Rice, Chess, Exponents

Rice, Chess, and Exponential Growth

Pentecost 105

“May you grow and thrive exponentially in your life!”  It might have seemed like the strangest autograph on the student’s yearbook until one considered it was written by the math professor.  Exponents are one of those things in mathematics that cause most of us to roll our eyes and close our ears.  We are convinced they are difficult and impossible to not only understand but also learn and use.  The truth is, we are the cause, the result, and the definition of exponential growth just by being.  How can it be such a foreign thing to us when it is what we are?

My previous blog discussed a chess board so you might think I am an avid player.  I like the game of chess but dislike some of its rigidity.  That should tell you that I know very little about actually playing the game because in truth, the possibilities are not rigid but endless, much like the game of life.

During political campaigns, it seems like there are a plethora of things a candidate can and cannot do.  Most recently, in the United States Presidential race, it would seem that a candidate should not contract an illness because that would not mean they are human but incompetent.  Of course, being on the campaign trail, eating at odd hours and getting very little sleep, as well as changing climates during a changeable time of climates could also have an effect but the public perception is that is one succumbs to a cold germ, one could not possibly be an effective leader.

We tend to allow exponential growth of a perceived enemy to exist while denouncing their good qualities.  It is ridiculous, of course, but it is how populations have reacted throughout time.  Populations themselves are a great example of exponential growth because populations exist, grow, change, and fade away all through exponential growth and its control.

Mathematically speaking, exponential growth is the increase that results when the growth rate of something is directly proportional to its current value.  Pretend we are standing on the banks of a lovely pond and we see one water lily pod floating on the water.  Each day we meditate by the pond and notice the growth rate of our water lilies.  The second day we have two; the third day, four.  The water lilies are doubling each day and by the end of the month, day 30, they cover half of the pond. So how long will it take the water lilies to completely cover the pond’s surface – another thirty days?  No.  When we visit the pond tomorrow we will see that it will be completely covered, due to exponential growth.

This series has been about making the ordinary time of Pentecost something extraordinary.  We haven’t invented anything new, cured any plagues, or discovered buried treasure.  What we have discussed is how to live better, create more happiness, and share the wealth that life has already afforded us.  We are using our being to exponentially grow a better world.

The following example from Khan Academy is a great way to explain exponential growth.  You are offered a job, which lasts for 7 weeks. You get to choose your salary:  First option –  you get \$100 for the first day, \$200 for the second day, \$300 for the third day. Each day you are paid \$100 more than the day before.   Second Option – You get 1 cent for the first day, 2 cents for the second day, 4 cents for the third day. Each day you are paid double what you were paid the day before.

This is a variation on the rice and the chessboard story of how chess was invented.  The Indian fable tells of a ruler being so delighted with an old man inventing the game of chess that he offers him a reward of the old man’s choosing.  The old man, according to the Indian tale, request a grain of rice be placed on the first square of the chess board, double that number on the second square, double that number on the third square, etc.  An Islamic version of this story was included in a book written by Ibn Khallikan in 1260 which uses wheat instead of rice.  In each version of this story, the game of chess was used to illustrate how the ruler should treat his subjects with humanity in order to be successful.

Also in each version, the request is thought to be frivolous and quickly granted.  However, soon the true exponential growth factor is apparent.  Exactly how much would such a request create in terms of rice or wheat?  You could try it yourself but you’d need to make a lot of trips to the market.  Such a reward would be enough to feed 100 tons of rice to every single human on Planet Earth. That’s 1 kg of rice per day per human for 275 long years. Economically speaking, that is more than a millennium worth of global rice production since we grow and produce approximately 100 million tons annually.

Let’s return to our example from the Khan Academy regarding salary.  Which choice would you have chosen?  For the first choice, the person earns \$2800 in week 1, then \$7700, \$12600, \$17500, \$22400, \$27300 then \$32200, for a grand total of \$122,500.  That is not a bad salary but the second choice, due to exponential growth, is the better choice.  For the doubling scheme, the person earns \$1.27 in week 1, then \$162.56, \$20807.68, \$2,663,383.04, \$340,913,029.12, \$43,636,867,727.36 then \$5,585,519,069,102.08 for a total of \$5,629,499,534,213.11. I certainly would rather have five trillion dollars than a little over one hundred thousand!

When we focus on someone’s faults, they seem to grow exponentially.  We seldom realize that goodness can do the same.  By allowing our strengths to double, by putting value on them rather than placing value on our faults, we allow ourselves a better future, an extraordinary future.  The choice is ours – positive growth based on kindness and respect or negative growth which results from fear and narrow-minded approaches.  Remember, the rate of exponential growth is determined by the current value.  A single grain of rice is not very big, neither does a single good deed seem like huge action.  However,  the results of the old man’s reward, all his grains of rice placed end to end, would cover a distance of 60,000,000,000,000 miles. How far is that? Alpha Centauri, the nearest star, is located 25,000,000,000,000 miles from Earth. Placed end to end, these grains of rice would reach farther than from the Earth, across space to the nearest star, Alpha Centauri, and back to Earth again – sixty trillion miles.  Never underestimate the value of a smile or a good deed.  Exponentially it could beextraordinary!