5. Galton's Message from the Ivory Tower

Sir Francais Galton was a Statistician who's work has speckled our history from the mid 1800's, to the early 1900's. He was the half-cousin of Charles Darwin, the father of Evolution. This influenced his perspective in such an interesting way. He believed that because of their common ancestry, they were better equipped to handle scientific postulation. That they were bred at a higher echelon of the genetic totem pole. He did not favor the minds of what he considered lesser people. He felt that the working class was incapable of taking part in representative democracy. Near the turn of the century, he set out to prove this. Ironically, he showed something of the contrary.

Galton wished to show that if people could not answer a seemingly easy question, that they could not be enlightened enough to offer up a vote in politics. He tested this by attending a livestock fair. At this fair was a contest which asked its contestants to guess the weight of an ox for a prize. However it would amuse me to know of his own guess. At any rate he must have believed this was a sufficient example to test lesser persons. He proceeded to record each contestant's guess, 800 in total. He was happy to find that each of the 800 individuals failed to guess the weight of the ox. However that was to change as he did what any good statistician would do with a large data set. Upon plotting the data, he noticed a striking resemblance to something he did not expect to see. What he found was that the data produced the Cumulative Distribution Function of the Normal Distribution! For those of you who don't know, the Normal Distribution is the bell curve. Taking the mean of the guesses yielded an approximation of the right answer.

Given some personal incentive, every participant offered up what they thought to be the right solution to the problem. All of which were wrong. However, together the group seemed to know the weight of the ox. How is this possible? Is this some kind of validation for collectivism? There is wisdom of crowds, but this does not validate collectivism. Rather it bolsters the contrary. Each participant had a personal incentive to guess the correct solution to the problem. A personal incentive is indicative of a want for personal gain. This however does not answer my question of how this is possible. Although, the clues to the answer of that question lie in what the data revealed. The Normal Distribution comes up all throughout nature. Why? I don't think anyone really knows why. Why does pi have the value that it does? Because it works? That to me seems like a half answer.

Consider the problem of being a tree. That is, the problem all life encounters which is persistence. What if there was only one solution to the problem of being a tree? There would only be one way in which to distribute your branches. One type of leaf to collect sunlight. One way in which to network your roots to provide stability and extract nourishment. Is it not obvious why this is not the case? Even within a species, variability provides adaptability in order to broaden your chances of survival as a species. More so, there is not one species of tree. Why? For the objective idea that is a tree to persist, would it not be beneficial to provide your own competition? This argument could go either way. However when discussing the persistence of the biological concept of what a tree is objectively, the concept enhances its survivability drastically by providing diversity within itself. This means that multiple species can better preserve the biological concept that is a tree while never attaining that objective reality. Not to sound cliche', but this brings new meaning to the phrase, "Don't put all your eggs in one basket." Each species offers up its own solution to the problem of being a tree. Each in effect gets the problem wrong, but together and yet independently, the tree may forever exist.

Often Free Marketeers offer up the argument of the invisible hand, regulating prices, correcting investments and providing the most stable market place. While many would argue against such a statement, many overlook the subtleties of how the market produces prices for particular products. In the same light of the argument of the previous paragraph, consider the problem of being a product. Is there only one way in which you are produced? No. Each competitor offers up its own solution to the problem of producing a product. The result being a variance in costs and so a variance in price. This also implies a variance in the level of quality of the product and the demographic for which it favors the most. Much like competing species of trees which share the same canopy, each independent solution fills a niche' by means of doing so most efficiently. The same phenomena occurs in the market. This competition for efficiency gradually produces lower prices from lower costs given a sufficient amount of resources. Together, competitors forever strive to reach an unattainable equilibrium of prices independent of one another. Obviously the market is much more sophisticated than this, but at its basics, this generalization gives us some insights into the distribution of variance within an Evolutionary System.

I have stated before that I believe an Evolutionary System to contain a sufficient amount of variation within itself. That a probability distribution would best represent such a system. I have also stated that Evolutionary Systems evolve and diversify according to rules precedent in Thermodynamics. That, evolution has more to do with how energy is distributed throughout a system, than it does with the result of this process. What probability distribution would best represent an Evolutionary System?

The Heat Equation is a partial differential equation which models how heat is distributed through a given medium with given boundary conditions and source of heat. The boundary conditions show how insulated the medium is. In fact you may recognize some of this language. All throughout my previous posts, I have been making a case for the Heat Equation to be my prime candidate for analytically testing my ideas. It wasn't until this past year that I learned something which I hold to be semi-conclusive in my assumptions. The solution of the Heat Equation is a multivariate of the Normal Distribution. Another interesting property of the Normal Distribution is that it is one of the distributions which reflects the Principle of Maximum Entropy. While the Principle of Maximum Entropy is reserved mainly for application in Information Theory, I believe the arguments there have great merits here for I believe even abstracts such as Information are also Evolutionary Systems. For a few years now, I have been asking myself where I should begin searching for a proper representation of a probability distribution, and yet here under my nose was my first best guess.

The moral of story here is that the best solution to any one problem is all solutions no matter how wrong each of them are. Let me elaborate and bring into focus my choice for the title of this post. No matter how enlightened a person or group is, they can never fully achieve what is to be an absolute solution to any one problem. When we provide solutions, we provide them with some degree of error always. Chaos Theory shows us that when we assume a solution to be accurate to within some degree of error, under iteration the error can grow in magnitude to be that of the solution itself. This concept is known as Sensitive Dependence on Initial Conditions, or what is commonly referred to as the Butterfly Effect. So to assume that your enlightened solution can provide lasting relief to any given problem is ridiculous. Over time, as the solution is processed through the feedback loop of generations, the solution will become distorted. As the solution becomes more and more distorted, the probability that it creates more problems increases.

We often hear of the idea that global problems must have global solutions. This is an oxymoron. There can never be a single solution to a global problem which will not present us with future global problems. Meaning global solutions will always present us with more global problems. Problems are resolved most efficiently at more local levels with higher degrees of efficiency because when local solutions fail drastically, the probability that they have drastic repercussions on larger scale environments is very small. If my farm this summer fails, it will only affect myself and maybe some of my closest friends who may receive the fruits of my labor. The probability that it will affect the global market is nearly nil. However when a nation subsidizes, mandates and regulates the Farming Industry, this could have greater implications. The problem inherit with doing so never comes into being until these national solutions fail. The probability that this drastically affects the global market must be higher than if my own personal farm failed. This example illustrates very plainly the cons of collective solutions.

My argument here is that no one can fully understand what the absolute solution is, because that kind of certainty does not exist. The absolute solution can only ever be approximated, whether it be at local or global degrees. The ramifications of those solutions are better distributed at more local levels, insuring society with a sense of stability. Be weary of the solutions which the Ivory Tower presents us. They are naturally distanced from reality. Some may argue here that because of our population size and voter turn out, that we are offering approximate solutions at each echelon of our Nation's government. Though I would remind those persons that our society is very much polarized. Our form of government currently only ever offers two approximate solutions to any one problem. Both tend to have harsh repercussions. This is the irony of government. They exist only to solve the problems for which they have created by solving previous problems.

Until next time, safe travels.