16 January 2011

From Linear to Exponential

Back in 1973 a fellow named Merle Haggard wrote a song about the tender optimism of a working man dealing with economic hardship. I relate to this particular song because at the time it was written I was dealing with economic hardship myself. In October of 1973 we were hit with the Arab Oil Embargo crisis and by Christmas that year and it seemed as though the lights were going out all over North America. There were gas lines everywhere and there was a line from that song that was on every one's mind at the time and it went:

If we make it through December
Every thing's gonna be all right I know...

Here in Mexico there is a similar sentiment but it differs in that the month that is the hardest to get through is not December but January. By the end of the year the Christmas holidays have taken their toll on the pocketbook and there is still "El Día de Los Reyes Magos" (The Feast of the Three Kings) on the Epiphany, January 6th to deal with. Many Moms and Dads literally go into hock at a pawn shop (casa de empeños) to get enough money to buy clothing and toys for their children who are expecting Melchor, Gaspar and Baltasar, the three wise men, to bring them gifts. The prudent parents buy the gifts (regalos) on "el plan de apartado" or "layaway plan" to be redeemed on the night of January 5th, the eve of the Epiphany, after the kids have been put to bed. To be sure, the Day of the Three Kings is a great day but after that there is a long hard climb out of debt. Many people who are caught off guard by emergencies during the holidays have had to borrow money from their employer or put off paying the rent or utilities and it is also a time when property taxes become due. That is why people often refer to January as "la cuesta de enero" or "the hill of January". A friend of mine noted recently that this year we will not only have "la cuesta de enero" to deal with but also "la cuesta de dos mil once" or "the hill of two thousand eleven".

This brings me to the title of this blog post, "From Linear to Exponential". I first encountered this phrase in the late 1980's while investigating the maintenance cost cycle of railroad equipment. The monthly maintenance cost would start out at next to nothing and rise very, very slowly over the years in a gradually rising straight line or in a "linear fashion". This would go on for many years until at some point, usually predictable, the various components would begin to wear out more or less simultaneously and the the maintenance cost would take an abrupt upward turn in an alarmingly steep manner or "exponential fashion" and this would indicate the end of a useful life cycle. The owner of the equipment would then need to decide to either completely refurbish the equipment or replace it. We now seem to be at that point with the debts of many nations and the availability of resources. The cause of this linear to exponential change in direction was also generally predictable and we were first warned about it by a man named Thomas Malthus. In 1798 he published An Essay on the Principle of Population which said that the growth of population will eventually reach the limit of the resource base, this resource base, of course, being the planet Earth.

It is hard to get one's head around the math behind exponential growth because our lives are linear and our activities generally don't involve the powers of ten. My father used to explain it by using the story of the chess board with 64 squares. One day a man brought a new game called "chess" to the king and the king enjoyed the game so much that he told the man that he could have anything that he wanted as a reward. The king asked what he would like and the man surprised the king by asking for one grain of rice on the first square, two grains on the second square, four grains on the third square etc. The king readily agreed and called for the rice to be brought in. All went well at first but by the time they got to the thirty-second square they needed 4,294,967,295 grains of rice or in other words about 118 tons. This is enough rice to fill a modern jumbo railroad covered hopper car full to overflowing. Then, on the very next square the amount doubled and they came to the point that some people refer to as, "the second half of the chess board" where the increase becomes so steep that it is almost impossible to deal with. In fact, if the king had kept on rewarding the man with rice according to the agreed upon plan, by the time they reached the sixty-fourth square there would be 18,446,744,073,709,551,615 grains of rice, weighing 501,270, 219, 565 tons, which would be a mountain of rice larger than Mount Everest.

The national debt of the United States is getting uncomfortably close to that "second half of the chess board". Not only that but scientists are telling us that the growing world population, falling energy sources and food shortages will create some almost insurmountable difficulties by the year 2030 if some drastic measures aren't taken immediately. Food reserves are already at a fifty-year low but by 2030 the world will require 50% more food, energy, and clean fresh water than we have available today. I think that more and more and more people at all levels are becoming aware of this all the time and that is why there is so much frustration with the world's leaders and politicians. No one seems to be able to step up and tell it like it is and do something about it NOW and for this reason there is a lot of built-up tension and the resulting strife. What occurred in Arizona recently may be an example. I don't think that what happened to Representative Gabrielle Giffords and the other shooting victims was necessarily politically motivated but the tensions caused by the realizations that I mentioned above could very well have been a factor and this tension may be enough to push some people over the edge. I believe that we must take this underlying tension into account with all of our relationships, both business and personal. The best advice that I have heard in this regard came from one of the world's oldest inhabitants, Ms. Mississippi ("Sweetie") Winn, who died last week at the age of 113 years. When asked what her favorite Bible verse was Sweetie unhesitatingly replied "Be ye kind one to another".

And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you.
(Ephesians 4:32)

AMEN !!!


norm said...

On the flip side of the problem of over population: odds are there is a holy person alive today that will change our world. If you look at how many people have lived, divide it by the number of holy people who have walked our earth and there should be more than a few here now. It is in the numbers.
I to fear we may be in for some interesting times, not so much for myself because I've lived a good life and am ready for what ever but for my children who have so many years ahead to deal with our problems. In my life I have never experienced anything like WWII, will my children? More than even odds on that.

Dan in NC said...

Excellent and erudite as ever. Thanks for the "brain cud" as I'll be chewing this info over for a while..
Dan in NC

Kevin and Ruth said...

Yes, interesting times. Wonder what the end will be for this U.S. debt problem...


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I was born and raised in Chicago, Illinois, U.S.A. I have been living in Mexico since January 6th, 1999. I am continually studying to improve my knowledge of the Spanish language and Mexican history and culture. I am also a student of Mandarin Chinese.