Linear to Exponential

When I was a little kid my father used to like to tell us the story about a king who received the gift of a checker board from someone in his court and he commanded the man to teach him how to play checkers. The man taught the king and the king enjoyed playing the game so much that he asked the man what kind of gift he would like in return. The man told the king that he would like one grain of rice on the first square, two grains of rice on the second, four grains on the third, etcetera. The king thought that the man must be nuts so he readily agreed and commanded that his servants give the man the rice according to what he asked for. For a little while everything went well but as the servants progressed through the 64 squares on the checkerboard by the time they got to about the 21^st square the requirement grew to more than a million grains of rice and by the time they got to the 41^st square they needed more than a quadrillion grains and there was no way that they could ever get to the 64^th square because there simply weren’t that many grains of rice anywhere in the world.

There is another story about a farmer who has a pond with some water weeds in it. The water weed patch doubles in area every day and if the farmer just leaves the pond alone the weeds will eventually cover the whole pond and choke off all of the oxygen and kill the fish and the frogs and all the other creatures that live in the pond. Day after day the weeds grow but the farmer is too busy to notice until one day he sees that the weeds finally cover half the pond and he tells his wife that “tomorrow” he will do something about it. The problem is that by the next day the weed patch had doubled again in size and now it covers the whole pond and the fish start dying.

So what am I getting at? Well, it seems to me that we are getting to the point where there aren’t enough grains of rice and the pond is getting all choked with weeds. By the year 2050, China will no longer be the most populous country in the world. That distinction will pass to India, where more than 1.8 billion people could be competing for their share of sun and sky and air and light, not to mention rice, and water, and all the other things necessary to life. That is an increase of 700 million people from the present population figure. How are these people going to survive? I am not talking about a “chicken in every pot and a car in every garage” either. I am talking about hand to mouth survival. Everyone wants to have what people in America consider to be basic rights but as I heard one Chinese official recently put it, “It would take three or four ‘Planet Earths’ to provide the necessary resources for everyone in the world to live according to the U.S. standard”. Nothing can keep growing forever. It reminds me of those stories about how many mice or locusts there would be if their growth went unchecked. Perhaps that is what wars and natural disasters and diseases are all about. It is nothing more than the Earth cleansing itself. For my part, every time I try to think this thing through, my head hurts.