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.
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 framew... (read more)