I think I understand patents as well as any average non-lawyer. What I'm trying to do is make sense of the language used to describe patents. It's clear that people can't agree on what they are, because the Supreme Court keeps needing to step in and refine the definition. The language seems not to make sense, which would help to explain why people can't agree on what they are.

Ok, you patent a machine. But that statement is vague and ambiguous at best. If I patent a machine that I built, then how could the patent apply to a different machine that I didn't build? Yet, that's the whole point: they apply to classes of machines, including machines that haven't even been built at the time that the patent is granted. The class would seem to be inherently something abstract.