Kinda I suppose. But the whole spreadsheet 'try this' trope is already unnecessarily hostile. You could put everything that spreadsheet exercise demonstrates into words.
And that's my main argument too. This equation/exercise is so simple as to be useless.
Human systems are multi-variate to the degree that a simple equation -- in this case showing that reliance on extractables is bad because their availability exponentially increases at the same time humans exponentially rely upon them more -- does not mean much of anything in the larger picture.
This equation sidesteps human ingenuity, free market adjustments that will be made, predicted population decline in developed countries, and if the equation did apply, where on the timeline of the curve would we be.
And those are just some of the criticisms of viewing the world through such a simple myopic lens.
The third assumption, that capital increases as a constant proportion of resources extracted, is even more questionable. I think it's fair to say that we are able to do more with less now than we could in the past. You might say that that is a function of the existing capital too. So what happens if you try something like C += r*q*(1 + .01*C)? Do you still get a peak?
And of course, there's the assumption that the next bit of resources you extract is a little harder than the last bit. Statistically this has been true for some time now, but you could imagine this rule reversing, at least temporarily, if we gained access to some new resource, say, asteroid mining.
So there's plenty in the model to attack, if you take the time to really consider it.
I do realize too that my model makes assumptions- which have not been demonstrated to be true. So, that’s where I would attack it. Which assumptions are false?
