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A pile of straw at the bottom of the cliff

[In Japanese — 崖の底にある藁の山 — Thank you, Masayuki!]


There is an old Russian saying: “If I had known where I would fall, I would have put down some straw there.” (“Кабы знал я где упал, я б соломки подостлал.”)

It is one of thousands of such sayings that are the repository of ancient folk wisdom. Normally, it is used to express the futility of attempting to anticipate the unexpected. Here, I am using it facetiously, to underscore the madness of refusing to anticipate the unavoidable.

I started thinking along these lines when I was invited to speak at the annual conference of ASPO (Association for the Study of Peak Oil), which was held in Washington in October of last year. It was shaping up to be something of a victory lap for the Peak Oil movement, now that the moment when global conventional oil production reached its historical peak is well and truly behind us, while the newer unconventional sources of liquid fuels have turned out to be insufficiently abundant and too costly both to the pocketbook and the environment. I wanted to use this opportunity to try yet again to correct what I see as a major flaw in the narrative of Peak Oil: the idea of a gentle, geologically-driven decline in oil production, which seems quite unrealistic, which I had detailed in my article “Peak Oil is History” more than a year before. But I also wanted to look beyond it and sketch out some plans that would work after oil production dives off a cliff, and what it would take to get them off the ground.

It's all well and good to present verbal arguments, but words don't stack up against numbers and curves, so I started looking around for a mathematical model that would capture the essence of what I was setting out. I put out a call for people to contact me if they wanted to collaborate, and was very happy to receive an email from Prof. Ugo Bardi of the University of Florence, asking what I had in mind. Ugo is an authority on the Club of Rome's much maligned but now indicated "Limits to Growth" model, having provided it with a recent book-length update.


I wrote back to Ugo:

“I would like to argue that whereas the method used to model Peak Oil using a Gaussian is reasonable when looking at individual oil fields, provinces and countries, it is not reasonable when looking at entire planets, because, unlike oil-producing provinces and countries in decline, planets can't import oil, while oil shocks cause industrial economies to collapse rather than decline gradually along some geologically constrained curve. In [my] article ["Peak Oil is History"] I have a long list of effects such as EROEI decline, export land effect, etc., to make the case for a stepwise decline rather than a gradual one.


“If we take our nice simple Gaussian model of Peak Oil and zoom out sufficiently far, it looks like an impulse. The peak amplitude and the width are not so interesting; but we do know what the area under the curve is: the ultimate recoverable. This is the "Odulvai Gorge" view of Peak Oil. Zooming back in, we see that the leading edge is the "growth" edge, influenced by economic growth, technological improvement, ever-wider exploration and so on, and we expect and see exponential growth. The trailing edge, on the other hand, dominated by the sudden collapse of industrial economies, due to all the factors I listed, would be expected to resemble exponential decay, but is so steep that we might as well approximate it as a step function. This is what we generally see when a growth process reaches a limit. Beer-making is one popular example: yeast population and sugar-use increases exponentially, then crashes.

“As oil is the "enabling" energy source, which makes it possible to deplete all other resources at a high rate, a stepwise decline in the availability of oil would halt the process of depleting (almost) all other resources (firewood in rural areas and a few others are the exceptions). So, the further the collapse is delayed, the less there will be left to start over with, making any attempt to prolong the oil age quite unhelpful. This is an ecological argument: the greater the overshoot, the more the eventual carrying capacity is reduced. Therefore, investing in "collapse-proof" schemes and businesses is harmful.

“An alternative is to set resources aside (supplies, tools and equipment, designs, skill sets) that can be rapidly deployed once collapse occurs. Entire turnkey business schemes can be developed and capitalized, in expectation of collapse.

These would 1. hasten collapse by withdrawing resources from the pre-collapse economy (a net positive) and 2. provide for rapid development of viable post-collapse businesses, such as manual, organic agriculture, sail-based and other non-motorized transport, and so on (also a net positive). Seeing as there is already a distinct lack of good ways to invest money (US "subprime" Treasuries? Gold bullion? African drought-stricken farmland?) this can be presented to the investment community as a way to hedge against collapse.”

Ugo wrote back:

“Hmmm.... let me see if I understand your point: you say that a Gaussian is no good; that the descent on the "other side" of the peak should be much faster than the growth. Am I right?

“If so, it is curious that I was working right on this concept today—and I think I cracked the problem just one hour ago! Maybe it was already obvious to other people, but it wasn't to me; maybe I am not so smart but, at least I am happy now. So, I can tell you that you are right on the basis of my system dynamics model. Descent IS much faster than ascent!

“When I received your message I was just starting to prepare a post for my blog "Cassandra's legacy" on this subject. So, if you can wait a couple of days, I am going to complete my post and publish it. Then you may give a look to it and we can discuss the matter more in depth. And I'll make sure to cite your post, because I think it is right on target.”

A little while later Ugo published his “Seneca Cliff” post. The name came from the quote from Seneca:

"It would be some consolation for the feebleness of our selves and our works if all things should perish as slowly as they come into being; but as it is, increases are of sluggish growth, but the way to ruin is rapid."
Lucius Annæus Seneca, Letters to Lucilius, n. 91

I wrote back:

“The Seneca Effect is splendid, and well-named. (Last winter I re-read Seneca's letters to Lucillus while laid up with the flu, and found a lot that's relevant.) I think I should be able to build on this model to include a few other effects.”

Ugo's post detailed two very simple models.

The first model reproduces the canonical depletion curve, which looks like a Gaussian. It is based on just a couple of intuitively obvious relationships:

  • firstly, the rate at which the resource base is exploited is proportional to both the size of the resource base and the size of the economy that is being used to exploit it;
  • secondly, the economy decays over time (depreciation, entropy, etc.) Set up the initial conditions, run the clock, and out comes the expected curve.


The second model incorporates the idea of pollution, or bureaucracy, or overhead: the inevitable external costs of exploiting the resource. About a third of the flow is diverted into the pollution bucket, which also decays over time. The first model, it turns out, must be filling the “pollution” bucket by exploiting some other resource, through imports. But since the planet as a whole imports nothing, the first model is not relevant to modeling global Peak Oil, and so we have to use the second model instead.

I found the Seneca Cliff model very easy to reproduce, first using a spreadsheet, then by writing a short program in Python:

I showed my results to Ugo, and he wrote back:


“Yes, it seems to be working.” I then started adding elements to this model, to see what it might take to “reboot” the economy into a post-fossil-fuel, post-industrial “operating system.” I made a highly idealized, wildly optimistic assumption: when a critical mass of people realizes that global Peak Oil has occurred and that the global economy is beginning to crash with no hopes of recovery, they will do the right thing: take 10% of the remaining industrial output, divert it and stockpile it, to be used to “reboot” into a post-industrial mode once the crash has largely run its course.


There is a problem with this plan: to a layman, global Peak Oil is rather hard to detect, leading to much confusion and dithering. Up to the final crash, it looks like a plateau, where oil production refuses to increase in spite of historically high prices.

But ignoring this issue (you have to idealize somewhat, for the sake of clarity, when working with conceptual models), if we start setting aside a “Peak Oil Tithe” around when Peak Oil occurs, and if we deploy all that we've stockpiled when the fossil fuel economy can no longer support us, the picture looks like this:
Zooming in, there are two triggers: when the “tithe” starts accumulating (shortly after the peak), and when it is deployed to build a post-collapse economy (when the fossil fuel economy is 50% down from its peak).


The resulting post-collapse economy is quite a lot smaller than the fossil fuel economy, but still large enough to support a significant portion of the current population, albeit at a much lower standard of living. There might not be indoor heat or hot water, certainly no tropical vacations in wintertime or fruit out of season, no advanced medical treatment and so forth. But it would still be better than the alternative, or, rather, the complete lack thereof.

I presented these graphs at the ASPO conference, where they were greeted with polite silence. There were some “investors” at the conference, but they were busy attending a session dedicated to discussing opportunities to invest in the fossil fuel economy. Nobody offered any counterarguments, but then nobody felt compelled to act based on what I said either. Why do you think that is? Why is that reasonably rational individuals who are able to follow an argument and who are unable to refute it are at the same time incapable of making the transition from thought to action? What is stopping them? Humans are clearly smarter than yeast, what does that matter if they are incapable of acting any more intelligently? I will attempt to address this question in a subsequent post.

What do you think? Leave a comment below.

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