Thursday 31 March 2016

Reason Observing Nature (Part II): The Truth Behind Complex Numbers and their relation to Nature

Reason Observing Nature
Part II



Introduction

Observing Reason has reached a stage of transition. I have decided to continue the journey of self-consciousness, towards verifying the certainty that it is itself the fundamental basis of all reality through the empirical and objective observation of nature, into two articles. Further, we must resist the psychological tendency to get lost in the details of Reason's development. Thus, it is necessary to explain again what it is that observing Reason is attempting to accomplish when it engages in empirical studies of Nature. Doing so will allow us to see why Reason unfolds the way it does. 

First, note that Reason is a shape of self-consciousness. The object which defines the Absolute True for Reason is the self. It is certain of itself, i.e. the supreme being for which Reason is concerned is its own self-conscious activity. For sense-certainty, its object was the immediate sensed particular, for perception the thing, for understanding the unconditioned universal, etc. Reason is a rationally self-interested agent. This self-certainty, in principle, extends beyond the finite confines of the physical body which self-conscious Reason inhabits. It is a particular being certain of its own universality. More specifically, it is a rational particular being, i.e. it operates in accordance with definite, universalizable, necessary, schematizable rules. This rationality should extend beyond the confines of its particular body, composed of organic and inorganic nature, and governs all reality. Thus, even Nature, which is the objective flux of appearances in which Reason finds itself as a living body, bereaved of all self-conscious activity, is nevertheless inherently rational.

The inherent rationality of nature is not a demonstrated truth. It is a bare, supremely self-confident, assertion. It is easy to confuse certainty and truth, however, it is possible for one to be certain that something is true, though in actual fact it is untrue. We saw this dynamic play out in the dialectic of sense-certainty. Like sense-certainty, Reason is attempting to raise its certainty of being all reality, i.e. that all reality is rational, to truth. It wants be certain of the truth of its certainty.

Like sense-certainty, Reason observing nature has three sub-shapes. In the first subshape, Reason will attempt to verify its certainty by objectively observing its object alone, seeking the true nature of inorganic and organic nature, without the confounding effects of self-consciousness. Nature is, by definition, bereaved of all self-conscious activity, yet for itself still behaves like a rational self-consciousness according to definite rules. It is these rules which Reason is attempting to discover. The second subshape will emerge when Reason discovers that no such rules can be found in objective nature that would verify its certainty of being all reality. Thus, Reason will turn inward, just as sense-certainty did, and seek the truth of its certainty in its own self-conscious activity, i.e. it will attempt to discover the laws of rational thought - logic.

At this point in the development, we have seen Reason observe nature first as an activity completely bereaved of all self-conscious activity, i.e. inorganic nature. The rules which it sought through observing inorganic nature emerged as recurring patterns, distinguishing marks, and finally, probabilistic laws. Reason had to verify that these rules were indeed universalizable, necessary, and schematizable. It found that recurring patterns lacked necessity, distinguishing marks lacked universalizability, and that probabilistic laws lacked both.

Through experimentation, Reason turned to mechanistic laws, but in doing so conflated inorganic and organic nature. This conflation occurred to the very nature of law, as we saw in the understanding, and reason's incapacity to know the underlying factors that determined the nature of its rational activity. These factors can only be grasped conceptually; we are discussing them in this very article. Organic nature, to some extent, is confined by the same mechanistic laws that confined inorganic nature. Organisms operate according to an internal logic that is in one sense dependent on the inorganic environment in which the organism is immersed, in another sense independent. Due to the latter sense, Reason finds that mechanistic laws are not universalizable. The organic being and its inorganic environment turn out to coexist, but are ultimately free and independent of each other. Organic nature and inorganic nature coexist, but are mutually indifferent to one another.

This mutual indifference between organic nature and inorganic nature shows that nature does not operate like a rational self-consciousness. Nature is irrational, if its rationality is to be based on mechanistic laws alone. Reason, concerned only with verifying the certainty that it is all reality, turns to teleology. The organism is allowed its freedom to set goals for itself, and accomplish them, while still being confined by the regularities of nature that Reason describes via mechanistic laws.

The organism's freedom to set goals for itself and actualize them, goals either in accordance to or opposed to the nature of the organism, is entirely predicated on the unobservable self-conscious activity of the organism. The external, purpose-driven, rule-governed behaviour, i.e. the activity, of the organism is predicated upon the life process of the organism, exhibited by the components of its observable, living body. Observing Reason must now find a universalizable, necessary, schematizable rule that relates these disparate aspects of the organism. This rule, i.e. law, once discovered would raise Reason's certainty of being all reality to truth. It would show that nature operates like a rational self-consciousness without the conscious activity of a self-consciousness.

The Organism: Inner and Outer

The internal purpose of the organism is posited by the pure activity of its self-consciousness. This inner activity can only be grasped conceptually, with the techniques developed by Hegel and in this blog. It cannot be observed. The expression of this self-preserving, self-moving unity is the outer. The outer, being a direct image of the inner, is observable. Observing reason now seeks a universalizable, necessary, and schematizable rule that circumscribes organic nature, inorganic nature, and self-conscious Reason through observing the relation between inner and outer.

The pure inner activity of the conscious organism involves the primary function of the organism's consciousness, i.e. its sentience. Consciousness is a simple awareness. It is aware of itself and others. Since the organism is aware of objects other than itself, and it inhabits a physical organic body, it must have the capacity to know and be conscious of another via its senses, i.e. it is irritable. Irritability is the capacity of the organism's physical body to respond to external stimuli, whether voluntarily or involuntarily. Further, the organism can respond to this response by engaging in rule-governed behaviour. Finally, since the organism loses the organic substance which composes its physical body, it is set in motion to preserve itself and replenish its lost substance by the feeling of hunger and thirst. The organism, as an individual, will die. Its activity is preserved through the genus to which the individual organism belongs. The organism is thus set in motion to produce offspring, in order to preserve its activity. The inner activity which sets the organism in motion to preserve itself as individual and as a member of a a genus is reproduction, i.e. the organism's desire to preserve itself and undergo growth, and to relate another and produce offspring. These three compartments of the inner, separate and distinct, are the primary impetus, the reason, behind purpose-driven behaviour. They cannot be observed.

The outer expression of this inner activity, however, can be observed. Observing Reason holds that the outer is an expression of the inner. Thus, there exist three observable outer processes that exhibit the essential character of the unobservable inner processes. The sentience of the organism is exhibited by its nervous system. The nervous system is the part of an organism's body that coordinates its voluntary and involuntary actions and transmits signals to and from different parts of its physical body.

The nervous system permits the organism to exhibit consciousness, consisting of the brain, spinal cord, sensory organs, and all of the nerves that connect these organs to the rest of the body. Together, these organs are responsible for the organism's control of the body and for the organism to communicate with its body, as well as for the body to communicate with itself. The brain and spinal cord form the control center of the body known as the central nervous system, where information is evaluated and decisions are made. The sensory nerves and sense organs of the peripheral nervous system monitor conditions inside and outside the body and send this information to the central nervous system.

All voluntary actions originate from the self-moving, free, and independent activity of self-consciousness. The central nervous system is the origin of the organic movement that brings that decision to act in a certain way into being. The peripheral nervous system carries out rule governed behaviour, maintaining the functions of the organism's body, as well as the organism's interaction with its environment. The nervous system is an also expression of the organism's sentience which observing Reason can observe. Through the nervous system, observing Reason observes the sentience of an organism as if it was an inorganic thing. The outer is an expression of the inner.

The irritability of an organism is exhibited to the senses of observing Reason by the muscular system of the organism. The muscular system permits the organism to move its body, maintain its posture, and circulate its blood throughout its body. Each muscle is a discrete organ constructed of skeletal muscle tissue, blood vessels, tendons, and nerves. Muscles are irritable; they receive and respond to external stimuli without any input from self-consciousness. The muscular response of external stimuli is a function of the periphary nervous system; a signal is sent to the central nervous system, and the organism qua consciousness responds by directing the motion of its muscles again via the nervous system. The inner purpose of the organism is carried out by the rule-governed behaviour of the muscular system. The muscular and nervous systems are not distinct and separate. They overlap.

Finally, the inner activity of reproduction, i.e. the primary impetus that sets the organism into motion in order to preserve itself as individual and as a member of a genus is exhibited to observing reason by the digestive and reproductive systems of the organism.

The digestive system is a group of organs working together to convert food into energy and basic nutrients to feed the entire body of the organism. Food passes through a long tube inside the body known as the alimentary canal or the gastrointestinal tract. The alimentary canal is made up of the oral cavity, pharynx, esophagus, stomach, small intestines, and large intestines. In addition to the alimentary canal, there are several important accessory organs that help the organism's body to digest food but do not have food pass through them. Accessory organs of the digestive system include the teeth, tongue, salivary glands, liver, gallbladder, and pancreas. The mouth and tongue allow the organism to communicate to others its internal conscious activity. It also allows it to eat, and preserve itself. The reproductive system is a group of sex organs within an organism which work together for the purpose of sexual reproduction. Many non-living substances such as fluids, hormones, and pheromones are also important accessories to the reproductive system.

The activity of the digestive system and reproductive systems overlap with the activity of the muscular and nervous systems. This overlap presents a problem for observing Reason's search for a unifying law that relates inner and outer. The divisions of the inner conscious activity of the organism which observing Reason made are not true divisions into separate and indifferent compartments of an organic whole; there is overlap in the outer expressions of the inner activity of the organism. There can be no true distinction in the inner conscious activity of the organism. Sentience, irritibility, and reproduction are parts of an inseparable unity. 

The process of the inner life of the organism has unobservable inner aspects, for-itself, which exhibited observable outer aspects, for-another, observing Reason. The observable outer aspect of the organism can be expressed teleologically, i.e. the organism uses these systems to set and accomplish goals for itself; these outer aspects can be shown to obey mechanistic laws. The transmission of neurons, for example, obeys the mechanistic laws of electromagnetism. However, the three compartments of the inner activity of the organism are presented as distinct and separate. Reason must make this distinction and separation in order to know the inner soul of the organism at all as something that is distinct from its body, yet interacts with it, and with it engages in purposive activity.

Reason observes that neither the muscular system nor the reproductive system can operate without input from the nervous system, nor can reproductive system operate without the muscular system. Further, Reason cannot observe the multitude of ways in which these systems interact with the environment of the organism, and with each other amidst this interaction, whether it attempts to do so qualitatively or quantitatively. Every possibility cannot be accounted for, since the range of possibility is infinite. Reason cannot deduce from the anatomy of the organism how the environment, which is independent of the organism, will affect it. Thus, it cannot reason how inner and outer will interact; it cannot find a unifying principle that could determine every possible permutation of inner and outer activity; it cannot find a rational law that unifies the inner and outer being of the organism.

These three systems are bound up with the self-conscious unity of the organism. The life process of the organism involves the unification of these outer processes. If they exhibit the same living process, then the inner which each outer expression is supposed to exhibit cannot be distinguished into three non-overlapping compartments. The self-conscious activity of the organism is a unitary, living process. To divide this unity from itself is to kill the organism; to observe these divided outer expressions of an organism is to observe something that is dead. No longer can observing Reason pertain to know a living organism, but rather a dead thing.

The organism is not the dead thing which anatomical explanation unwittingly presumes; it is a living thing, i.e. a self-same fluid unity that differentiates itself from itself while remaining self-same. No two aspects of the organism can be separated and distinguished, as observing Reason has done by making the distinction between inner and outer, without sacrificing the organic significance of the organism. The processes that sustain the life of the organism cannot be separated into distinct non-overlapping categories, i.e. sets, because in truth these processes overlap and blend into each other. The functions of the nervous system must overlap with the functions of the muscular, digestive, and reproductive systems. Otherwise, the organism cannot be alive. The fundamental observable characteristic of life is the organism's capacity to move its limbs, via the muscular system, at the command of its brain and spinal cord, via the central nervous system. But observing Reason finds itself ignoring this overlap, instead observing the parts of the organism, all while the organic unity which gave it any significance has flown away.

The Whole of Nature: Inner and Outer

The inner organic unity of the organism is a part of a fluid process, i.e. a whole that cannot be ignored. Thus Observing Reason will now attempt to generalize the organic unity of the organism, while taking for granted that it has an inner and outer aspect - that it is a fluid whole whose life is sustained by differentiated, yet overlapping, parts. The overlap of these differentiated parts of the living organism suggest that they have a common origin. This common origin serves as the observable basis of organic unity, and it is to be distinguished from the organism as a self-unfolding activity of consciousness. The organism, therefore, is no longer being treated as a living, holistic, process, that fundamentally involves a sentient, conscious being. Rather, Reason seeks an observable basis for the organic living unity of the organism. Once the observable basis for this unity has been established, Reason will seek to explain it with universalizable, schematizable, necessary rules.

In other words, a second relation between inner and outer has been posited; this time, however, the organic unity of the organism as a whole, with its own inner and outer character discussed in the above section, is taken to be the new inner. More specifically, observing Reason considers the physical shape of the organism to be the inner, and sets it up in opposition to the new outer, which is the existence external to the organic shape of the organism, i.e. the environment. This organic unity develops cohesively, changing gradually from a simple unity to a complex whole.

The simple unity that serves as the holistic basis of all organic life is the cell. For this blog, we will only consider the animal cell in some detail.

Like the organism, the cell is a whole that observing Reason divides into parts. These parts are overlapping processes. Cells have various functions within the body of the organism. Like the organism, cells must feed and reproduce. Cells are a part of the organism which reflect the nature of the whole organism. In other words, the constitution of the organism as a whole, and the constitution of the cell, are self-similar. The purpose which the conscious organsm sets for itself is identical to the purpose which each cell functions - to subsist and reproduce. Thus, the cell too has an inner purpose, which it realizes by means of rule-governed, goal-oriented behaviour.

When observing Reason realized that the organism as a whole has an inner purpose which it accomplishes by means of external, observable, rule-governed and goal-oriented behaviour, it divided the organism into inner and outer aspects that correspond to its inner purpose and outer purpose. The inner conscious activity of the organism was directly expressed by the rule-governed, purpose driven behaviour of the organism's anatomy. However, observing Reason ended up carving the organism into various, disjoint, parts, killing it both literally and conceptually. This happened because of one of the very first axioms: to know is to make distinctions, literally to cut or pull apart, and to identify, to put back together.

The cell, being the basis of all organic life, has its own inner and outer purpose, and like the organism its outer is the direct expression of its inner. The nucleus of the cell corresponds to the nervous system of the organism. It controls many of the functions of the cell, and contain the basic unit of all cells, its genetic material, organized as DNA strands. The nucleus maintains the integrity of these genes of which DNA is composed and controls the cell by regulating gene expression. This gene expression is the driving mechanism behind the observable and unobservable traits of cells, and a fortiori, of organisms.

The internal purpose of the organism is identical to the internal purpose of the gene, though unlike the organism, the gene lacks consciousness. The organism reproduces and sustains its own life for the purposes of transmitting its genetic material to the next generation. Besides sustaining itself, what has been called being-for-self, the gene is responsible for the organism's desire to exhibit itself, what has been called being-for-another.

The transmission of genes to an organism's offspring is the basis of the inheritance of phenotypic traits, i.e. an organism's observable characteristics, such as its morphology, development, behaviour, products of behaviour, etc. A phenotype results from the expression of an organism's genes as well as the influence of the environmental factors in which the organism is immersed, and the interaction between the two. In other words, genes are the fundamental basis behind all the traits that organic nature has exhibited to observing Reason. Some genetic traits are instantly visible, such as eye color, or number of limbs, while some are not, such as blood type, risk for specific diseases, or the thousands of biochemical processes that comprise life. Observing Reason finds that the fundamental basis of all life, the cell, is predicated on its genetic material, which has an internal purpose that is identical to its external purpose - to be exhibited to another. Observing Reason finds that the basis of all life is its observability.

When observing Reason turns towards the mechanisms behind genetic expression, it finds not a simple conscious unity, but chemical processes, physical processes, and ultimately, numerical processes. The life of the organism is predicated on a gene, a self-contained code that writes itself; its basic unit of operation is the complex number; the law that governs the exhibition of genes is the same law that governs the processes of inorganic nature, i.e. the law of fractal self-similarity. Complexity emanates from the self-contained repeated iterations of simplicity: this is the universalizable, necessary, schematizble law which observing Reason has sought in its observation of organic and inorganic nature.

Repeated iterations of the equation in the above picture, where z and c are complex numbers, have an identical shape with cell-division.

However, by finding this law, Reason is not able to assert its certainty of being the universal substrate of all reality. The fractal is a pure concept that is the basis of all of observable reality, the objective flux of appearances, yet it is bereaved of all conscious activity. No consciousness, according to this law, is involved in the iteration from simplicity to complexity, even though consciousness itself is the basis upon which such a phenomenon may be understood. Yet, consciousness itself is an iteration from a simple awareness of immediate being, to self-consciousness, to Reason itself. The law of fractal self-similarity cannot acknowledge that it circumscribes both the activity of self-conscious Reason and nature.

Fractal self-similarity is explored in fractal geometry, which is devoted to the study of diverse aspects of diverse objects, either mathematical or natural, that are not smooth, but rough and fragmented to the same degree at all scales. The objects of fractal geometry reflect the rough and fragmented nature of observing Reason itself. Even though a unifying law has been found that allows observing Reason to provide a rational account of the diverse, yet lawful, complexity of inorganic and organic nature, this law proves to be no unifying principle. Instead, it is more a theory of probability. The seemingly successful application of a universal, necessary, schematizable rule that circumscribes both self-conscious Reason, inorganic nature, and organic nature, fails to serve as the vehicle through which Reason asserts the certainty that it is the basis of all reality.

The failure of observing Reason is due to its having undertaken the habit of framing laws, i.e. the universalizable, schematizable necessary rules that circumscribe the inner and outer of organic nature, inorganic nature, and self-conscious Reason, which turned out to be the law of fractal self-similarity. That is, Reason takes at least two aspects of self-conscious Reason, say inner and outer, and holds them apart as static mathematical disjoint sets composed of observable particulars, distinct from each other and indifferent to each other. Then Reason seeks to relate these disjoint static sets with a static rule of relation. This tactic cannot work because these aspects which Reason sets up as being mutually opposed in truth fluidly transition into one another. Ultimately, Reason makes a distinction between self-consciousness and nature, and seeks to assert its certainty of being the basis of all reality (as the cell is the basis of all life), which is a self-certainty, by finding a universal law, a unifying principle, of a medium that is bereaved of all self-conscious activity, nature.

Having found the law it sought as fractal self-similarity, it finds the basis of all nature. Nature is engaged in the process of transition, from simplicity to complex, from chaos to order, through repeated iterations of a simple, self-same unity that results in a complex self-same unity. The end, complexity, resides in the beginning, a complex number. Organic nature engages in this movement by means of the gene, which dictates the internal and external purposes of the cell, and the organism which comprises it. The ultimate purpose behind this movement is the exhibition of traits, which in turn propel this movement forward beyond the life of a single organism. These traits are transmitted from an organism to its offspring.

The exhibition of traits, however, mean nothing without a consciousness to observe those traits with its senses. Since organic nature cannot operate in accordance with mechanistic laws alone, the presence of consciousness is necessary in order to see the exhibition and act upon it in accordance with its own internal purposes and external, rule-driven, goal-oriented behaviour. In order for a consciousness to relate what it sees to universal laws, it must engage in Reason. Reason, however, presumes the existence of self-consciousness.

Since, self-consciousness is engaged in this same movement from simple to complex through repeated iterations of the same simple notion that begins with the statement: the knower is distinct from the known, for the first time observing Reason sees self-consciousness as an objective phenomenon. The law of fractal self-similarity expresses the basis of all nature, i.e. objective reality bereaved of all self-conscious activity. In order to find this law exhibited in the activity of self-consciousness, asserting the certainty that self-conscious Reason is the basis of all reality, Reason turns inwards and observes the Laws of Thought.

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