one physical unit produced or measurable service rendered would be equal to one monetary unit.

Of course his 45 degree slope could be true depending on how he chose his units.

If that's the relationship he wants to discuss, why isn't it the one graphed? Why are the axes energy vs. gdp instead of manufacturing output vs. gdp? Or, since you're including services, perhaps non-financial gdp vs. overall gdp.

Of course his 45 degree slope could be true depending on how he chose his units.

The two values he said were 1:1 related aren't even linearly related. There's no reasonable way to change the units to fix that.

The curve he graphed has a constantly-decreasing slope, and looks roughly like e^(-1/x). Sure, graphing -1/x vs. ln(y) will give a straight line, but that's not any kind of meaningful comparison.

I think his point was to show how it diverges from this linear relationship

If he's trying to show there's no linear relationship, then perhaps he should not say there is one:

"If I take the consumption of primary energy and compare it with GDP, what I observe is almost a one to one relationship (almost a straight line)"

He also shouldn't be begging the question by completely ignoring efficiency gains:

"The fact that there has been a change in the measuring system over time is probably the reason why there is now a difference between the growth of primary energy sources and the growth in GDP"

This argument does not read like a conclusion of the evidence; it reads like a preconceived notion with some largely-irrelevant numbers tacked on.

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As an aside, is there any reason every new graph in this sequence is getting its own article? There have been three articles on the same discussion in half a week, and the latter two appear to be minor additions without enough to justify a new article - witness how they have only a handful of comments (currently 14 each). It seems as though keeping the pieces of this discussion together would be more productive.