This chapter examines perspectives and relationships that show a connectedness between the parts and the whole. These models are not parts of a proof, but examples of a method of perception.
Reality cannot be described directly by any one model, but is seen in the common structures displayed by different models, indirectly. Objective models are comparable to subjective models, with a difference.
By using a proportional array, objective concepts are seen to be modeled by equation.
The same proportional array shows how subjective concepts are modeled by relation.
Quantitative relationships use objective equations, and qualitative relationships use subjective relations. They can both be represented by a proportional array that separates each element of interest from the others. This array is the division of the unity into four parts, seen along and across two dimensions. Each new overlay of concrete existence adds new information for further parallel correlations of subjective existence. The better understood each model is, and the greater the number of parallel correlations made between models, the clearer an actual indirect perspective of the whole of all things becomes. By aligning several contrasting patterns out of the vast array of existent models, a lateral higher perspective may be perceived.
Einstein’s famous equation relates the four components of the physical universe; mass, energy, space, and time. Einstein’s said that in cases where the atoms emitting and absorbing photons are at rest relative to each other, E=mc ² . E is energy, m is mass, and c is the speed of light. All motions (including that of light) are expressed in a rate of distance per time. Distance is the one-dimensional expression of space. (Area would be the two-dimensional expression of space.)
The equation E=mc ², in this form, does not show the proportional array it naturally contains. Simple algebra will suffice to restate the equation as the parts of a proportional array.
Divide both sides of the equation by m and the result is E/m=c². The c representing the speed of light (which is squared) can be rewritten as (s/t) ², which is equivalent to s²/t², so the equation now reads E/m=s²/t².
The proportional array is now evident. Energy is to mass as space squared is to time squared. It is also evident from this array that energy is to space squared as mass is to time squared.
E=mc²
E/m=c²
E/m=s²/t²
The relationship between the four components of the physical universe can be seen to parallel the relationship between the four components of formal linear logic; the A, E, I, and O propositions.
These four propositions are assertions about a relationship between things and there is a relationship between the four different logical assertions and the possibility of each to exist in the case of the others.
The A proposition is ‘All A is B’
The E proposition is ‘No A is B’
The I proposition is ‘Some A is B’
The O proposition is ‘Some A is not B’
These propositions can be visualized topologically.
The relationship between the possible truth of one formal proposition in relationship to the possible truth of another formal proposition parallels the possible case of one kind of physical existence for an entity in the presence of another kind of physical existence for that same entity. The array of formal propositions in logic parallels the array of physical components of objective reality.
Each term of reality is defined by the others, and is a term used to define the others. This array is a definitive study on the relationships between the physical entities of existence; matter, energy, space, and time, and also the relationship between conditions of existence.
A definitive study will encompass all the parts that make up that whole. Each part is a term in the display of relationships within that whole. Each term of a definitive set describes a facet of that object. Such a facet is described relative to the elements that are not that facet. Facets are not only abstractly descriptive of models, but are objectively descriptive of physical objects as well. Atoms accumulate into groups by bonding and linking to other atoms in regular geometric patterns. The patterns involved create defined ends and edges to the real physical extensions of the object. Even the attributes of sub-atomic particles are arrayed as polyhedrons when their measurable properties are quantitatively extended along the three mutually perpendicular axes of the Cartesian coordinate system. Facets bound the extension of space used for an object’s representation.
A facet's boundaries are the edges of the polyhedron where the crossing planes of orientational symmetry of the object intersect. The area of the facet is functionally proportional (as with the cube/ square law) to the volume of the object, and is inversely proportional to the number of facets in the polygon. An object may have only a few facets and be some simple polyhedron, or the object may be full of many tiny facets that are so smoothly angled as to resemble a perfect sphere. Infinitely many small flat facets on a polyhedron make it indistinguishable from the smooth curved surface of a sphere, yet always the object is a polyhedron with facets.
In any regular polyhedron, every facet is perpendicular to the object’s center and will reflect that center point back to itself. As the number of facets grows toward infinity, the object nears spherical perfection, having every point on the sphere reflect the center point back to itself.
Objective facets (surfaces) and subjective facets (surfaces) both reflect and project waves.
The whole can be divided into any number of parts. Parts are indirect descriptions of the whole. Since each model is a qualitative representation of some quantitative aspect of the whole, each model is a useful representative for a description based on the common feature of the number of facets in the object. The overlay of model upon model allows differences and distinctions between models to be filtered out, leaving bare the generalized abstract base. That which cannot be described directly can be indirectly seen in the abstract parallels of reality. Detailed lists of parallel models for different numbered divisions are in later.
Each part is, in its own way, a whole with parts. Each whole is, in a way, a part of a greater whole. Each thing is connected to all other things. Each of us is in the universe and the universe is in each of us in a two-way relationship with a two-way flow of objectivity and subjectivity across and through each other. Whether any particular entity is seen as part of a whole, or as a whole in its own right, is only a matter of perspective or context. As example, a heart is one part of the circulatory system, but as a whole, the heart has its own parts like valves and chambers.
Generality relates to abstractness just as specificity relates to concreteness. As example, imagine describing a transport device by its parts. In the abstract, the parts are not specified, just as a “transport device” is not specific, but rather vague.
Such a list of parts might include such vague descriptives as power source, support structure, amenities, and modes of operation.
If the transport device’s parts are given more specifically, the examples become more concrete. The transport device includes among its parts such things as radial tires, an internal combustion engine, automatic transmission, bucket seats, and stereo cassette player. The transport device is a car. This more concrete description is still somewhat vague. A more concrete description of the car might yield a specific model and year. An even more concrete description would include all the embellishments that describe an individual vehicle.
Each new level of objective information creates a more concrete specific description of reality. Even more concretely, one could describe a specific car at a specific time or place. Concrete objectivity is the explicit.
In the totally concrete objective, everything is different from everything else. Every concrete event is specific and separate from all other events. Objectively every moment changes the world. As the saying goes, “You can’t step in the same river twice.”
Abstractness is the vague and subtle world of the indirect, the implicit. To be grouped only by a common feature is to be abstracted. In the totally abstract, no specifics are available at all because all things are abstractly part of the one indescribable unity. In the totally abstract subjective, everything is part of the same thing that everything else is.
While objectively, all things are changing constantly, subjectively, everything is the same as it has ever been. As participating entities in the existence of all things, we can view other entities and be viewed by other entities in the abstract and in the concrete. Our surface facets of interaction reflect and project similarities and differences both at the same time. Everything is related to everything else by their similarities and differences. Both dimensions are needed to create and describe the field. All items have their specific resonant similarities and resonant differences as well. Mutual reflective resonances interfere both concretely and abstractly.
Awareness is of the similarities and differences of perceived events. An event is registered in the abstract as similar (or parallel) to other events. The same event is registered in the concrete as different from (or perpendicular) to other events. These two views are in opposition to each other, and expected conflicts of agreement between the two views are reconciled to differing ways of seeing (perspectives of) the same thing. This is the holographic record of the past that events and patterns of events resonate against into conscious awareness and memory. Experience occurs on a lattice of similarities and differences and is on the diagonal of both together and of neither one alone. Non-linear systems do not require a condition to be either/or, and instead can be somewhat so and somewhat not-so.
When we observe some new event, we notice that in some ways it is similar to other events of experience. We also notice that in other ways this event is different from the previous events of our experience. By aligning the similarities and difference, we describe and relate things to create meaningful expressions like analogy, simile and metaphor. Our language uses many different parallels of description.
These distinctions are used to describe how one thing is related to another. In each case, some level of similarity is expressed. In language, words are just sounds, which are auditory parallels of ideas that we have and know about.
It is our ability to create these parallel comparisons in a world of many differences, (and differentiations in a world of similarities) that makes the universe comprehensible.
Our experience of each moment is in similarities and differences as compared to what we already know and feel. A current event will resonate against the memory of past events. Each current event is observed in the context of the reflected resonances relative to past events already experienced and the projected resolutions likely to occur in the future, from the observer’s point of view.
An event follows a path through time and space, as the flow of energy and the information of mass, from the beginning of its occurrence to the end of its occurrence. In this perspective of our universe we experience one timeline and three perpendicular spacelines for the past events to reflect against and resonate with. Deeper representations are illustrated as higher dimensional perspectives. Reflected patterns in memory will resonate positive or negative reinforcement depending upon the feedback from previous outcomes.
Knowing the history of past paths and comparing them to new paths, similar beginnings can project similar future outcomes or resolutions. Subjectively, all outcomes are possible. Objectively, some outcomes are just more probable than others.
Objective equations and subjective relations can both be expressed as proportional arrays. Equations link physically oriented entities and events and quantitatively express an objective perspective of reality. Relations link non-physical entities and events and qualitatively express a subjective perspective of reality. Our level of self-awareness is attributable to the extreme resolution of our projections into the future and the depth and subtlety of our ability to detect resonances to the pattern of reflections of the past.
Thought is along a line of reasoning, or many. Awareness of an event is the taking of a position, (a perspective), that includes the knowledge and belief that certain futures to occur are more probable than others. Choosing actions to alter the probabilities of events is a process of consciousness. Points of resonance where the actions in one dimension can influence the actions in another can be graphed in space on harmonizing, interfering grids. Events are described as patterns of resonance and patterns of patterns.
The process of consciousness propagates through resonance points of being. Exchange is two-directional. That which occurs moves in one direction along the grid. What does not occur travels along the grid in the opposing direction. Consciousness creates order in the subjective direction, and therefore, it creates disorder in the objective direction. Order and disorder are subject to a point of view. From different perspectives, order and disorder can each be the other. That which changes is the arrangement within ordered groups.
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Sub-atomic particles are described by their ordered groups of properties. Exchanged particles are themselves properties of higher ordered groupings of properties. An exchange of properties is an exchange of one order for another order. Similar particles may decay and give up their properties into differing groupings of particles. Similar events may have differing possible outcomes. The outcome of one possibility is the non-outcome of all the other possible possibilities.
Patterns of emitted decay (into one event or another) are paralleled on the level of human consciousness interactions. As events occur and are registered into consciousness, other events of non-occurrence are also registered into consciousness. This is like the weaving of a tapestry creating an opposing weave in the threads yet to be incorporated into the work. The weaving work cannot continue unless the future threads are unwoven regularly. In this same manner, dreams allow consciousness to unweave the events and non-events in the future threads of awareness. These dreams may be processed in images that are similar to and/or different from experienced events.
Deductive reasoning goes from the general cause to the specific effect. Deduction determines the various reasonable effects concurrent with a set of causal facts, and is an objective perspective. As example, we know that running heats the body and makes one sweat. Also, running consumes oxygen, leaving the body starved for air. Now, if a running person covers a distance of two miles in less than nine minutes, we can predict that the runner will be hot, sweaty and breathing hard, even if the race is unseen. This process is of logical linear reasoning that projects inevitable effects from accepted premises. This is formal logic.
Inductive reasoning goes indirectly from the specific effects to the general cause. Induction looks for the most common causes for a concurrent set of facts and is subjective. (When an African hears hoofbeats, the thought is less likely of horses than of zebras.) As example, One enters a stadium to see people dressed for running and standing on the track beyond the finish line. They are bent over, breathing hard, and sweating profusely. Inductive reasoning concludes this to be the end of a race where the participants were running at a furious pace. This is lateral, non-linear reasoning and reflects a probable cause for the case at hand.
Our level of consciousness is a function of our ability to compare similarities between different things, and contrast differences in similar things. Consciousness reflects upon current events and resonates the relevant harmonics significant to events of the past. We analyze for patterns, and project a realistic probable perspective of futures events. Our brains are designed to make sense of conflicting information. In fact, the two hemispheres of the brain view things in two different ways and presume a conflict. One half of the brain compares different events of the past and present for similarities that might have some common cause, while the other hemisphere contrasts similar events of the past and present for differences that might create some expected effect. These are the two reasoning systems: induction and deduction.
Linear deductive thought is direct problem solving. It is A to B, and as such, finite. Deductive reasoning works only as well as the considered propositions agree with reality.
Lateral inductive thought is indirect feeling about the problem. There are innumerable paths of thought around a problem, and as such is infinite. Inductive reasoning (deciding how one state was brought on by another) accepts all cases as possible, and judges in the moment as to which process is most probable.
The similarities and differences in all things are unending. No two things are any more similar than different, nor more different than similar. As example, one cannot say that men are more similar to women than different from them, or more different than the same. Men and women, like all paired object of comparison, are both incomparably similar to and different from each other.
One can say that object A is more like object B than it is like object C, but the manner of comparison must be expressed. As example, compare a 200-pound rock, an ant, and a man. The man is more similar to the rock than the ant if one is comparing mass, but a man is more similar to an ant than a 200-pound rock if one is comparing complexities of feedback systems.
With sub-atomic particles, the manner of comparison equates to the properties of the particles. Similar times and spaces are as valid a basis of comparison as similar masses and energies.
Opposites exist in all things. The yin and yang each have the other’s opposite at its center. One would not experience darkness, except for the existence of light. A push in one direction is a pull from the other direction. For one person to have more than another, the other must have less. For good to exist, evil must also exist. Good and evil, God and devil, perspectives of opposition are universal.
The simplest extension of space is a one-dimensional representation, (a taught wire representing a line), that involved two opposing forces for the extension of space to exist. One force is the tension that pulls the two endpoints of the wire apart, the force of expansion. The other force is the tension that holds the wire together, the force of contraction. Each force has its own positive or negative resonances, depending on the feedback response of the other.
Surfaces are stable places between levels of opposing forces, whether the stable surface is found in the layer between fluids of different densities, isometric lines of force, or in the harmonic geometric node set of a taught vibrating wire. Push and pull together define extension into space. The tension between two forces creates the surface for waves to travel through space on. Two tensions feed back to each other, together creating surfaces of vibrational stability and a place for constant change. Each entity supports opposing tensions to hold standing waves. When opposing forces are out of balance, disease occurs. As example, growth and no growth are at odds with each other. If no growth is unduly dominated by growth, cancer can result. If growth is unduly dominated by no growth, a vital organ might fail.
What exists in the one-dimensional universe is the line, which is between two points. The two endpoints of a line are opposite each other. Any choice of motion along the line is one way or the other. There are two directions for potential flow. Every point on a line is at a unique and complementary set of distances from the opposing end points. Each point on the line exists in two ways. A point exists both as a potential non-moving nodal surface point fixed harmonically between two endpoints and a point also exists as a part of the transitional wave moving across the surface of tensions, (position and momentum).
As a standing wave vibrates on a wire, oscillating on a motionless surface. A wave moving resonantly along the vibrating surface will eventually also be reflected back in a standing wave manner and so also be a surface.
Wave projections and reflections move through each other across every point on the line. The motion of the line is the sum of all the waves on the line. Each point on the line boasts a unique position, making the points on the line all part of a single complete set of points having uniqueness as their common feature.
Each person is an individual, unique unto that single self. In some way, each of us is special and like no other. But since everyone is special, no one is special. We are inescapably similar, bound by our common differentness. We are all different in the same way.
For good to be possible in life, bad must also be possible. Both must exist for either to exist.
Agreement and disagreement both exist in all compared things. No two things can be in complete agreement or disagreement. If they both register complete disagreement with the other, then on that disagreement they agree. If two entities were in complete agreement, they would have to be in the exact same place and time, and there would be only one entity, not two.
An entity exists by its interactions with the rest of the universe, with the not-self. To interact with the universe, an entity creates a model of the universe inside of itself. Entities exist by interacting as the self and by being the image that is not the self.
For an entity to be what it is, it must also be not what it is. Two contradictory assertions that come from this are; This is this, and this is not this. These statements are icons of similarity and difference. Being and not-being are integrated onto the consciousness of each entity.
Expanded, these two contradictory expressions are stated more fully. This is this and this is only this. This is the deductive linear perspective. Freud cautioned in his dream therapy that sometimes a cigar is just a cigar, and not necessarily representative of something else in contrast to a cigar.
This is not this, but all things like this. This is the inductive lateral perspective. Magritte spoke of this in his painting of a pipe with painted words asserting it (in French) not to be a pipe. Instead, the painting is representative of things that are comparable or similar to a pipe.
The first statement is exclusive, projective, objective, and left brained. The second statement is inclusive, reflective, subjective, and right brained. Consciousness integrates linear and lateral opposites to diagonally represent both and neither.
Linear thought is one axis of understanding. Objective reasoning is required to create objective models, but one who is to firmly grounded in objectivity sees only the trees and misses the forest. Restated, one can mistake the examples for the pattern.
Lateral thought is the other axis of understanding. Subjective reasoning is used to give meaning to the patterns, but subjectivity alone fails to justify the meta-pattern by using only objective verifiable examples for comparison.
An integrated perspective sees the examples as the pattern, and not the pattern. The higher truth is not one or the other; it is both and neither. Whether two lines are parallel or perpendicular, (whether the lines cross or not) is dependent upon perspective. The two lines can exist in more than two dimensions. The simplest three-dimensional structure is the tetrahedron. From different perspectives, opposing edges of a tetrahedron can be seen as either parallel or perpendicular. From differing perspectives, a particular set of opposing edges can be seen to cross or not cross.
