Seneca's gamble: why the road to ruin is rapid

Originally published on "Cassandra's Legacy" on Monday, February 2, 2015

Why people can so easily destroy the resources that provide their livelihood? Fishermen, for instance, have destroyed fisheries over and over, and every time they refused to take even the most elementary precautions to avoid disaster. Eventually, I came to think that it is related to a basic miswiring of the human mind: the "gambler's fallacy". Fishermen, it seems, see fishing as it were a lottery and they redouble their efforts thinking that, eventually, they will get lucky and strike it rich. Alas, it doesn't work in this way and all what they obtain is to destroy the fish stocks and create a spectacular collapse of the fishing yields. This way of creating one's own ruin could be termed "Seneca's gamble", from the words of the Roman philosopher Lucius Annaeus Senecawho stated that "the road to ruin is rapid". 

The "Martingale" is a strategy to be played with games which have a 50% chance of winning. It consists in doubling one's bet after every loss, believing that, eventually, a win will pay for the previous losses and provide a gain.

The Martingale is an example of the "gambler's fallacy". Typically, gamblers tend to think that some events - such as the numbers coming out of the wheel in the roulette game - are related to each other. So, they believe that, if the red comes up several times in a row, it is more probable that the black will come out the next spin. That's not true, of course, and the Martingale is a surefire way to ruin oneself, and to do that very rapidly. Nevertheless, many people find the idea fascinating enough that they try to put it into practice. It is the effect of a bad miswiring of the human mind.. 

The gambler's fallacy may explain some aspects of the human behavior that would be otherwise impossible to understand. For instance, in a previous post I was showing this figure, describing the yields of the UK fishing industry (from Thurstan et al.).

Compare the upper and the lower box, and you'll see that the fishing industry was ramping up at an incredible speed their "fishing power," just when fishing yields had started to decline. Note also how they still had a lot of fishing power when the fisheries had all but collapsed. How could it be that they kept fishing so much even when there was little or nothing left to fish?Thinking about this matter, we can only come to the conclusion that fishermen reasoned like gamblers at a betting table. In other words, they were playing a sort of "fishing Martingale", doubling their efforts after every failure.

Gamblers know - or should know - that casino gambling is a negative sum game. Yet, the gambler's fallacy makes them think that a streak of bad results will somehow increase the probability that the next bet will be the good one. So, they keep trying until they ruin themselves.

Now, consider fishermen: they or should know  that, at some point, the overall yield of the fishery has become negative. But, like gamblers playing roulette, they believe that a streak of bad luck will somehow increase the probability that the next fishing trip will be the good one. So, they keep trying until they ruin themselves.

The mental miswiring that gives rise to the behavior of gamblers and fishermen can create even larger disasters. With mineral resources, we are seeing something similar: operators redoubling their efforts in the face of diminishing returns of extraction; the story of "shale gas" and "shale oil" is a typical example. Maybe it is done hoping that - somehow - the destruction of one stock will increase the probability to find a new one (or to create one by some technological miracle). So, instead of trying to make mineral stocks last as long as possible, we are rushing to destroy them at the highest possible rate. But, unlike fish stocks that can replenish themselves, minerals do not reproduce. Once we'll have destroyed the rich ores that created our civilization, there will be nothing left behind. We will have ruined ourselves forever.

In the end, the gambler's fallacy is one of the factors that lead people, companies, and entire civilization to a rapid collapse. It is what I have called the "Seneca Cliff" from the words of the ancient Roman philosopher who first noted how "the way to ruin is rapid". In the case described here, we might call it the "Seneca gamble" but, in all cases, it is a ruin that we create with our own hands.

The shale oil "miracle": how growth may falsely signal abundance

Originally published on "Cassandra's Legacy" on Tuesday, February 24, 2015

Oil production (all liquids in barrels per day) in the US and Canada. (From Ron Patterson's blog). Does this rapid growth indicate that the resources are abundant and that all the worries about peak oil are misplaced? Maybe not....

Sometimes, we use a simple metric to evaluate complex systems. For instance, a war is a complex affair where millions of people fight, struggle. suffer, and kill each other. However, in the end, the final result is seen in terms of a yes/no question: either you win or you lose. Not for nothing, General McArthur said once that "there is no substitute for victory".

Now, think of the economy: it is an immense and complex system where millions of people work, produce, buy, sell, and make or lose money. In the end, eventually, we think that the final result can be described in terms of a simple yes/no question: either you grow, or you don't. And what McArthur said about war can be applied to the economy, as well: "there is no substitute for growth".

But complex systems have ways to behave and to surprise you that can't be reduced to a simple yes/no judgement. Both victory and growth may well create more problems than they solve. Victory may falsely signal a military might that doesn't really exist (think of the outcome of some recent wars....), while growth may signal an abundance which is just not there.

Take a look at the figure at the beginning of this post (from Ron Patterson's blog). It shows the oil production (barrels/day) in the US and Canada. The data are in thousand barrels per day for "crude oil + condensate" and the rapid growth for the past few years is mostly due to tight oil (also known as "shale oil") and oil from tar sands. If you follow the debate in this field, you know that this growth trend has been hailed as a great result and as the definitive demonstration that all worries about oil depletion and peak oil were misplaced.

Fine. But let me show you another graph, the US landings of North Atlantic Cod, up to 1980 (data from Faostat).

Doesn't it look similar to the data for oil in the US/Canada? We can imagine what was being said at the time; "new fishing technologies dispel all worries about overfishing" and things like that. It is what was said, indeed (see Hamilton et al. (2003)).

Now, look at the cod landings data up to 2012 and see what happened after the great burst of growth.

I don't think this requires more than a couple of comments. The first is to note how overexploitation leads to collapse: people don't realize that by pushing for growth at all costs, they are destroying the very resource that creates growth. This can happen with fisheries just as with oil fields. Then, note also that we have here another case of a "Seneca Cliff," a production curve where the decline is much faster than growth. As the ancient Roman philosopher said, "The road to ruin is rapid". And this is exactly what we could expect to happen with tight oil

Sandeels: another Seneca cliff

Originally published on Cassandra's Legacy on Thursday, January 22, 2015

Image from http://www.climateandfish.eu/default.asp?ZNT=S0T1O-1P192

Once you start looking for "Seneca Cliffs" in the exploitation of natural resources, you find them all over the scientific literature. This is my latest find of a production curve where decline is much more rapid than growth: the landings ofsandeels. If you don't know what a sandeel is, here is one: 

In the report (2007), where I found the curve shown above, the authors discuss the causes for the collapse of the fishery, especially in view of climate change. They don't seem to arrive to any definitive conclusion and they don't use the dreaded term "overfishing". But from the fact that trawlers were used in this fishery, I think it is clear that the fish stock was being destroyed in a process similar to the one that led to the collapse of the whole UK fishing industry. The more resources were aggressively thrown at trying to maintain production, the more the fish stock was depleted. The end result was the rapid collapse observed.

So, as in several other cases, we have a classic example of the "Seneca Collapse", that is a production curve where decline is much more rapid than growth. Below, you can see the Seneca curve as shown in a simulation carried out by system dynamics that takes into account the increased capital expenditure in fishing equipment (the model is described here). 

As Seneca said, "the road to ruin is rapid", indeed.

Seneca again: the collapse of the UK fishing industry

Originally published on Cassandra's legacy on Jan 6 2015

Image from a 2010 article by Thurstan, Brockington, and Roberts. It describes the cycle of the UK fishing industry, which collapsed because ofoverfishing in the late 1970s.

The two graphs above (from a 2010 article by Thurstan et al.) speak by themselves. We have here a real life example of the overexploitation of natural resources; that is, of the tendency of people of destroying their own sources of wealth. Other classic examples can be found with the 19th century whaling industry and with the Canadian cod fishery.

Overexploitation typically generates the "Hubbert curve," the name given to a bell-shaped production cycle best known for the case of crude oil, but affecting all the resources which can be exploited faster than they can reform by natural processes. This behavior can be explained by means of mathematical models, but, qualitatively, it is the result of the falling profits generated by the diminishing resource stock. In the long run, lower profits discourage investments and the result is a general production decline. A particular case of this mechanism is when the industry initially reacts to diminishing returns by aggressively increasing the amount of capital invested. In this case, the stocks of the resource are depleted very fast and the result is a crash of the production rate; we still have a bell shaped curve, but skewed forward. The rapid decline that occurs after the peak is what I called the "Seneca Cliff." 

There are several historical examples of the Seneca cliff; in the case of fisheries, it is especially evident in the case of the Canadian cod fishery and for the Caspian Sturgeon; but it is evident also in the case of the UK fishing industry. Note, in the figure above, the steep decline of the landings of the late 1970s, it is significantly steeper than the growth of the left side of the curve. This is the essence of the Seneca mechanism. And we can see very well what causes it: the start of the decline in production corresponds to a rapid growth of investments. The result is the increase of what the authors of the paper call "fishing power" - an estimate of the efficiency and size of the fishing fleet.

The results were disastrous; a textbook example of how to "push the levers in the wrong directions", that is, of a case when the attempt to solve a problem worsens it considerably. In this case, the more efficient the fishing fleet was, the more rapidly the fish stock was destroyed. This is a classic mechanism for falling down the Seneca cliff: the more efficient you are at exploiting a non renewable (or slowly renewable) resource, the faster you deplete it. And the faster you get into trouble.

This case, as others, is such a staggering disaster that one wonders how it was possible at all. How could it be that nobody in the fishing industry or in the government realized what was happening? In their article on this subject, Thurstan and his colleagues don't comment on this point, but we can cite an article by Hamilton et al. on the Canadian Atlantic Cod fishery, where they say "Some say they saw trouble coming, but felt powerless to halt it."That seems to be not describing not just the fishing industry, but our entire civilization.

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

Originally published on Cassandra's Legacy on Monday, December 15, 2014

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 newtechnology 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 modeldescribing 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 byBardi 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!