I guess my purposes are different. In the Physics in the Economy series, my goal is to create a sequence that makes the basic physical ideas (which are amazing, really, when one stops to review them, which I haven't done in a long time) accessible to people without much physics background - the energy economics literature just kind of assumes the basic physics background is there. I think the enormous layer of mathematics that physicists slather over everything, because they know how, really interferes with making it remotely accessible to anyone else. (For an example, I was looking this evening for a simple way to explain Noether's theorem, which I think is a mindblowing result, and look what the Wikipedia says. What are they thinking? How is anyone without a PhD in theoretical physics already supposed to make anything of all that gobblydegook? Even working experimental physicists would probably struggle to understand it. It displays an utter lack of clue about the purpose of an encyclopedia. I used to know what cotangent bundles where, but I've long since forgotten and am not inclined to go figure it out again.) So I'm going to use as little math as I can get away with, and take all my examples from economically relevant cases, rather than rollers on inclined planes, etc. I'm not striving to train physicists, but rather hoping to help people gain enough physics ideas that they can conceptualize the economy as a dissipative system, understand the general implications of that, and make sense out of energy economics papers.

Here in this post, I couldn't think of a way to explain why this graph has anything to do with Hubbert's peak without showing the differential equation. You're right it's not consistent in level. I call Emerson to my defense:

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do.

(I always imagine him being taken to task for some slip-up and coming up with this arrogant, imperious gem of a quotation as a response).

I guess more to the point - the beauty of this kind of blog is commenters can and do add all kinds of value. So you can explain all the important parts that I leave out to those with the desire and sophistication to appreciate it.