### Exponential Growth and what that means (and what Rod Smith meant)

In a previous blog entry I quoted Monbiot, who was quoting Rod Smith in talking about this doubling effect of global resource usage. Rod figured out that over the next 23 years we will use double the amount of resources than we did in the preceeding 23 years (assuming 3% growth). And, shockingly, that this equates to, over the next 23 years, to us using more resources than the whole of humanity has ever used to date - more than the WHOLE OF HUMAN EVOLUTION, INDUSTRIAL REVOLUTION, STAR WARS PROGRAMMES, COLD WAR MISSILE STOCK PILING, BUTTER MOUNTAINS AND WINE LAKES - more than ALL OF THAT!

Wow.

A few people (one is a Fellow of the IMechE so I need to watch my figures!) have been asking me more about it and I've added a few more links to the original presentation but questions still remain and I haven't yet got a hold of all of Rod's slides. What is he talking about? Is he talking about ALL RESOURCES or just those relating to generating energy? How does his model work if we consider than many aspects of GDP don't produce anything because they are services and not goods? What about the fact that we are getting ever more efficient - how is that factored in? I have discovered something called The Kaya Identity which I will talk about on another blog post. For now though, let's consider what Expoential Growth means.

Here is what Rod Smith actually said,

... I argue that the economy is actually driven by the physical processing of natural resources into materials than goods and services which are transported to consumers. When we have finished with the goods, we dispose of them, often with very little effort to recycle. This physical view of the economy is governed by the laws of thermodynamics and continuity. The question of how much natural resource we have to fuel the economy, and how much energy we have to extract, process and manufacture is central to our existence.

It has been calculated that if all the present population of the earth was consuming in the present style of the USA, we would need about three earths to sustain ourselves and about nine earths to absorb the wastes and toxins

generated. But we have an economic model predicated on growth. Many features of our economic consumption can be described by the exponential growth function.

A key characteristic of any variable which multiplies proportional to its current size is its doubling period. It is elementary to show that relatively modest annual percentage growth rates lead to surprisingly short doubling times. Thus, a 3% growth rate, which is typical of the rate of a developed economy, leads to a doubling time of just over 23 years. The 10% rates of rapidly developing economies double the size of the economy in just under 7 years.

These figures come as a surprise to many people, but the real surprise is that each successive doubling period consumes as much resource as all the previous doubling periods combined. This little appreciated fact [...] lies at the heart of why our current economic model is unsustainable.

It is therefore the EXPONENTIAL nature of this growth that is described by this doubling Rod is talking about. This is what exponential growth looks like - the GREEN line (from Wikipedia)...

Here are some graphs showing exponential growth curves, I think it begins to become clear what Rod Smith was talking about...

(This is from the BBC Planet under pressure series which I found from an interesting Blog called Past Peak)

Finally, I have just found another awesome video called 'The Most IMPORTANT Video You'll Ever See' and was made by the teacher that made another video I showed recently. This one explains some of the maths concerning exponential growth very well. It's an eight part series. I'll embedd the first one here and leave you to find the others if you want to. Before hitting play, remember that Rod Smith, in his calculations, was using just 3% as his growth figure.

I hope this starts to support what Rod was saying. Later I'll come on to The Kaya Identity which allows us to start to answer some of the other questions people raised.

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