Just the other day, I saw a disparaging reference to Al Gore. Not the first one I’ve seen of course but, considering it is six years since the release of his documentary, An Inconvenient Truth, it is surprising that he is still being pilloried for giving us all that bad news and for ‘inventing the hockey stick graph.’ Well, I can say without fear of contradiction, that he did no such thing.
His film certainly brought the image of the hockey stick graph to life, but all he was demonstrating is what exponential growth looks like on paper. Professor Albert Bartlett has been using this graph in a lecture that he has given over 1600 times in the 32 years since he first delivered it in 1969. The title of the lecture is Arithmetic, Population and Growth, and is a discussion of how exponential growth affects the human species and its behaviour on this planet.
According to Professor Bartlett, ‘the greatest shortcoming of the human race is our inability to understand the exponential function.’ I am no mathematician (although I did enjoy a very successful, if somewhat curtailed, career as a land surveyor in the days before calculators and computers) but the arithmetic behind exponential growth is simple. The exponential function is used to describe anything that is growing steadily – i.e. at a certain fixed percentage per period of time. Within the function is the means to calculate what is known as the ‘doubling time,’ the time it takes for something to grow by 100%.
Those of you who are mathematicians will be able to establish quite easily that the number 70 is the key to calculating the doubling time of anything. Simply divide 70 by the % growth per unit of time, and you have the answer. Thus, for instance, if we want to calculate the doubling time for something growing at 5% per annum, we divide 70 by 5 – and the answer is 14. Therefore, at 5% per annum growth, it will take fourteen years for the original figure to double. More interestingly, it will take a mere ten doublings for the original figure to be over one thousand times bigger. Plotted diagrammatically, this would show a line that rises ever more steeply – and there we have the hockey stick graph.
The simple fact is that exponential growth moves us rapidly from small numbers to astronomical numbers. Taking world population for instance, at the beginning of this century it was around six billion and growing at 1.3% per annum. This seems like an insignificant (some might say ‘sustainable’) percentage, but it equates to a doubling time of only 54 years (70 divided by 1.3), which would translate into a total of around 12 billion by the middle of the century. Of course other factors will be introduced into the equation as the years unfold, and we may never get to this level of population, but the principle of exponential growth does not go away.
Taking an illustration from Professor Bartlett’s lecture, let us look at bacteria in a bottle. Imagine the bacteria are growing in a bottle, doubling every minute. At 11.00am there is one bacterium in the bottle, and at 12 noon the bottle is full. The good professor’s first question is, “At what time was the bottle half full?” Very clearly, the answer is 11.59, because a minute later the population had doubled and filled the bottle. Then he asks, “If you were a bacterium in that bottle, at what time would you realise you were running out of space?” The answer here is more difficult, as there would appear to be a huge amount of space left right up to the last minute. For instance, at 11.58 the bottle would still be only a quarter full, or three-quarters empty, and at 11.56 it would only have been one sixteenth full!
Such an illustration can be applied to anything that grows exponentially, which includes world population and all of the resources that population needs to survive. Applied to the consumption of resources, the exponential function shows us another invariable constant: the growth in each doubling time is greater than the accumulated growth in all preceding periods. Illustrated simply, if we consume, say, one barrel of oil in the first period and multiply by two, ten times, we will have consumed 1024 barrels in the 10th period alone, one more than the 1023 barrels consumed in the nine periods up until then.
Alarmingly, this kind of steady growth is the central beam of our economic model, yet we hear virtually no discussion of the implications of applying a steady percentage growth to a finite resource. Like the bacteria in the bottle, we seem blissfully unaware of the inevitable crisis for humanity that is just around the corner. Professor Bartlett poses another question during his illustration of the bacteria in the bottle. He asks us to imagine that, at 11.58, some of the bacteria realise they might be running out of space and so instigate a search for more bottles, which results in the discovery of three more. What a result! That’s three times what they knew about before, and it gives them a total of four times the space they thought they had. The professor’s question is, “How long can the growth continue as a result of discovering three more bottles, a quadrupling of proven resources?” The answer is simple – two minutes. The first bottle is full at 12 noon, and the second will be full by one minute past twelve. A minute later, the population having doubled again, all four would be full.
This puts into perspective all of our hand-wringing about the problems facing society today. There are those who worry about climate change, and there are those who worry that the world is about to be taken over by snake-headed aliens. Meanwhile, however, our cherished economic model of prosperity, based as it is on the false flags of materialism and consumerism, has now been adopted by virtually every country on the planet, and we are all madly scrabbling to dig up the last remaining deposits of all the raw materials and minerals we need to keep the whole thing going. But we are right on the curve of the hockey stick, vindicating Al Gore’s explicit Power Point graphics.
In this context, worrying about climate change, or indeed worrying about anything, is fruitless. It is unlikely we will change our ways before we fill our bottle. As Professor Bartlett said all those years ago, our greatest shortcoming is our inability to understand the exponential function. He is not alone in trying to warn us of our folly. Like all prophets, his destiny is to be ignored. And the destiny of the human race is to extinguish itself by overrunning and consuming the habitat on which it depends for survival. Oblivion awaits. It’s not all bad news though – with the demise of this most alien species, at least Earth will have a chance to recover.