[fallingfrog]

Here's a fun little exercise: Open up a spreadsheet.

Label the first column C for capital. This starts at 1.

Label the second column T for total resources extracted. This starts at 0.

Label the third column r for resources extracted this step.

Label the fourth column E for extraction efficiency.

Label the 5th column m for maintenance. Make it proportional to capital.

Now, for each step:

E is some positive function of T with a negative slope. It doesn't have to have a finite area under the curve (you don't have to assume total resources to be finite, in other words). You just have to assume that the next unit of resources to be extracted requires a bit more effort than the last one. Use E = .1*exp(-.01*T) or something like that.

r = C*E

m = C*k where k is any positive number between 1 and 0- .01 is a good constant to use.

C += r*q - m where q is again some constant, say .2

T += r

Now observe the behavior of the system. Plot the value of C over time. For the above constants you'll want to include about 3000 steps.

(Edit: forgot the maintenance term)

[carapace]

I didn't have a spreadsheet handy:

    from math import exp

    k = .01
    q = .2
    C = 1
    T = 0
    E = lambda T: 0.1 * exp(-0.01 * T)

    for step in range(3000):
        r = C * E(T)
        m = C * k
        C += r * q - m
        T += r
        print('%5i %g' % (step, C))

[reedjosh]

Because human economics in the realm of energy and or resource extraction are easily predicted by simple equations in a spreadsheet.

So much so that this trivial exercise imparts real wisdom and is definitely not mental masturbation.

[fallingfrog]

Unfair - I didn't say that all human economics are easily predicted by a spreadsheet. It's an exercise. A starting point for discussion. As in: to start with, point out the assumption that is wrong. Rather than just insult me.

[reedjosh]

> Unfair

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.

[fallingfrog]

I'll give you a hint: Each one of those equations has an assumption embedded in it. The first and last one seem pretty solid. The middle two, though- The second assumption is that maintenance on capital is some constant proportion of total capital. That might be true, but also might not be, especially if you consider knowledge to be a form of capital. Maybe maintenance should scale with the log of capital, or something like that. But even then, I'm pretty sure that unless maintenance goes to zero, this doesn't affect the general shape of the curve.

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.

[fallingfrog]

Well, I majored in physics, so to me the cow is always a sphere.. but you know, all models of reality are imperfect, no matter how complicated. And it’s true that I have no idea where on the curve we might be. I would certainly not use this model to make specific predictions- that would be silly. It’s more the general behavior of the system I’m interested in. But you can definitely make refinements. For example, if you add renewables then you still get a peak, but it doesn’t go all the way to zero afterwards.

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?

[bckr]

I've got a lot of other homework... Could you provide a filled out worksheet or describe the behavior?