Sunday, February 26, 2017

Catastrophism is popular, but not necessarily right. Debunking the "Hill's Group" analysis of the future of the oil industry



"The Hill's Group" has been arguing for the rapid demise of the world's oil industry on the basis of a calculation of the entropy of the oil extraction process. While it is true that the oil industry is in trouble, the calculations by the Hill's group are, at best, irrelevant and probably simply plain wrong. Entropy is an important concept, but it must be correctly understood to be useful. It is no good to use it as an excuse to pander unbridled catastrophism. 


Catastrophism is popular. I can see that with the "Cassandra's Legacy" blog. Every time I publish something that says that we are all going to die soon, it gets many more hits than when I publish posts arguing that we can do something to avoid the incoming disaster. The latest confirmation of this trend came from three posts by Louis Arnoux that I published last summer (link to the first one). All three are in the list of the ten most successful posts ever published here.

Arnoux argues that the problems we have today are caused by the diminishing energy yield (or net energy, or EROI) of fossil fuels. This is a correct observation, but Arnoux bases his case on a report released by a rather obscure organization called "The Hill's Group." They use calculations based on the evaluation of the entropy of the extraction process in order to predict a dire future for the world's oil production. And they sell their report for $28 (shipping included).

Neither Arnoux nor the "Hill's Group" are the first to argue that diminishing EROEI is at the basis of most of our troubles. But the Hill's report gained a certain popularity and it has been favorably commented on many blogs and websites. It is t is understandable: the report has an aura of scientific correctness that comes from its use of basic thermodynamic principles and of the concept of entropy, correctly understood as the force behind the depletion problem. There is just a small problem: the report is badly flawed.

When I published Arnoux's posts on this blog, I thought they were qualitatively correct, and I still think they are. But I didn't have the time to look at the report of Hill's group in detail. Now, some people did that and their analysis clearly shows the many fundamental flaws of the treatment. You can read the results in English by Seppo Korpela, and in Spanish by Carlos De Castro and Antonio Turiel.

Entropy is a complex subject and delving into the Hill's report and into the criticism to it requires a certain effort. I won't go into details, here. Let me just say that it simply makes no sense to start from the textbook definition of entropy to calculate the net energy of crude oil. The approximations made in the report are so large to make the whole treatment useless (to say nothing of the errors it contains). Using the definition of entropy to analyze oil production is like using quantum mechanics to design a plane. It is true that all the electrons in a plane have to obey Schroedinger's equation, but that's not the way engineers design planes.

Of course, the problem of diminishing EROEI exists. The way to study it is based on the "life cycle analysis" (LCA) of the process. This method takes into account entropy indirectly, in terms of heat losses, without attempting the impossible task of calculating it from first principles. By means of this method, we can see that, at present, oil production still provides a reasonable energy return on investment (EROEI) as you can read, for instance, in a recent paper by Brandt et al.

But if producing oil still provides an energy return, why is the oil industry in such dire troubles? (see this post on the SRSrocco report, for instance). Well, let me cite a post by Nate Hagens:

In the last 10 years the global credit market has grown at 12% per year allowing GDP growth of only 3.5% and increasing global crude oil production less than 1% annually. We're so used to running on various treadmills that the landscape doesn't look all too scary. But since 2008, despite energies fundamental role in economic growth, it is access to credit that is supporting our economies, in a surreal, permanent, Faustian bargain sort of way. As long as interest rates (govt borrowing costs) are low and market participants accept it, this can go on for quite a long time, all the while burning through the next higher cost tranche of extractable carbon fuel in turn getting reduced benefits from the "Trade" creating other societal pressures.

Society runs on energy, but thinks it runs on money. In such a scenario, there will be some paradoxical results from the end of cheap (to extract) oil. Instead of higher prices, the global economy will first lose the ability to continue to service both the principal and the interest on the large amounts of newly created money/debt, and we will then probably first face deflation. Under this scenario, the casualty will not be higher and higher prices to consumers that most in peak oil community expect, but rather the high and medium cost producers gradually going out of business due to market prices significantly below extraction costs. Peak oil will come about from the high cost tranches of production gradually disappearing.

I don't expect the government takeover of the credit mechanism to stop, but if it does, both oil production and oil prices will be quite a bit lower. In the long run it's all about the energy. For the foreseeable future, it's mostly about the credit

In the end, it is simply dumb to think that the system will automatically collapse when and because the net energy of the oil production process becomes negative (or the EROEI smaller than one). No, it will crash much earlier because of factors correlated to the control system that we call "the economy". It is a behavior typical of complex adaptative systems that are never understandable in terms of mere energy return considerations. Complex systems always kick back.

The final consideration of this post would simply be to avoid losing time with the Hill's report (to say nothing about paying $28 for it). But there remains a problem: a report that claims to be based on thermodynamics and uses resounding words such as "entropy" plays into the human tendency of believing what one wants to believe. Catastrophism is popular for various reasons, some perfectly good. Actually, we should all be cautious catastrophists in the sense of being worried about the catastrophes we risk to see as the result of climate change and mineral depletion. But we should also be careful about crying wolf too early. Unfortunately, that's exactly what Hill&Arnoux did and now they are being debunked, as they should be. That puts in a bad light all the people who are seriously trying to alert the public of the risks ahead.

Catastrophism is the other face of cornucopianism; both are human reactions to a difficult situation. Cornucopianism denies the existence of the problem, catastrophism (in its "hard" form) denies that it can be solved or even just mitigated. Both attitudes lead to inaction. But there exists a middle way in which we don't exaggerate the problem but we don't deny it, either, and we do something about it!






Tuesday, February 21, 2017

MEDEAS: The Next Step after the Paris Climate Agreement


Jordi Solé, coordinator of the MEDEAS project speaks in Brno (Czekia) on Feb 15th, 2017. The European project MEDEAS has the ambitious goal of providing the tools necessary to put into practice the 2015 Paris agreement on climate


Let me start with something to dispel the confusion about what models are for. When you deal with complex, adaptive systems, models are NOT meant to predict the future. As John Gall said in his book on complex systems, "systems always kick back" - to which I may add, "and sometimes they kick back with a vengeance". (another way to express this concept is "forecasting always fails.")

But if dynamic models cannot predict the future, what are they good for? Simple, they are about being prepared for the future. Think of the Paris climate treaty of 2015. It was the result of millions of runs of various climate models, none of which claimed to predict "the" future. But these models are tools to prepare for the future; they tell you what may happen, depending on what you do. They are tools to shape political decisions. Out of all those runs, a goal was extracted, a setpoint, a number: "we don't want temperatures to rise of more than  2 °C and, for that purpose, there is a limit to the amounts of fossil fuels we can burn." It was a political decision that took into account not just what the models say, but what could be concretely achieved in the real world.  No model would give you that number as an output.The Paris agreement was a masterpiece of diplomacy and of communication strategy because it concentrated so much noise into a simple, stark, number: a goal to reach.

And there we stand: with Paris, we set the goal, but how do we get there? This section of policy planning was poor in Paris, where the best that could be done was to line up the INDCs, the intended nationally determined contribution; that is how single countries think they could reduce emissions. That's not planning, it is a first stab at the problem; it shows the good will to do something, but no more. As they stand, the INDCs won't get us far enough.

So, we are again at the task of getting prepared for the future. We know that we need to reduce carbon emissions, but how fast? Besides, it is not just a question of reduction, it is a question of substitution. We need to maintain the essential energy services to the world's population: surely, as a society, we can shed a lot of fat and keep going, but without a minimum of energy input, the system collapses. At the same time, we need to maintain the current input without exceeding the emissions limits. A difficult challenge, although not an impossible one.

Here, we need models, again. No model can tell you exactly how to get there, but models will tell you what is likely to happen given some choices and some decisions. And out of the models, you have to extract a concrete, politically feasible goal: how to invest the remaining resources into attaining the Paris objectives? In other words, what fraction of the world's GDP need to be invested in the transition to a renewable economy?

Giving an answer to this question is the ambitious task of the MEDEAS project which has now reached a full year of work and set up the basis for an extensive modeling effort. MEDEAS takes an approach mainly based on system dynamics, similar to the one of the well-known "The Limits to Growth" approach. It is not the only ongoing project in this area, others projects take different lines of approach. But in al cases the idea is to build up knowledge on what is needed for the transition. Some data are already available that tell us we need a major effort to replace fossil fuels fast enough. The transition that won't come by itself, pushed by purely economic forces. But we need to explore the issue more in depth before these considerations can be turned into a number that can be agreed upon by the interested parties. We need to take into account both what's needed and what is politically feasible. Then, we will have a goal to reach.

If you want to know more about MEDEAS, you can see the MEDEAS website. There is also a MEDAS newsletter, still in a preliminary phase. And, if you would like to be involved, contact me (ugo.bardi(strangething)unifi.it)


Below: an intense discussion held in Brno about the project with the coordinator, Jordi Solé from Barcelona and two Italian researchers from Florence, Sara Falsini and Ilaria Perissi. 









Thursday, February 16, 2017

Seneca and Medea



Sara Falsini (left) and Ilaria Perissi (right), researchers from Italy, illustrate their results at the MEDEAS project meeting in Brno, Czekia, on Feb 15-16 2017


I try to put up a post every week on this blog, but this week I was really swamped by a zillion things. Of these, two really overwhelmed me. The first is the MEDEAS meeting, right now ongoing in Brno, Czekia. The second is completing my new book, "The Seneca Effect". (the cover on the right is fanciful, also the title will be a little different),

Both things have a certain "ancient history" flavor, even though Seneca is a historical character whereas Medea is a mythological one (as far as we know). But they have many things in common, the book and the project are both aiming at understanding the future on the basis of the idea that the key of the future is in the past. (and, after all, Medea and Cassandra are similar mythological figures)

So, I can tell you that the MEDEAS project is going well, although it is an awful lot of work with several models being developed at different levels of detail and scope. The book, too, is almost finished, needs some retouching and some figures are being drawn. It should appear soon in English. Also the German version is being prepared.

Once all this has been accomplished, I can go back to blogging. Soon, I hope.



Monday, February 6, 2017

Checkmated on the "Climate Pause". The Mistakes Scientists Make


David Rose popularized the concept of the "pause" in global warming in a 2012 article on the Daily Mail. There never was such a thing, but it became a highly successful meme (*), still widely cited today as proof that global warming doesn't exist or it is nothing to be worried about. By now, the rapid rising temperatures of the past few years should have been consigned the "pause" to the oblivion it fully deserves. But a group of scientists offered to Rose the occasion to double down and to accuse them of manipulating the data. 


Years ago, I used to play chess, even though I always remained, at best, at a low-medium skill level. Once, I found myself playing with a local high-level player and I was thoroughly trashed, quickly checkmated. I offered my congratulations to him and he answered to me with something like, "Ugo, it is not that I am especially good. It is you who made mistakes with your moves. Make no mistakes, and nobody will ever checkmate you."

I think that was good advice that I still try to remember after many years. If you are defeated, it may be that your opponent is especially good, but it is also likely that he or she simply exploited your mistakes. Avoid making mistakes, and your life will be easier. But you need to recognize the mistakes you made and admit them.

This seems to be the problem with the present debate on climate science. Facing aggressive criticism, scientists keep making the most elementary communication mistakes. The latest disaster for science is the recent article by David Rose in which scientists are accused to be manipulating the data. Rose, you may remember, is the journalist who first diffused in the media the idea that there had been a "pause" in global warming. His 2012 article in the Daily Mail was a milestone in the meme war; with the "pause" (or "hiatus") still widely known and repeated as "proof" that global warming doesn't exist or that, at least, climate models don't work (*).

Obviously, the "pause" never was anything more than a perfectly normal oscillation - amplified by carefully choosing a specific interval of temperatures. The recent temperature increases broke all the warming records and that should have buried forever the "pause", together with other legends such as the claimed arrival of the planet Nibiru in 2012. But, no. Now David Rose doubles down with a new article in which he, this time, accuses scientists of having manipulated the data in order to make the pause disappear.

I don't think I need to tell you that Rose's latest article is a textbook example of logical inconsistency. First, he claimed the existence of the "pause" on the basis of temperature data that, evidently, he trusted. Now, he says that the data shouldn't be trusted because they don't show a pause. If there ever was an example of motivated reasoning, this is it.

Yet, communication is not just a question of formal logic. Take a tour of the Web and you'll see how many people are gleefully commenting on Rose's latest broadside against science. It is a landslide; the dam has given way: it is a true disaster for science. Maybe Rose is an evil genius in communication, but I think he is not. He is just exploiting the mistakes made by climate scientists.

This story is all about an article published in 2015 by a group of NOAA scientists who claimed that there is no evidence of a slowdown in the world's temperature increase. The article was perfectly good in scientific terms, but it was a terrible mistake in terms of communication. Why? Because it ignored a simple fact of life: in the mass media debate, mentioning a concept, even if for debunking it, has the effect of reinforcing the public perception that the concept is real.

This is a well known concept. On this issue, you may read a good article by Chris Mooney describing the "backfire effect" or, sometimes, the "boomerang effect". Among the many cases, it was found that having Barack Obama explicitly stating that he is not a Muslim tends to reinforce some people's belief that he is. And you surely remember the story of the "weapons of mass destruction" in Iraq. There never was any proof for their existence (and, indeed, they never existed). But the more the subject was debated, the more people became convinced that they existed.

In the end, it is simple: debunking doesn't work; on the contrary, it often reinforces the perception that the belief being debunked is true. So, it should have been obvious that a paper that attempted to demonstrate that there never was a "pause" would generate a backlash, one day or another. And it did.

Let me repeat: For what I can say, there is nothing wrong in scientific terms in the work by Karl et al. But place yourself in the shoes of a person who is not a scientist, won't you get the impression that the scientists are fiddling with the data? That's the point that the critics of science are making over and over and this message seems to be going through.

Maybe it was unavoidable that a review of the temperature data would lead to this result, but was it appropriate to publish a minor correction of a data set in a high-visibility journal? If it was in order to affect climate policies, it was a perfectly legitimate target, but only if based on rock-solid data. Didn't the people involved in this work realize that their corrections are debatable, to say the least? And how is it that no one in NOAA thought that in some quarters the corrections would be understood and described as politically motivated data manipulation? Do scientists always have to be so naive? 

Now, many scientists are trying to debunk Rose's article (**), but the problem remains the same: the more you mention the "pause", the more it becomes real for the public. And that's a victory for the enemies of science. It seems that, as scientists, we are falling over and over into the same traps. As long as we do that, we'll keep being checkmated by people who exploit our mistakes.





(*) About the power of the "pause" as a meme, note that even a Nobel prize in physics, Carlo Rubbia, became convinced that it was something real. You can hear him (in Italian) here saying that on minute 2.40 

(**) Note that climate scientists are debunking Rose who was debunking NOAA that was debunking Rose who was debunking climate scientists. Quite a trophic chain of debunking and counter-debunking. A true "metadebunking" that only confuses people and plays in the hand of the enemies of science.





Sunday, January 29, 2017

Another Defeat for Science: "Metallic Hydrogen"




This blob is supposed to be "metallic hydrogen" according to the claim of a group of Harvard scientists. Maybe. For sure, it is another disaster for the reputation of science and of scientists.


Another day, another disaster for Science. A group of researchers from Harvard claimed of having obtained for the first time "metallic hydrogen" in their laboratory. That gave rise to a series of improbable claims about the cornucopia of abundance that humankind could obtain from the discovery. Especially lyrical was "The Independent", in an article that was soon retracted and replaced with a more sober one their page, where they now say it was all a mistake. But the first article contained such gems as:

Now, in a stunning act of modern-day alchemy, scientists at Harvard University have finally succeeded in creating a tiny amount of what is the rarest, and possibly most valuable, material on the planet, 

metallic hydrogen could theoretically revolutionise technology, enabling the creation of super-fast computers, high-speed levitating trains and ultra-efficient vehicles and dramatically improving almost anything involving electricity. And it could also allow humanity to explore outer space as never before.

And more like this, and thank God they didn't mention flying cars but they got close.

Now, let's examine this story. First of all, "metallic hydrogen" is a legitimate target of investigation. It was theoretically predicted already about a century ago and believed to exist in the core of giant planets. From here onward, however, the whole story is just a mix of fantasy and bad science.

The claim comes from a test in which the researchers placed a sample of hydrogen inside a diamond anvil and compressed it at very high pressures. At some point, they saw something shiny appearing and they concluded that it was "metallic hydrogen." Immediately afterward, they proceeded to publish their story with all the associated outlandish claims of spaceships, alchemy, ultra-efficient vehicles, etc.

Now, when you start a career as a scientist, you are told that

1) Your experiments should be repeatable.

2) There be should be always proof - say, a blank test - that what you claim is not an artifact of your experimental setup.

3) You should never claim anything for which you have no evidence.

Consider this as a checklist and you'll see that the Harvard researchers should mark all three items as "failed." (1) Unbelievable but true: they didn't repeat their experiment, they didn't make a blank experiment, and they engaged in wild fantasies on what their result could mean or, at least, they didn't object on such fantasies being reported over the press.

Note that it is perfectly possible that the blob in the anvil could turn out to be metallic hydrogen but, at present, there is no justification for this early claim. Besides, there is strictly zero proof that metallic hydrogen could turn out to be stable at or near room temperature and hence useful for the multiple claimed miracles. To say nothing of the fact that a diamond anvil processes micrograms and it would be interesting to calculate how many of these anvils would be needed to produce the tons of fuel needed to power a spaceship (hint: trillions).

More evidence, if it was ever needed, of the general decline of science, underfunded, poorly organized, pushed and pulled in all directions at the same time by politicians, businesses, journalists, the public, and more - a disaster. And the results are what you would expect: the general defeat of science that we are witnessing nowadays.

The big problem, here, is that a lot of people are clearly starting to perceive that some scientists are trying to fool them. They don't like that and they may well arrive at the conclusion that all scientists are trying to fool them. And that's very bad because there are still plenty of good scientists who are producing good science and who are trying to alert humankind of the dangers ahead. But, in the general sinking of the scientific ship, bad and good science are lumped together and sent heading to the bottom.

Can this trend be reversed? Hard to say but, at least, we should do something to avoid that the overinflated ego of some scientists continues to lead science into this kind of disasters.




(1) Incidentally, this is exactly the same series of failures that we can attribute to Stanley Pons and Martin Fleischmann when they claimed to have discovered "cold fusion" in 1989. An even worse defeat for science, whose consequences are still felt.



Sunday, January 22, 2017

Trump: the Defeat of Science





Minutes after Donald Trump took office as President, the page on climate change of the website of the White House disappeared. This may be just a result of some internal protocol, but also the first stage of a coming "purge" of climate science and climate scientists. In any case, the election of Trump is a major defeat for science and we need to understand what mistakes we made to arrive at this point. I am writing here something that probably won't make me popular with my scientist colleagues, but I thought I had to write it.



Defeats are supposed to teach people how to do better; in theory. In practice, it often happens that defeats teach people how to become masters in blame-shifting. With some exceptions, this seems to have been the main result of the recent defeat of the Democrats in the 2016 presidential election, where we saw a truly spasmodic search for culprits: Putin, the Russian hackers, the Fake News, the Rednecks, the FBI, Exxon, the aliens from Betelgeuse, and more. Everything except admitting one's mistakes.

Even less soul searching has been performed by those who turned out to be among the major losers in this story: science and scientists. In particular, climate scientists saw their field wiped out from the White House Website minutes after President Trump took office. That may have been simply a question of protocol, but surely it is not a good omen for the future.

So far, scientists have reacted with appropriate outrage to possibilities such as Trump repudiating the Paris climate treaty. However, on the average, scientists seem to be completely unable to even imagine that there may be something wrong with what they have been doing. We may have here a good illustration of the principle expressed by James Schlesinger that "people have only two modes of operation: complacency and panic". Even though some scientists are starting to show symptoms of panic, most of them seem to be still in complacency mode.

Yet, for everything that happens there is a reason and if you invaded Russia in winter it is no good to blame the snow for the defeat. So, what did scientists do that led them to a situation that may turn out to be even worse than the retreat from Moscow for Napoleon's Grande Armée?

One problem, here, is that if scientists had wanted to present themselves to the public as a priesthood of acolytes interested only in maintaining their petty privileges, they succeeded beyond the rosiest expectations. Yet, I don't think that this is the problem. Overall, science is still a sane profession and very few scientists have been directly involved in financial scandals. The public perceives this and normally rates scientists as much more trustworthy than - say- journalists or politicians. And modern climate science, as part of the field of Earth sciences, is nothing less than a triumph of human knowledge. Truly a major advance of what we know on the way our planet and our ecosystem work.

The problem, in my opinion, is a different one. It goes deeper and it is not related to individual scientists or to specific scientific fields. It has to do with science as a whole and, in particular, with the inconsistent messages that scientists are beaming to the public. According to the results reported by Ara Norenzayan's in "Big Gods" (Princeton, 2013), people have a built-in "lie detector" in their minds that works by a heuristic algorithm: people will evaluate the truth of what they are told on the basis of consistency. Not only the message must be consistent in itself, but also the messenger must be consistent with the message carried. This is a fundamental point: people don't normally care about data and factual evidence: they care about the consistency of the message in their social environment; it is something that Dan Kahan has shown in a series of studies on the public perception of climate science.

So, if your local prophet tells you that you must be chaste, he'd better be chaste himself. If he tells you that you must make sacrifices and accept poverty, he'd better be poor himself. And chastity/poverty must be acceptable in your social environment. These are things that Francis of Assisi understood already long ago. Then, think of Donald Trump: why was he elected? It was, mainly, because Trump's political message was consistent with Trump himself. Trump was telling people that he would make America rich and powerful and that was perfectly consistent with the fact that he is rich and powerful himself. Because of this, Trump's message didn't trigger people's lie detector and Trump the unthinkable became Trump the unavoidable.

Getting back to science, the message of climate change is intimately linked to the need of making sacrifices. We are asking people to reduce their consumption, reduce waste, travel less, and the like. It is a perfectly legitimate message and many religious groups have been carrying similar messages successfully. Of course, it would never work if Donald Trump were to propose it; but why can't scientists propose it successfully? Scientists are not Franciscan monks, but normally they are not rich. I often tell my PhD students that they are exchanging three years of starvation for a lifetime of unemployment. I don't really need to tell them that: they know that by themselves.

The problem is that there exists another side of science where scientists are beaming out exactly the opposite message of that of the need of making sacrifices. It is the side of the "gee-whiz science" or, maybe, "Santa Claus Science", scientific research still operating along the optimistic ideas developed in the 1950s, at the time of the "space age" and the "atomic age". The message that comes from this area is, "give us some money and we'll invent some magic device that will solve all the problema." It is a message that's ringing more and more hollow and the public is starting to perceive that the scientists are making promises they can't maintain. Not only the various scientific miracles that were promised are not materializing (say, nuclear fusion) but many pretended scientific revolutions are making things worse (say, shale oil). Still, many scientists keep making these promises and a certain section of society accepts - even requires - them.

So, the name of the problem is inconsistency. Scientists are taking two different and incompatible roles: that of doom-sayers and that of gift-givers. And "inconsistency" is just a polite way to say "lie." White scientist speak with forked tongue. Ye can't serve God and mammon.

The result is that not just Donald Trump despises science; it is a consistent fraction of the public that just doesn't believe the scientific message, especially about climate. The fraction of Americans who think that climate change is a serious threat has remained floating around 50% - 60%, going up and down, but not significantly changing. It is trench warfare in the climate communication war. Things may get worse for science under the Trump presidency. It already happened at the time of McCarthy, why shouldn't it happen again?

At this point, good manners dictate that when you write about a problem, you should also propose ways to solve it. Of course, there are ways that could be suggested: first of all, as scientists we should stop asking money for things that we know won't work (the "hydrogen-based economy" is a good example). Then, science badly needs a cleanup: we should crack down on predatory publishers, fight data fabrication, establish transparent standards for scientific publications, provide for free results of science to those who pay for it (the public), get rid of the huge number of irrelevant studies performed today, and more. Personally, I would also like a science that's more of a service for the community and less of a showcase for primadonnas in white coats.

But, as we all know, large organizations (and science is one) are almost impossible to reform from inside. So, where is science going? Difficult to say, but it may need a good shake-up from the outside (maybe from Trump, although he may well exaggerate) to be turned into something that may be what we truly need to help humankind in this difficult moment. The transformation will be surely resisted as much as possible, but change is needed and it will come.



"No man can serve two masters: for either he will hate the one, and love the other; or else. he will hold to the one, and despise the other. Ye cannot serve God and mammon." (Matthew 6:24)











Tuesday, January 17, 2017

Amelie the Amoeba: How Things Grow



This academic year, I gave a lesson on the growth mechanism of complex systems. It is a fascinating subject that can be applied to several fields, from biology to economics. Since the students I was talking to were not specializing in complex systems (they were students of geology), I used a light tone and used "Amelie the Amoeba" an image for the growth mechanism of bacteria in a Petri dish of many other things dish. Then, the image above summarizes what I told them.

If you know about these matters, you can probably understand what the drawings show. If you don't, some notes are appropriate. So, here is a very brief summary of how things grow in the universe.

1. The "Solow" mode, or exponential growth. The name refers to the economist Robert Solow who proposed this model, but most economists today seem to argue that exponential growth is the natural, actually the only possible, mode of growth of the economy. They may not be completely wrong; after all, it is the way bacteria grow (for a while) in a Petri dish. So, Amelie the Amoeba is very happy to be growing exponentially, too bad that if she were to continues for a long time, she would eventually devour the whole universe.

2. The "Malthus" mode, also "Verhulst" or simply "sigmoid" mode. It takes into account the fact that the Petri dish contains a limited amount of nutrients and Amelie can't keep growing forever. Malthus was the first to apply this model to the human population, assuming that it would reach a certain limit and then stay there: contrarily to what commonly said, Malthus never predicted collapses. The concept of "collapse" was alien to him, but at least he was right in noting that all physical systems have limits.

3. The "Hubbert" mode or the "bell-shaped" curve. That's more like what could happen to Amelie in a Petri dish. Grow for a while, reach a "peak amoeba" size, and then shrink and die for lack of food. Hubbert applied the model to the oil production of the United States, predicting reasonably well the future of the extraction of "conventional" oil. And, if you try to do the test for bacteria (or amoebas) in a Petri dish, it works as well.

4. The "Seneca" mode. This is the name I gave to the kind of growth kinetics where the decline is much faster than the growth. It comes from something that the Roman philosopher Lucius Annaeus Seneca said in one of his letters ("increases are of sluggish growth, but the way to ruin is rapid") and it happens all the time, even to amoebas in a Petri dish.

5. The "Hokusai" mode. The Japanese painter Katsushita Hokusai never made mathematical models and he probably never knew what an amoeba is. But with his famous painting, "the wave", he provided a good visual impression of what happens when things get real bad. Not only decline is faster than growth, but the curve actually starts chasing you! Even amoebas can get nasty and eat your brain.

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)