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Wednesday, March 04, 2015

A really simple bit of maths.......

For those that don't understand the exponential function (i.e. politicians, teachers of economics, those that watch endless consumerist rubbish on television, the main stream media, in fact just about everyone it seems), here is the simple maths behind it:

Let's assume something is growing on a compound basis. School text books like to talk about nice things like the money in your bank or irrelevant things like octopuses. However, the same maths applies to important things like global economic growth which on average has been about 3% per annum since the Second World War. What we are particularly interested in is the  doubling time. The maths is simple if you know just a little bit about logs, if not go to the last line below and find the log function on your calculator.

Now we want to think about what this means in the real world - we are particularly interested in the area under the curve. The reason is that as all economic activity is dependent on energy, the area under the curve is proportional to the total energy consumed.

With a little bit more simple more maths, this time basic integration, we can get an expression that compares the two areas in the chart above, i.e. the area to the start of the doubling point (given by alpha) and the area in the doubling period.

Anything that grows exponentially will have this same property, as the curve is simply stretched vertically and horizontally to match what ever set of data we have.

So what is the significance of this?

It means in the next 24 years (the doubling time we calculated above), we will use the same amount of energy as we have consumed since we crawled out the caves at the end of the Stone age. We will also produce the same amount of greenhouse gases as we have ever produced; rather disturbingly we will do this when the planet's ecosystem has already entered into a period of free fall. 

If you are still not disturbed by this,  then consider it a bit further. We will have to do all the above when the fossil fuel energy we consume is increasingly carbon intensive to extract and process. We will also have to consume increasingly large amounts of energy on climate change impacts, such as adaptation  (relocating cities, decommissioning coastal nuclear power plants and oil refineries), mitigation (building low carbon energy sources) and increased competition (fighting wars and maintaining increasingly complex and large military industrial complexes).

The adaptation issues, such as shutting down nuclear power stations and oil refineries will also reduce available energy just when we need it the most.

Oh, and by the way, to fund all the adaptation, mitigation and defence that climate change causes, we need more fossil fuel driven economic growth.

Anyone still wondering why we don't teach the area under the exponential curve in our schools? 


Kevo Downunder said...

Fantastic update on the great unraveling. You labours on this are greatly appreciated

Mark Tweedie said...

Eye-opening and very sobering! Great stuff which everyone should read and ponder. Thanks for putting this together.