I could discuss everything within a few very concrete examples. A concrete example tends to create a working understanding in a way mathematical abstraction fails to. I want to give my readers real knowledge, so I do often insist on describing concepts in the world without numbers or equations or proofs.

However, math exists for a reason.

Some patterns generalize so strongly that you simply cannot communicate the breadth of its applications in concrete examples. You have to describe the shape of it by constraint. To do otherwise would render it a handful of independent parlor tricks instead of one sharp and heavy blade.

I could discuss everything within a few very concrete examples. A concrete example tends to create a working understanding in a way mathematical abstraction fails to. I want to give my readers real knowledge, so I

dooften insist on describing concepts in the world without numbers or equations or proofs.However, math exists for a reason.

Some patterns generalize so strongly that you simply cannot communicate the breadth of its applications in concrete examples. You have to describe the shape of it by constraint. To do otherwise would render it a handful of independent parlor tricks instead of one sharp and heavy blade.