Mind Exponentially Boggled

Exponential growth is a mind boggling concept. It is most easily explained by an old story. Once there was a king who loved games. But alas, he had grown tired of all the games he knew how to play. So he put forth a call to everyone in his kingdom. Anyone that could invent a new game that could keep his interest for more than a week could name their own reward. If they were unsuccessful however, the king vowed to cut off their head.

Soon a gentleman arrived at the gate of the castle with a bag. He told the guard that he had a game that would entertain the king for years on end. The guards laughed at him and said he’d be better off going on his way and keeping his head on his shoulders. The gentleman insisted and so they led him in to see the king.

The king could barely contain his excitement. He told the gentleman that this was his last chance to leave with his head intact unless he really did have a game that could entertain the king for more than a week.

The gentleman assured him that this game would keep him entertained for the rest of his life. At which point he pulled a chess board and pieces out of his bag and proceeded to teach the king to play.

The king was enthralled. He played chess before breakfast. He played chess in the bath. He played chess all day long and into the night until he could no longer keep his eyes open. He played chess for days and then weeks, and after three months it occurred to him that he had made a bargain with the gentleman who had taught him this wonderful game.

The king sent for the gentleman and when he arrived he asked him what he wanted in return for teaching him this wonderful game. At first the gentleman declined saying that the kings happiness was plenty reward for him. But the king insisted. So the gentleman said, “Okay. I want you to place one grain of rice on the first square of the board. Then double that amount and place two grains of rice on the second square of the board. And continue on, doubling the number of grains of rice on each successive square until you have done that for ever square on the board.”

The king thought the man was daft. What was a little bit of rice compared to this wonderful new game he had learned? He immediately agreed to the man’s request. Of course, this was his big mistake because by the time you get to the sixty-fourth square of the chess board, the last square has 2 to the 64th power grains of rice on it which far exceeds all the rice in the world.

That is the power of exponential growth. Now a fun fact based on that principle. In 1969 Intel invented the first microprocessor. That was the first computer on a single chip. It ushered in the era of the personal computer. Several years later, Gordon Moore wrote an article for a technical magazine in which he described the rate of growth that he had observed regarding the number of transistors that they were able to fit on a chip of a given size. The number of transistors in a computer is a rough measure of how powerful it is.  Moore observed that they were able to double the number of transistors on a chip approximately every eighteen months.

This was coined Moore’s Law and has held from then until now. Consequently, we now have computers that we carry around in our pocket and hold in our hands that are much much more powerful than the computers that used to fill entire buildings before the invention of the microprocessor. We call them cell phones but the phone function is one of the least amazing of their capabilities.

And now for the truly mind boggling fact. Moore’s Law has been projected to continue at it’s current rate for at least another six or twelve years. What are we going to be using for computers by then? Are we going to implant them in our brain? Will they float around like dust? The imagination runs rampant.

Sweet dreams, don’t forget to tell the ones you love that you love them, and most important of all, be kind.