That is what I expected, thank you. That's a puzzling omission by the author: he's declined to include the details of his key piece of work. It appears the book did not provide a look behind the wizard's curtain afterall! Let's dig into that bit by bit:
Yes, that is indeed where the missing equation should be, but isn't. I saw that the first time you posted about the "ETP Model" and pointed out that it was missing. It's the source of the problem we're discussing. Thanks for getting it for me so I didn't have to go back and find it again. What is odd about it is that these two sentences appear to contradict each other:
So he says there is no ("explicit"?) equation, then provides an equation...albeit with the key piece missing(which should be its own equation)!
But the entire passage screams "Handwaving!" I see the following issues, at least:
1. Obviously, the first sentence begs the question: if there is no equation, then how, exactly were they generated? Next, it says:
2. Logistic curves have equations. What is the equation?
3. What does derived numerically mean (show me!)? It implies a curve fit from some data. But even a curve fit has an equation - does he not understand how to have Excel show the equation when he does a curve fit?
That's an intriguing nugget. But there are a couple of problems in that:
4. The maximum theoretical energy that can be extracted from a unit of crude is a constant. It doesn't change over time, so it can't be a curve -- there must be much more to the curve than just that.
5. "Maximum theoretical energy" must have units like Joules or BTUS -- the graph is in dollars. Did he take curves with different units and lay them over top of each other? Or did he just misspeak and there is really more to it than that?
6. The energy content of crude not only does it not change over time except insofar as its usage will change, but it's often above 71% and you don't need to dig into the combustion equations of hydrocarbons to get it.
7. That's an equation. So does it follow an equation or not? Obviously, if time factors into this anywhere, it would be in a changing "ETP Value", which is obviously the part we are missing. It should be it's own equation in the form:
ETP Value = -L/(1-e^-k(x-x0))
Sorry, I don't do latex, but you can find the form of the equation here:
https://en.wikipedia.org/wiki/Logistic_function
All we need is the constants and if he's having trouble extracting them from an Excel curve fit, I can show him how to do it.
8. Where does the 42 come from? Arbitrarily selected number to make it fit what he wants it to fit?
9. "BTU/$" appears to be unit correction inserted to cover the fact that "energy" and "$/barrel" don't match. You can't do that in math. You can't just arbitrarily change the units in an equation by sticking in extra unit signs that aren't associated with values in the equation.
So, this has all the hallmarks of handwaving nonsense generated by someone who is woefully inept at math and graphical analysis of data. I do believe you that he apparently didn't include the "ETP Value" equation, but since this entire effort is supposed to be about "The ETP Model", he's left-out of his book the very punch line of his joke! It would be like Einstein leaving e=mc^2 out of his book on Special Relativity (caveat: the real equation is more than that)!
So now what, futilitist? We're still left with not having access to the details of the key claim. We still don't have access to "The ETP Model" itself! Whether that's an equation, a curve fit that he couldn't figure out how to generate the equation for, or a piece of spaghetti that he traced around, we still need to see it.
Claim as a question aside, you should be able to see clearly from the fact that oil prices dropped by half in a very short period of time that it is
not closely tied to the energy required to produce it. It is much closer tied to supply and demand economics. How do I know that? Because the energy required to produce the oil did not drop by half in a few weeks -- indeed, the whole point of Peak Oil is that the energy required to produce the oil is
rising, not falling: As I said before, the data you are using to support your latest claim of the apocalypse is pointed in the wrong direction: it should be pointed up, not down. But you did that throughout your previous incarnations of this issue: up is down and down is up and an improving economy is a worsening economy and all roads lead back to Peak Oil even if they lead away from it.
That, by the way, is an example of me understanding the ETP Model better than you do, even though neither of us have seen it. I understand how it
must work, at least in broad strokes, and you don't.