Earlier quoted context omitted.
Billing by the day is good advice, but > Engineering is creative work, and you're paid to think - code is just the end product. No you aren't. No one cares if you think. They care about what thinking is (supposed to be) getting them. It just so happens, though, that whatever that is requires thinking. So you do charge for that. But no one is paying you "to think".
> No you aren't. No one cares if you think. If you are a manager, an architect or a scientist, all you do is think. You literally don't do anything else. The only reason diagrams, meetings, documents and research papers exist is to communicate your thinking to others
First of all, no; it's not true that, "You literally don't do anything else". Even if we were to accept that, though, it's besides the point, because what you're saying right now is a change of subject.
What I said was that you don't get paid to think. You're getting paid for what the customer (hopes) they'll get from you. (And yes, that's true even if they never get anything from you.)
To say it again: nobody cares if you're thinking. The exercise of thinking has no intrinsic value to the people who people who are paying you. All of the value is consequential. Ergo, even if you are thinking over the course of your work day, you are not really getting paid to think. If you could somehow manage to deliver the same results without thinking, you'd still get paid--because you're not actually getting paid "to think".