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Exponential growth is a short term thing

During a discussion with other board members of the National Space Society, someone noted this lecture by Albert Bartlett, a retired Physics prof. at the University of Colorado-Boulder on the subject of “Arithmetic, Population, and Energy,” After watching it, I felt a discussion was in order on how someone can say things that are absolutely correct and yet not map them correctly to the boundary conditions in the reality we actually inhabit.

I had been putting this off due to an overly busy schedule but I finally had a little time free this morning and watched all eight sections. 1-6 are math; the remaining two are primarily politics. What I find wrong is what is missing. We all know how exponentials work and we all know that they do indeed stop in real life. In electronics a rising exponential means clipping, feedback, etc as the circuit response transitions from linear to nonlinear.

It is also present in economics and in demographics both of which have the S curve as a fundamental form. The S is a combination of a rising exponential and a falling exponential glued together at an inflection point. This is the ‘growth’ curve that matches the Bell Curve he shows for oil production. The two are closely related mathematically.The inflection point on the S-curve is the peak on the Bell.

A very big missing fact in his discussion is that population growth peaks in the mid to late part of this century by all the demographic studies I have seen. I was part of a University wide collection of summer seminar givers on this subject at CMU back in the early 1980′s (I presented in one course on the implications of the space option naturally). The UN projections that were part of our study guide showed a family of curves of which we seem to have followed the lower growth curve in the ensuing decades.

Even then it was known that the biggest factor reining in population growth is women’s education and per capita wealth. One could even say the faster economies of the third world grow, the sooner they are likely to get through the demographic transition (ie the S curve in populations) and the lower their final population will be. Europe went through the transition a century ago; the US in perhaps the 40′s (I would have to research that timings, I do not remember them precisely). China has gone through it also now and the population is still going up only because there is a coasting phase due to previous growth. In the terms I used earlier, they have passed the inflection point of the S curve or the peak of the Bell Curve.

Europe faces a collapsing population, a falling exponential, something that was not really predicted 30 years ago. Russia has a demographic disaster on its hands. Very few places still show population growth and those are primarily in the Middle East. It is no surprise this an area dominated by a culture where women are allowed the least control of their lives and bodies and are least likely to be educated.

The good professor also ignores economics although they show indirectly in his curve. Economics, not a bunch of self-congratulatory tree huggers, is the driving force behind a growing efficiency in products or the useful part of that efficiency at least. The market gives a price signal on a resource; capitalists then innovate to find ways to do the same with less or with different so they can make more money. This was the most important message from Julian Simon’s writings.

I found it interesting how he went out of his way to denigrate Julian Simon rather than engage the very real ideas Simon espoused. Most notable was the uncomfortable fact of the bet Simon won against Paul Erlich on the declining real price of resources. Perhaps the difference is that Simon’s world is one in which nonlinear dynamics rule. Simple linear models of classical physics are simply not a good model for economics or civilizations over the long term.

So, absolutely, long term exponential growth would be a bad thing if it ever really happened. But it will not. Population on the planet will stabilize; per capita use of resources will rise for a while after that until everyone in the world comes up to the wealth level of us hated capitalist Americans who have the temerity and the creativity to make our lives better than those with crap governments and worse cultures. They will emulate us, not vice versa.

Market signals and competition will drive down the per capita use of resources and the energy per unit of production; if we get lots of solar power satellites the actual energy per capita may go way, way up… but not necessarily as an exponential, or at least not one that runs for a long period of time.

I foresee stable planetary populations living at levels of wealth beyond the wildest dreams of our most creative billionaires. Since I just saw “Atlas Shrugged” yesterday afternoon, I very much hope we do not make our billionaires go on strike. They are the ones who make real things happen. Without the generations of their kind we would all still be spending our days watching the backside of a mule.

8 comments to Exponential growth is a short term thing

  • Laird

    “Population on the planet will stabilize; per capita use of resources will rise for a while after that until everyone in the world comes up to the wealth level of us hated capitalist Americans”

    Or until our wealth level declines to theirs. Which, frankly, seems more likely given current trends.

  • Richard Thomas

    Very true, Laird. Population follows resources. Government growth -> wasted resources -> less resources (all other things being equal) -> population decline.

  • John B

    Market signals and competition will drive down the per capita use of resources and the energy per unit of production; if we get lots of solar power satellites the actual energy per capita may go way, way up… but not necessarily as an exponential, or at least not one that runs for a long period of time.

    This will cause a massive energy input to the planet if it occurs on a massive scale, and the result of that will be?

    Additionally.
    I admire your optimism but you do leave out the problem of human nature.
    My perception is that mankind’s technological ability has outstripped its wisdom.
    There is an answer to that, in human terms though – a benevolent Big Brother!!
    Although, when Big Brother’s technological ability outstrips his wisdom, what will we do then?

  • JohnB writes:

    My perception is that mankind’s technological ability has outstripped its wisdom.

    That is an interesting thought (and I’ll not comment on his religious follow-on).

    However, whenever such interesting thoughts are expressed, I want to go further.

    Could we please have plots over time (at least say 3,000 years; anyone can contribute, not just JohnB) of mankind’s technological ability and mankind’s wisdom.

    Then we can see if one is outstripping the other.

    Best regards

  • I went and looked at where the videos come from; it’s wonderingmind42.

    I then went to their main page where there is a video on what we should do about global warming. The duration is a second under ten minutes, so it is a shorter watch than Dale’s marathon of 8×9:30 minutes.

    Their thesis is that the call of Armageddon, combined with the argument from authority, outweighs any counter-argument.

    Guess where that puts them WRT my opinion.

    Now, it is true that a person or group can be wrong on one thing and right on another. But if substantially their whole philosophy of argument and science on the one thing is built on sand, …

    Best regards

  • Dale Amon

    But the math is correct. It is just applied with an linearity assumption that is not realistic over an extended period. He also says as much; but he embraces a doom and gloom result whereas I am a bit more positive about how things will change.

  • Bill Johnson

    exponential ‘growth’ is always short term. If you ever looked at a graph of exponential growth, you see the line on the graph shooting damn near straight up on the right hand side. That ‘damn near’ is the short term of which I speak. notice it takes very little of the x-axis (usually time). that’s exponential – muddling along, until one day, bang, we’re all in the stratosphere.

    And if you only see the previous portion of the curve, you’re hard pressed to discover the exponential hidden within. but then one day, bang.

    as in – when the world finally quite trusting the US government to cover it’s debts, fecal matter will distribute quite rapidly from the Air Movement Device (actual IBM name for a fan). bang. you won’t have time to react before it’s just too late.

  • Bill Johnson

    sorry – quite ===> quits