish and disconnected just build a higher-level framework on top of more basic concepts that have been successfully utilized over and over again.
That gives us a solid framework on which we can base our reasoning about abstract ideas. Just a few decades ago most people believed the theory of probability was just a useless mathematical game, disconnected from any empirical reality. Now people like you and me use it every day to quantify uncertainty and make better decisions. The connections are not always obvious.
Is it not the purpose of math to tell us "how" to connect things? At the bottom, there are some axioms that we accept as basis of the model, and using another formal model we can infer what to expect from anything whose behavior matches our axioms.
Math makes it very hard to reason about models incorrectly. That's why it's good. Even parts of math that seem particularly outlandish and disconnected just build a higher-level framework on top of more basic concepts that have been successfully utilized over and over again.
That gives us a solid framework on which we can base our reasoning about abstract ideas. Just a few decades ago most people believed the theory of probability was just a useless mathematical game, disconnected from any empirical reality. Now people like you and me use it every day to quantify uncertainty and make better decisions. The connections are not always obvious.