population growth not exponential

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  • Wed, Apr 14, 2010 - 09:11am

    #11
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    Re: population growth not exponential

Hi VF

Please bear in mind that Dr Martenson has had the Crash Course completed for over a year, with all possible chances to change information within it with supporting arguement from ‘Working Joe’s’ to Mathematical Scientists, based on close to 1.5 million viewings.

The crash course should be as open to criticism now as when it was first posted. Just as scientific theories are as robust as the latest test regardless of how many tests have previously been carried out. If we stop questioning something because it has survived challenge up until now then we might as well stop thinking for ourselves altogether. Sorry but as a scientist my training pretty much forces me down this line!

I do agree that the message about human population is important and that the human footprint is huge and getting worse. Maybe I am nitpicking the detail but CM made a point in the first chapter to explain the importance of the difference between fact, opinion and belief. It is the facts that provide the edifice for the whole argument and belief construct that follows. And it is a fact that population growth is no longer exponential. You may believe this doesn’t make much difference but, as I’ve responded to Set, you can get widely divergent results depending on it. For one thing it is not even open to question that continued exponential growth is unsustainable – as someone once said only an economist would believe such a thing! But it is very much open to opinion/belief as to whether a population leveling off at 9bn is sustainable – we won’t know until or if we get there.

The belief that the facts need to be dumbed down or approximated is again a complete anathema to me as a scientist. It’s not difficult to present growth extrapolations based on current rate changes and such extrapolations are not hard to grasp for anyone capable of reading a graph (see Wiki entry posted previously). Without such facts being presented accurately CM is in danger of not only misrepresenting the situation but also of losing credibility in the wider community, or at least the more scientifically minded part of it. Which would be a shame because, as I’ve said, I completely agree that the message about our impact on the planet and its resources is extremely important.

  • Wed, Apr 14, 2010 - 12:54pm

    #12
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    Re: population growth not exponential

All of my work is open to critique at all times.

Without such facts being presented accurately CM is in danger of not only misrepresenting the situation but also of losing credibility in the wider community, or at least the more scientifically minded part of it.

As a scientist, I think precision is important, and it is a trait I share – to a point.

Briefly, I would like to point out that I have (very carefully) never made any claims that human population will continue to expand exponentially, you might have inferred that into the presentation.

Here’s the text:

In this particular case you are looking at a chart of something that historically grew at less than 1% per year. It is world population and because it is only growing at roughly 1% per year we need to look at several thousands of years to detect this hockey stick shape. The green is history and the red is the most recent UN projection of population growth for just the next 42 years.

I have drawn the very clear and completely defensible conclusion that human population has been growing exponentially up to now, but all I do for the next 42 years is cite the most recent data that exists from the UN.  I never actually state anything about my own predictions for human population growth over that time frame (precisely because I didn’t want to get bogged down in the arena of making and defending such predicitons). 

However, I could also say that right now human population is still growing on a percentage basis every year which means that it is still growing exponentially.  You’ve made the claim, based on extrapolating a recent change in the rate of growth, that the future will see population growth will go to zero or even negative growth which itself is a prediction – something I studiously avoid because predictions open up a whole can of logical worms, are hard to defend, and leave your critics a lot of easy territory to exploit.  Once you start making predictions the next thing you know you are stuck in a sea of pesky facts.

For example, I might trot out that US fertility rates have been going up lately:

The fertility rate among Americans has climbed to its highest level since 1971, setting the country apart from most industrialized nations that are struggling with low birthrates and aging populations.

The fertility rate hit 2.1 in 2006, according to preliminary estimates released by the National Center for Health Statistics. It’s a milestone: the first time since shortly after the baby boom ended that the nation has reached the rate of births needed for a generation to replace itself, an average 2.1 per woman.

Then I might note that despite this “flattening out” you’ve cited, that for some reason we still seem to be adding record breaking numbers of new babies to the landscape:

The journal Pediatrics has published its annual report on birth and pregnancy in the United States, and it found that the number of babies born in 2007 — 4,317,119 — was the highest ever recorded.

The birthrate rose in all age groups, including teenagers, whose birthrate had been declining since 1996. (A Guttmacher Institute report last month came to a similar conclusion.) Rates for women in their 30s were the highest since 1964, the last year of the postwar baby boom.

Births to unmarried women in 2007 increased to the highest levels ever measured, rising 4 percent over 2006. Almost 40 percent of all births were to unmarried women, and there were increases in births to single women of all races, including those identified as Hispanic.

So even though the rate might have come down some in the past, it is now headed up again in the US and we are still adding more new humans than at any time in history to the surface of the planet year after year.  Perhaps this will decline to zero at some point in the future as you’ve predicted.  Maybe not.  Perhaps we could argue that for something to be considered “exponential” as a purist would define it in a textbook that the rate has to be constant, and not wobbling about.  Okay, but what does that do for us in terms of effectively communicating the crux of the issue to the widest possible cohort of people?  See? We’re down a rabbit hole.

The facts, as they stand are precisely what I put in Chapter 3 and which VF has recited above.  We know how fast population has grown up to now, and we can extrapolate into the near future using currently available data on lifespans and birth rates.  That gets us to 9 to 10 billion by 2050.

What additional clarity, or illumination, do you see as being offered by wading into a relatively complicated prediciton about the precise mathematical characterization that we may, or may not, experience in 40 years?

How will this help to make a better decision today?  How does this deepen our understanding or change the nature of the predicament?  If it turns out that even 7 billion people are too many to sustain, what changes in our thinking by knowing that the final rate of growth that brings us to 9 billion in 2050 is not really exponential because its either falling, or rising, or doing something that doesn’t quite fit the definition?

After all this discussion, are any of us any closer to accepting the nature of our predicament, our responsibility for the future, and taking concrete actions to try and make the best of it?  If so, then I’ll have these sorts of discussions all day long.  If not, then I respectfully suggest that there are more important things to be doing.

  • Wed, Apr 14, 2010 - 01:51pm

    #13
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    Re: population growth not exponential

Touche!

  • Wed, Apr 14, 2010 - 02:49pm

    #14
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    Re: population growth not exponential

Cool
~ VF ~

  • Wed, Apr 14, 2010 - 07:09pm

    #15
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    Re: population growth not exponential

Hi Chris

Firstly thank-you for taking the time to respond in such detail. Before replying to your points I should perhaps put my original post in context because I imagine it must have come across as rather confrontational, esp for a new member! Overall I think you’ve done an excellent job of bringing together some difficult but important issues and that’s the main reason I’m here. If I appear critical it’s a consequence of my scientific training and natural awkwardness to focus and criticise what I see as being weak points rather than praising the much larger volume of praiseworthy effort.

Briefly, I would like to point out that I have (very carefully) never made any claims that human population will continue to expand exponentially, you might have inferred that into the presentation.

Fair comment although I would stick to my original assertion that the impression from the presentation is that population growth is currently as well as historically exponential. And as we all know impression is everything. The fact that the responses I got were along the lines of how important it was that I understand the exponential function (I do!) suggests that others got the same initial impression that I did.

You’ve made the claim, based on extrapolating a recent change in the rate of growth, that the future will see population growth will go to zero or even negative growth which itself is a prediction – something I studiously avoid because predictions open up a whole can of logical worms, are hard to defend, and leave your critics a lot of easy territory to exploit.  Once you start making predictions the next thing you know you are stuck in a sea of pesky facts.

Also fair. However when you present the perils of exponential growth and include population in that presentation then you make an implicit if not an actual extrapolation in the mind of the reader – i.e. that population growth will continue to grow exponentially. Even if the small print sais otherwise 😉 Also I would say that extrapolating from an existing trend is fair play as long as you make the caveat that it is valid only if the current trends continues. Which is where we get to my main point – that extrapolation from a true (constant rate) exponential growth rate is very divergent from extrapolation from a reducing rate. They have hugely different implications for both future population levels and the perils those levels may bring.

The facts, as they stand are precisely what I put in Chapter 3 and which VF has recited above.  We know how fast population has grown up to now, and we can extrapolate into the near future using currently available data on lifespans and birth rates.  That gets us to 9 to 10 billion by 2050

True but there is still a big difference between 9bn and still growing and 9bn and plateaud.

What additional clarity, or illumination, do you see as being offered by wading into a relatively complicated prediciton about the precise mathematical characterization that we may, or may not, experience in 40 years?

How will this help to make a better decision today?  How does this deepen our understanding or change the nature of the predicament?  If it turns out that even 7 billion people are too many to sustain, what changes in our thinking by knowing that the final rate of growth that brings us to 9 billion in 2050 is not really exponential because its either falling, or rising, or doing something that doesn’t quite fit the definition?

Understanding whether we are likely to plateau around 9bn or continue growing exponentially makes a potentially huge difference and how we might go about tackling the issue. If we are confident (acknowledging the uncertainty we’ve both highlighted) that 9bn is going to be a plateau then we can more easily and quantifiably address the question as to exactly how the Earth can sustain such numbers (I think you and I are probably in agreement that it can’t but that’s another debate). If the belief is that population will still be growing exponentially even at 9bn then it’s a whole different predicament!

After all this discussion, are any of us any closer to accepting the nature of our predicament, our responsibility for the future, and taking concrete actions to try and make the best of it?  If so, then I’ll have these sorts of discussions all day long.  If not, then I respectfully suggest that there are more important things to be doing.

Happy to draw a line under this discussion and move on. For what it’s worth I do recognise stubborness as one of my character flaws! No offence intended with any of my comments and I reiterate my support for what you are attempting. Who knows I might post something complimentary one day 😉

  • Wed, Apr 14, 2010 - 09:04pm

    #16
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    Re: population growth not exponential

“The fact that the responses I got were along the lines of how important it was that I understand the exponential function (I do!) suggests that others got the same initial impression that I did.”

But do you…?

As I explained in an earlier post (as Chris himself said) if the population is still growing at ANY percentage, then it is still growing exponentially.  Changing the number in front of the % sign changes the current steepness of the exponential curve, but that’s all…..  Until we get to negative numbers of course which is when the curve starts diving, exponentially too!

Mike

  • Thu, Apr 15, 2010 - 07:39am

    #17
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    Re: population growth not exponential

Hi Mike

As I explained in an earlier post (as Chris himself said) if the population is still growing at ANY percentage, then it is still growing exponentially.  Changing the number in front of the % sign changes the current steepness of the exponential curve, but that’s all…..  Until we get to negative numbers of course which is when the curve starts diving, exponentially too!

Sorry but that’s just wrong. If you change the rate of growth then you no longer have an exponential curve. Of course whilst the sign is positive you have growth but it’s not exponential. Whilst it is subject to error, an extrapolation of current trends in growth gives a plateau in population around 9bn. If growth were currently exponential then simple extrapolation would give a continued exponential curve. Big difference.

Also, whilst Chris makes a valid point about continued growth of the US population, it’s worth pointing out that there are now regions of the developed World where populations have plateaud or even started to decline slightly – large parts of Europe and Japan are examples. Whilst this alone doesn’t prove World population can or will plateau it does show it is at least possible. And as I’ve said careful analysis of birth vs death rates lends credence to the Global plateauing theory.

  • Thu, Apr 15, 2010 - 09:38am

    #18
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    Re: population growth not exponential

Just come across this interesting article in NS which talks about population trends both wrt growth rates and demographics;

http://www.newscientist.com/article/mg20627550.100-the-shock-of-the-old-welcome-to-the-elderly-age.html?page=1

…….First, we are not producing babies like we used to. In just a generation, world fertility has halved to just 2.6 babies per woman. In most of Europe and much of east Asia, fertility is closer to one child per woman than two, way below long-term replacement levels. The notion that the populations of places such as Brazil and India will go on expanding looks misplaced: in fact, they could soon be contracting. Meanwhile, except in a handful of AIDS-ravaged countries in Africa, people are living longer everywhere.

 

  • Thu, Apr 15, 2010 - 08:27pm

    #19
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    Re: population growth not exponential

I’ve got to agree with Damnthematrix. Changing the percentage doesn’t suddenly make the growth non-exponential. True enough that the overall graph isn’t the graph of the same function over time, which would exhibit the classic exponential curve. It’s possible to draw graphs over whatever time period one desires. If one takes a small enough time period, that period will show exponential behaviour, if there is any percentage growth at all, during that period. If each period is showing exponential growth then all periods together are showing exponential growth.

To put it another way … if population was growing 0.2% per month for three months, then that is exponential growth for those three months. If population then grows at 0.15% per month for the next three months then those three months are showing exponential growth (though the curve will be different from the previous three months). If both periods are exhibiting exponential growth, then why isn’t the 6 month period showing exponential growth? Of course, the answer is that it is showing exponential growth; it’s just that the curve is a concatentation of various exponential curves.

So, population is certainly rising exponentially and it’s worth pointing this out. Global population growth rates had been steady or increasing since 2004 but it looks like the rate dipped down again last year. I think it’s wrong to assume that population will level out and, somehow that will solve the population problem. As Chris points out, no one knows the maximum sustainable population (though there have been many guesses around 1-2 billion) but you can bet that the higher it goes, the more likely it is to reach an unsustainable level, if it hasn’t already.

  • Thu, Apr 15, 2010 - 09:26pm

    #20
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    Re: population growth not exponential

[quote=piquod12]

Sorry but that’s just wrong. If you change the rate of growth then you no longer have an exponential curve. Of course whilst the sign is positive you have growth but it’s not exponential. Whilst it is subject to error, an extrapolation of current trends in growth gives a plateau in population around 9bn. If growth were currently exponential then simple extrapolation would give a continued exponential curve. Big difference.

[/quote]

Sorry mate, but YOU are plain wrong……  you can only get a plateau at 0%.

All that happens when you lower the number in front of the % sign is you change the shape of the curve.  Yes it’ll take longer (maybe a lot longer!), but eventually the curve will again go skywards, ESPECIALLY as it starts from an already very large number, unlike the current one which starts (pick a date, any date) around 2000 years ago when world population was 200 million as opposed to today’s 7,000 million….

I can’t put it any clearer than this.  If you don’t get it, well you just don’t get it!

Mike

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