Disorder, Chaos, and Existence
[NOTE: An expanded, 2005 version, of this article is available here.]
Chaos and disorder are frequently associated with political anarchy, but this chapter is only about what order means and the confused idea that disorder means chaos or destruction and the interesting mathematical concept of chaos. Interestingly enough, there is a relationship between chaos, in the mathematical sense and the "chaos" that, supposedly, anarchy would lead to. Since that would be a digression from the subject at hand, political chaos will be fully explicated in the, "Social Chaos," chapter.
This chapter is partly about that branch of mathematics called chaos, including fractals and strange attractors, it is not a technical discussion of that subject, but a way of introducing some related philosophical ideas having to do with disorder, existence, and the limits of mathematics.
There is some math, and there are some technical terms, but for the most part, this is not a very technical discussion.
What is Order?
What exactly is chaos? The common view, I think, is that chaos is extreme disorder, or even complete disorder. Without understand what order is, however, this description is not very helpful.
Ironically, one of the most confusing of concepts is the concept of order. The word itself has more than one meaning or connotation, and those meanings are often confused and include: 1. relational order, 2. functional order, 3. natural order, 4. uniform order, and 5. entropic order. For the sake of explanation, the first three kinds of order (relational, functional, and natural) will be referred to as positive order and the last two kinds of order (uniform and entropic) will be referred to as negative order.
1. Relational order—is numerical or hierarchical order such as order that can be identified by the ordinal numbers, first, second, third, fourth, etc. Numerical order is an epistemological method of identifying relationships in space or time, and by analogy relationships between values and concepts. For example, "the third tree from the left," "the fourth time today," "the most expensive of the three houses," "the fourth priority," and "the penultimate syllable," for example. Taxonomy and geneologies are examples of hierarchical order.
2. Functional order—is any order that is based on the intended purpose of a method, process, or design and may include numerical oders (a recipe for example). When a method fails, (because a rule has been violated), or a process fails, (because a step is missed), or design fails (because a machine part is missing or wears out) the failure is a kind of disorder.
3. Natural order—is the order of the natural world, determined by the nature of material existence which are the laws discovered by the physical sciences. When natural events, determined by physical laws, are described as order, it is not functional order. There cannot be any disorder in nature, and whatever happens in the natural world is natural order. Though natural order is often mistaken for functional order, natural order has no intrinsic objectives or purposes.
Natural order is the order arising from the ontological nature of physical existence. The most important aspect of that nature to order is the, necessity of difference, described as the second corollary of the axiom of identity: "Anything that exists must be different in some way from everything else that exists. No two things can be identical." [See the chapter, "Ontology Introduction.]"
4. Uniform order—is any order that limits or eliminates differences. Things have uniform order to the degree they are the same in either their attributes or their behavior. It is this kind of order that is usually meant by social order, for example, meaning everyone conforms the same behavioral rules. In a very real sense umiform order is always destructive (eliminating difference which is necessary for existence) and is the converse of both functional and natural order.
5. Entropic order—is the oder of distribution of either useable energy (in thermo-dynamics) or data integrity (in information theory). Like uniform order it is the converse of other meanings of order. More entropy means less difference in usable energy or data, less entropy means more difference in usable energy or data.
Existence Requires Disorder
The second corollary of existence is, "The Necessity of Difference—Anything that exists must be different in some way from everything else that exists. No two things can be identical in every way." The difference must be a difference in qualities or attributes; no two existents can have exactly the same qualities.
Ontologically, then, existence depends on disorder in the uniformity sense. If everything were uniformally the same, if there were not differences, there would be nothing. To illustrate what this means the nature of information (as in information theory and entropy) can be used.
[NOTE: "Information theory," is not about information in the sense of knowledge or cognition. The, "information," in information theory is about the integrity of stored or transmitted patterns which can represent anything, but in themselves have no meaning. So long as the patterns are faithfully stored or transmitted the entropy of the system is zero.]
What is odd about information theory is that perfect order, in the uniformity sense, is maximum entropy, meaning zero information. The reason is because information, like existence, requires difference to exist. Consider the following illustration:
The string of dots represents states of the medium of transmission or storage of information. The actual medium could be a light beam, radio signal, or a physical state (voltage, static charge, or magnetic polarity). So long as there is no difference, either a change in the transmitted medium (constant amplitude, frequency, or phase of the radio signal, or steady light beam) or difference in the storage state (same voltage, static charge, or polarity), no information is possible. (The dots represent potential points of change or state in a medium.)
In order for any medium to carry or hold information a change or difference is required either in the transmitting medium or storage medium. (The, "#s" represent a a change or difference in the medium.)
What meaning the information data represents, if any, is irrelevant to information theory. Information theory is only interested in the integrity of the transmitted or stored data. If the data sent or stored and the data received or retrieved is identical, there is zero entropy in the information system.
If the data received or retrieved has none of the changes or differences transmitted or stored the system has total entropy.
In information theory, the degradation of the integrity of transmitted or stored data directly determines entropy. In the following example, the entropy has doubled.
Though the data in information theory is neither knowledge or cognition, it can be used to transmit or store knowledge, just as written language does. The knowledge does not exist in the data, however, but only in the minds of individuals who are able to interpret the data used to, "encode," knowledge. The following illustration is the exact same string of dots and #s as the original example. The original represents a continuous string. The interpretation below is made by dividing the string of data into separate strings of twenty one units. The method of encoding and decoding the data must be predetermined by a human being.
You might notice the interpretation of the encoded, "message," is based on a kind of order—relational order. Breaking the string of data into groups of twenty one units interprets the message. Also notice, the disorder (variation of the data itself) must be maintained for the interpretation to work. Any method that in any way decreased the disorder of the data would destroy any intended message.
Positive Order Vs Negative Order
Both positive order and negative order are based on the fact that an existent's attributes are its identity. The idnentity of all existents are the attributes that are those existentsd. Positive order identifies things in terms of attributes they have—the attributed that differentiate them; negative order identifies things in terms of attributes they do not have—attributes that would differentiate them.
Everything that exists is different in some way from every single other thing that exists. If any two things were not different in some way from each other, the would not be two things, there would only be the one same thing. What makes things different from each othere are their attributes (qualities, properties, or characteristics). For things to be similar, there must be some attributes that are the same. Things are similar to the degree they have attributes that are not different.
Ontologically every entity is different, even if most of there attributes are not different. The similarity of existents is an epistemological observation of entities that have some attributes that are the same. The fact that they have those attributes is ontological. The fact that having those same attributes makes them the same kind of existents is strictly epistemological. Ontologically, every entity is unique, and every individual (particular) entity of the same kind has some attribute that differentiates it from all other entities of the same kind. Positive order is racognition of the ontological fact that every entity is unique.
Negative order recognizes entities only in terms of their same attributes, ignoring the fact that every entity is ontologically unique.
Epistemological vs. Ontological Order
Every single entity that exists is different from all other entities. An entity is whatever its attributes (qualities, characteristic, or properties) are. No two entities can have exactly the same attributes or they would not be two entities by the one same entity. Since every enitity is different from every other entity, every entity has some attribute or attributes that are different from any other entities.
Entities of the same kind have some attributes that are not different. Those same attributes of entities of the same kind are what make them the same, but ontologically, each of those same entities must also have some attribute or attributes that are different, or they would not be separate entities.
Entities of the same king are only the same epistemologically, because ontologically they are all different. The epistemological sameness is recognition of the ontological fact, the same kinds of entities do have some same attributes, which is what makes them epistemologically similar, while ignoring (not denying) the ontological fact of the unique attributes that make them separate entities individually. [Please see the chapter, "Epistemology, Concepts."
The physical universe has natural order, determined by the nature of physical existence, but that order is not at uniform order. It is, in fact, the opposite. Physical existence is totally chaotic. Everything is different, no two things are the same or behave the same way. Ontologically the universe is dominated by constant change and total differentiation.
It is the ability of the human mind to identify attributes, relationships, and behavior that are similar or different that produces epistemological order. The formation of universal concepts which identify existents of the same kind creates a kind of uniformity (the recognition of the sameness of entities), "as if," the ontological differences did not exist (which is why it is called negative order).
The order of the universe determined by the laws discovered by the physical sciences is the order of differentiation and change which makes existence possible (which is why it is called positive order).
Disorder And Existence
An "ordered," universe, in the uniformity order sense, is not possible. Consider a hypothetical universe that is totally uniform. Whatever aspect is considered, entities, attributes, or events, total uniformity would mean no difference, everything would be identical, have the same attributes, and behave in the same way. There could only be one thing in one place with nothing else for it to be related to or different from in any way. It is impossible.
While the so-called, "heat death," of the universe is described as, "total disorder," it is, in fact, the exact opposite. Just as entropy in information technology means total uniformity without any change or difference in the transmission or storage media, total entropy of the universe would mean total uniformity in the distribution of energy. It is order, not disorder that eliminates usable energy and existence itself.
In one sense, this confusion about the nature of order is semantic, of course, based on the two different meanings of order, but the misunderstanding has significant consequences to philosophy. It is not disorder that is a danger to existence and life, but order—the relentless push to make everything uniform and the same. It is disorder and whatever produces change and difference that is the only creative principle, and the more disorder there is, the more existence there is. Extreme disorder is called chaos. The fear of chaos is fear of existence itself.
The order of uniformity or sameness is malevolent to both life and existence. It is the order of death itself.
The Universe is Not Orderly
The universe is not orderly, it is chaotic, and if it were orderly it could not exist. It is difference and change that make everything possible, and both are disorderly.
The disorderliness of the universe is neither random or haphazard. It is a determined disorder. If it were not for this disorder, the so called heat death of the universe would be assured. In fact, that heat death is probably not possible because most of the behavior of the universe is not, in the normal sense, geometric or linear. While heat, itself, cannot violate the first law of thermodynamics, entities and substances are not restricted by that law, and since it is entities in which heat is distributed, (the existence of infrared, for example, is only known if some body is heated by it).
In a sense, Maxwell's demon exists, and its name is Fractal Chaos. Nothing physical can violate the second law of thermodynamics, and if the universe were orderly and uniform it's heat death would be asured—it is not orderly and uniform, however, and has a tendency to "clump up" and distribute itself in unpredictable ways. While heat is distributed evenly, the matter in which it is manifest is not, which assures, on a cosmic scale, heat itself can never be uniformly distributed.
Determined But Not Predictable
There is a branch of mathematics called "chaos," which includes such forms as "fractals" and "Lorenz attractors." Most events have some elements of behavior that are described by that kind of mathematics. Most people have heard of the esoteric fractal "Julia," "Mandelbrot," and "Lyapunov," sets, and my have seen images produced to represent them.
Phenomena described as, "chaotic," has the following mathematical characteristics: 1. determined, 2. non-repeating, 3. non-linear, 4. unpredictable, 5. limited (finite), 6. small initial inputs produce enormous differences, 7. fractal forms display self-similarity.
1. Chaotic events are not random, not matter of chance or probability, but absolutely determined. The same chaotic pattern, beginning with the same initial values will always result in exactly the same pattern.
2. No part of a chaotic event is exactly repeated. Mathematically, a chaotic pattern is a non-repeating series of numbers that never repeat.
3. No part of a chaotic event can be described by linear mathematics. A chotic pattern has no linear description.
4. No part of a chotic event can be predicted from any other part of that event. A chaotic series is totally unpredictable.
5. Chaotic events are finite limited events that cannot exceed values determined by the mathematical description of those events. Events that mathematically go to infinity cease to be chaotic at that point. Most chaotic events have no mathematical termination.
6. Mathematically described chaotic events will produce very different events depending on different initial conditions, no matter how small the differences in those initial conditions are.
7. Though no part of a chaotic event is ever identical to any other part, there is a kind of pattern to chaotic events that is called, "self-similar." It is difficult to describe exactly what self-similar means, because no part has exactly the same measureable attributs as any other part. The similarity is approximate, very close but never identical. This can be seen in most fractal demonstrations.
The mathematics of chaos is actually an approximation of the natural phenomena they reflect. In reality, the chaotic behavior has the same kind of determined but unpredictable nature as fractals, but fractal math is discrete and natural chaos is analog. Some early experiments with Lorenz attractors, used analog computers for modeling things like the weather and fluid dynamics. Today, digital computers approximate the analog functions by means of equations with discrete outputs.
What Is a Fractal Equation
Fractals are called "iterative," functions, which only means, a particular equation is repeated over and over. In fractal math, the "output" of each iteration of an equation, is used as one of the input variables of the equation for the next iteration.
Most iteratie functions simply produce a series of evern increasing and decreasing values. For example, X2 + c = X`, (the basic equation for both Mandelbrot and Julia sets), simply means X "squared" (or X times X), plus c equals X`. The value of c, called a variable, is "fixed" (if a Julia set) but varies (if a Mandelbrot set). The right side of the equation (X') is the value of X to be used in the next iteration.
If the output value of the equation X2 + c = X, if c is a real number, for each iteration the value of X simply keep increasing, for example, if c is 3: (02 + 3 = 3). The next iteration uses the result X' (3) as the input value of "X" in the next iteration. Therefore, the next iteration is 32 + 3 = X', and the result is 12 (32 + 3 = 12). Since 12 is the new value of X for the next iteration, the equation will be 122 + 3, or 147. This is obviously a simple increasing series.
A fractal equation uses a complex number, which is a combination of real and imaginary number (the square root of a negative number), as the value of X and some value for c which is less than 1. Because of the peculiar nature of the square roots of negative number, a iterative series with those inputs does not produce and linear increasing series, but a series that is non-linear and non-repeating.
Fractals are not the only kinds of chaotic events, however. The following is an example of a simpler chaotic equation no requiring imaginary numbers:
(X-c)/X = X', with the following values: X=1, c=3, X` is the value of X for the next iteration. The first iteration is therefore: (1-3)/1 = X', or -2/1= -2. The series begins as follows:
X = (1-3)/1 = -2/1 = -2
X = (-2-3)/-2 = -5/-2 = 2.5
X = (2.5-3)/2.5 = -.5/2.5 = -.2
X = (-.2-3/-.2 = -3.2/-.2 = 16
X = (16-3)/16 = 13/16 = .8125
X = (.8125-3)/.8125 = -2.1875/.8125 = -2.692307
X = (-2.692037-3)/-2.692037 = -.307692/2.692307 = -.114285
X = (-.114285-3)/-.114285 = -3.114285/-.114285 = .355918
X = (.355918-3)/.355918 = 3.355918/.355918 = 9.428899
X = (9.428899-3)/9.428899 = 6.428899/9.428899 = .681829
X = (.681829-3)/.681829 = -2.318170/.681829 = -3.399928
The output of all equations produces a series of values: -2, 2.5, -.2, 16, .8125, -2.692307, -.114285, .355918, 9.428899, .681829, -3.399928, .... (All values have been truncated to 6 decimal places.) The series is indefinite and never repeats. Notice that the change in signs seems to be random. It is not random, because it is determined by the equation and input values, but cannot be predicted. In fact, no part of the series can be predicted.
Given the same starting values for c and x, however, the identical series is always produced. In fact, if any value of x at any point in the series is used as the starting value, the series will continue from that point just as if the whole series were produced.
It is impossible to determine the starting values or equation from any portion of a fractal series, and even if the equation is known, the starting values cannot be determined.
Most importantly, the values seem to be random. A series like the one above has no obvious or apparent pattern. Nevertheless, it is determined, and if plotted by a computer program designed to make a fractal series, "visible," like the images illustrating this article, it is obvious there is a pattern with the parts that seem to repeat themselves, but in fact, no two parts are ever identical.
A Chaotic Universe
The entire universe illustrates chaos and is chaotically determined. The human heart beat is never absolutely even, because the electronic nature of the heart behaves, apparently, like a Lorenz attractor. It is a feedback mechanism (like taking the output of one equation and using it as the input of the next). In fact, if the heartbeat were perfectly symmetrical, it would race uncontrollably, a condition which does happen called fibrillation.
Snow flakes are examples of fractals. Each is completely different, because the physics that forms them, though identical, begins with a different value for each snow flake (because the particles of dust all snow flakes form on are slightly different).
Ferns are another an example. While ferns all look very similar, they are never identical. Broccoli exhibits the same fractal characteristics. There are, in fact, chaotic characteristics in all life. The venous and arterial systems in a human kidney, flowers, and trees are all examples, and DNA clusters form shapes that resemble Julia sets. Non-living examples include clouds, frost and ice formations, lightning, and galaxies.
Perhaps the most interesting example of chaos examples is the weather. It was while studying weather that the famous Lorenz attractor was discovered. Edward Lorenz, an MIT meteorologist was attempting to create a program that all meteorologists dream of. It was believed if one could map all the meteorological states of the world, one cold predict all the weather, indefinitely. What they discovered was, because weather "feeds itself" it behaves chaotically, and therefore was unpredictable, which came as no surprise to anyone except meteorologists.
These examples demonstrate that chaos is part of almost every aspect of physical existence. Without it, there would be no existence.