Sunday, October 17, 2010

Exponential growth is a funny thing...

Note: This is the first in a series which, over the next few weeks, will hopefully help everyone understand the reasons behind the 1:1 learning initiative in the Okoboji School District.  Today we will talk in general terms about the world we are preparing our children for....

There is a legend that is told about the invention of the chessboard.  It goes something like this;

When the games inventor brought his chessboard to the king, the king was so pleased that he asked the inventor to name his price for the game.  The king was surprised when the man asked simply for one grain of wheat for the first square on the board, two for the second, four on the third, and so forth, doubling the number of grains with each square.  Since the king did not have a great handle on arithmetic, he quickly accepted and ordered the treasurer to count out the wheat for the payment.  The image below illustrates how this accounting would go.

Much to the king's surprise, by the time he got to the 64th and last square he would have owed the inventor 2 to the 63rd power grains of wheat.  This equates to  9,223,372,036,854,775,808 grains of wheat.  That amount of wheat is approximately 80 times what would be produced in one harvest, at modern yields, if all of Earth's arable land could be devoted to wheat.  This type of growth, in which the amount of something doubles at each time interval, is known as exponential growth.  As you can see, on the first half of the chessboard, the number grew but it is the second half of the chessboard in which the number skyrockets.  When plotted on a graph, exponential growth looks like this:

At first, exponential growth is not that distinguishable from linear or geometric growth.  The funny thing about exponential growth, as you can see from the graph, is that by the time the rapid rate of growth is noticeable, it is about to take off at a rate you could not have imagined before.

Examples of exponential growth can be found in nature.  One example is the rate at which bacteria in a culture will grow until one of the essential nutrients is exhausted.  Another is the rate at which a virus can spread until there is a vaccine.  Population growth can also be exponential at certain times under certain conditions. 

By now you are probably wondering why I would devote so much time to explaining and discussing exponential growth.  The reason has to do with the rise of computing technology and specifically the processing power of computers - which is defined as the number of discreet calculations that can be completed per second.  Below is a graph that displays the increase in processing power over the past 100 years.

As you can see, the white line is the graph of an exponential curve.  The graph shows the number of calculations per second, per thousand dollars of computing investment.  In short it shows what $1,000 worth of computing power will get you in processing ability.  The red dots are actual data points showing, in that moment in time, the processing power, or calculations per second, that could be achieved for $1,000 of computing investment.  As you can also see, for the past 100 years, the increase in processing speed and ability has followed an exponential curve - exactly.  This is not an estimate, this is not a theory.  This is fact that has been documented over the past 100 years.  If the increase in computing speed has followed an exponential curve for the past 100 years, it stands to reason that it will most likely continue on this track.  

The dashed lines show specific benchmarks of computing speed.  The data points are a bit dated but the trend in the past 10 years has stayed the course.  The number of calculations per second accomplished by the average computer now exceeds the speed of a mouse brain.  Assuming the trend that has stayed constant for the past 100 years remains so, we can expect that a $1,000 computer will be able to conduct more calculations per second than a human brain sometime within the next 15 years.  Projecting out further, we would expect that $1,000 computer to have greater computational power than the entire human species somewhere around the year 2050.  Some of those reading this may not be around by then.  But this post isn't about us. It is about our children and grandchildren.  This year's kindergarten class will be 45 years old that year.  They will need to be able to live, work, and thrive in what can only be described as a "brave new world."  

When sharing this information recently, I was asked - do you think this advance in technology is a good thing?  My answer was and is - it isn't about good or bad.  It simply IS.  Barring some unforseen intervention or obstacle, this rate of technological advance will continue at an exponential rate.  We have two choices - do what we can to prepare our children for the future, or stick our heads in the sand.  Our job is to prepare them for their future, not our past.  

Have a great week!


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