Saturday, May 12, 2007

Complex Theory and Power Laws, With Philosophical/Economic Implications
An artist's depiction of fractals in complexity/chaos theory

These are concepts set out to replace linear causality. Instead of event A causing a response called event B, events A, B, C, D and so on act as either points, planes, or spatial objects, with or without mutual exclusivity, push and pull in tandem or in flux or with mutual influence but not to the full extent, either cause some other group of events to occur, cancel themselves out, or somewhere in between.

I suppose that's where things get complicated (thus, complex theory, what a cool name), but it is certainly a concept more befitting of economics than linear algebra--and not just economics either, but maybe existence itself too. Of course that's beyond what I'm trying to do in a blog entry. But what's amazing about complex theory is its scope of application, in back-testing of what's happend in the past, in understanding how we got to where we are now, and in setting a framework for any sort of art in predicting the future. After all, to make an example of a commonly known process: evolution, the beginnings of life were once considered humble and quite easy to understand. Now, to define life itself as an academic pursuit would take years of not decades of categorical work. As the theory goes, single celled organisms divided itself and combined with other organisms to form living beings planet earth is teemed with today. First with simple structures and organelles to sustain itself and reproduce--a cell wall to house cytoplasm, a nucleus to shelter chromosome, mitochondria to generate energy, and some endoplasmic reticulum to distribute resources. Then on to sexual reproduction and combination with the genetic codes of other cells to create intergenerational adaptation and evolution through the shared replication of superior genes. Then, as cells moved beyond being isolated phenomenons, vessels of massive size are created to house groups of cells who have found ways to co-exist under mutually beneficial arrangements--we can think of these as plants and animals at any given stage of evolutionary complexity. Some remain very simple as rudimentary genomes find no reason to evolve beyond what is necessary to survive in a simple, unchanging environment--phytoplankton, algae, and various other microorganisms. Some, in order to exploit changing circumstances and power over other organisms evolved into a complex entanglement of organs and biological fluids working together for the goal of common survival and reproduction. And some of these organisms even evolved an executive cell group created solely for the purpose of intellectual thought called the brain. And it didn't end there. Intellectual thought (at least only in humans on this planet) quickly became a means for what was once cellular organisms to go beyond biological fluids and structures, to create social interaction, common history, civilization as we know it recorded in the form of knowledge--the rise and fall of empires, the evolution of media and the press, religion, economics, politics, and most recently the creation of the most complex web of virtual ideas known as software. And who knows what the future holds. But what's clear to scientists and philosophers is that each stage of evolution and change can be traced and graphed as according to a secret order, and the magnitude and timing of each tipping point or critical state could be related back to a statistical power law. Changes of a certain magnitude will happen less likely the bigger these changes themselves are. The frequency of such revolutions in biology, science, knowledge, ways of thought will happen statistically less—as according to a power law, with some physicists and scientists pointing to a factor of four times as likely or not as likely. But these critical states of change happen in natural phenomena, and it gets quicker and more complicated with every branch of development expanding ever rapidly. It took longer for single-celled organisms to go from asexual reproduction to sexual reproduction, than for a moth to develop chameleon-like skin as according to their environment to avoid predators (a process that takes only a couple of generations, each lasting a couple of years). By the same token it took much longer for man to develop and pass on agriculture and basic technologies to the next generation, than for modern innovation to take a foothold in everyday life (remember the most daunting advancements in technology and social organization came about in the 19th and 20th century). This example of evolution, and the frequency of critical turning points in its progress (the second derivative), is just one of what modern intellectuals can attribute to complex theory and power laws--which, as the trend of our scientific times has determined, the origins of virtually everything on this planet, hardware and software, can be ascribed.

As any model goes, it serves very well as a framework for organizing and back-testing data collected on historical data and developments. Simple and seemingly linear progressions would start very easy, but accelerate into multifaceted networks of causality weighing on one another and create systems of stable equilibrium that expand infinitely. This is mathematically beautiful (I personally think so). You could look at the development of anything with a new perspective, from evolution as we've just mentioned, to the development of our current government (from townhouse meetings to national democracy to national committees and agencies to bureaucratic glut), the great monotheistic religions (from simple beginnings of monotheism to Judaism to the crucifixion of Christ and the spread of 'the word' by Paul to the arrival of Mohamed and the thereafter split between Sunni and Shia to the splits in Christendom of Eastern Orthodoxy, Catholicism, Coptic Christianity, Protestants, Evangelicals, and the arrival of Islamic fundamentalism), to why one should do well early on in school (from As in math, science, and english, to an A in subjects derived from these subjects, history and economics for example, and then knowledge of each subject in detail, which is virtually every subject from the beginning ones, and the detrimental effects of having to catch up if full understanding of simple origins of such knowledge is not achieved) to categories in science, politics, economics, philosophy, you name it. And all knowledge and existence could be related to a tree, with which metaphorical branches spawn even more branches, and it doesn’t stop. Sometimes branches get old and die, in existence and in knowledge, and when branches wither and fall from the tree the other branches fall with it—like an act of god or maybe the inability for the environment to support certain phenomena or without the environment going head-to-head against its very existence. And thus a web is disturbed. The example would be like a tiny moth going extinct due to an external factor such as human intervention to control their population, leading to certain smaller birds of prey unable to feed their young, leading to tree-dwelling mammals unable to find birds eggs as a source of food, and larger predators unable to secure a steady supply of these mammals as prey, and extinction occurs at the top of the food chain more often than the bottom, ect. Sometimes branches continue their upward and outward growth, far outpacing what its original host had intended, due to its prolific potential as a basis to develop offspring—knowledge, for one, has several of these: monotheism, mathematics, literature and philosophy, or even the more modern ones such as the Einstein’s theory of relativity, Darwin’s theory, game theory, critical state ubiquity (the most recent). Sometime knowledge could be destroyed or rarified in human knowledge, and rendered antiquated and useless—such as geocentric theory, medieval treatment of lunacy through exorcism, Zoroastrianism, countless languages from extinct tribes of people, and the list goes on.

To put it in a nut-shell, "complex theory" serves to describe an underlying order to what seems to be the complete chaos of modern day life, by first ascribing the origins of any categorical phenomenon under consideration and then, with a model--either scientific or philosophical, slowly branching out these origins and fitting more modern manifestations under these models, and be able to explain their evolution or destruction and the prospects of the “branch” going forward. The "power law" describes the speed and the frequency at which the branching out occurs—for example, outlining the occurrence of earthquakes and its statistical frequencies according to their magnitude—the famous Gutenberg-Richter theorem, or the accumulation of wealth being defined as being a certain power of more or less frequency as the amount of wealth increases or decreases by a certain factor in the individuals of a population, or just the normal curve under any statistical study delineating the expected normal occurrences spread across standard deviations—with events getting rarer as sigma grows.

Anyway, that was quite a bit of description, but hopefully one can see the implications that these theories can have on economic development, whether macro or micro, and the relevant policy or investment decisions might be derived from understanding such models. But, as any model, it's very good for hindsight. We should keep in mind the adage "Models do not provide answers, they only serve to detail questions". So what would this theory tell us in the world of finance and economics? Could we use something like this to learn more about how the world of practical matters such as money, employment, social security, empire building, etc.

Let’s leave that for another time.

Just another suggestion, pick up these books, they are insane and make you go "holy shit this kicks ass" with every page:

Ubiquity - Mark Buchanan, Deep Simplicity - John Gribbins, The Selfish Gene - Richard Dawkins

They may mention finance/economics only seldomly, but the concepts and simple truths delineated in the pages is something that everyone in perhaps every profession would benefit to know.

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