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.

4. The Hierarchy of Einstein and the Universe.

What is the probability of Einstein ever existing? What is the implication of even pondering such a question? What necessary events had to occur in order for Einstein's life to unravel for all the reasons we take care to remember? While seen as a pioneer, Einstein mostly synthesized already known ideas. The difference between him and another who may have done the same is the conclusions he came to. These conclusions not only changed things, but they changed almost everything on this small blue world. I know in my life, that I would be most proud to have changed only a fraction of things to occur. We all should feel that way. What is the difference between the probability of Einstein existing, and myself, or even you? What is the difference between Einstein existing and the Universe?

The difference must be a number. Be careful to assume that it is less likely for the Universe to exist, than it is Einstein. For Einstein to exist, the Universe must have first existed. We must change our point of view of what defines existence. What is the probability of an event occurring which directly influences to some degree, all proceeding events within some locale of time and space? In this case, the event known as the existence of the Universe has less of a probability of happening than Einstein. This means that because the Universe happened, it directly influences all proceeding events. That given the Universe, Einstein is likely to happen and not as often as me or you. I am not trying to discredit our lives in any way. Rather, I am illustrating just how much we can accomplish with our lives. That our accomplishments are all the events which we influence, both during and beyond our lives.

To equate this to my model for Evolutionary Systems, we must establish what Einstein was to his system. He among many prominent members of the physics community diversified physics. Prior to these peoples lives, Physics had exhausted its resources in understanding. It was inevitable for it to evolve and diversify. Its only other choice was stagnation. For these reasons, we can assume that Einstein, and many others of his caliber, contribute to the ordered part of their evolutionary system. Further, that the probability of Einstein existing forced Physics as an evolutionary system to evolve, and subsequently diversify, because the probability of high caliber individuals existing is lower than that of the rest of us. We have already established in previous blogs that the systems we discuss as being evolutionary, are best represented as a probability distribution. But which distribution? This is not a question I like answering at this stage, but if I were to guess, I would guess that the distribution would be very closely related to the normal distribution. I will give you my full reasoning for this in a later blog.

The less likely that something exists implies its capacity to influence its environment is greater than the average member of its population. This is observable and evident in any evolutionary system. For example, it is less likely for a lion to be born who happens to be stronger and faster than the rest of the members of its pack. The implication of it being stronger and faster means that it is more capable of making the kill than the next. This changes the environment that the entire pride exists in. It further forces the prey to evolve, to be stronger and faster still. This in turn provides pressure on the pride as a whole to evolve further still. This is what it means to be less likely to exist. The more ordered part of the system has less of a chance of existing, because if it was otherwise, the evolution of the system would lead to more detrimental implications to the environment of which it persists. This in turn undermines and mutates the system into homogeneity. There is a fine line, a optimal hierarchy for every evolutionary system to have. It is at the point where the system's progress in evolution does not undermine its future generations. When that line is crossed, the system homogenizes and it becomes something else than what it once was.

Imagine for a moment, that nothing else exists. Instead, everything that is, is a nearly perfect sifted space of energy. It is static, and of near perfect inhomogeneity. What is the probability of an event occurring which directly influences to some degree, all proceeding events within some locale of time and space? The answer is "a very small probability", nearly infinitesimal. There are many lesser order states which could occur more frequently, but they are not ordered enough to ever make an irreversible set of events from ever happening. A nearly infinitesimal probability of an event occurring in this environment would bring into existence a nearly perfect ordered system. This is under the basis of everything I've discussed in this blog, given my assumptions to be correct. While the probability of this super ordered state to exist is nearly infinitesimal, it will still exist eventually. When you take into account all of time, as we understand it, a nearly infinitesimal probability could occur nearly an infinite amount of times, given all of time for it to occur. What is this super ordered state? By our understanding of entropy, it's first course of action is to break down into a more diverse population of lesser ordered systems. It must do this, because it must correct itself for ever existing, by distributing its energy to ever more local levels. This now is the inflationary period of the birth of our universe. Every transaction between ordered states and the energy needed to sustain them, takes place after this point. It leads the universe to producing things such as you and me, and all the Einsteins to come.

Until next time, safe travels.