In the discussion of global warming, the time it takes for a process to double is often one of the key issues, and has come up a couple of times in the comments thread. There’s a neat rule on this which I thought was worth a short post. For moderate growth rates, you can get the doubling time just by dividing the percentage growth rate into 70. That is, an economy with a 1 per cent growth rate doubles its output in 70 years, 2 per cent takes 35 years and so on.

The key to this rule is the fact that the natural log of 2 is just about 0.7. Actually it’s 0.693, but 69 doesn’t have as many prime factors and ‘The Rule of 69’ is hard to say with a straight face.