Entropy and the Laws of World-creation and World-maintenance
In the beginning, when nothing yet existed and when the whole of our Universe was empty endless space ... our Most Great and Most Most Holy Sun Absolute existed alone in all this empty space. . . It was just during this period of the flow of time that there appeared to our Creator All-Maintainer the imperative need to create our now-existing Megalocosmos, that is, our World. . . The Sun Absolute, on which He dwelt with His cherubim and seraphim, was almost imperceptibly, yet steadily, diminishing in volume.As this fact ascertained by Him appeared very serious, He decided to review immediately all the laws which maintained the existence of that still unique cosmic concentration. During this review, it became clear to our Omnipotent Creator for the first time that the cause of this gradual diminishing of the volume of the Sun Absolute was simply the Heropass, that is, the flow of Time itself.
What causes the wind to blow? What causes a river to run? A simple inquiry into the source of all movements makes it clear that contrasts, oppositions, or contradictions are the requirements of all movements and therefore of life. Compared with animals, man can be freer in his movement because he is capable of placing himself under the influences of wider variety of forces. If he fails to reconcile contradictory forces while remaining open to them, that freedom is replaced by various manifestations of disharmony, split, and indecisiveness. Indeed, it is rare to find a man whose movement is more grand and beautiful than that of an animal.
We all know at least subconsciously that movements are the measure of truth as in the case with a lie detector. Impartial observation of the movements of the world and of ourselves is a serious undertaking that may reveal falsities in what we believe. It has been so in science also. The study of movements in science since the mid 19th century has first ascertained our helplessness in resisting the universal tendency of everything going into the drain. Then it became gradually aware of some peculiarities in the working of physical laws that brought us a hope which appears to me more objective than the hope it had before.
The development of a certain line of science after Gurdjieff's time has been very much in confirmation of what he has written in the Beelzebub's Tales to His Grandson. Even though Beelzebub had a very low opinion about the planet Earth's scientists when he was speaking to Hassein in the year 1921, he may change a part of his opinion after reading this article through his Etherogram connection. Readers of this article on the planet Earth, on the other hand, may discover that many statements made by Beelzebub are not as absurd and unscientific as they are generally thought to be.
In this manner, this essay aims to demonstrate that the difficulty in relating the exact science and Gurdjieff's cosmology particularly with regards the law of entropy, mentioned by James Moore in his book Gurdjieff: The Anatomy of a Myth (pp. 345-348), may not be as great as it might have looked a few decades ago. This essay does not address fancy theories such as of multiple dimensions and parallel universes but focuses on the study of laws that govern the movements of matters in the world of reality we are directly in touch with.
Is the Creator Really a Maintainer?
Around the time of Gurdjieff's birth, science made it clear through its law of entropy that the universe is constantly losing its potential for all types of movements. This potential is nothing but the sharpness of contrasts, oppositions, or contradictions that I mentioned earlier. All contrasts that we see in the current universe are developments of one primordial contrast between existence and nonexistence. The potential for further creation is consumed by all cosmic processes including the formation of galaxies, planets, and organisms. The universe is slowly but irreversibly moving toward death.
In the above quotation from the Beelzebub's Tales, it is easy to understand why our Creator had to create the universe. On the other hand, it is difficult to understand how the created universe can be maintained without going down the drain. The Sun Absolute's state described in this passage is characteristic of a thermodynamic system that has reached equilibrium at a high energy level. It cannot survive without creating lower worlds. The owner of a commercial organization burdened by the excess of money may make a similar decision. The manager of a power plant producing more excess heat than it can handle will also make the same decision. How can we be assured that the decision was not an egoistic one? A great suspicion arises about the goodness of the Creator and his ability as a Maintainer.
From this point of view, creation appears distinct from maintenance. Creation can be a one-time affair requiring only one push. All subsequent events might have proceeded automatically. We are horrified to find that Beelzebub seems to confirm this view. How then can maintenance be achieved? Beelzebub mentions two general directions of all cosmic processes. He calls them involution and evolution. I associate involution with the top-down flow of events in the process of creation; evolution with the bottom-up flow of events in the direction of returning to the source. Biological evolution is not necessarily a process of evolution in this sense. We understand how involution follows the act of creation but how can evolution happen?
What we might call the law of involution is called the law of entropy in science. Toward the end of 19th century, following Rudolf Clausius' formulation of the law of entropy, scientists became aware that whatever they studied in the physical world obeyed this law. They also became convinced of their inability in detecting any law that might act against it. Young Gautama Siddhartha must have had a similar realization before he left his palace. The entire universe was slowly moving toward death; local and temporary exceptions would never change the general direction of this movement. The more they tried to see the whole picture of what's happening, more hopeless they became. The following description about the law of entropy will explain you why.
Entropy and the Terror of the Situation
The law of entropy is another name of the second law of thermodynamics. Later on, the concept was found to be applicable to a great variety of academic fields including biology, ecology, economics, information theory, and the study of human mind as an information processing system. The applicability of the law of entropy to the information theory confirms Gurdjieff's insistence about the materiality of knowledge.
In terms of thermodynamics, the first law called the law of the conservation of energy ensures that the total amount of energy within a closed cosmos shall remain always the same in spite of anything that may happen in that cosmos. The second law of thermodynamics, the law of entropy, does not deny the conservation of energy in a closed cosmos but predicts gradual loss of its quality with time. This exactly is the problem that our Creator All-Maintainer took very seriously. The law of entropy is defined as follows:
Understanding the basics of the law of entropy does not require any scientific training. However, one has to be familiar with the usage of some words. Higher entropy within a system means less potential for dynamic movements within that system. The term system is similar to what Beelzebub calls cosmos, which can be of various scales.
Imagine that you have a container that have two compartments, one filled with cold water another with hot water. If you remove a wall between the two containers, convective movements will take place within the container, which is taken here as a closed (insulated) system. The contrast between the higher and lower in terms of temperature enables these movements. With time, the movements will become smaller and eventually cease. This gradual loss in potential is referred to as increase of entropy.
Another example can be of an electric battery. In the initial state of a battery when it has a sharp contrast between its positive and negative poles in terms of chemistry, much energy is available for use. The amount of available energy decreases as a process toward chemical uniformity proceeds in the battery.
In the second example, you may try to reverse the process within the battery by connecting it with a new battery, even though this connection will make the first battery no more "closed." It will surely decrease the entropy within the first battery. If we enlarge our vision and take the two batteries together as a single cosmos, however, we find that the connection of the two batteries has caused the entropy of this larger cosmos to increase. Thus, science admits that each decrease in local entropy must be compensated by a sharper increase in global entropy. It implies that the interest of a part can never match the interest of the whole. It also implies that larger a cosmos, more susceptible it is to the law of entropy. Conclusion: the entire universe is slowly but steadily moving toward death.
The above conclusion, scientifically arrived at with such a sane logic, turned out to be far ominous and persuasive than any doomsday prediction. Various scientists and theorists tried to argue against this conclusion. Here I describe failings of many of such arguments to help discriminate between real hopes and false hopes.
The first reaction against the theory of entropy took the form of a craze over the invention of a machine that would prove the possibility of defying entropy; that is, in Beelzebub's words, a mechanism that would run forever without requiring any material from the outside:
Seeing the failure of purely mechanical means, some have thought that they might have a better chance if they employed in their machines something a little less mechanical: our so-called intelligence. A famous physicist James Maxwell (1831-79) proposed a conceptual model of perpetual motion that employed what became known as the "Maxwell's Demon." The proposed machine has a container divided into two compartments. The Maxwell's Demon sits by a hole in the wall that separates the right and left compartments. He is intelligent enough to discriminate between fast-moving and slow-moving molecules. He allows only fast-moving molecules to pass from left to right; slow-moving molecules from right to left. This work of the Demon would make the right compartment hotter in defiance of the law of entropy. Since the level of intelligence required for this job is not quite high, it must be possible to invent an apparatus that takes his role.
Technical evaluations of this concept have shown the impossibility of such an invention, the main reason being that the working of the Demon and the preparation of conditions for the Demon to work would require more energy than his work can produce. These technical evaluations are showing us that the working of our mechanical mind is upsetting rather than beneficial in trying to control the situation. The failure of the Demon is the defeat of our so-called intelligence, which Beelzebub describes as: "Look! Look! He already begins to distinguish mama from papa!" In spite of a huge difference in intelligence between Beelzebub and Maxwell's Demon, however, they might be in a collaborating relationship in a certain sense.
Many popular books written on the subject of entropy console the readers by inviting them to pay attention to the apparent state of orderliness in the universe we see now. They argue that the richness and beauty of forms and structures that we see in the world prove the existence of a hidden law of evolution. This sounds true. However, these arguments often ignore the fact that the universe is losing its potential constantly by creating these forms and structures. Are these forms and structures helping in counterbalancing the law of entropy in any observable way?
Another serious error behind this way of thinking is the misleading definition of entropy as the factor of chaos and inverse of orderliness. This is not a part of the original definition of entropy but is the result of what is known as the Boltzmann's interpretation. This interpretation may be correct in what scientists call "ideal states" but not in reality, where the definition of orderliness becomes very subjective. For example, in purely thermodynamic sense, our universe in its initial chaotic state was in a state of lower entropy than in its current state of orderliness. In a wider sense, when particles stop fighting with each other and begin to co-exist "harmoniously," we often see it as orderliness while it actually may be a process of running down. There are two types of chaos and likewise two types of orderliness: one that holds much potential and another that results from the loss of potential. Rather than making a judgment about entropy based on the state of apparent orderliness and chaos, one should apply the concept of entropy to discriminate between these two types of chaos and of orderliness. This subject came to be addressed remarkably well in the field of complex system dynamics but only very recently. Readers should be aware of the Boltzmann's interpretation because many popular books and scientists still accept it in spite of recent criticisms that are more persuasive.
Finally, there are those who tried to look for a hidden law of evolution in the working of forces that enabled the appearance of organic life on Earth. This also is a valid line of inquiry but here also it is easy to fall into the pitfall of wishful thinking. It is again useful to return to the original thermodynamic concept of entropy. Each organism constitutes a thermodynamic system and its survival depends on keeping one's own entropy lower than that of the environment. In other words, each organism feeds on negative entropy and excretes positive entropy. No organism can be beneficial for the environment by its survival. Vegetation on Earth is exceptional because its openness to the sun helps the Earth. Still, in a larger scale, our sun is constantly dissipating its energy through its radiation, thereby increasing the entropy of the entire universe.
Theoretically speaking, for anything in the universe to be able to be of any use for the whole, it must be connected with a source that never dissipates itself by its radiation (or in contact with a certain emanation that never dissipates its source). Beelzebub speaks of such and laughs at the poor scientists of the planet Earth who are ignorant of this. He makes an absurd statement: Our Sun Neither Lights nor heats. What he calls Our Sun may not be the same with what we call our sun.
Law of World-creation and Law of World-maintenance
Hearing the absurd statement of Beelzebub and his contemptuous remarks on our scientists, we are tempted to conclude that whatever Beelzebub says about the World Laws is allegorical of what happens in our inner world but does not apply to the outer world. I can never support this view because I take it seriously when Gurdjieff emphasizes that similar laws govern our inner world and outer world; only some laws are more available for observation in one of them. Let us trace further the history of scientific inquiry into the physical laws of movements while maintaining our interest in how they may apply to our inner world.
As mentioned earlier, the development of a certain line of science after Gurdjieff's time has been very much in confirmation of what he has written in the Beelzebub's Tales. What changed the direction of scientific inquiry toward the direction pointed by Beelzebub? It is the scientists' growing awareness about that which Beelzebub describes as follows: "the contradiction between the concrete results flowing from the processes of all the cosmic laws and the results presupposed and even definitely expected by their sane logic" (Beelzebub's Tales, Chapter 39).
The efforts of scientists in earlier decades were mainly focused on describing reality in terms of theories in a neat, logical way. In doing so, they presupposed lawful movements of matters in what they called "ideal states." In reference to what we have examined together, you must have found all preceding discussions about the law of entropy very understandable and undeniable because they were clearly based on a sane logic. But logic cannot cover all faces of reality. It never occurred to the earlier scientists that new discoveries were yet to be made with regards the most probable patterns in the earlier-mentioned definition of the law of entropy.
Scientists gradually became aware through their observation of reality that particles within a more or less complex system do not move in the way they are supposed to move in an ideal state. Phenomena like flow and turbulence that have a vital significance in our organic universe were found to be explainable only when we take account of complex interactions that take place among different processes and physical laws involved in creating the phenomena.
The dependence of a part of a process on another process or another part of the same process and real-time interactions between ongoing processes, both competitive and collaborative, are the main causes of what science calls nonlinearity, which is a major peculiarity brought about by the changes our Creator has introduced to the working of the Law of Heptaparaparshinokh in his hope to ensure maintenance of the universe, according to Beelzebub. Similar interactions among different processes and physical laws in a complex system are also known to cause emergence of unexpected patterns. In other words, collective development of processes, which essentially are the lawful execution of the law of entropy, may produce patterns that betray our preconceived images of most probable patterns. This is the central subject of study in the field of complex system dynamics.
Our mind lacks capacity to understand the complexity of interactions among multiple processes that take place simultaneously. So the best way to grasp the reality of these phenomena is to be assisted by computer programs designed to simulate such phenomena in a graphical way. There are two types of such programs: programs that draw a fractal figure and programs called automatons.
A typical program that draws a fractal figure simulates a top-down process of creation. Such a program is mathematically defined as successive fractioning of a primordial law according to a predefined set of rules. In the process of fractioning that the computer executes automatically according to the rules, one finds both the nonlinearity of the whole process and unexpected emergence of a pattern that is often redolent of an organism or natural object. The following words of Beelzebub accurately describe this process and its significance in relationship to the concept of entropy:
It should be noted that in the Great Universe all phenomena, without exception, wherever they arise and are manifest, are simply successive, lawful "fractions" of some whole phenomenon which has its prime arising on the Most Holy Sun Absolute.
Another type of simulation program called automatons (or automata or artificial life) shows the down-up process from multiplicity to simplicity. An automaton program simultaneously moves multiple residents of a created cosmos according to a set of rules to simulate emergence of patterns in collective movements of these residents. Using these programs, researchers try to identify a set of rules that would cause the emergence of patterns that realistically resemble those of biological adaptation and habitat segregation, competition and collaboration, health and disease, process between birth and death, and so on. More interesting for researchers may be the study of how a small change in the working of these laws would change the state of affairs.
Gurdjieff preceded those researchers by decades with his Movements, some of which bearing the title Automaton, that use real living human beings instead of virtual creatures. The merit of using real human beings is immense, because only by doing so one can expect to find a real factor in man that would enable him to reestablish a connection with the source, counterbalancing the law of entropy working on his physical body. In this connection, it is interesting to note that many researchers in the field of complex system dynamics, notably John Holland, like to compare the objects they study with "dances" but very "unusual" because of the irregularities they show in their progressions and also because of the image of complexity they produce through combinations of simple laws. These are well-known properties of the Gurdjieff Movements.
Informational Entropy and the Purpose of Organic Life and Man
Many recent studies in the field of complex system dynamics seem to have been made in the right direction pointed by Beelzebub. However, we must remember that none of the researchers has proved the real possibility of counterbalancing the law of entropy. They simply point to the existence of a certain principle that allows forms, structures, and organisms to emerge out of the top-down processes of creation governed by the law of entropy. As mentioned earlier, it is doubtful whether these forms, structures, and organisms can help decrease the general level of entropy in the universe. Such is not happening so far, as evidenced by the current ecological crisis on the planet Earth, and the chance for such to happen in future is very small. To help this very small chance, we must identify the conditions under which such may happen.
Some scientists rejoiced in discovering what looked like a universal principle that so far had enabled automatic emergence of living organisms, biological evolution of species, and development of so-called intelligence in man. The same group of people developed what they believe as a computer-simulated model of self-learning, self-evolving creatures. They are happy because they believe that this principle they have found will guarantee automatic evolution of human beings into a bright future. But then, what is the purpose of us being a man rather than a machine? They should have been ashamed in knowing whatever they believed as development and intelligence was the result of automatic adaptation and learning that are possible even for a computer virus.
For further inquiry into the subject of entropy and the role of organic life on Earth, we must study the relationship between thermodynamic entropy and informational entropy, and the role of consciousness in this connection. Science takes thermodynamic entropy and informational entropy officially as different subjects, but their similarities are evident. The mathematical formulas describing the law are identical between the two. Aren't they basically the same law? Though science hesitates to make this claim, the interrelationship between the realms of thermodynamics and information is evident at least in the organic universe of genes, cells, vegetation, animals, and men. If this interrelationship exists only in our organic universe, on the other hand, it proves the paramount importance of organic life in maintaining the whole universe.
Information - what we know and what we are aware of - naturally determines how we move as particles of the universe. The movements of these more-conscious particles and the movements of less-conscious particles both seem to be under a similar set of laws while consciousness can be a critical factor that may bring unexpected consequences. However, there's no clear demarcation between what we call exchange of information and what we call physical interaction. The impression of this continuity is particularly strong when we pay attention to how mechanical processes of physics and chemistry must have first produced genes on Earth. Genes are clearly more intelligent than inactive matters because they are informational entities "conscious" of time (past and future) and therefore of entropy. So what we see here is a hierarchy among different modes of exchanges according to their degree of materiality, which is the inverse of the degree of consciousness involved. A body of information consists of particles that allow more penetration of consciousness; so the presence of consciousness acts more effectively in counteracting the involution of these particles than in preventing the involution of denser particles that belong to the realm of thermodynamics.
Information theorists measure the degree of truth (negative entropy) at a certain point in the process of transmission by evaluating the purity of information at that point against the purity at the source. Purity here means the proportion of correct information against the whole body of information. Now if we leave information theorists behind and become concerned about something more than the mere correctness of information, namely the meaningfulness and purposefulness, and also accept the above-mentioned continuum between the world of physics and the world of information, we arrive at a more satisfactory but very surprising definition of zero entropy or original source: maximum meaning in least materiality. Now we finally reached, through our pondering, what Beelzebub called the Sun that Neither Lights nor Heats.
In this connection, it is interesting to note how cognitive science almost reached the same conclusion but denied it hurriedly by a childish logic. The fact that a man is able to be aware of the movements of his attention suggests that this awareness belongs to a deeper layer in man. While attention is quantifiable in terms of its strength and distribution, deeper awareness is less quantifiable and therefore less material. A man who proposed a theory about the layers of attention and deeper levels of control was "pecked to death" by his colleagues, who insisted that this should never be the case because then they would have to assume: man within man within man within man within man...ad infinitum. But what to do? This is the reality experienced by all explorers of the inner world: infinite regression back to the source of our arising.
Information theorists today do not effectively address the role of consciousness in information exchange. Their main focus is on mechanical processes of cognition, memory, and inference. Still it must be possible for researchers to comparatively study the processes of various degrees of mechanical learning: absolutely unconscious as with self-evolving computer virus, organically unconscious as in genes, mostly unconscious as in biological adaptation, generally subconscious as in infants, slightly conscious as in us. Comparing their consequences in terms of informational-thermodynamic entropy may give us an idea about the role of consciousness in the universe. With these variations of mechanical learning, however, its effect in decreasing thermodynamic entropy is expected to be null or negative, as in the case with the Maxwell's Demon. We cannot even be sure whether such mechanical learning can decrease informational entropy as such or not, because more learning means more material in the head, which means higher entropy by definition.
Official definition of informational entropy (Shannon's formula):
Amount of information = - log (Proportion or probability of truth)
- The amount of information is sinonymous to informational entropy.
- The amount of information is inverse-logarithmically proportionate to the proportion of truth.
- More distant from truth; more is the amount of information.
Feel again the power of this formulation: maximum meaning in least materiality. In this formulation, Meaning is another name of Purposefulness. The second half of this formulation again shows impossibility of connecting the Purpose with the survival of organic forms. We may choose to make such a connection in our mind at the cost of negating the whole meaning of all that exists, making ourselves totally at the mercy of the law of entropy. Since all forms of mechanical learning are motivated by survival needs, they can neither free us nor serve the universe except through preparing the ground where something higher may grow. Since this something higher is not growing in most of us, a daily-life formulation of the law of informational entropy in relationship to its dynamic consequence could be like this: more knowledgeable a man is, less freedom he has in life.
However, we know that there are exceptional cases. A man clearly has in him a reconciling principle that allows him to extract truth from a larger body of information. Understanding is a process that decreases informational entropy. It relieves man from the burden of knowledge. Unlike thermodynamic entropy, the amount of informational entropy (confusion) removed from one person's head in this manner will not enter other persons' heads. This major difference from thermodynamic entropy seems to prove that we are actually able to make contact with a source of negative informational entropy through our consciousness. Otherwise where does that excess amount of entropy disappear?
Informational entropy should be a subject of vital interest for those who are concerned with the transmission of a spiritual teaching. In the context of what we discussed, however, transmission of a spiritual teaching should be understood in terms of sharing the opportunity to come closer to the source of our arising rather than in terms of transmitting information. The formulation "maximum meaning in least materiality" is very close to the precept of Zen with regards its tradition of direct transmission with no word. Zen also knows another form of transmission, the tradition of existential questioning (koan), in which words are used not as containers of information but as a means to evoke contradictions in man to the effect of awakening in him the sacred law of reconciling. Beelzebub uses words in very much the same way.
On a larger scale, however, the transmission of any true teaching inevitably follows the law of entropy, which will destroy it within three or four generations, according to Beelzebub. Specifically in the case of Gurdjieff's teaching, what might be the best way to protect it against this rapid decay? With traditional views about the law of entropy we discussed earlier, there seems to be no hope: imparting the teaching cannot be achieved without diluting the message. Preserving the teaching within a small circle will not work either: the amount of entropy within a closed system irreversibly increases with time. Beelzebub's advice which you may guess from Chapter 44 of the Beelzebub's Tales is more in line with the emergence theory of complex system dynamics and still deeper because it takes account of vivifying effects of the reconciling principle present in man.
In Gurdjieff's illustration of man as a three-story factory, the realms of thermodynamics and information theory interact by a contact between the air octave and the octave of impressions, a contact that requires the work of consciousness. Through an inner exercise mentioned in the Third Series, an exercise of establishing a contact between the energy associated with information and the energy associated with breathing, one may be able to confirm how this contact may change the climate within oneself and how it can be shared within a group of people.
In summary, the various lines of reasoning presented here, while they may not be quite sufficient in proving something in the favor of Beelzebub, make us more aware of the inevitability of a choice between life and death: either start on a journey toward the pointed direction or lose the entire ground and meaning of existence, including any reason for further inquiry, scientific or unscientific.
Listening to Beelzebub and reading reports from recent works in the field of complex system dynamics, and as I begin to see potential sacredness of all interactions, I am tempted to give the broadest possible meaning to such words as consciousness and awareness. Can we say, for example, that the Newton's apple and earth are aware of each other though the law of gravity? What are those physical laws anyway? Aren't they all means that enable matters to be aware of each other? In this sense, isn't it reasonable to see awareness as the real source of creation that preceded the working of these laws? Isn't it also the case that everything in the world, animate or inanimate, is aspiring to become more conscious through its interactions with others, the totality of which may have the effect of canceling out the decaying action of Time?
Looking at some creatures of lower forms, like those that live in the depth of ocean, one wonders why the Creator had to give consciousness even to such forms. While seeing the obvious cruelty of containing consciousness in such forms, can we see it as an evidence showing how badly needed is consciousness in the universe?
Exactly at this point, we must remember a grim fact about living organisms that I mentioned earlier: no organism can be beneficial for the universe by its survival. So we are confronted with this paradox: the eventual goal of all those evolutionary processes cannot be the creation of life because life kills the universe. This forces us to see life and consciousness as interdependent partners with opposing purposes and our presence as the reconciling ground for the two opposing principles.
Even though Beelzebub speaks about the emergence of evolutionary processes out of involutionary processes and calls the former as strivings to reblend with the source, what he sees as the real spiritualizing force in the universe is the third reconciling force resulting from collisions between the involutionary processes and evolutionary processes. This brings us back to the subject we started with: man's responsibility to be open to and reconcile contradictory perceptions as well as contradictory forces at work both inside and outside him.
Thanks to what we have learned about the basics of the law of entropy, we can now understand better that reconciliation doesn't necessarily mean resolving conflicts and that avoiding the above-mentioned responsibility will make us more susceptible to the law of entropy. We can also understand why Gurdjieff refers to "inner tension of forces" as an honorable state of man. I hope you consciously assist "collisions" happening to you after reading this essay so as to be able to have a real taste of this reconciling principle working in your presence now.