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The Myth Of The Exponential Phase
Introduction
It is a commonly stated "fact" that the last two centuries (or some other timeframe) are somehow unique in terms of the exponential growth of our human population. This fact has grown to such an extent that it is worthwhile spending a short while stripping away the myth to reveal the actual facts. This article will reveal that, in fact, no law of nature has had to change to accommodate the prodigious increase in human numbers of the last two hundred years or the last ten thousand years. In fact, the same universal law of nature has applied to all population of any species across all time...and always will.
Part of the issue is that people get easily confused over what exponential growth actually means. I highlight some of that confusion in my articles Paul R. Ehrlich and The Prophets Of Doom and What Is Exponential? For those expecting a discussion on the exponential phase of bacterial growth see Bacteria - An Exponentialist View.
Two Centuries Of Exponential Growth?
No less a person than Stephen Hawking (The Universe In A Nutshell, 2001) is one of many luminaries which have mislead the public on this point:
"In the last two hundred years, population growth has become exponential; that is, the population grows by the same percentage each year. Currently, the rate is 1.9 percent a year. That may not sound like very much, but it means that the world population doubles every forty years..."
Firstly, pure logic must dictate that Hawking believes that our global population has been growing at 1.9% for the past 200 years. Hawking clearly states that exponential growth means that a population "...grows by the same percentage each year...". Therefore, if the population has been growing exponentially for 200 years then it must have been growing at the current annual rate of 1.9 percent. Has it? No!
Any demographic history of the world will reveal that, in fact, our global population has been growing at variable annual rates through time. Take, for example,, the U.S. Census Bureau's figures: Historical Estimates Of World Population.
A simple test of Hawking's assertion is to establish whether our global population has doubled 5 times in those 200 years (exactly every 40 years). The United Nations Population Fund issued Press Release OBV/53 POP/675 on 9 July 1998. In it they stated that it took until 1800 for humanity to reach 1 billion, and that by 1930 our population had doubled to 2 billion. Then it took only a further 30 years to reach 3 billion and fourteen years later, in 1974, we reached 4 billion. In 1987 we reached 5 billion, and 12 October 1999 was officially designated as "The Day Of Six Billion".
What is apparent is that we have only doubled twice (and not five times) in 200 years, and we're on our way (perhaps) to a third doubling (1, 2, 4...8?). Five population doublings would put our population at 32 billion! What is also clear is that the doubling period itself is not a constant 40 years (nor, indeed, any other constant period). The fact is that our population has been growing at variable annual rates, and doubling at varying periods as that rate speeds up or slows down.
I doubt that most people have a problem with Hawking's assertions on exponential growth - after all, he is a physicist not a demographer. Well, too bad. The problem is, as you will come to understand if you read the articles on this website, that exponential growth is so poorly explained by demographers and scientists of all callings. I therefore find myself unwilling to let any such incorrect explanation stand unchallenged.
Ten Thousand Years Of Exponential Growth?
Carl Sagan (Billions And Billions, 1998) asserted that:
p.18 "Exponentials are also the central idea behind the world population crisis. For most of the time humans have been on Earth the population was stable, with births and deaths almost perfectly in balance. This is called a "steady state". After the invention of agriculture ... the human population of this planet began increasing, entering an exponential phase which is very far from a steady state. Right now the doubling time of the world' population is about 40 years. Every forty years there will be twice as many of us. As the English clergyman Thomas Malthus pointed out in 1798, a population increasing exponentially - Malthus described it as a geometrical progression - will outstrip any conceivable increase in food supply. No Green Revolution, no hydroponics, no making the deserts bloom can beat an exponential population growth."
Both Sagan and Hawking are making the same mistake. They implicitly assume that some fundamental law of nature changed at some landmark time in human demographic history. A common misleading theme is the requirement for a constant population doubling period (both assume 40 years). This is already shown to be a fallacy.
Sagan's landmark is the agricultural revolution of 10,000 years ago, Hawking's landmark is (effectively) the industrial revolution of 200 years ago. Nobody, least of all me, would deny that these were landmarks in human demographic history. Each marked a period when our global annual rate of population growth increased.
Sagan also slightly misrepresents Malthus. As Malthus himself put it in An Essay On The Principle Of Population (1798):
"Population, when unchecked, increases in a geometric ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the immensity of the first power in comparison to the second."
As noted by Sagan, Malthus uses the older term - geometric - whereas these days we are used to the term exponential (even if it is commonly then incorrectly explained these days). It is also worth noting that the term arithmetic can be taken to mean linear.
So, what Malthus means is that exponential growth is more powerful than linear growth. He's most definitely right about that. See Linear Growth Versus Exponential Growth for more. However, where I believe that Malthus is wrong is asserting that our food supply increases in a linear ratio. Confusing, isn't it?
Well no, not really. You see, if we assume that Malthus is right to believe that his Principle Of Population is a universal law of nature (for all populations of all species for all time), then suddenly it all becomes very clear. To make Malthus' assertion true, we must assume that all populations of all species are subject to variable rate compound interest at all times. I call this the Couttsian Growth Model to differentiate it from the Malthusian Growth Model. We must assume that all populations are either growing exponentially, or shrinking exponentially (which is negative growth anyway). Most of the time, this can be simplified by saying that all populations are subject to population halving and population doubling. See Malthus - An Exponentialist View for more.
Conclusion
How does this help? Does this mean that Sagan is wrong? Well, yes and no. Sagan was wrong to put words into Malthus' mouth. If Malthus had thought that food supply could increase exponentially then he would have been able to see how food supply could in theory keep pace with population. Exponential growth can match exponential growth. This is, in fact, the deep secret of the "steady state" to which Sagan refers. The balance of nature, the state of dynamic equilibrium, is a never-ending struggle for existence between competing populations within and between species within Nature's dynamic and often deadly arena. This fine balancing act pits exponential forces against exponential forces for as long as any replicator exists.
Where Sagan and Malthus would rightly agree is that no population can sustain a positive rate of population growth indefinitely. Especially if that population is limited to the finite resources of the Earth. In time, all growing populations must face the limits to growth.
I leave you with a thought from Carl Sagan's Billions And Billions (1998):
p.23 "If you understand exponentials, the key to many of the secrets of the Universe is in your hand."