I’m a mathematician and numbers appeal to me. But the numbers in this example are simple enough for all to understand. And they are the numbers we are taught all our lives to worship in the guise of wealth and economics.
They are the numbers of growth exponential growth compound interest. They are the numbers economists talk about when they talk about GDP and the growth rate. They are the numbers we hope drive our superannuation policies to grow magically into nest eggs to make us rich in retirement.
They are simply the numbers of steady and regular growth.
The clearest example the one that also applies to us is population growth. It also applies to inflation resource extraction consumption of goods compound interest the volume of malignant tumours and many other things which tend to grow over time.
Whether we are talking about a population of bacteria in a test tube or the population of people on earth the issue of growth rates is the same. If there is enough food and few predators and a steady growth rate the population will have a steady [url=http://en.wikipedia.org/wiki/Doubling_time]doubling time[/url].
There is a simple sum to enable us to estimate the doubling time from the growth rate. Divide the growth rate into 72 and you have the doubling time. For example if the growth rate is 6% per annum the doubling time is about 72 divided by 6 which equals 12 years.
In the example of a population in a closed finite system like a test tube or the earth we can then ask how the population behaves as it grows and doubles.
Let’s start with one bacterium in a test tube with sufficient food supply to keep doubling for 60 minutes. After one minute there are two bacteria. After two minutes there are 4 bacteria. After three minutes there are 8 bacteria.
Now let’s work backwards. If the test tube is full at 60 minutes completely reached the limits of the available food supply when is it half full?
The answer is at the 59th minute. Think about it. The population doubles every minute. If it is full at 60 minutes it is half full at 59 minutes.
It is a quarter full at 58 minutes. It is an 8th full at 57 minutes. It is a 16th full at 56 minutes. It is a 32nd full at 55 minutes.
Let’s think about what this is saying. At 5 minutes before the test tube is completely full and run out of food for the bacteria population the test tube is only one 32nd full. That is about 3% full.
Imagine if one of the bacteria said at 5 minutes before the 60th minute: “Hey guys. It’s getting crowded around here!”
It is almost impossible for us to get our imaginations around how much change population doubling with steady growth rates makes.
Yet in only 5 minutes that test tube is going to be full.
When I was born the world’s population was already well past the 5 minutes before the hour mark. It was at 2 billion. There was heaps and heaps of space. We didn’t even think about it.
In my lifetime the population has doubled to 4 billion and is moving towards doubling to 8 billion. At the moment it is around 7 billion and growing fast.
We are past the 59th minute. We need to think of what comes next when the test tube is full. In less than a minute’s time.