C4CC(5): The accumulating crises of our time (1)

So with this chapter I am wanting to zoom out from the specific question of oil supply and look at what it is an example of, ie the pursuit of perpetual growth in a finite environment. What I describe in this chapter is now more often called a ‘polycrisis’ by the Archons of the Outer Church… Anyhow, today’s extract is an introduction to exponential growth.

~~

"...if way to the better there be, it exacts a full look at the Worst"
Thomas Hardy, In Tenebris II

Peak oil is a problem. Taken on its own, and dependent upon the wisdom and maturity of political leaders and followers – the ordinary people who set the weather that the politicians have to sail in – peak oil is more or less manageable. We will experience a great dislocation in our economies, but we have faced such things before, such as through the 1930s and 1940s, and so, whilst peak oil is something that we have to address and deal with, it is not, in itself, something that will cause our civilisation to collapse. This Chapter will explain the predicament which will cause our present way of life to collapse: the phenomenon of exponential physical growth within a finite environment.

I follow the author John Michael Greer in believing that the word 'predicament' is appropriate to describe this issue, and not 'problem', because when we talk about problems there seems to be an expectation that for every problem there is a corresponding solution. There is no solution for a predicament; it is something that we have to learn to deal with. So: working out what to say to a boss when you have overslept and are late for work – this is a problem. Facing the fact that you will one day die – this is a predicament. In the same way, as a result of exponential growth, our culture is now in a predicament; and our culture as we have known it for the last few centuries is going to die.

Professor Albert Bartlett, of the University of Colorado, has written that, “A misunderstanding of exponential arithmetic is one of the most dramatic shortcomings of mankind.” Exponential growth occurs whenever something grows at a constant rate – for example, an economy that is growing at 5% a year. So if we begin with 100 widgets of production, and our production grows by 5%, then after one year we will have 105 widgets. If the growth continues then after another year, we will have 110.25 widgets. After another year we will have 115.7625 widgets. Notice that the amount added on increases each time – five widgets in the first year, five and a quarter in the second year, five and a half in the third year. That is because the underlying quantity has increased. So exponential growth is not simply adding on a fixed amount each year, it is adding on an increasing amount each year. If a fixed amount is added on each year (say five widgets every year) then we are not looking at exponential growth, we are looking at linear growth.

The interesting thing about exponential growth, and what makes it so marvellous and miraculous and devastating, is something called 'doubling time'. When a certain percentage of growth is maintained over time then we can expect the underlying quantity to double at a particular rate. For example, if growth is maintained at 7.5% a year then the underlying quantity will double (approximately) every ten years. This brings us to the famous tale of the chessboard and the king. The tale goes – and it is entirely apocryphal so it has been told many ways – that a great inventor gave the king a chess set. The king was greatly pleased with the gift and asked the inventor what he would like as a reward. The inventor asked that a grain of rice be placed on the first square, two grains of rice on the second, four on the third, eight on the fourth round all the 64 squares of the chessboard, doubling each time, and that he be given the total quantity of rice that would end up on the board. The king readily agreed and asked his treasurer to dispense the rice. After taking some time to work out how much this would be, the treasurer told the king that it amounted to more rice than was available in the whole world¹ at which point the king decided the inventor was more trouble than he was worth and had his head chopped off.

The point about doubling time is that it allows very large numbers to be reached remarkably quickly. Consider another example – if you folded a piece of paper 42 times, how thick would it be? (Leave aside the physical impossibility of folding paper more than around half a dozen times.) The answer is that it would reach to the moon. Consider an example that is apparently used in French classrooms: there is a beautiful pond, and some water-lilies have begun to grow in the pond. The lilies are growing exponentially, doubling in size each day, and we know that in 30 days it will have covered the entire surface of the pond. At what point will the surface be half-covered? On day 29 – when there is only one day left to do something about the infestation (consider that on day 27 only one-eighth of the surface will be covered by the water lilies). Now imagine that three new equivalent sized ponds were built adjoining the existing pond, in order to preserve the wider pond-life. How long before they are also covered in water-lilies? The answer is just two days – for on the first day an entire extra pond will be covered, and on the second day the two remaining ponds would be covered. To preserve wider pond-life, whilst doing nothing about the water-lilies themselves, requires an ever-accelerating building of ponds!! That is the nature of exponential growth.

118,446,744,073,709,551,615 grains.