Saturday, October 8, 2011

Exponential growth

Doomer literature is replete with stories of exponential growth and then collapse. It's one of their favorite themes. Some doomer sources (like Albert Bartlett, or the 7th fold) focus on exponential growth as their primary topic. In fact Albert Bartlett has famously claimed (famously in doomer circles anyway) that the inability of most people to understand exponential growth is one of the great problems facing the world today.

The reason exponential growth is a topic in doomer circles, is because exponential growth of almost any important quantity will lead to disaster before very long. For example, exponential growth of population, by 4% per year, would lead to 6.5 million times as many people in the world in 400 years, necessitating a massive die-off. And exponential growth of energy usage, by a few percent per year, would lead to the oceans boiling in only a few centuries. In most cases, sustained exponential growth leads to die-off or collapse before very long. Just look at colonies of bacteria or yeast, which (as doomers frequently point out) grow exponentially until they suffocate in their own waste or exhaust their food supply.

There is only one big problem, with all this talk of exponential growth and then collapse. The problem is: no important quantities are growing exponentially.

Take energy consumption as an example. Energy consumption is not growing exponentially. In fact, energy consumption per capita isn't growing at all, not even linearly, and hasn't grown much for decades. This point should be obvious to anyone over age 40, by just looking around and then remembering how things used to be. Do you use exponentially more electricity than in 1970? Do you set your thermostat 3% higher every year? Do you use exponentially more gasoline than in 1970? In fact, you probably use less gasoline, if your car in 1970 was anything like my parents' cars, which got about 10 mpg.

In fact, energy usage per capita has been essentially flat for the last 5 years or so, and was growing only very slowly in the 2 decades before that, and not at an exponential rate.

Well, even if energy usage per capita isn't growing exponentially, isn't the world population growing exponentially? Don't we face exponentially more people, and so exponentially more resource usage even if resource usage per capita remains the same?

No, the population of the world is not growing exponentially. In fact, the population is growing, but at a declining rate. Already, the rate of population growth has reached 0% in many industrialized countries, and is declining rapidly in developing countries. Furthermore, there is every reason to believe that the rate of population growth in developing countries will also reach 0%, since they're basically following the same pattern which industrialized countries have laid down. As a result, most professional demographers believe that world population will level off at between 10 and 12 billion people.

Well, isn't the economy growing exponentially? We see figures like "3% growth this year" which seems to imply it's growing exponentially, right? And, since we need energy for economic growth, doesn't that mean that the rate of energy usage is also growing at 3%?

First, economic growth isn't the same thing as growth in energy consumption. (This mistake is very common). The term "economic growth" refers to growth in production of things you can buy. If someone invents a new drug, he has caused the economy to grow, even if manufacturing that drug takes less energy than manufacturing the older equivalent.

Second, the economy is not growing exponentially. The rate of economic growth is delining everywhere. As economies mature, their rates of growth decline. This has already happened in all first-world countries, which do not enjoy anyhwere near the rates of growth of (say) China or India.

Thus, essentially no important physical quantity is growing exponentially1. Population is not growing exponentially. Energy usage is not growing exponentially. Industrial output is not growing exponentially. The economy is not growing exponentially. Food production is not growing exponentially.

Since these quantities are not growing exponentially, it would be a basic mathematical error to use exponential functions to model them.

Both population and energy usage will grow and then level off before very long. There is ample historical precedent for this.

NOTES

1 The term "exponential growth" refers to a mathematical function like this: f(t)=bt where b is constant. If b is not constant, then it's not an exponential function. None of the quantities listed in this article are growing according to an exponential function.

21 comments:

  1. Unfortunately Tom, I don't find this post very comforting at all. The Al Bartlett video provides a model and a concept which isn't invalidated by the fact that things in the real world aren't following f(t)=b^t. In fact, in the real world bacteria/yeast don't always follow exp. growth, but still they can overshoot then die off.

    Take an economy, which like it or not is a subset of the environment or the other way round. Our current way of living requires economic growth, at least according to those pretending to be in charge. Any percentage growth on previous growth will still follow what Al's video was saying; it is no comfort to economists to say the growth will level off, as then all the people that rely on growth will lose their livlihoods and eventually the whole thing collapses...as we're seeing right now in the financial world. Reality disagree's with what you are stating. Economic growth *has to* eventually relate to something from the Earth in the end. The new drug in your example wont be created from nothing and if the drug extends people's life..well there you go you now need more growth to provide for that as well.

    Human population, whilst not following the exponential function, still is growing, just not at as much as before. It is still going to be a massive problem. To disagree with that statement is a matter of faith, not mathematical. Within that population, amount consumed per person is increasing still in places like India and China. In your example, I'm sure the old China man remembers his childhood as using a *lot less* energy and probably didn't even have a thermostat.

    Species loss is increasing. Habitat loss is increasing. Whether this is linear or exponential or geometric isn't important, its still happening and it still greatly threatens us. I know you and DB think this is irrelevant, but we still rely on the environment no matter how much technology we have.

    Lastly, I disagree with your notion that it is wrong to use the exponential function to *model* the future. Egg's aren't spherical, but when modelling how long it takes to boil one you can approximate. In physics, my field of study, we use the exponential function all the time in models knowing that in the real world this isn't the case, but very close.

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  2. I'm also interested in this 'tribal' doomer versus non-doomer thing going on within the blogsphere; you might find this essay interesting. I met this guy and he was really interesting, you might also like it:

    http://www.energybulletin.net/node/53651

    Blogs like yours are good as they do provide something different to read, but I'd tone down the 'doomer thinks this' thing - it seems very playground. 'Doomers' aren't all stocking up on ammo, myself included (well the UK doesn't allow it). If it wasn't for the 'doomed' mindset, we wouldnt have people raising awareness on extinction or climate change.

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  3. "...the economy is not growing exponentially. The rate of economic growth is delining everywhere."

    Yes, and what a party it is. We're seeing right now what happens when an economy is predicated upon growth. Our fiat currency is loaned into existence - with interest - and the money supply must grow to keep up this "growth" and growth is the word every politician with a prayer of being elected will utter thousands of times on the campaign trail.

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  4. This might be of interest:

    http://ourfiniteworld.com/2011/10/10/the-united-states-65-year-debt-bubble/

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  5. The comments board seems to be broken right now, as I can't post anything longer than this msg. I'll post my response when the comment function is working again. Sorry for the delay, -john

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  6. gJ:
    "as then all the people that rely on growth will lose their livlihoods and eventually the whole thing collapses..."

    The economy won't collapse as people lose their jobs. We may have a recession, but not collapse! The economy will adjust because it's always adjusting.

    The economy can withstand zero growth without posing any risk of collapse.

    "In fact, in the real world bacteria/yeast don't always follow exp. growth, but still they can overshoot then die off."

    Almost nothing in the real world follows an exponential curve for very long. The question is: what is the mechanism for the attenuation of that curve. Die-off is only inevitable if nothing else is attenuating the exponential growth until die-off occurs. However that's not the case with population or energy consumption.

    "amount consumed per person is increasing still in places like India and China. In your example, I'm sure the old China man remembers his childhood as using a *lot less* energy and probably didn't even have a thermostat."

    I grant this, but economic growth will level off in China and India as they approach first-world standards of living.

    The reason those countries have a high rate of growth is because they're playing catch-up.

    "Economic growth *has to* eventually relate to something from the Earth in the end. The new drug in your example wont be created from nothing"

    Economic growth could just as easily be a reduction in the amount of materials or energy needed to accomplish something.

    Granted, that can't go on forever, since we can't reduce materials to zero. But I'm clearly not claiming that economic growth will continue exponentially forever at a constant base.

    "Species loss is increasing. Habitat loss is increasing. Whether this is linear or exponential or geometric isn't important, its still happening and it still greatly threatens us. I know you and DB think this is irrelevant..."

    Why do you assume I don't care about the environment? You're wrong about this. For example, I think that global warming is a serious crisis, and we must do something about it.

    However, that's just a different issue, which has nothing to do with energy doomerism. For some reason, these things get conflated. Global warming and energy doomerism get put in the same "camp", solely because they both predict something bad, even though they're not logically related.

    Whereas global warming is an accepted scientific conclusion, energy doomerism is a folk fringe economic theory, based upon a whole series of mathematical and logical errors.

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  7. gJ:
    "Lastly, I disagree with your notion that it is wrong to use the exponential function to *model* the future. Egg's aren't spherical, but when modelling how long it takes to boil one you can approximate. In physics, my field of study, we use the exponential function all the time in models knowing that in the real world this isn't the case, but very close."

    Eggs may not be spherical, but they're close enough that a sphere is a good model.

    On the other hand, an exponential function is not at all a good model for a non-exponential function, because the two will diverge drastically almost right away, and will diverge even more drastically the further you project into the future.

    An exponential function would only be a good model for a logistic function for very brief periods until an inflection point is reached.

    When creating a model, it would often be more reasonable to omit or alter every other detail in your model but retain the distinction between exponential and non-exponential growth. For example, look at the field of mathematical analysis of algorithms in computer science. In that field, people often use models which omit or alter everything except whether the running time is increasing exponentially, logarithmically, etc.

    In the doomer case, doomers are projecting decades into the future using exponential functions for quantities which aren't growing exponentially. By doing so, they obtain a result which is very different from, and not at all a good approximation to, what they would have obtained if they'd used the correct mathematical function. In this case, exponential functions do not constitute a good approximation.

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  8. Anon:
    "Our fiat currency is loaned into existence - with interest - and the money supply must grow to keep up this "growth" and growth is the word every politician with a prayer of being elected will utter thousands of times on the campaign trail."

    This may be true, and it may pose serious consequences for us. However the economy will still never collapse because it will adjust and eventually regain full employment.

    There may be recessions, bubbles, downturns, increasing prices, financial panics, prolonged unemployment, banking crises, and so on, in the future, as there have been repeatedly in the past. But there will never be collapse. The US and other industrialized countries will never revert to a pre-industrial state, short of nuclear war.

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  9. But there will never be collapse. The US and other industrialized countries will never revert to a pre-industrial state, short of nuclear war."

    I hope someone is able to retrieve that statement from a server someday for your edification.

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  10. Nuclear war is not that far-fetched. Neither is a handful of states seceding from the US. Maybe you should define "collapse" before you assert what can and cannot happen.

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  11. Tom thanks for your replies:

    The economy won't collapse as people lose their jobs. We may have a recession, but not collapse! The economy will adjust because it's always adjusting.

    I think this is in the eye of the beholder. To a very wealthy land-owner with a full pantry trading with other wealthy land owners the economy is still doing fine. The guy made jobless then homeless, in his mind it has collapsed. I think youre understating the severity of how bad things will get if there is mass unemployment - there will always be a base-line/basic economy, but I define collapse as the current system failing a large number of people so much so that it is forced to 'adjust' into something unrecognisable to the original form via a period of mass inactivity.

    The economy can withstand zero growth without posing any risk of collapse.

    Not for very long as we are seeing right now - as a previous poster said its not much of a party. There has to be some sort of reason why all western nations are obsessed with growth?

    Almost nothing in the real world follows an exponential curve for very long.

    This was ultimately the point of Al Bartletts video.

    I grant this, but economic growth will level off in China and India as they approach first-world standards of living.

    The reason those countries have a high rate of growth is because they're playing catch-up.


    By the time this happens, the Earth will be f**ked. If the population of China AND India reach even Europe's energy consumption levels, let alone the US's, in trying to approach 'first world standards' the level off will be irrelevant due to the amount of pollutants and carbon released. I personally don't think the resources, or energy, exist to make this possible in the first place. It will level off but only due to limits rather than human decision

    However, that's just a different issue, which has nothing to do with energy doomerism. For some reason, these things get conflated. Global warming and energy doomerism get put in the same "camp", solely because they both predict something bad, even though they're not logically related.

    Whereas global warming is an accepted scientific conclusion, energy doomerism is a folk fringe economic theory, based upon a whole series of mathematical and logical errors.


    Why aren't they related? Global warming is caused by carbon emissions which is caused (primarily) by energy consumption and resource consumption. The two are inextricable.

    doomers are projecting decades into the future using exponential functions for quantities which aren't growing exponentially. By doing so, they obtain a result which is very different from, and not at all a good approximation to, what they would have obtained if they'd used the correct mathematical function. In this case, exponential functions do not constitute a good approximation.>

    I think 'doomers' refer to the exponent function as its something the layman can relate to, even if it isn't mathematically correct (incidentally economics is far from mathematically correct but more notional). If you look at the human population graph (http://en.wikipedia.org/wiki/File:Population_curve.svg) it *looks* fairly exponential. If you couple energy usage with population then it isn't unreasonable to assume that energy usage *looks* exponential, and their point is, as you say, 'nothing in the real world follows an exponential curve for very long'. Whether you interpret this as a good thing or not comes back the to 'tribalist' view of doomers vs non-doomers. I personally think that an increasing population (exp. or not) coupled with a declining main energy source (inadequate replacements ) and declining environment (irrefutable) is a bad thing, and I don't think that's an unreasonable stance to take hence me being a 'doomer'.

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  12. Nuclear war is not that far-fetched. Neither is a handful of states seceding from the US. Maybe you should define "collapse" before you assert what can and cannot happen.

    I don't think this is an unreasonable request either - your definition of collapse would be useful. I'd define collapse as:

    the current system (economic, financial, environmental) failing a large number of people/organisms so much so that it is forced to 'adjust' in a violent and chaotic fashion into something unrecognizable to the original form.

    Thus financial collapse is *not* the end of financial transactions forever, but a period of violence and chaos with an emergent system that is unrecognizable to our current global economy - most likely localized and scaled down.

    Environmental collapse is *not* the end of life forever, but a period of violent and chaotic extinctions, die offs, die backs etc with an emergent recovering ecosystem unrecognizable (and unreliable for humans) to the original one.

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  13. gJ:
    "I think youre understating the severity of how bad things will get if there is mass unemployment ... I define collapse as the current system failing a large number of people so much so that it is forced to 'adjust'... via a period of mass inactivity."

    Don't assume that energy=jobs or anything similar. We had full employment in 1920 despite 75% lower per-capita energy usage.

    The consequences of declining oil will be a modest reduction in standard of living compared to what it would have been. We'll all drive Priuses in 25 years, and we'll transport goods using trains more and trucks less. But there still will be full employment much of the time, barring recessions which will be temporary.

    "If the population of China AND India reach even Europe's energy consumption levels, let alone the US's"

    Presumably they will reach Europe's energy consumption levels, and not those of the US. They have a population density and distribution similar to that of Europe.

    "I personally don't think the resources, or energy, exist to make this possible in the first place. It will level off but only due to limits rather than human decision"

    Don't assume that energy=oil. The Chinese and Indians will use any kind of energy to continue their economic growth, including breeder reactors and (in the last case) solar thermal, as those become necessary. They will also use any kind of resources available, if there are any substitutes. This would affect the rate of growth, but would not prevent their growth outright. Their growth will only stop when there is no additional usable energy of any kind.

    There are more than enough resources available for them to become 1st world nations, since we're not even using even 1% of the energy or minerals available at present and there are many substitutes for various things.

    "By the time this happens, the Earth will be f**ked... due to the amount of pollutants and carbon released."

    This may be true. I doubt we'll do anything serious to prevent global warming.

    "Why aren't they related? Global warming is caused by carbon emissions which is caused (primarily) by energy consumption and resource consumption. The two are inextricable."

    That's incidental. They're related in the sense of using the same word or dealing with the same very broad topic (energy, fossil fuels). In that sense, global warming is "inextricably related" to the phlogiston theory of fire, since they both deal with heat transfer, or the abiogenic theory of oil production, since they both deal with fossil fuels.

    Global warming and energy doomerism aren't logically related in any way. One doesn't imply the other, and they don't rely on the same evidence or even the same kind of evidence.

    In most regards, global warming contradicts energy doomerism. I've read the IPCC report, and they obviously aren't assuming a near-term peak in fossil fuels.

    "I think 'doomers' refer to the exponent function as its something the layman can relate to, even if it isn't mathematically correct"

    I think that's a charitable reading of the doomer literature. You're explaining their failed predictions by claiming that they never really meant it.

    From what I recall, many doomers were speaking of "overshoot" and "die off" around year 2006, and they meant it. They claimed that the human population would imminently revert to 2 billion. I'm not cherry-picking the outliers here. I'm talking about Savinar, Ruppert, Kunstler, Simmons, Heinberg, Orlov, Hanson, and many, many others, who were the leading figures in the doomer movement at that time.

    If you're claiming that these doomer theories are technically incorrect, then we agree on that point.

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  14. Anon:
    "I hope someone is able to retrieve that statement from a server someday for your edification."

    This is just asserting your conclusion.

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  15. Anon:
    "Maybe you should define "collapse" before you assert what can and cannot happen."

    The topic of this blog is energy doomerism, so I'm referring to collapse as defined by Savinar, Orlov, Heinberg, Kunstler, dieoff.org, etc etc.

    Obviously we could all die from a meteor hitting Earth and killing everyone, or from nuclear war, or from a large solar flare, or from an emergent disease. However those would be surprises. There is no mathematical curve indicating collapse as a mathematical inevitability by just extrapolating from present trends.

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  16. Tom:
    Global warming and energy doomerism aren't logically related in any way. One doesn't imply the other, and they don't rely on the same evidence or even the same kind of evidence.

    Tom I'm not sure I'm understanding you or vice versa. Im not saying that peak oil implies climate change. The two have futures that are bound together, and I think thats what the 'doomerism' is about (If we could not use the word 'energy doomerism' as I have said before it seems a bit playground - how about 'energy concerns'?). I don't think anyone has said peak oil *implies* or is the cause of climate change; that makes little sense.

    My general impression was that global warming caused by, among other human contributions, the release of CO2 into the atmosphere. With the aim of limiting CO2 emission this then has an effect on our energy policies. Surely the decline of oil, and in your previous post, the conversion to coal are a problem in relation to GW. Future historians could say "due to the peaking of oil they turned to coal, which was their fatal error". The fallout from the climate changing such as droughts and floods (as we have seen a sharp increase in severity in recent years) place additional strain on our energy systems. Additional irrigation requirements, changing patterns of food production, increased reliance on fossil fuel derived chemicals for food production, increased reliance on imported food etc all need additional energy. Everyone wont be driving priuses in the future if that particular city is under water, or the countries that export rare-earth metals fall into conflict due to the pressure of climate change. Kunstler, for all his faults of insisting on predicting actual dates, does have a good name for this which is 'converging crises'. Yes maybe if energy was our *only problem* then it could be dealt with or 'muddled through'. The colliding problems of climate, debt, popualtion, energy, antibiotic resistance, war on terror etc are real cause for concern.

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  17. "Im not saying that peak oil implies climate change. The two have futures that are bound together, and I think thats what the 'doomerism' is about"

    Wouldn't the peak of fossil fuels serve to mitigate climate change? Wouldn't it cause our co2 emissions to contract abruptly?

    It seems to me that global warming and "peakism" are mutually exclusive. If we face a near-term peak in fossil fuels, then concerns about global warming have been greatly overblown.

    I've read the IPCC report, and it assumes continued increasing use of fossil fuels for most of this century. That is the basis for its assumptions about how much co2 will be released, which in turn is the basis for its predictions of temperature increases.

    "If we could not use the word 'energy doomerism' as I have said before it seems a bit playground - how about 'energy concerns'?"

    I'm definitely not trying to sound insulting by using the term "doomer". I wouldn't even use the term, but I have no other terms which uniquely identify the people (Savinar, Orlov, Hall, etc) and theories (overshoot, etc) which I'm referring to. Saying "energy concerns" doesn't quite capture it, because almost everyone has energy concerns (for example, I have energy concerns, and so does the CEO of Exxon-Mobil). The term "energy concerns" is casting too wide a net.

    I'm referring to the ideas found in the works of Jevons, Charles Hall, Herman Daly, James Hanson, Orlov, Heinberg, Kunstler, Simmons, Duncan, and many, many others; and also the ideas found in books such as "The Population Bomb" and "Limits to Growth". These ideas are closely related, and are based upon the same assumptions, and are derived using the same methods. These ideas have been around for decades (centuries if you count Jevons). The ideas rely mostly upon certain kinds of curve-fitting and various incorrect assumptions.

    When I say "doomerism" I am referring to that network of closely-related ideas. The reason I use the word "doomerism" is because that's the only word in common usage which refers to those ideas.

    "climate, debt, popualtion, energy, antibiotic resistance, war on terror"

    I realize we face serious problems, as we always have. I acknowledge that some of the problems you listed are menacing (esp climate and war). I'm not trying to paint a rosy future.

    I was making a narrower point about energy doomerism, overshoot, die-off, etc. Even if we face serious problems, our problems are not the ones which doomers have identified.

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  18. Wouldn't the peak of fossil fuels serve to mitigate climate change? Wouldn't it cause our co2 emissions to contract abruptly?

    You're correct in saying CO2 emissions would contract abruptly and the current recession also did just that (http://www.euractiv.com/climate-environment/recession-cut-eu-co2-emissions-record-72-news-504252). However there is a little sting in the tail that quickly cutting emissions may make the problem worse due to 'global dimming' (where current atmospheric pollutants reflect some radiation into space. If we emitting tomorrow for whatever reason, these pollutants rinse out of the atmosphere in weeks). It's a bit of predicament as either fuels don't peak and the climate situation becomes ever more grave, or they do peak and the current Western way of living ceases to be viable.

    It seems to me that global warming and "peakism" are mutually exclusive. If we face a near-term peak in fossil fuels, then concerns about global warming have been greatly overblown.

    Not really - the CO2 is already out there in the atmosphere, and will stay there for hundreds of years. A near term peak in fossil fuels would result in other sources such as forests being used. Forests act as sinks of carbon as well as their use resulting in carbon emissions. A near term peak, as we are seeing, is resulting in more desperate and dirtier methods of oil extraction such as 'tar-sands' which apparently is the largest source of man made carbon to date (http://warincontext.org/2011/06/24/canadas-tar-sands-carbon-bomb/)

    "climate, debt, popualtion, energy, antibiotic resistance, war on terror"

    I realize we face serious problems, as we always have. I acknowledge that some of the problems you listed are menacing (esp climate and war). I'm not trying to paint a rosy future.

    I was making a narrower point about energy doomerism, overshoot, die-off, etc. Even if we face serious problems, our problems are not the ones which doomers have identified.


    Thats fair enough - I still think 'doomers' have/are serving a useful purpose by bringing these issues to the forefront and countering the corporate feel-good-noise out there. Ive been reading a book called Deep Survival by Laurence Gonzales which talks about people in life-threatening situations and who lives and who dies. A strong point he makes is that a consistent theme in survival, whether its disease or natural disaster or accidents, is that the ones who survive don't sugar coat the truth. The ones that don't survive are strangely the ones filled with 'hope'. I just have concerns that if we all start talking about 'could' solutions, hot fusion, solar arrays, artifical leaves, priuses - people get side tracked or placated into not caring as much because 'everything will be ok'.

    In a much used example of the proverbial boat hitting the proverbial iceburg I imagine the ones that don't survive are the ones that either run around screaming 'were doomed!' and the ones that run around saying 'back to the cabins, I'm sure they'll fix it! Boats don't sink exponentially anyway! :P'. The ones that would survive would be the ones that quickly accept the current situation and calmly find something that floats to cling on to.

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  19. "Thats fair enough - I still think 'doomers' have/are serving a useful purpose by bringing these issues to the forefront and countering the corporate feel-good-noise out there."

    The difficulty is that "doomers" try hard to tether themselves to legitimate scientific concerns like global warming. If "doomers" successfully associate themselves with climatologists, then make wrong predictions again (which they always will except by random chance, because their methods are mistaken) then they could easily throw AGW and other legitimate concerns into disrepute.

    Bear in mind that the political right will seize upon the minutest mistaken detail from anyone in the AGW community. Imagine the field day they would have if they could poke fun at the drastically wrong predictions of Charles Hall et al.

    Few people remember now that energy doomerism was actually quite common in the late 1970s. Few people know that many of the doomer ideas which are current now (like declining EROI, etc) are recycled from the late 1970s. For a brief period during the 1970s, doomers actually convinced a president of the United States (Jimmy Carter) that energy decline was imminent. Carter then had a televised address in which he claimed that fossil fuels were near their peak and we faced catastrophe unless we started adjusting right away. When the catastrophe didn't happen, it did not create a respectful legacy for Carter.

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  20. You can quibble over whether debt, population or energy use is growing in a strictly exponential rate or not, but it really doesn't matter - they're all growing at a nice clip. The inescapable facts are that we humans have tripled our numbers since oil was first pumped, we've just passed 7 billion, and despite all of that, the US standard of living is declining even as we consume oil faster per capita than any other nation on earth.

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  21. "In fact, the energy available to us can grow exponentially with any EROI higher than 1. The reason is because the output of any plant can be used to build several other plants, each of which can then be used to build several more plants, and so on......"

    The fantasy lives on.

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