Alternative Socioeconomics/Why look at alternative systems?/Exponential Growth

The Nature of Exponential Growth

The feature of exponential growth forms an essential part of our socioeconomic system. We quote the current growth rate of the economy in percentages such as We expect the economy to experience growth of 3% this year. If the economy doesn't grow then we have a recession which has the potential to create economic hardship for many people. Governments carry out economic policies to maintained economic growth.

Exponential growth has a number of interesting features.

Doubling Time

Firstly, it has constant doubling period; it doubles in the same time period and then double again in the next time period. We often use percentages to specify a growth rate. We can find the approximate doubling period if we divide the growth rate into 70. For example a growth rate of 3% means a doubling time of about 23 time periods (70 / 3 = 23.333). A growth rate of 1% gives a doubling of 70 time periods and a growth rate of 7% gives a doubling of 10 time periods. So, an economy that grows at about 2-3% doubles every 23 – 35 years. Doubling means twice as much resources and twice as much strain on the environment at each doubling.

Explosive Growth

When compared to other forms of growth such a liner growth or growth to the power of three, exponential growth appears slow to start with. However, after some time it starts to take off and then it reaches a period of very rapid growth when compared to other forms of growth.

Humans often predict the future based on the past. We look to our past experiences to assess future possibilities. However, with exponential growth our past experiences can let us down. Things that growth exponential appear to grow well for some time and then suddenly fail as if a bolt from the blue suddenly hit the system.

Impossibility to Maintain

Take a piece of paper and fold it half, fold it again and again. How many times can you fold it? Most people manage 7 or 8 folds. What happened? Why can't you fold any more?

The Emperor of China, so the story goes, was so pleased with the inventor of the game of chess that he promised the inventor anything he wanted. The inventor asked for a grain of rice on the first square, double the amount on the second square, double again on the third and so on till the end. How much rice would you have at the end?

Both of the above form examples of exponential growth. They also illustrate another characteristic of real, physical, exponential growth; it comes to an end. All natural, real, physical systems cannot grow exponentially indefinitely. You run into problems folding the paper as the thickness doubles each time as the area halves. Keep doubling the amount of rice from one square to the next and you will eventually have more rice than exists.

Our economic system exemplifies another form of a physical system; a resource allocation system. An economic system effectively allocates raw materials to production which produces goods that we demand. Each stage forms an example of a physical system. The raw material, the rocks in the ground or the crops in the field all form examples of physical resources. So do the factories and transport systems we use and they all require energy to run.

Yet, we try to grow this physical resource based system exponentially; a system that has nothing about it that separates it from other physical systems and therefore, we cannot maintain exponential economic growth. Sooner of later, the system will fail.

Bacteria in a Bottle - A thought Experiment

Imagine, if you will, a bottle. In that bottle we will grow some bacteria exponentially. Lets have a doubling time every minute and let's start our thought experiment at 11:00. Let's say it takes an hour to fill the bottle so the bacteria will fill the bottle up at 12:00.

We should now ask ourselves at what time will the bottle become half full?

Switching to New Resources

For 59 minutes our growing of bacteria will work nicely. At 59 minutes we would have used half of the bottle. One minute later and the bacteria fills the whole bottle.

However, human beings differ from bacteria; we have the attribute of intelligence. If we have problems with one resource we can apply our intelligence to acquire a new resource. In our economic system, if we start to run out of resources the price of that resource will increase. The increase in costs will motive people to seek an alternative; as in the past (so in the future). Alternatively, we could come up with more efficient ways to use the resource we have so it lasts longer. Either, we can model both increased efficiency and the acquisition of new resources as the same; an increase in resources.

Let's imagine we have some intelligent bacterial who realise when the bottle reach quarter full (quarter full means two minutes to dooms day) they will soon run into trouble. So, our clever bacteria initiate a programme to acquire more resources and they add three more bottles. Now, it takes the bacterial from 11:00 to 12:00 to fill one bottle, how long before they fill all four?

It will take them another minute to fill a second bottle and a minute to fill the next two bottle. All they did was delay dooms day and added a couple more minutes.

If we should maintain exponential growth we would also need to acquire new resources at an exponential increasing rate.

Summary

Our socioeconomic system is an example of a type of physical resource allocation system that operates with the real world. No physical systems can sustain exponential growth. Therefore, we cannot sustain the rate of our socioeconomic.

We could, however, cut back and then grow again like a rose bush. To do that we would need to kill of large number of people and destroy infrastructure and buildings. Wars, disease, famine and natural disasters would help to achieve that.