Welcome to the age of diminishing returns

Friday, December 19, 2014

Peak pyramids: the way to ruin is rapid

The graph above is a little exercise in cliodynamics, the attempt of quantitatively modeling historical data. Here, the size of the great Egyptian pyramids is plotted as a function of their approximate building time, taken as the last year of the reign of the Pharaoh associated to them. The data are fitted with a simple Gaussian, which approximates the cycle of the Hubbert model of resource depletion.


The great Egyptian pyramids built during the 3rd millennium BCE are the embodiment of the power and of the wealth of the Egyptian civilization of the time. But why did the Egyptians stop building them? Not lack of interest, apparently, since they kept building pyramids for a long time. But they never built again pyramids on such a giant scale.

Probably, we will never have sufficient data to understand the economics of the Egyptian pyramid building cycle of the 3rd and 4th Egyptian dynasties. But we can try at least to examine the quantitative data we have. So, I went to Wikipedia and I found data for the size of pyramids and their approximate dates. The result is the graph above. Here, I show only the data for completed pyramids as a function of the last year of the reign of the Pharaoh associated for each one.

As you can see, it is possible to fit the data with a Gaussian curve, which approximates the Hubbert curve, known to describe the depletion of a limited, non renewable resource. This suggests that the Egyptians had run out of resources, possibly in the form of the fertile soil necessary to sustain the large workforce needed to build pyramids. Or, perhaps, in an age of increasing warring activity, they were forced to funnel more and more resources into the military sector, taking them away from pyramid building.

Another phenomenon we can note in the graph is the rapid collapse of the size of the pyramids at the end of the cycle. The last pyramid of this cycle, the one associated to Pharaoh Menkaure, is even smaller than the first one of the cycle, the "stepped pyramid" of Pharaoh Djoser. Perhaps, this rapid decline is a manifestation of the "Seneca Effect", a term that I coined to describe economic cycles in which decline is faster than growth. Unfortunately, however, the data are too scattered and uncertain to be sure on this point. But surely there was no "plateau" nor a slow decline after the construction of the largest pyramids andit is suggestive to think that even pyramid building may be described with Seneca's words "increases are of sluggish growth, but the way to ruin is rapid."










 

Monday, December 15, 2014

Seneca cliffs of the third kind: how technological progress can generate a faster collapse


The image above (from Wikipedia) shows the collapse of the North Atlantic cod stocks. The fishery disaster of the early 1990s was the result of a combination of greed, incompetence, and government support for both. Unfortunately, it is just one of the many examples of how human beings tend to worsen the problems they try to solve. The philosopher Lucius Anneus Seneca had understood this problem already some 2000 years ago, when he said, "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."


The collapse of the North Atlantic cod fishery industry gives us a good example of the abrupt collapse in the production of resources - even resources which are theoretically renewable. The shape of the production curve landings shows some similarity with the "Seneca curve", a general term that I proposed to apply to all cases in which we observe a rapid decline of the production of a non renewable, or slowly renewable, resource. Here is the typical shape of the Seneca Curve:


The similarity with the cod landings curve is only approximate, but clearly, in both cases we have a very rapid decline after a slow growth that, for the cod fishery, had lasted for more than a century. What caused this behavior?

The Seneca curve is a special case of the "Hubbert Curve" which describes the exploitation of a non renewable (or slowly renewable) resource in a free market environment. The Hubbert curve is "bell shaped" and symmetric (and it is the origin of the well known concept of "peak oil). The Seneca curve is similar, but it is skewed forward. In general, the forward skewness can be explained in terms of the attempt of producers to keep producing at all costs a disappearing resource.

There are several mechanisms which can affect the curve. In my first note on this subject, I noted how the Seneca behavior could be generated by growing pollution and, later on, how it could be the result of the application of more capital resources to production as a consequence of increasing market prices. However, in the case of the cod fishery, neither factor seems to be fundamental. Pollution in the form of climate change may have played a role, but it doesn't explain the upward spike of the 1960s in fish landings. Also, we have no evidence of cod prices increasing sharply during this phase of the production cycle. Instead, there is clear evidence that the spike and the subsequent collapse was generated by technological improvements.

The effect of new and better fishing technologies is clearly described by Hamilton et al. (2003)

Fishing changed as new technology for catching cod and shrimp developed, and boats became larger. A handful of fishermen shifted to trawling or “dragger” gear. The federal government played a decisive role introducing new technology and providing financial resources to fishermen who were willing to take the risk of investing in new gear and larger boats.
 ...

Fishermen in open boats and some long-liners continued to fish cod, lobster and seal inshore. Meanwhile draggers  and other long-liners moved onto the open ocean, pursuing cod and shrimp nearly year round. At the height of the boom, dragger captains made $350,000–600,000 a year from cod alone. ... The federal government helped finance boat improvements, providing grants covering 30–40% of their cost.
....
By the late 1980s, some fishermen recognized signs of decline. Open boats and long-liners could rarely reach their quotas. To find the remaining cod, fishermen traveled farther north, deployed more gear and intensified their efforts. A few began shifting to alternative species such as crab. Cheating fisheries regulation—by selling unreported catches at night, lining nets with small mesh and dumping bycatch at sea—was said to be commonplace. Large illegal catches on top of too-high legal quotas drew down the resource. Some say they saw trouble coming, but felt powerless to halt it.

So, we don't really need complicated models (but see below) to understand how human greed and incompetence - and help from the government - generated the cod disaster. Cods were killed faster than they could reproduce and the result was their destruction. Note also that in the case of whaling in the 19th century, the collapse of the fishery was not so abrupt as it was for cods, most likely because, in the 19th century, fishing technology could not "progress" could not be so radical as it was in the 20th century.

The Seneca collapse of the Atlantic cod fishery is just one of the many cases in which humans "push the levers in the wrong directions", directly generating the problem they try to avoid. If there is some hope that, someday, the cod fishery may recover, the situation is even clearer with fully non-renewable resources, such as oil and most minerals. Also here, technological progress is touted as the way to solve the depletion problems. Nobody seems to worry about the fact that the faster you extract it, the faster you deplete it: that's the whole concept of the Seneca curve.

So take care: there is a Seneca cliff ahead also for oil!


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A simple dynamic model to describe how technological progress can generate the collapse of the production of a slowly renewable resource; such as in the case of fisheries. 


by Ugo Bardi

Note: this is not a formal academic paper, just a short note to sketch how a dynamic model describing overfishing can be built. See also a similar model describing the effect of prices on the production of a non renewable resource


The basics of a system dynamics model describing the exploitation of a non renewable resource in a free market are described in detail in a 2009 paper by Bardi and Lavacchi. According to the model developed in that paper, it is assumed that the non renewable resource (R) exists in the form of an initial stock of fixed extent. The resource stock is gradually transformed into a stock of capital (C) which in turn gradually declines. The behavior of the two stocks as a function of time is described by two coupled differential equations.
R' = - k1*C*R C' = k2*C*R - k3*C,
where R' and C' indicate the flow of the stocks as a function of time (R' is what we call "production"), while the "ks" are constants. This is a "bare bones" model which nevertheless can reproduce the "bell shaped" Hubbert curve and fit some historical cases. Adding a third stock (pollution) to the system, generates the "Seneca Curve", that is a skewed forward production curve, with decline faster than growth.  

The two stock system (i.e. without taking pollution into account) can also produce a Seneca curve if the equations above are slightly modified. In particular, we can write: 
R' = - k1*k3*C*R C' = ko*k2*C*R - (k3+k4)*C.
Here, "k3" explicitly indicates the fraction of capital reinvested in production, while k4 which is proportional to capital depreciation (or any other non productive use). Then, we assume that production is proportional to the amount of capital invested, that is to k3*C. Note how the ratio of R' to the flow of capital into resource creation describes the net energy production (EROI), which turns out to be equal to k1*R. Note also that "ko" is a factor that defines the efficiency of the transformation of resources into capital; it can be seen as related to technological efficiency.
The model described above is valid for a completely non-renewable resource. Dealing with a fishery, which is theoretically renewable, we should add a growth factor to R', in the form of k5*R. Here is the model as implemented using the Vensim (TM) software for system dynamics. The "ks" have been given explicit names. I am also using the convention of "mind sized models" with higher free energy stocks appearing above lower free energy stocks





If the constants remain constant during the run, the model is the same as the well known "Lotka-Volterra" one. If the reproduction rate is set at zero, the model generates the symmetric Hubbert curve. 

In order to simulate technological progress, the "production efficiency" constant is supposed to double stepwise around mid-cycle. A possible result is the following, which qualitatively reproduces the behavior of the North Atlantic cod fishery.




Among other things, this result confirms the conclusions of an early paper of mine (2003) on this subject, based on a different method of modeling.

Let me stress again that this is not an academic paper. I am just showing the results of tests performed with simple assumptions for the constants. Nevertheless, these calculations show that the Seneca cliff is a general behavior that occurs when producers stretch out their system allocating increasing fractions of capital to production. Should someone volunteer to give me a hand to make better models, I'd be happy to collaborate!















Friday, December 12, 2014

First, thou shalt not scare them



Watch the clip on youtube


A fundamental tenet of scientists and climate concerned people is that "you must not scare people about the climate threat". Sure: we all know that. It is reasonable, it makes sense, it is even obvious: if you say how bad you think the situation is, if you even mention the worst case hypothesis, they will close their ears singing to themselves "la-la-la!" while they run away. If you are not careful, they will not want to hear what you are telling them, and if they don't hear you they will do nothing. And if they do nothing, the problem will not be solved. It is standard practice in risk management.

So, we have always been careful to follow the instructions: avoid scaring people, avoid looking like scaremongers, avoid even hinting that things may be worse, much worse than anyone could imagine. We have been careful to end all warnings with a list of solutions; saying that, sure, it looks bad, but the problem will go away if you just insulate your home, buy a smaller car, and turn off the lights when you leave a room. What we need is just a little bit of good will.

To no avail: the climate problem is still there, bigger and more fearsome everyday. Nothing changes, nothing moves, nothing is being done. Nothing even remotely comparable to the scale of the threat. And, sometimes, you feel that you have had enough; you feel like screaming that this is NOT a problem you can solve with double-paned windows and smaller cars; it is NOT a problem for the next century; it is NOT a problem for another generation, It is here, it is now, it is big, it is damn big, and it is out of control. You feel like screaming that aloud.

So, the scene written by Aaron Sorking for "The Newsroom" is astonishing and refreshing at the same time. It is fiction, sure, it is something that will never happen, but it is an incredible jolt. It is a moment of truth, miraculously appearing in a place where it never appears: in the news. For instance:

"The last time there was this much CO2 in the air the oceans were 80 feet higher than they are now. Two things you should know: Half the world's population lives within 120 miles of an ocean." "And the other?" "Humans can't breathe under water."

I know, I know.... We should never, never even dream of saying this kind of things in public. We should not..... And yet.....


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Below, an excellent commentary on this scene by Randy Malamud on "The Huffington Post" (there is also a commentary by David Roberts on Grist which I found rather underwhelming)








Randy Malamud Headshot

It's The End of the World As We Know It



A scene on Aaron Sorkin's The Newsroom recently struck me, at first, as simply an astute and amusing commentary on global warming... until the real world chimed in with one of those life-imitating-art occasions suggesting that R.E.M.'s apocalyptic song is destined to be the soundtrack of our future.

First, the HBO moment: Anchor Will McAvoy (Jeff Daniels) interviews an EPA administrator (Paul Lieberstein, who will always be Toby Flenderson from The Office no matter what role he's playing) about a report that carbon dioxide levels have hit extremely dangerous new highs.

McAvoy begins in the usual mode for this sort of story, poised to emphasize the urgent threat of climate change while reinforcing the conventional platitudes that people need to take this seriously and work hard to remediate the problem.

His conversation, though, quickly goes off the rails.

"If you were the doctor and we were the patient," the anchor asks, "what's your prognosis? A thousand years, two thousand years?" The scientist's response takes him aback: "A person has already been born who will die due to catastrophic failure of the planet."

McAvoy: You're saying the situation is dire?

EPA guy: Not exactly. Your house is burning to the ground, the situation is dire. Your house has already burned to the ground, the situation is over.

McAvoy: So what can we do to reverse this?

EPA: Well there's a lot we could do...

McAvoy (interrupts): Good...

EPA: ...20 years ago, or even 10 years ago. But now, no.

McAvoy (becoming increasingly uncomfortable): Can you make an analogy that might help us understand?

EPA: Sure. It's as if you're sitting in your car, in your garage, with the engine running and the door closed, and you've slipped into unconsciousness. And that's it.

McAvoy: What if someone comes and opens the door?

EPA: You're already dead.

McAvoy: What if the person got there in time?

EPA: Then you'd be saved.

McAvoy: OK. So now what's the CO2 equivalent of the getting there on time?

EPA: Shutting off the car 20 years ago.

McAvoy: You sound like you're saying it's hopeless.

EPA: Yeah.

McAvoy: Is that the administration's position or yours?

EPA: There isn't a position on this any more than there's a position on the temperature at which water boils.

Then last week, an actual piece of journalism, the lead story in Monday's New York Times, confirms that things are indeed pretty much as desperate as Sorkin depicted on his pretend newscast. As the latest UN summit on greenhouse gases convenes in Peru, climate scientists report that a 3.6 degree rise seems inevitable, which they believe is "the tipping point at which the world will be locked into a near-term future of drought, food and water shortages, melting ice sheets, shrinking glaciers, rising sea levels and widespread flooding."

Flipping back to one last bit of patter from The Newsroom: The EPA administrator tells McAvoy, "The last time there was this much CO2 in the air the oceans were 80 feet higher than they are now. Two things you should know: Half the world's population lives within 120 miles of an ocean." "And the other?" "Humans can't breathe under water."

I propose that it is time for us to accept as a premise in whatever environmental discussions we have -- or indeed, in any deliberations on anything taking place in the future -- the fact that the world is coming to an end.

Well, not the world itself: The planet is actually pretty resilient, and will likely continue on its orbit unbothered by the warm spell; it's just people, along with most other life forms, that will disappear. Geologically, there's not so much to worry about; biologically, on the other hand, we have a situation.

Over the past decade -- since Al Gore's documentary An Inconvenient Truth brought global warming into the mainstream consciousness -- the rhetoric has been dire, but at least minimally hopeful: If we start doing this and stop doing that now, we can perhaps just barely salvage what is left of our ecosystem.

For a while it made sense, as Will McAvoy was trying to do on his newscast, to cling to a thread of hope in order to motivate reform and prevent people from descending into a paralyzing sense of helplessness.

But now it's time to accept our impending demise. Those are profoundly difficult words to write, but they are necessary: Our times demand a new rhetorical honesty. It is deceitful and irrelevant to sustain the charade that things may improve. Instead, it's time to start talking about how we will die.

(Maxine Kumin has a poem called "Our Ground Time Here Will Be Brief." It was.)

As depressing as this is, it has at least the virtue of being true, unlike the kick-the-can-down-the-road policies that pretend the solution for global warming lies in producing (someday!) cars that get 150 mpg and cities powered by wind farms. And expecting Westerners (the 12 percent of the world's population who consume 60 percent of its resources) to use less stuff.

If there's a silver lining, it is not a very satisfying one, but for what it's worth: I think it may prove refreshing, even exhilarating, to develop a new trope, a new truth, that lets go of the pretense that things will turn out ok.

"The progress narrative" that has undergirded Western culture for millennia was nice while it lasted, but it's also responsible for getting us where we are today, as it stoked the fantasy that we were invincibly moving ever forward, and that our rampantly voracious overdevelopment (exploration, imperialism, conquest, growth, "civilizing" nature) had no costs, no limits, no consequences.

As an English professor, I find it exciting to consider the possibilities for a new voice, a new style, a new writerly consciousness that may accompany and chronicle the winding down of our sound and fury.

Other cultures at similar points in their trajectory -- past the zenith, clearly waning yet close enough to the glories of the past -- have often produced keenly insightful literature and art. Being on the cusp of decline provokes incisive self-reflection -- as the Greeks called it, anagnorisis: recognition.

Cervantes achieved this in Don Quixote toward the end of Spain's Golden Age, as did T. S. Eliot in "The Waste Land," his report from the front lines of the cultural disintegration that accompanied the collapse of European imperialism and the War to End All Wars: "These fragments I have shored against my ruins."

On a personal level, we have lately begun to do a better job of dying, and of accepting death -- writing "death plans," forsaking heroic measures of resuscitation. So too as a species we may learn to accept the inescapability of our impending ecological fate. We can celebrate the bright spots from our past human heritage, acknowledge our follies, and finally, deal with it: It is what it is.

There will be a limited future audience for this brave new art, since we're hovering on the verge of extinction, but it will leave an interesting time capsule for whoever might come to recolonize the planet after we're gone.

"Anthropocene," a recently coined term for our present epoch, reflects the unique phenomenon of human impact that has changed (disrupted, ruined) the earth. Complementing this scientific assessment, a parallel aesthetic movement must acknowledge, better late than never, that we have irreparably fouled our nest.

We might demarcate our cultural expressions of this period as "epitaphal": our last words, as on a gravestone, inscribed with a solidity that will outlast our mortal frames and will announce for eternity (even in its conscribed scope) what kind of people we wanted to be and how we hoped we might be remembered.


Randy Malamud is Regents' Professor of English and chair of the department at Georgia State University.

Sunday, December 7, 2014

Fossil fuels: are we on the edge of the Seneca cliff?



"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 Anneaus Seneca, Letters to Lucilius, n. 91

This observation by Seneca seems to be valid for many modern cases, including the production of a nonrenewable resource such as crude oil. Are we on the edge of the "Seneca cliff?"



It is a well known tenet of people working in system dynamics that there exist plenty of cases of solutions worsening the problem. Often, people appear to be perfectly able to understand what the problem is, but, just as often, they tend to act on it in the wrong way. It is a concept also expressed as "pushing the lever in the wrong direction."

With fossil fuels, we all understand that we have a depletion problem, but the solution, so far, has been to drill more, to drill deeper, and to keep drilling. Squeezing out some fuel by all possible sources, no matter how difficult and expensive, could offset the decline of conventional fields and keep production growing for the past few years. But is it a real solution? That is, won't we pay the present growth with a faster decline in the future?

This question can be described in terms of the "Seneca Cliff", a concept that I proposed a few years ago to describe how the production of a non renewable resource may show a rapid decline after passing its production peak. A behavior that can be shown graphically as follows:



It is not just a theoretical model: there are several historical cases where the production of a resource collapsed after having reached a peak. For instance, here are the data for the Caspian sturgeon, a case that I termed "peak caviar".




Do we risk to see something like this in the case of the world production of oil and gas? In my opinion, yes. There are some similarities; both fossil fuels and caviar are non-replaceable resources; and in both cases prices went rapidly up at and after the peak. So, if Caspian sturgeon showed such a clear Seneca cliff, oil and gas could do the same. But let me go into some details.

In the first version of my Seneca model, the fast decline of production was interpreted in terms of growing pollution that places an extra burden on the productive system and reduces the amount of resources available for the development of new resources. However, I found that the Seneca behavior is rather robust in these systems and it appears every time people try to "stretch out" a system to force it to produce more and faster than it would naturally do.

So, in the case of the Caspian sturgeon, above, growing pollution is unlikely to be the cause of the rapid collapse of production (even though it may have contributed to the problem). Rather, the main factor in the collapse is likely to have been the effect of the growing prices of a rare and non replaceable resource (caviar). High prices enticed producers to invest more and more resources in raking out of the sea as much fish as possible. It worked, for a while, but, in the end, you can't fish sturgeon which isn't there. It ended up in disaster: a classic case of a Seneca Cliff. 

Can this phenomenon be modeled? Yes. Below, I describe the model for this case in some detail. The essence of the idea is that producers need to reinvest a fraction of their profits in developing new resources in order to keep producing. However, the yield of the new investments declines as time goes by because the most profitable resources (e.g. oil fields) are exploited first. As a result, less and less capital is available for new investments. Eventually production reaches a maximum, then it declines. If we assume that companies re-invest a constant fraction of their profits in new resources, the model leads to the symmetric bell shaped curve known as the "Hubbert Curve."

However, as I describe in detail below, decline can be postponed if high prices provide extra capital for new productive developments. Unfortunately, growth is obtained at the cost of a fast burning out of capital resources. The final result is not any more the symmetric Hubbert curve, but a classic Seneca curve: decline is more rapid than growth.

Is this what we are facing for fossil fuels? Of course, we are only dealing with qualitative models, but, on the other hand, qualitative models are often robust and give us an idea of what to expect, even though they can't tell us much in terms of predicting events on a precise time scale. The ongoing collapse of oil prices may be a symptom that we are running out of the capital resources necessary to keep developing new fields. So, what we can say is that there are some good chances of rough times ahead - actually very rough. The Seneca cliff may well be part of our near term future.


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The Seneca curve as the result of increasing fractions of profits allocated to the production of a non renewable resource

by Ugo Bardi - 07 Dec 2014


Note: this is not a formal scientific paper; it is more a rough "back of the envelope" calculation designed to show how increasing capex fractions can affect the production rate of a non renewable resource. If someone could give me a hand to make a more refined and publishable study, I would be happy to collaborate!


The basics of a system dynamics model describing the exploitation of a non renewable resource in a free market are described in detail in a 2009 paper by Bardi and Lavacchi. According to the model developed in that paper, it is assumed that the non renewable resource (R) exists in the form of an initial stock of fixed extent. The resource stock is gradually transformed into a stock of capital (C) which in turn gradually declines. The behavior of the two stocks as a function of time is described by two coupled differential equations.

R' = - k1*C*R
C' = k2*C*R - k3*C,

where R' and C' indicate the flow of the stocks as a function of time (R' is what we call "production"), while the "ks" are constants. This is a "bare bones" model which nevertheless can reproduce the "bell shaped" Hubbert curve and fit some historical cases. Adding a third stock (pollution) to the system, generates the "Seneca Curve", that is a skewed forward production curve, with decline faster than growth. 

The two stock system (i.e. without taking pollution into account) can also produce a Seneca curve if the equations above are slightly modified. In particular, we can write: 

R' = - k1*k3*C*R
C' = ko*k2*C*R - (k3+k4)*C.

Here, "k3" explicitly indicates the fraction of capital reinvested in production, while k4 which is proportional to capital depreciation (or any other non productive use). Then, we assume that production is proportional to the amount of capital invested, that is to k3*C. Note how the ratio of R' to the flow of capital into resource creation describes the net energy production (EROI), which turns out to be equal to k1*R. Note also that "ko" is a factor that defines the efficiency of the transformation of resources into capital; it can be seen as related to technological efficiency. These points will not be examined in detail here.

Here is the model as implemented using the Vensim (TM) software for system dynamics. The "ks" have been given explicit names. I am also using the convention of "mind sized models" with higher free energy stocks appearing above lower free energy stocks




If the k's are kept constant over the production cycle, the shape of the curves generated by this model is exactly the same as with the simplified version, that is a symmetric, bell shaped production curve. Here are the results of a typical run:





Things change if we allow "k3" to vary over the simulation cycle. The characteristic that makes "k3" (productive investment fraction) somewhat different than the other parameters of the model, is that it is wholly dependent on human choice. That is, while the other ks are constrained by physical and technological factors, the fraction of the available capital re-invested into production can be chosen almost at will (of course, there remains the limit of the total amount of available capital!).

Higher prices will lead to higher profits for producers and to the tendency to increase the fraction reinvested in new developments. It is also known that in the region near the production peak prices tend to be higher - as in the historical cases of whale oil and caviar and whale oil. In the case of caviar, the price rise was nearly exponential, in the case of whale oil, more like a logistic curve. Assuming that the fraction of reinvested capital varies in proportion to prices, some modeling may be attempted. Let me show here the results obtained for an exponential increase of the fraction of reinvested Capex.
  


I have also tried other functions for the rising trend of k3. The results are qualitatively the same for a linear increase and for a logistic one: the Seneca behavior appears to be robust, as long as we assume a significant increase of the fraction of the reinvested capex

Let me stress once more that these are not supposed to be complete results. These are just tests performed with arbitrary assumptions for the constants. Nevertheless, these calculations show that the Seneca cliff is a general behavior that occurs when producers stretch out their system allocating increasing fractions of capital to production. 










Who

Ugo Bardi is a member of the Club of Rome and the author of "Extracted: how the quest for mineral resources is plundering the Planet" (Chelsea Green 2014)