Saturday, April 14, 2012

Linear Vs Exponential, or Exponential Vs Exponential

Most readers of Malthus note his argument that the exponential growth of populations will outstrip the linear growth of food supply. Many, sadly, leave it there - they assume Malthus has made his point. A few notice that food always grows in populations and, therefore, must also grow exponentially.

So, on the one hand, "Malthusians" argue that because growth with an exponential nature of 1,2,4,8,16,32,64,128,256,512,1024 will always outstrip growth of the linear nature 1,2,3,4,5,6,7,8,9,10 Malthus must be right.

Sure, a mild acquaintance with numbers will indeed show that exponential growth does easily outstrip linear growth.

However, it is Malthus himself who demonstrates that food - in the form of sheep or grain - also grows exponentially. Hence, the competition is between the exponential growth of populations (1,2,4,8,16,32,64,128,256,512,1024) and the exponential growth of the populations of the food sources for those populations (1,2,4,8,16,32,64,128,256,512,1024).

It would seem that the problem of human overpopulation is solved by the equivalent overpopulation of the food sources to feed us. Yet roughly 1 billion people are said to be starving.

Imagine the exponential series (1,2,4 etc) is in billions. Now imagine that the series for human population is ever so slightly out of step with the same series but for food supply. So, a human population of 7 billion is fed with enough food for 6 billion. This is the world we live in.

Sure, we might produce more than enough food in the rich developed world, so perhaps 3 billion people's worth of food is fed to 2 billion people. And in the poorer nations it might be that 3 billion people's worth of food is fed to 4 billion people.

What matters are not the numbers relating to those populations who are overfed and overweight, but those who are underweight and underfed.

It's like for the poorer nations food is 1,2, whereas population is 1,2,4. The exponential series for food and population are the same, but out of step with more people than food .Of course, it is never quite so neat, numerically (the actual numbers can lie anywhere between the numbers on the exponential scale).

But this is nonetheless the true nature of exponential growth, that although food does indeed have the potential to keep up with population or sometimes exceed it, it also has the potential to fall short.

Falling short in an exponential series can be just as devastating as falling short when comparing linear growth to exponential growth. The result is still millions who starve.

Thanks for reading,

David Coutts


Blogger Sandra said...

Lucid and thoughtful thinking, with the same bottom line all should care about most, whether considering linear or exponential examples of 'playing with numbers:' large numbers of people are underfed due to reasons beyond the mathematical in the world at any point in history.

10:28 PM  

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