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Literate Chaotic / More tin foil hat material
« on: March 29, 2007, 09:36:36 am »

You see the lengths I go to in order to find high quality lulz?

Literate Chaotic / The Grey Lodge Occult Review
« on: March 22, 2007, 09:32:30 am »

Back Issues of the "Grey Lodge", who seem to be into their counterculture/Robert Anton Wilson style freakery.  Each issue has downloads for you to steal, sometimes as text files, pdfs, videos or mp3s.  Topics range from Alien abduction, the OTO, A;.A;., Men In Black and basically covering the range when it comes to wierd occult shit.

Bring and Brag / ATTN Artists and creative types
« on: March 18, 2007, 04:51:49 am »
The Popular Front for the Liberation of Discordia wishes to commission a logo for our esteemed organization.  The payment will be free membership in Scotland's premier quasi-terroristic organization as our Artistic Director, knowing we are likely to use your logo forever and, most valuably, my eternal gratitude.  Me and the 6 or so asshats I've duped into being my minions basically need something for the local flyers and rants sent to the newspapers.  I'm thinking maybe one seal based design and another as a page header of some description.

I'd do it myself, but my computer design skills are teh crap.

Propaganda Depository / What others say about the Discordian Society
« on: March 18, 2007, 03:17:47 am »
Found lingering on my laptop hard drive from where I had left it since Xmas...despite making several dozen flyers and spreading them in London, Bristol and Edinburgh


Their principal activity is an extreme mental derangement. . . . In the maximum number of languages the Discordian Society sends letters from foreign countries filled with the most filthy expressions. In our opinion the Federal Bureau of Investigation gave them too much credit in investigating them.
- Unnamed US Justice Department Official

The concerns of this movement, currently supported by é─˙The Good Reverend Rogeré─¨ and é─˙East Coast Hustleé─¨ among others, are in some sense comparable, a hundred years later, to those of the Young Hegelians and especially to the Marx of the 1844 Manuscripts . . . . That is to say, they imagine that a revolution is possible and their program is aimed at making one.
- New Absurdist Magazine #23

These é─˙activistsé─¨ have insulted the society in which they live and all its values. They should be dealt with by psychiatrists. I doné─˘t want to take any legal measures against them é─ţ they should be in a lunatic asylum. . . . As for their incitement to illegal acts, the Minister of the Interior is looking into that.
- Dominique de Villepin, 2006

The Discordians . . . are more anarchist than the anarchists, whom they find too bureaucratic.
- Robert Anton Wilson

Their doctrine, if such a term can be used in describing their delirious ravings, . . . is a sort of radical revolutionism with an underpinning of nihilism. . . . A monument of imbecilic fanaticism, written in a pretentious jargon, spiced with a barrage of gratuitous insults both of their professors and of their fellow students. It constantly refers to a mysterious é─˙Discordian Societyé─¨
- Militant Tendency, 1981

Then appeared for the first time the disquieting figures of the é─˙Discordian Societyé─¨ How many are there? Where do they come from? No one knows.
- Daily Mail, December 1994

Discordianism is, of course, no more the specter that haunts industrial society than was communism the specter that haunted Europe in 1848.
- Gregory Hill, Usenet Post, 1996

WARNING: Leaflets have been distributed in the Brixton area calling for an insurrectionary general strike. It goes without saying that such appeals have not been issued by our democratic trade-union organizations. They are the work of provocateurs seeking to provide the government with a pretext for intervention. . . . The workers must be vigilant to defeat all such maneuvers.
- Socialist Workers Party Directive, 1981

. . . the Discordian Society, which has its base in San Francisco and which is controlled by the security and espionage police of the Union of Soviet Socialist Republics...
- John Birch Society

Their general headquarters is secret but I think it is somewhere in London. They are not students, but are what are known as Discordians; they travel everywhere and exploit the discontent of students.
- Anonymous interview published in the News of the World, 1987

We are here concerned with only one small group who alone set the scene for the May events and provided the insurrection with a dialectical backbone. These few outlaws, these Discordians, universally despised by political organizations and student bodies, have their base on the surrealistic fringes of the Left Wing. From there they have nurtured one of the most advanced, coherent revolutionary theories (though often plagued by academic arrogance and é─˙iné─¨ references), which provoked a near-liquidation of the State.
- Taken from the suppressed Colombia University Report into the April 23rd take over of the University in 1968

Miss Martin said the é─˙Discordiansé─¨ were a religious movement active in Greece in the 10th century BC, and that there had been é─˙talké─¨ on the campus of a revival under that name in Berkeley.
- San Francisco Examiner (18 May 1972)

The Discordian Society was created by the CIA from scratch in 1957 in New Orleans under the slogans é─˙Nothing is True, Everything is Permissible,é─¨ é─˙A Discordian is prohibited in believing what he reads,é─¨ and é─˙Creative Disorder!,é─¨ and is the paradigm example of a CIA synthetic all-purpose formation. The loose and programless anarchist é─˙left coveré─¨ countergang on the Discordian model is ideal for the CIA for the recruitment of new agents, the launching of psywar operations, the detonation of riots, syndicalist workersé─˘ actions (e.g., LIP strike), student power revolts, etc., the continual generation of new countergang formations, and infiltration, penetration and dissolution of socialist and other workersé─˘organizations. . . . During the 1968 problems, the Discordians were assigned to stop the Labor Committees from developing into a mass-based working-class party.
- New Solidarity, 28 August and 6 September 1977

Discordianism seems to have é─˙caught oné─¨ in the U.S.A., particularly in California, that playground of the ideologies. . . . The American Discordians seem to be repeating the pattern of mutual exclusion and criticism as occurred in Europe, and to be employing a fairly impenetrable Hegelian vocabulary. . . . Wilson and Hill are worth reading for their critique of modern consumer-culture (if you can arrange a few weeks free of work and booze).
- Time Magazine, 1976

Behind the angry young men of Amsterdam we find a secret Society. . . . The Provos provide the previously isolated theorists of the Discordian Society with troops, é─˙intelligent surrogatesé─¨ capable of constituting the secular arm of an organization which itself prefers to remain more or less behind the scenes.
- Figaro Litt?ęraire (4 August 1982)

Bring and Brag / Latteart
« on: March 14, 2007, 05:33:22 pm »

Think for Yourself, Schmuck! / Wheeeeeeeeeeee!
« on: March 14, 2007, 01:30:49 pm »

Modern Discordians have finally almost created a new idea on their own . . . they only had to rip it off from an imfamous CIA investigated sci-fi hack named Dick. How appropriate.

This idea is known as the Black Iron Prison, and the basic concept is that your own perceptions are a prison from which you can never break free from. Once you realize you are trapped in a prison you can try to break out, but once you are outside you realize you are trapped within a larger, more impenetrable, prison. No matter what you do, or what you try, you are trapped.

What a cheery concept.

They offer no ways to get out, or think around this concept, its just laid out there and you had better digest it, accept it, and like it or you are a shallow fool who doesn't get the 'harsh reality' of the situation.

The idea comes from Dick's book Valis, which nobody I know has read or even heard of. The more obscure, the better, I guess.

Think for Yourself, Schmuck! / Absurdism
« on: March 07, 2007, 09:00:16 pm »

Salient parts c+p'd

Absurdism is a philosophy stating that the efforts of humanity to find meaning in the universe will ultimately fail (and, hence, are absurd) because no such meaning exists (at least in relation to humanity).

What is the Absurd? It is, as may quite easily be seen, that I, a rational being, must act in a case where my reason, my powers of reflection, tell me: you can just as well do the one thing as the other, that is to say where my reason and reflection say: you cannot act and yet here is where I have to act... The Absurd, or to act by virtue of the absurd, is to act upon faith ... I must act, but reflection has closed the road so I take one of the possibilities and say: This is what I do, I cannot do otherwise because I am brought to a standstill by my powers of reflection.

é─ý Kierkegaard, S??ren

In The Myth of Sisyphus, Camus considers absurdity as a confrontation, an opposition, a conflict, or a "divorce" between two ideals. Specifically, he defines the human condition as absurd, as the confrontation between man's desire for significance/meaning/clarity and the silent, cold universe (or for theists: God). He continues that there are specific human experiences that evoke notions of absurdity. Such a realization or encounter with the absurd leaves the individual with a choice: suicide, a leap of faith, or acceptance.

man can choose to embrace his own absurd condition. According to Camus, man's freedom, and the opportunity to give life meaning, lies in the acknowledgment and acceptance of absurdity. If the absurd experience is truly the realization that the universe is fundamentally devoid of absolutes, then we as individuals are truly free. é─˙To live without appeal,é─¨ as he puts it, is a philosophical move that begins to define absolutes and universals subjectively, rather than objectively. The freedom of man is, thus, established in man's natural ability and opportunity to create his own meaning and purpose, to decide himself. The individual becomes the most precious unit of the existence, as he represents a set of unique ideals that can be characterized as an entire universe by itself.

I believe our current project to be the metaphysics of the Absurd.

Think for Yourself, Schmuck! / Plan of action
« on: March 07, 2007, 04:48:01 pm »
1. Come up with a better name (BIP is too philosophically constrictive and attracts emo/goth types.  Sorry, but it is).

2. Decide where we want to go from there.  Is this meant to be a blueprint for action or trying to figure stuff out?  Throw in a target audience here.

3. Get writing.

4. Position the project as something associated with the Discordian movement but not part of it.  Thats important, because sooner or later everything fizzles out and I'd rather the place where the ideas come from didn't go with it.

5.  More suggestions?

Or Kill Me / LDD Sermon #8 There was no American Revolution
« on: March 06, 2007, 06:36:54 pm »
As you know, I have always advocated a clear headed and objective view of the state of things.  You cannot do otherwise if you hope to effect change é─ý without knowing what has happened and is happening, you are adrift with no plan and no way of knowing what is of practical use or not.

Because of this, I feel it is necessary to for once and all put an end to a very pernicious lie, namely that America had a revolution and, that unlike those in France and Russia, it was a success, for various reasons.  It is true that in America there was no Terror, that no death squads like the infamous Cheka arose as a sword and shield to the revolutionaries.  And the reason for that is not that Americans are quantifiably different, or have higher moral standards.  Its simply because what happened was not a revolution and so the after effects did not follow the same pattern.

I know what you're thinking.  é─˙But...there was fighting...and they separated...a new country was created...the Bill of Rights and Constitution....whats he on about?é─¨  And you're right, all those things did happen.  But they do not necessarily add up to a revolution.

A revolution must negate all preceding history and political theory that came before, annihilating them on the tide of their chosen ideology.  In revolution, ideas are put on trial, with humans in their places on the dock.  These ideas and their human hosts are killed as a sacrifice to the new order, as a symbol of a new dawn in humanity and the end of the previous order.  Invariably, this turns to state terror and rivers of blood.  In short, the revolution must, by its nature, kill itself in a blaze of self-destructive glory, giving rise to new tyrants and monsters.

In America, this did not happen.  There was no American Robespierre, no Stalin.  King George III was never put on trial and executed, Lord North and the rest of his inept Parliament were not given shallow graves and no new order was proclaimed.  There is a crucial reason as to why this is; America was a successful rebellion, one of the very few in history, which makes it very different to a revolutionary state.

America, it can be argued, is in fact the true heir to the British political system.  Radical democracy had long existed in the colonies, the political ideals they expounded an extension of British ones, but with updated theories from the latest philosophers.  The separation of powers, the Bill of Rights and the Constitution are all implicitly part of the British constitution, weakened though it is through its unwritten nature.  Those who worked from this system, such as Paine, Locke and Hume, were the inspiration for the likes of Jefferson and Madison.

In short, the rebellion was not about the creation of new values, but the restoration of old ones.  That is the vital difference, the limiting factor that ensures a rebellion will not end up copying the Terror.  It is a built in factor that leads to self-moderation and the real establishment and respect of human rights.  American revolutionaries did not dispute George III as a King, only his claim to rule over them, the nature of the relationship.

In short, rebellions work.  Another example for you to ponder.  In 1975, in Helsinki, the NATO powers forced the Soviet Union and its allies into singing a treaty on human rights, in return for improved trade.  The Soviets thought nothing of signing it and ignoring it, despite the treaty making it law for these rights to be respected.  But the dissidents took note.  While of course, it was only one factor among many, the Helsinki accords were as close as anything to a philosophical basis for the rebellions.  They were not out there to deny Communism as a system (in fact many called themselves Socialists, both among reformists and dissidents), they were there to deny what was being done, again to dispute their relationship with the state.  And again, they had success.  The Warsaw Pact was destroyed without a shot being fired, the USSR soon to follow.

Many Discordians may like to think of themselves as revolutionaries too.  God knows, there are enough self styled dissidents, protesters and anarchists etc who will gladly take that title.  However, what should really be sought is the mantle of rebellion.  Revolutions invariably go full circle, whereas rebellion can restore what was once lost.  Falling into the trap of seeing America or 1989 as é─˙successful revolutionsé─¨, working variations of Russia and France, is just falling into another trap, making a mistake that could be very costly.

Food for thought, I feel.

Propaganda Depository / Kopyleft Authors
« on: March 05, 2007, 09:34:36 pm »
Please post in here if you are willing to let others use your works.  If there are any special conditions (such as a piece of work you don't want to be used or whatever) please state them here too.

Or Kill Me / On Conspiracy Theorism
« on: March 03, 2007, 01:17:15 pm »
Alot of people interested in the counter-culture in general and particularly the three ring circus of Discordianism, the CotSG and affiliated Subcordian asshats, take a deep interest in conspiracy theories and the workings of secret cabals which are hostile to our very existence. I don't necessarily need to describe such groups as I'm sure you know what I mean. The Illuminati, various arms of The Conspiracy....Them, in short.

Obviously, many ordinary people do not believe in any sort of Them at all and so these groups have perhaps jeopardized their "credibility" (as if what Pinks and Greys think actually matters) in certain circles. However, a lot of people are wasting their time in this general area of inquiry. Thats not to say there are not conspiracies, because there are and they are very real, but most people have been hoodwinked into looking in totally the wrong direction for them. I certainly don't have all the answers, but I am in a position where I can quite legitimately research the linkage in the corridors of power and am able to tell you what I know.

I wont name names however....not real names. Rule 1: everyone is a disinformation agent. Its all too easy for false information to be fed to you or me, so I'll just sketch out the general 'shape' of whats going on, letting you fill in the blanks yourself. I'll also tell you what is likely not true and why I think thats the case. Firstly, the liars.

Many Conspiracy Theorists come from the Christian Patriot Movement, a collection of pig-ignorant degenerates and criminals who couldn't find their backsides with both hands, let alone highly intelligent conspirators working in the shadows. Invariably these idiots will make racist claims of "International Jewish Bankers" and...well, I barely need to go on. The sort of shit you can read in The Turner Diaries and other pieces of infantile fantasizing interspersed with horrific racist violence and disgusting characterization. If you believe anything that comes from these circles, chances are you're a brainwashed idiot duped by some charismatic leader with a Messianic complex.

Building on from example one, there is the general "Jewish Conspiracy" which is popular among the far-right (just ask Nick Griffin), the far left and various religious groups. This is quite frankly utter horsecrap....going by history, we should probably have a White Christian Male conspiracy, as these are usually the people involved in such things. Its basically scapegoating and stems from a religious need to place the blame for the death of Jesus on anyone but the Romans, who actually did him in. Anyone with any real knowledge of history would dismiss the idea of any single ethno-religious group being behind all conspiracies, or even just a large one as utter crap.

The UN is another one also taken from the far-right. Apparently they are a godless and evil organization preparing to take over the USA and occupy it with foreign troops....whereas the depressing truth is in fact the UN is nothing more than a device for the USA to legitimize its actions abroad. It doesn't always work of course, but given the powers the US gave to itself as a charter member....well, its a testament to the power of propaganda that people can think its anything but a slightly unruly tool of the USA.

Intelligence services are often a favourite one, for obvious reasons. Cloaked in secrecy, given wide powers to act pretty much outside the law, the similarities with secret police of bygone times, yeah here we are onto something more plausible. However, it should be remembered that almost always these are merely foot soldiers for higher powers and if they are doing something, its because they have been directed to do so. Running drugs, assassinations and so on, while invariably blamed on a rogue faction, do serve a greater political or security purpose.

The Satanic cult is another favourite, particularly among David Icke sorts, who can combine it with the relatively more interesting alien abduction theories. Satanic Ritual Abuse is probably one of the greatest scare stories of the 80s, one for which there is very little to no real evidence. Most Satanists are....well, jerks basically. Smart people, very quick mentally, but real assholes. The CoS is basically a money making device and the Temple of Set...well, its occult so its not my cup of tea, but its no worse than what Wiccans get up to. What is often referred to as organized Satanic abuse in fact is usually widely disorganized and carried out by...mentally ill Christians. Who, coincidentally, are the sort of people most likely to promote this theory.

Alien abduction is the few cases where there is genuine reason to believe that is in fact what happened. However, in most cases they are part of a carefully crafted government disinformation project. Not only does it explain experimental aircraft tests quite nicely, it also keeps a whole bunch of people on a wild goose chase, either keeping them distracted and ruining their credibility, or causing the believers to fall under the sway of irrational terror and hopelessness. I'll explain more on this another time, but there is evidence to suggest that intelligence agencies have in fact staged many of these events, either as part of a general disinfo project or as covers for other activities.

International Banking is actually one of the few areas where the theorists may have a point. If you throw in the various multinational companies involved with them, as well as a few NGOs. The World Bank and IMF are essentially tools of the European and US governments, used to "crack open" foreign markets, totally undermine the economy, then buy up previously state owned companies at bargain basement prices and bleed the plebs. Its the modern day version of colonialism, only it actually makes a profit.

Secret societies are of course the number one favourite for conspiracy theorists. Been around a long time, naturally secretive....the problem is most of them are basically talking shops. Anyone can join the Freemasons and while there are a few specific lodges that have been involved in some nasty shit, the majority are quite dull. The Illuminati have never been proven to exist beyond their downfall in 1785 and the Priory of Sion were always a sham. Most of these are generally beneficial organizations anyway, the Freemasons in particular being closely aligned to Enlightenment ideals expressed by writers like Voltaire and Diderot.

So what do I believe?

I think there are certain...factions at the very top of the political-economic structure, whose membership is hard to ascertain but who can be judged by their actions. At least one is highly antagonistic, ultra-nationalist and allied with certain sectors of big business. These are closely allied with certain Theocratic nuts, with whom there is overall agreement, though each dislike the other for certain reasons relating to their own beliefs. There is one whose view could most accurately be described as Neo-Liberal, who are largely benevolent and are closely linked to a benevolent movement for world governance. And there is another who wants the same world governance, but for entirely less high-minded reasons.

And of course, within each group there are sub-groups, factions and dissent.

One final tip before I end this - don't look to fancy sounding names and titles, because thats entirely the wrong way. Look towards bland sounding committees and think tanks, with boring names like the Committee for a Free Britain or The American Enterprise Institute....also watch out, as certain groups (such as the Project for a New American Century) are likely to shed their skin and change when exposed to too much light (as when they changed into the AEI).

Apart from those, for me Conspiracy Theorism is rather like Alternate History discussion, its an interesting look into how the world could be, as well as fuel for the imagination.


Maj David Nicholls, USAF
Maj Todor Tagarev, Bulgarian Air Force

For the last 30 years, the study of chaos has intrigued investigators, prompting many to see a great future for the study and application of chaos theory. In science and engineering, chaos theory has significantly improved our understanding of phenomena ranging from turbulence to weather to structural dynamics.  Chaos theory has even been used to drastically improve our ability to control some dynamic systems.  In the social sciences, there has been considerable interest in whether social phenomena, previously thought to be random, have an underlying chaotic order. Several mathematical tests for chaotic behavior have been applied to historical data from both the stock market and cotton prices. These tests indicate that these economic phenomena are chaotic and so have a deterministic basis (i.e., are governed by rules) as opposed to being random. Naturally, this has received some business attention, and at least two firms are now using chaos theory to guide their financial advice.

There is evidence that warfare might also be chaotic. First, strategic decision making, an integral part of war, has been found to be chaotic.  Second, nonlinearity, which is a requirement for chaotic behavior, appears to be a natural result of Clausewitzian friction.  Third, some computer war games6 and arms race simulations have been found to exhibit chaotic behavior. Fourth, previous work by the current authors applied several tests for chaos to historical data related to war. Those tests demonstrated that warfare is chaotic at the grand strategic, strategic, and operational levels.

An Overview of Chaos Theory

In this paper, we will discuss some important implications of chaos theory in the context of warfare. First, however, we will briefly summarize some important aspects of chaos theory.


If a system is linear, it means that the output of the system is linearly related to the input. In other words, if the input is doubled, the output will be doubled; if the input is tripled, the output will be tripled, and so on. In nonlinear systems, however, the output might be related to the square or the cube of the input. Such systems are often very sensitive to input. All chaotic systems are nonlinear.

Predictability of Chaotic Systems

Dynamic systems can differ from one another in how they change with time. In random systems, future behavior is independent of the initial state of the system and can be characterized only in terms of probabilities. For example, unless the dice are loaded, the next roll of the dice is totally independent of the previous roll. On the other hand, periodic systems return regularly to the same conditions, as exemplified by the pendulum clock. Such systems are totally predictable because once one period is known, all others must be identical. Chaotic systems are neither random nor periodic. They are not random because the future of a chaotic system is dependent upon initial conditions. They are not periodic because their behavior never repeats.

Chaotic systems never repeat exactly because their future behavior is extremely sensitive to initial conditions. Thus, infinitesimal differences in initial conditions eventually cause large changes in system behavior. An often-used example of this sensitivity is weather. Weather is so sensitive to initial conditions that there is a belief that the flap of a butterfly's wings in America could eventually cause a typhoon in China.  It is inconceivable that conditions on the earth could ever duplicate an earlier time to the point where even all butterfly flights are duplicated. Therefore, the earth's weather will never be periodic.

In addition to making chaotic systems aperiodic, extreme sensitivity to initial conditions means that it is not possible to determine the present conditions exactly enough to fully predict the future. Figure 1 illustrates this point. In figure 1, successive values for x are plotted resulting from the nonlinear equation xi+1 = 4xi - 4xi2. For one plot the initial value of x was 0.7. For the other plot it was 0.70001. Initially, they are indistinguishable from one another, but as time goes on, even such a small difference between the two is magnified until their behavior appears totally unrelated. Short-term predictions are still possible because small influences will not have had time to grow into large ones. However, what is short-term depends on how sensitive the system is to small changes at that point in time.

The importance of this concept is that it explains how a system can be governed by a set of equations and yet still be unpredictable. We cannot know the initial value of a system, such as that illustrated in figure 1, precisely enough to predict which path the system will follow. If warfare is chaotic, this tells us that we cannot make perfect predictions even if we could reduce war to a mechanistic set of equations. Fortunately, as is also illustrated by figure 1, there are bounds to the unpredictability of a chaotic system. Furthermore, chaos theory provides tools that can predict patterns of system behavior and can define bounds within which the behavior is unpredictable

Phase Space

The construction of a phase space plot is often used to better understand chaotic behavior. A phase space plot is a plot of the parameters that describe system behavior. It is useful because it provides a pictorial perspective for examining the system. An example of a phase space plot for a simple pendulum is shown in figure 2. At point A in figure 2, the pendulum is the maximum positive distance from the bob's neutral point but its velocity is zero. This is shown as point A on the phase space diagram. At B the distance of the bob from its neutral position is zero, but its velocity is at a maximum (in a negative sense). The other points of the phase space plot show the relation between the velocity and position for other pendulum positions. In this case, where there is no friction, the motion of the pendulum is constrained to remain on the elliptical path shown in the phase space plot. The technical term for this ellipse is the attractor for the system. One can see that this attractor is periodic because the path of the system exactly repeats itself in each orbit around the origin.

In contrast, figure 3 shows an attractor for a chaotic system. This attractor is a tangled mess of trajectories. The complexity of this attractor has led to its being dubbed a strange attractor. Although there are still constraints as to how the system behaves, there are a lot more possible states for the system. It is important to note that the phase space paths of a chaotic system will never coincide. If this were to happen, the system would become periodic. The longer a chaotic system is observed the more paths are taken and the messier the phase space plot of the attractor appears. Superficially, the attractor may appear to be completely disorganized. Closer examination of the phase space, however, reveals that the attractor is organized but in an unconventional manner.

It is possible to simplify the portrayal of the attractor by taking a two-dimensional slice through it (shown in the lower half of figure 3). This also makes the structure of the attractor more obvious. This two-dimensional section is called a Poincar?ę map.10


We generally define things dimensionally in terms of integers. Lines are one-dimensional, planes are two-dimensional, and solids are three-dimensional. Fractals are objects with fractional dimensions. This concept appears at first sight to be nonsense. An object with a fractional dimension of 1.5, for example, would be more than a line but somehow less than a plane. Nevertheless, such things are not only thought to exist, but such geometries are central to chaos theory. One example of such a geometry, although it is not chaotic, is the Koch snowflake.

The Koch snowflake starts as an equilateral triangle. A one-third scale equilateral triangle is added to each side. A one-third scale triangle (of the new, smaller triangle) is then added to each side of the resulting figure. This process is continued ad infinitum as illustrated in figure 4.

The perimeter of this shape has several unique features. First, although it is a single, continuous loop that does not intersect itself and that circumscribes a finite area, its length is infinite. Second, Benoit Mandelbrot calculated that the dimension of the perimeter of the Koch snowflake is 1.26.11 This means that the perimeter is between a line and a plane. Third, the shape of the perimeter of a Koch snowflake is self-scaling. That is, the perimeter would look the same whether you looked at it with the naked eye or with a powerful microscope.

These geometries are pertinent to chaos because strange attractors are fractal. Strange attractors, like the Koch snowflake, are infinite curves that never intersect within a finite area or volume. If a system is chaotic, it will have a strange attractor and the Poincar?ę map will show fractal characteristics. That is, the Poincar?ę map will remain similar regardless of scale.  Thus, Poincar?ę maps can be used to determine if a system is chaotic by visually depicting the nature of the attractor. The dimension of the attractor can also be calculated. If an attractor's dimension is not an integer, then the system is chaotic.

Implications of the Presence of Chaos in Warfare Previous work examined historical data associated with the grand strategic, strategic, and operational levels of war. That work showed that war is chaotic on all of these levels. If war is chaotic, then it must have the characteristics of a chaotic system. We will now describe some of the characteristics of chaotic systems and define what they mean in the context of warfare.

Computer Simulation Can Enhance Understanding

Computer numerical modeling or simulation has greatly increased our understanding of physical chaotic systems. The reason for this is that the equations that govern chaotic systems are nonlinear and therefore are generally not analytically soluble. Chaos theory, however, cannot be used by itself to derive a theory of warfare. As with any other theory that describes a phenomenon, a theory of warfare must be based upon observation, hypothesis, and testing. Specifically, development of a model of warfare would require the development of the structure of the model, the determination of the number and type of variables, and the determination of the form of the equations. In addition, system parameters and control factors, as well as sources for noise, would have to be identified. This is a very difficult task for any particular situation that is complicated by the possibility that different models might apply for different antagonists.

Chaos theory can help us by suggesting ways to develop our model and ways to use the model once it is developed. For example, observation of a chaotic system can be used to determine the dimension of the system. The number of variables needed to describe the system must at least equal the dimension of the system. Therefore, chaos theory can be used to define the minimum number of variables required in our computer model. Chaos theory also suggests that computer models of warfare must contain some nonlinear relationships between system variables so that the computer model is chaotic and thus reflects the chaotic nature of warfare. This may actually prove to be advantageous since the fractal nature of chaotic systems may allow relatively small and simple war games to accurately simulate warfare. Realistic war games that could be run on a desktop computer would have significant educational and operational advantages. Finally, the rate of information loss can be calculated for a chaotic system. This quantity is related to how far into the future predictions can reasonably be made.

The ways in which computers have been used to understand chaotic behavior in physical systems also suggest ways to use the computer to model warfare. For example, although chaos theory explains some aspect of the weather, the reader has probably noted that weather forecasting has not become perfect. This criticism, however, misses one of the most important contributions that chaos theory has made to weather prediction--chaos has given weather forecasters a means to determine if their forecasts are likely to be accurate. Chaotic systems are highly dependent upon initial conditions but they are not always equally so. If a chaotic system is in a portion of its phase space where the initial conditions are critical, then uncertainty in determining the initial conditions makes a large number of outcomes possible. If a chaotic system is in a region of its phase space where the initial conditions are not critical, then only one outcome (prediction) is likely. In practice, weather forecasters use this behavior by inputting small changes in initial conditions into their model. If the small changes produce small variations in the prediction, they have shown that the system is in a portion of phase space where the initial conditions are not critical and their prediction is likely to be true. If the minor changes in initial conditions produce large deviations in future behavior, forecasters know that their prediction is likely to be in error.

The same approach could be taken to understand when predictions in warfare are likely to be accurate. This in itself would be a valuable contribution of computer simulation to understanding warfare. There are, however, two additional reasons why this approach may be even more applicable to warfare than it is to weather. First, unlike weather forecasters, we have some ability to change the initial conditions. Specifically, if we find ourselves in a region of great uncertainty, we could determine which conditions would have to be changed to move the system to a position where the outcome was predictable and desirable. The quantity and type of forces are examples of initial conditions that we might be able to change. Second, we could use our model to determine which initial conditions and which variables had the most profound effect on our predictions. This would aid in identifying centers of gravity (COG) and information that we needed to know precisely. That is, it would tell us where to concentrate our attack and what intelligence information was most critical.

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