we didn't agree on terms, and dictionary arguments are boring

If someone can come up with a dictionary definition that defends their use, I'll accept that there are multiple common uses of a term. Sometimes utterly contradictory ("inflammable", "citation", "oversight", etc.) It's when I find people dismissing common terms or arguing against the dictionary that I rapidly lose interest. What's the context/field for your use of decoupling?

"Population growth is exponential, but the exponential rate keeps changing"

Mapping different fits to different portions of a curve is neither unknown nor invalid. A mathematical model simply describes the behavior of data. The underlying mechanism isn't itself described by the model (which itself is something of an orrery). Instead, as Murphy notes, population was responding to markedly different circumstances at different points along the line. You've neatly skipped over his explicit recognition of this: "What accounts for the discontinuity in slope?", and:

Plotting global population in the last thousand years (below), we see a few breaks in the slope. For most of this period, we saw a modest 0.12% growth rate, amounting to a 600 year doubling time. Around 1700, the rate stepped up to 0.41%, doubling every 170 years. The next break happens around 1870, jumping to 0.82% and 85 years to double. Then around 1950, we see another factor-of-two rate jump to 1.7%

What happened at those dates? 1700 marks the nascent beginning of the Industrial Revolution (Newcoman's steam engine pumps in coal mines) and more abundant coal. 1870 marks (roughly) electricity and modern sewerage, sanitation, antisceptics, and anesthesia. 1950 marks the beginnings of the Green Revolution as well as the great advance of manufacturing and post-war renaissance around the globe. The earlier 0.03% growth to ~6000BC marks the period prior to advanced agriculture and urbanization. Noting where your tidy mathematical model breaks is just as important as seeing where it fits.

In the "Economist" dialog, you're failing to recognize the point that it's the economist who's positing eternal growth:

Physicist: "So what’s a typical rate of annual energy growth over the last few centuries?"

Economist: "I would guess a few percent. Less than 5%, but at least 2%, I should think."

The remainder of Murphy's analysis is to demonstrate the patent absurdity of this.

I've observed that this leads to a number of fairly typical responses from Murphy's critics:

⚫ He's extending a growth trend which has broken down in recent years (your objection). The point is that the energy growth he demonstrates is tightly coupled (correlated) with economic growth. And if you want the latter, you're going to need the former.

⚫ Economic growth has been decoupled from energy growth. The graphical evidence I've shown suggests otherwise.

⚫ Technology will fix everything. "Growth doesn't depend on increasing material consumption at all". /u/geezerman at reddit and Tim Worstall at The Telegraph essentially make this argument.

⚫ "There is no energy/resource shortage". Humans will find and tap endless sources of new energy and raw material ... somehow.

I don't accept the fundamental premise

So: what would be a valid basis for a model of future resource availability? How do you address Hubbert peaking and depletion curves and the accuracy with which they've predicted known peaks in local, national (US and elsewhere), and by appearances, global oil production, as well as other resource peaks?

Rubbishing models without presenting a more accurate one yourself (or pointing at one) isn't science, it's denial.