Wednesday, February 5, 2014

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Zen Theory: An Exploration of Space, Time, and Consciousness via the Cycle of Change Between Binary Opposites. By Kigen William Ekeson

Zen Theory: An Exploration of Space, Time, and Consciousness via the Cycle of Change Between Binary Opposites.
By Kigen William Ekeson

In Zen Buddhism there exists a way of understanding how objective consciousness arises by describing the universe and everything in it in terms of a simultaneous interaction between two opposing functions. As an extended philosophical thought exercise, it will be shown how this approach can be used to create a topological model based on the Mobius strip.  This model outlines a  unified and logical way to understand everything from quantum entanglement and gravity, to objective consciousness in a way that can be organized through a progression of discrete levels of topological complexities. Finally, this model will be applied to the Double-slit experiment in order to present a new and logically coherent explanation for the quantum measurement problem.

1.1  Introduction

Albert Einstein revolutionized our understanding of time and space when he discovered that the causes and effects of any event couldn’t travel faster than the speed of light. These ideas were first published in 1905 as The Special Theory of Relativity (SR). One of the most useful and common tools for illustrating SR's description of causality is a Minkowski space-time diagram (Fig.1). The Minkowski space-time diagram is just a diagram depicting a set speed limit (the speed of light) for how fast any classical-level event can be caused or can affect anything else. Each light-cone illustrates a particular frame of reference oriented to a specific event. Differing frames of reference are often compared to each other in order to help illustrate the relative differences brought about due to the constancy of the speed of light. The diagram for each frame of reference can be divided into four main parts: 1) the past light-cone of an event, 2) the event itself, 3) the future-light cone of an event, and 4) all of the remaining space- time "outside" of the light cones.
The past light-cone of an event represents the history of all the previous causes (moving at the speed of light or slower) that converge in order to create any event. The future light-cone of an event represents all the effects generated by a particular event, again limited by the speed of light. The event itself in SR is represented by a point particle. A point particle is a conceptual representation of an event whose size, shape, and structure are irrelevant to its given relativistic context. For example, even a galaxy can be considered and behave as a point-particle within the relativistic framework of SR. When the history of a point-particle through time and space is plotted, a world-line is formed (see Fig. 1) with each point along the line having its own past and future light cone. The fourth part of a space-time diagram includes everything outside of the past or future light cones of an event existing in an “unknowable” or "causally disconnected" state called a space-like separation. SR makes clear that when something is in a state of space-like separation from a particular event it should have no causal influence on that event whatsoever because in order to do so, that influence would have to travel faster than the speed of light. A classic example of this is that it takes light leaving the sun about eight minutes to reach the earth. Until that sunlight hits us, according to SR, the earth and sun exist in a state of space-like separation and can have absolutely no causal impact on each other.
However, there is another well-proven theory that raises some interesting complications about basic ideas set forth in SR. That theory is called Quantum Mechanics (QM). Soon after Einstein published his work at the beginning of the 20th century it was correctly posited that at the quantum level of interactions certain causal influences not only happen faster than light; they can happen instantaneously. For example, it was experimentally shown that it is possible to split certain fundamental particles into two, oppositely polarized sub-particles. If these sub-particles are then separated by some distance and only one is changed in a certain way, its separated half instantaneously reflects an equal and opposite change regardless of the distance between them. This "spooky action at a distance" (as it was labeled by Einstein) is a characteristic of what is called quantum entanglement. Because at the instant that one of the sub-particles is influenced they must (as defined in SR) be in a state of space-like separation with respect to each other, they should not be able to have any causal influence on each other...but they do! Furthermore, the mere act of observing one of these separated opposites is enough to bring about a corresponding causal change in the separated half. Trying to find a way to reconcile the theoretical disparity between the “classical level” causality of SR and the “spooky” behaviors of the quantum-level has proven to be very difficult and persist even today. Up until a couple decades ago a shaky peace had existed between these two great scientific theories by arguing (via the Copenhagen Interpretation) that QM's instantaneous transfer of "influence" (as opposed to a transfer of “true” information) belongs to another level of reality entirely and that Quantum level influence has little or no direct corollary in the large scaled classical-level (i.e. the non-quantum, everyday world).

Why is this instantaneous influence evident at the quantum level but not at the classical level? Is it truly, as posited in the Copenhagen Interpretation, because the quantum level operates by completely different rules than those of our classical-level world, or is there some other more principled explanation? An even more profound question is how is it that at the quantum-level, the instantaneous physical influence mentioned above can be brought about through the mere act of observation?  What role does observation play within causal processes? Is it merely as a passive, uninvolved witness, or does it somehow play an active role within the cause and effect interactions of its surroundings? 

When comparing various frames of reference to each other using Minkowski space-time diagrams, we must always assume the role of a “detached” observer. Perhaps there is no possible way to represent or account for the observer or the act of observation within a typical space-time diagram because observation requires some internalized contrast of information. Until we create a model that somehow depicts this necessary internalized contrast of information within the framework of a space-time diagram, we must continue to accept observation (the only thing that can create a relativistic comparison) as a necessary yet inexplicable assumption in S.R. What this paper suggests is that although every object can be conceptualized and diagramed as a point particle, in order to account for the action of observation within the system in a way that is valid at both the classical and quantum levels requires a different depiction of a space-time diagram.

1.2 A Different Approach
Simply put; SR holds that every reference frame shares the exact same relationship relative to the speed of light. This implies that no single reference frame is “correct” relative to others. Therefore, the inverse should also be true; every reference frame exists in some uniquely "true" state for itself relative to the rest of time and space. In SR, the internal dynamics within any historical event (i.e. every event expressed as a point-particle) are ignored and focus is exclusively put on determining the relative differences of perception that would occur between different frames of reference. Conversely, the ZT approach will be to completely ignore the relative differences of perception between differing reference frames and instead identify and focus on a common principle necessary to give rise to (and decay) the internal dynamics of any real event in space-time. It is only by adopting such an approach that the inclusion of any space defined by an internal contrast within the causal model becomes possible. Therefore, one might describe the approach presented in this paper as a kind of general theory of individuation.
1.3 Boundaries and Binary Opposites
In order to begin to model how individual real events occur within space-time within a space-time diagram, a simple set of postulates must be introduced. Using these we will attempt to reinterpret the basic Minkowski’s Space-time diagram in a way that ultimately allows for the phenomenon of observation to be identified within it.
The postulates are:

First, there is an aspect of something we call “reality” (for lack of a better word) that reflects our experience of boundaries in time and space.

Second, All perceived physical or mental boundaries within this reality change continuously over time. Everything has motion (i.e. no bit of space can be completely lacking in energy).
Third, Together with our perception of changing boundaries, we have an aspect of our existence that shares a common field of reality. Despite all boundaries within time and space, the Cosmos is ultimately “one”.
If the experience of our single universe somehow fosters the arising of distinctions within it, then the simplest hypothetical distinction would be to posit a single contrast between two conditional inverses that when taken together would include all of time and space. For example, that table in front of you is the perfect and unique inverse of everything that is not that table at this moment in time and space (from any single frame of reference). The physical size or temporal duration of any chosen set of conditional inverses is irrelevant because all such variations when considered in this manner serve only to further define the unique and perfect contrasting relationship between a "thing" and its conditional inverse i.e. “not-that-thing”.

However, such co-dependent polarities are not only limited to such an extreme example as a particular thing contrasted to the rest of time and space. Any limited boundary within time and space (i.e. real event) can likewise be objectively isolated and internally sub-divided into a binary set of conditional opposites which when taken together define the totality of that real event. For example, our afore mentioned table can be divided into a left side and right side, a specific period of time can be divided into the beginning half and ending half, even a photon can be divided into "spin up" and "spin down" opposites. ZT holds that all we need do to define any spatially or temporally shared boundary is to identify some set of binary opposites of which it is composed.
Of course, as events become more and more complex, descriptive conditional opposites need not be limited to only one pair. For example, there are a number of ways to identify a particular circle (e.g. center and circumference or via any two conjugal portions of that circle). However, within the context of this paper this fundamental dichotomy as it exists at every level will be synonymously understood as either a binary opposition or as conditional opposites.

To satisfy the second of our three postulates, both halves of any binary opposition must be in a state of simultaneous change with respect to each other. Alternatively put, for some action to happen it must always have some context within which to do so. Thus both parts of any binary opposition have a gestalt-like relationship and can also be alternately be understood as context and active subject changing in perfect synchronicity with each other. By defining every real event as being brought about through the simultaneous action of some pair of binary opposites we are merely acknowledging the fact that no event can occur that is unconditionally or completely independent from some co-dependent context. For example, one cannot move the afore mentioned table forward even the smallest amount without the context within which that table exists simultaneously changing in some uniquely corresponding way.

Therefore, as Einstein showed us, the speed for any particular entity to go from Point A to Point B within some given context is indeed limited by the speed of light, but a simultaneous interaction between that entity and its defining conditional context (most broadly described as its binary opposite) is a necessary prerequisite in order to give rise to any speed at all. Interestingly, what becomes clear once this action is identified is that this simultaneous and complimentary causal action between binary opposites always adheres to a uniform cycle of change (involving time and/or space). This cycle of change between binary opposites (Fig. 2a) is illustrated and listed below. It is followed by the corresponding reinterpretation of a Minkowski Space-time Diagram (Fig. 2). The diagram simply expresses the idea that all real events are created and model change through the simultaneous interaction between some set of conditional inverses following a fundamental pattern.

Fig. 2a
The ZT Cycle of Change
Polarity I (Initial polarization of binary opposites)
Unification I (First unification of binary opposites)
Polarity II (“Switched” or "changed" polarization of binary opposites)
Unification II (Second unification of binary opposites)
Polarity III (Return to initial configuration of binary opposites)                           

1.4 Polarity I - A Simple Circle  

In order to exemplify the ZT cycle of change between binary opposites and how this cycle ultimately allows for the arising of consciousness we have only to draw a circle. This circle will represent any single shared boundary imaginable. Let us divide that shared boundary into a binary pair by contrasting the perimeter of the circle (radius = 1) with its center (at 0) (Fig. 2). Perimeter and center define both the single circle they create as well as each other by way of their perfect conditional co-dependence.
To illustrate the ZT cycle of change for our circle let the perimeter and center (i.e. 0 / 1) alternate their positions with respect to each other. Supposing that their alternation will happen at the speed of light, we will begin at the first polar extreme (Polarity I, Fig. 2). Since no direct contact (or communication) between the opposites has occurred at this point, neither opposite can observe the parameters of the total action in which they are engaged in. Such a pre-informational condition corresponds to the example of the space-like separation between the earth and the sun before its rays have reached us. The salient point here is that there is always a pre-informational binary condition (Polarity I) necessary to evolve into an informed binary condition. Thus, the ZT version of space-like separation would run something more along the lines of; a pre-informational relationship comprised of two conditionally inverted variables that together make up some dynamic shared boundary. The same contrast exemplified by the perimeter and its center, or the sun and earth, can also be identified in the relationship between the earth and any distant star, or between two sub-atomic particles.

1.5 Unification I
Continuing to the second stage for the cycle of change between binary opposites, there will come a point where the perimeter and center of the circle meet and perfectly unite (See Unification I, Fig. 2). At this point they become indistinguishable from each other; their binary relationship changes from one functionally characterized by pre- informational polarity to one characterized by pre-informational unification. Thus, in perfect contradistinction to usual denotation of an event in a Minkowski diagram, the point of convergence of causes within a particular ZT cycle represents the unique part of the cycle that is (from within the reference frame of that event) utterly incapable of being defined as a historical event because at that point, no contrast exists within their single shared boundary. One might also call this the point of maximum uncertainty in the ZT model. However, even though the union between opposites cannot be internally observed, any act of unification must still express some non-zero real spatial dimension (although that dimension will be meaningless from the perspective of the two opposites creating it). That is, at the exact point where two real conditional opposites come together (which is only truly possible to consider at the quantum-level because at macro-levels the opposites involve are made from compounded complexities), nothing can be measured from within that system of opposites. Consider the possible relation to the standard ideas of QED in the following excerpt from Richard Feynman (one of the fathers of Quantum Electro-Dynamics [QED]).
Feynman writes; “When calculating terms with (subatomic) couplings, we must consider (as always) all the possible points where couplings can occur, right down to cases where the two coupling points are on top of each other – with zero distance between them. The problem is, when we try to calculate all the way down to zero distance, the equation blows up in our face and gives meaningless answers – things like infinity...Perhaps the idea that two points can be infinitely close together is wrong – the assumption that we can use geometry down to the last notch is false.” (Feynman, QED, p. 127, 1985, Princeton University Press)
Perhaps the above quote reflects a real-world example of the unification aspect of change within the ZT cycle; an aspect that is fundamentally indefinable but only becomes truly clear when it is examined at the simplest levels of complexity.
1.6 Birth of a Historical Event / Information
As the cycle of change between the opposites continues, perimeter and center move beyond their state of unity and adopt a completely new relationship with respect to each other. That which was acting as the center of the circle now lies outside of what was once its own perimeter, i.e. is now acting as “perimeter”, and that which was once the perimeter now lies inside of what was its own center, i.e. is acting now as the relative “center” in the relationship. This switching of functions has two important implications. The first has to do with each binary opposite “doing” its inverse function, and the second is that a new and unique sub-space has been defined by the area formed by their functional overlap.
This area of co-mingling can also be understood as the point of “creation” of some form of information between the original binary opposites. That is, in order for information to be produced (i.e. a real historical event to “occur”) two things must not only first somehow encounter each other; they must actually switch places and assume the character (to some degree) of its opposite function.
Therefore, all but the simplest points in space-time can be understood as some union of both the "inner" and "outer" space-time surrounding it (all cases will be categorized more completely in section 2). Extrapolating this still further, ZT posits that this newly “born” overlap of the original opposites has the unique potential to (at the highest levels of complexity) be able to draw relative contrast between itself and the inner and outer surroundings from whence it arose. Unlike the previously (Polarity I) two space-like separated ‘parents’, the newly created area has the potential to know its "mother" and "father" in a new and unique way because it not only shares a relational context with the two discrete, binary opposites from which it arose but also exclusively experiences the content of its own individual “reality” as their unique product i.e. child. The above expresses the foundational principle within the ZT model used to explain both the formation of any historical event as some relative space-time and (ultimately) the arising of reflective consciousness.
1.7 Polarity II - Maturation
After the original perimeter and center of the circle have begun to switch their functions, the process continues until the perimeter finally reaches the “limit” of what was once its center, and the center expands out to the limit of what was once its perimeter. This expresses the second complete polarizing of binary opposites within the ZT model (See Polarity II, Fig. 2).
This second, “switched” polarity indicates the completion of the “growth” phase for any historical event because it reflects the complete realization of the full potential for the internalization of the original binary opposites by their (now fully matured) overlap. It is that aspect of the cycle that expresses the full physical individual “is-ness” of every point (i.e. boundary) in space and time. As we know, some of these overlaps can be extremely complex, and can give rise to animate beings. The ability for an animate being to (via consciousness) internalize their inner and outer surroundings as “personal experience” or qualia (more on this later) is one example of this aspect of the ZT cycle.
1.8 Decay –Information and Entropy
Upon reaching the absolute limits of their polar opposites (at Polarity II) there is only one thing that the original binary opposites of perimeter and center can do in order to continue their dynamic cycle of change with respect to each other; they must return to their original orientation. Because the historical event was ultimately formed by the overlap of two polar opposites, when they begin to cycle “back” towards their original “pre-birth” orientation the historical event that was formed by their overlap simultaneously begins to decay. This is merely to state that the same factors that gave rise to any historical event (or bit of information) will eventually destroy it by the exact same process that created it.
A second, far more sophisticated way to conceptualize historical decay is limited exclusively to animate objects and involves the area formed by the overlap (i.e. the child) of “parental” polarities in some way participating in the process of its own decay by “giving” its own constituent parts back to the polarities (inside and outside) from which they originated. This is done by the child somehow influencing both its inside and outside (i.e. his or her foundational binary opposites) through some new first-person experience of connection with its surroundings. Decay in all its forms will also be dealt with more extensively in Section 2.
1.9 Unification II - Death
On their way back to their original polar positions the returning original center-turned-perimeter and the original perimeter-turned-center will eventually participate in a second point of unification with each other (See Unification II, Fig. 2). This second expression of perfect unity completes the negation (i.e. death) of any historical space-time event that was begun by the process of decay.
1.10 Polarity III – Rebirth
However, immediately after the second unification, the two opposites switch again and begin to regain their original polar orientation (albeit in a ‘new’ way) to each other until a new expression of the original polarity is fully realized (See Polarity III, Fig. 2). This third “polar” expression can also be thought of as the maturation of the "negative" or “new” version of the (now deceased) prior historical event. 
1.11 Dynamic Fields of Interaction
Although the cyclical process outlined above was presented in a linear format, it is important to understand that each pair of binary opposites can be understood as simultaneously expressing every other part of the cycle merely through any subjective reconfiguration of relevant boundaries. For example, the burning head of a match can be simultaneously understood as a historical expression created between match and air (aka fire) or as manifesting one half of a binary pair contrasted with the part of the match that’s not burning whose ‘child’ will ultimately be the consumed match. Because of the staggering complexity of the countless “over-lapping” sub-cycles that make up the both the quantum and classical-level universe, all expressions of binary opposites (that give rise to real points in time and space) are most accurately imagined as dynamic “fields” of interaction simultaneously sharing all parts of the cycle as opposed to objects or events defined by objective boundaries or states. This simply mirrors our three original Zen assertions that can be summarized as conditional and limited binary relationship existing as some shared boundary that is engaged in some dynamic and oscillatory relationship with respect to each other. If we were to graph this changing polarity and their revolving functions over time they would appear as a pair of alternating sine waves meeting at a shared axial connection and then polarizing from each other at opposing extremes before returning to another axial connection and each then progressing to the opposite extreme. ZT posits that this pattern can be identified in the history and evolution of every action within space and time including the universe as a whole (This suggests a new way to understand the origin, nature, and fate of the universe based on the simple large-scale cycle involving fundamental opposites giving rise to a single great ZT cycle**).
2.1 The Mobius Effect
The ZT space-time diagram (Fig. 2) describes the causal history and evolution of every real event in a way that allows for the possibility of a first-person perspective to be accounted for. In Section 2 this cycle will be expressed as a topological model showing how real events can be further categorized into an interdependent system of discrete orders of complexity. Through mapping these discrete orders, explanations for the nature of light, gravity, and mass as well as a clear transition from inanimate to animate matter (and ultimately the development of reflective consciousness) can be deduced. 

The tool we will use to topologically illustrate the relationships between different binary opposites is a modified Mobius strip. It will be modified in such a way so that it more clearly reflects the ZT cycle (Fig. 2a). The Mobius strip is a surface with only one side and only one boundary component. The Mobius strip has several curious properties the best known being that if we were to take our finger and trace it along the length of the strip after one 360o time around we would be at the same place we started but on the other face of the strip.
If we continued around once more we would finally arrive at the starting point of our journey. This continuous 720º loop demonstrates that the Mobius strip has one side but that that one side can be divided into two faces at every point along it. This clearly illustrates the ZT assertion that any shared boundary within real space- time is divisible into two purely conditional binary opposites.
In order to make the Mobius strip express the aspect of continuous change posited in the ZT model to an even greater degree, let the longitudinal dimension (length) of the strip represent the cycle of change between binary opposites (i.e. as time). To do this, let black and white represent the polarized aspect of some binary pair (on opposite faces) within the ZT cycle and let grey reflect their unified aspect. When this is done, one half of the Zen Mobius strip (ZMS) (see Fig. 3) has black and white on opposite faces and the other half has uniform gray on both faces with a gradual transition between these two extremes. Thus, at any point along an entire 720º “trip” around the loop the relationship between the opposing faces reflect the ZT cycle; starting out polarized (an arbitrary starting point), unifying as grey, switching their polar orientations (relative to the starting point) then unifying again as grey, and finally reaching their original polar configuration in exact accordance with the ZT cycle of change (Fig. 2a).
The Mobius strip also has the mathematical property of being a non-orientable surface. When something is non-orientable it means that there is no way of statically defining the ‘original’ orientation between some pair of shapes moving along the single shared surface of the strip. For example, if we were to draw two pinwheels pointing in opposite directions on a transparent Mobius strip, if we were to slide one of the pinwheels (360º) once around the loop we would find that the orientation of the pinwheel would now be the same as the orientation of what was once its opposite. It's not until we make another full 360º ̊ loop (720º total) that the two pinwheels would again be twisting in opposite directions. This means that we have no way of knowing what the original orientation of either one of the pinwheels was unless we would have drawn them ourselves, i.e. unless we had the initial information before we made our observation. That is, any qualities identifying either shape relative to each other has no static “reality” as is due solely to their conditional and dynamic interaction along the shared the surface.
The last parameter that needs to be set in order to create a Mobius strip that topologically reflects the real-world ZT cycle of change is the relative complexity between differing sets of binary opposites. Therefore, let the latitudinal dimension (width) of our ZMS represent the relative complexity between different sets of polar opposites. 
2.2 First-Order Complexity
What happens when binary opposites express only the simplest examples of physical complexity? Let us form the simplest ZMS using one of the simplest pair of opposites possible: the largest and the smallest. One real-world example of this could be a single photon (smallest) in contrast to the rest of the cosmos (largest). Such a first-order complexity might be thought of as generally analogous to some massless subatomic particle (in the Standard Model of particle physics) paired with the rest of the cosmos.
Applying the Zen Theory cycle of change to the above example, we know that somehow these opposites will polarize and unify with respect to each other. However, because the photon can travel (i.e. polarize) only the smallest measurable distance before coming into contact (unifying) again with the rest of time and space (its conditional inverse) the change between phases (i.e. polarizing and unifying) happens at an incredibly fast rate. In fact, ZT posits that because it is the simplest it is the fastest rate possible. Therefore, the speed of light, which Einstein discovered as a universal constant (but for which there is no known explanation as to why it is so), is defined in the ZT model as the rate at which each successive photon-universe polarizing-unifying cycle occurs.
Although the direction and speed of a photon-cosmos polarity can be measured and verified (as a wave-function), the individual photons themselves are never distinguishable while they are actively cycling with the cosmos as a whole. It’s an all-or-nothing deal; either the first-order complexity is defined by (i.e. polarizes with respect to) its relationship to the cosmos as a whole or as a “relative” particle within some other binary relationship embedded within the cosmos (although “quantum” characteristics are always involved to some degree). Therefore, although other complexities can exert certain influences on a freely moving photon/cosmos polarity (due to influence on the particle as it polarizes from the cosmos for a micro-second, e.g. gravitational lensing), the particle involved remains exclusively defined by its cyclical relationship with the entirety of the cosmos (happening at the speed of light) until that primary relationship has been superseded by another (involving for example, photosensitive film, or a banana leaf).
Because of this, it also stands to reason that no matter how fast any particular macro-level (non-wave-function) object within the universe is traveling, the speed of the “light” originating from it will always be the same (when measured by any macro-level observer) regardless of that object’s speed because every photon is by definition (as a first-order complexity), engaged with the cosmos as a whole. Therefore, as far as photons are concerned it's as though any pair of eyes are the universe's eyes and every pair sees photons polarizing from itself at the same rate regardless of how fast different sets of “macro-level” eyes (different reference frames) are moving relative to each other. One could paraphrase John Donne's famous lines from “Devotions Upon Emergent Occasions” to read 'Ask not from what the beam of light is bursting forth from (nor be concerned with the speed of its point of origin) for it bursts forth from Thee! (i.e. the universe as a whole)'. Therefore, as Einstein so brilliantly discovered, the speed of light stays constant for everything and each observer adjusts his or her own relative perceptions of space-time in order to reflect the foundational nature of the binary relationship between the simplest of particles and the rest of the cosmos. Although this is a rather radical assertion it's difficult (or impossible?) to come to any other logical explanation concerning the very real and unique characteristics expressed by light and its definitive universal speed.
As mentioned in Sec. 1.2, the entanglement of a single divided particle with itself is one of the hallmarks of quantum level behaviors. This mysterious “influence" between the separated halves seems to contradict (or at least stretch) Einstein's discovery about information transfer being limited to the speed of light. However, once we assert that any particle involved in a first (or second)-order complexity is literally engaged in a binary relationship with the cosmos as a whole (rather than just a probabilistic one), then even though a kind of odd “sub-polarity” is created by splitting the particle into entangled halves (via some “subtle” influence), from the perspective of those entangled halves their relationship i.e. contact with their definitive polar opposite (i.e. the cosmos as a whole), has not been altered in the least. That is, even though from our perspective within the cosmos we can measure a relative distance between the entangled halves, from the point of view of the split particle that distance is meaningless; there is still only a single photon engaged with the rest of the cosmos; polarizing and unifying with each other regardless of any split. Thus, Einstein's "spooky action at a distance" is rendered into perfectly ordinary behavior. ZI asserts that the speed of light, and quantum entanglement are two behaviors that arise from the same simple principle: namely, sharing a definitive polar relationship with the cosmos as a whole.
As so beautifully shown in QED, all the opposing probabilities for the general direction that any first-order particle/cosmos ZT cycle will propagate, cancel each other out, and the behavior of an electromagnetic wave always manifests in a very predictable way (the angle of incidence always equals the angle of reflection). However, even though the behavior of a photon/cosmos-wave-function is very predictable the exact location that a particular photon (or other particle) will polarize from the cosmos still has an aspect of quantum indeterminacy or randomness. That is, if individual photons are unifying with the entire cosmos (represented via the "grey" areas of its ZMS) the exact location where a particular photon will polarize again from the cosmos can never be precisely predicted. One of these simplest of particles could potentially polarize from the cosmos at any location in time or space (even backwards or forwards in time!). This randomness in first- order complexities also exists (in some form) at all higher orders of complexity as reflections of the same cyclic principle but the particular character that that randomness takes will vary according to the particular order of complexity expressing it.
2.3 Second-Order Complexity – Gravity and Mass
Particles capable of manifesting as freely moving wave-functions are not limited only to massless particles. Certain, subatomic particles, atoms, and even large molecules that have actual mass can also be described as participating as one half of a binary pair of opposites in relationship with the cosmos as a whole. However, because of their far greater complexity these opposites traverse the ZT cycle at slower rate (but still often really fast) than massless first-order complexities. Because of their added complexity (relative to first-order expressions) the width of the ZMSs representing any of these more complex pairs will be wider than first-order ZMSs. But in order to accurately reflect the profound character change for such an evolution within the context of our ZT topology the edges along this “second-order” Zen Mobius strip must not only become wider (as would be the case for larger first-order [massless] particles) they must actually begin to curve inwards towards each other.

Fig. 4a The Klein Bottle

The addition of this lateral curve is not arbitrary but reflects the natural topological progression necessary for a Mobius strip to evolve towards a Klein bottle-like topology (See Fig. 4a. A 'standard' Klein bottle is a combination of two laterally convex Mobius strips). Any such curvature for a single ZMS (or sometimes combined ZMSs, as in the case of a molecule) represents the second-order of complexity in the ZT model (see Fig. 4). ZT posits that the latitudinal curved dimension of second-order ZMSs is the topological representation that accounts for both mass and gravity.

With the evolution of a lateral curve to a ZMS we can identify two other dimensions of topological asymmetry. First, the topological orientation of the convex/concave curve (white/black convexity or concavity), and second, the width differential between the expanding “bulb” and contracting “handle” of the evolving ZMS (See Fig. 4) regardless of orientation. That is, first-order ZMSs are flat (have no concavity) and their topological width is uniform all the way around the loop (Fig. 3). Therefore, for the first-order complexity the topological “form” of its ZMS remains the same for the first time around (1/2 of a ZT cycle) as well as for the second (i.e. one full ZT cycle). In the first-order, it is only the black/white to grey orientation polarities that alternate over time. What this means (per the ZT cycle) is that a first-order “particles” can share the same spatial and temporal topology (at Polarities I, II, or III within the ZT cycle) with “other” first-order particles (or even as past or future versions of the same particle over time). To use the example presented in Sec. 2.1, if instead of opposing pinwheel shapes we just draw two dots on a transparent Mobius strip we find that without that extra dimension of the oppositely pointing pinwheel arms, the non-orientabilty "effect" becomes less complex. That is, unlike the pinwheel shape, when one of the dots is moved one 360º loop around the strip (i.e. spin* 1) both dots still look exactly the same as each other and can "occupy" identical positions along the strip and would just still look like a single dot (even though there would technically be an “upside-down” aspect that would remain). But ZT suggests that this lack of topological asymmetry in a simple flat ZMS topology corresponds to the real-world characteristic of two or more first-order complexities (e.g. bosons**) being able to occupy the same place at the same time with no one being the wiser.
By way of the evolution of a lateral curve to the topology of the second order ZMSs, another layer of non-orientable complexity is added to the model...again, like drawing two oppositely turning pinwheel shapes instead of just dots. That is, in addition to the existing oscillation in orientation from black to white faces (via grey), a unique black- white-grey / convex-or-concave topological character is also added to every point along the entire 720º ZT cycle. Therefore, while first-order complexities require only one revolution around the ZMS (360º or 1/2 a complete ZT cycle) to polarize into their original topological state (i.e. spin 1, 2, 3, etc.), second-order complexities require the full two rotations around the ZMS (i.e. 720º, or one complete ZT cycle) before they can again topologically express their original polar state. That is, (for the simplest second-order particles (e.g. an electron), upon one 360º trip around their ZMS, they only complete one half (i.e. spin 1⁄2) of the full 720º necessary for them to polarize as a “new” particle (any discrete moment of space-time can only come about after a full 720º ZT cycle). This means that Polarities I and III (0º and 720º for any second-order particles) are topologically distinct from the “switched" polarized state at Polarity II (360º). Thus, in contrast to first-order complexities, second-order complexities can occupy only one unique “place” in space-time at any given instant. This distinctive character of the topology of the second-order ZMS is reflected in the characteristic we call mass. Thus, this description of the difference between first and second-order particles seems to reflect the Pauli Exclusion Principle that states that no two particles with mass can occupy the same place at the same time. It might also be a simple way to visualize the difference in spins between massless particles (e.g. bosons) and those with mass (e.g. fermions). 

*Spin is a kind of internal angular momentum peculiar to quantum-level particles. The spin of an elementary particle is currently understood as a truly intrinsic physical property of these particles without any accepted explanation for how or why it comes about. The ZT model seems to suggest one such explanation.

**Some bosons do indeed have mass (and gravity). These can be explained by two "fused" second-order ZMSs where each grey handle (area of unification) is fused to the black and white area (polarity) of its co-joined partner.  Thus, the topological shape of this ZMS after one trip around is identical to the shape of its point of origin (spin 1. (illustrations pending)

Gravity is unique among the four fundamental forces because; 1) it is the only force that can “distort” a light-cone, which is the same thing as saying that it actually affects the “shape” of space-time itself, and 2) at the smallest scales it is incredibly weak compared to the other forces. A way has been posited above showing how the natural evolution of a lateral curve of some ZMS coupled with spin (i.e. the ZI cycle of change) can be linked to the creation of mass. That is, when a second-order cosmos/particle pairing polarizes (at Polarity II), the particle aspect of the polarity will have the character of mass, but what ZI also suggests is that the lateral curve that causes mass also imparts that curved character to any expression of mass and to some degree of its local surroundings (binary opposite). It is this curving of space-time expressed by all second-order (or higher) complexities that we call gravity.
With respect to gravity’s relative weakness compared to the other forces at the smallest of scales; in the ZI, the nuclear and electromagnetic forces relate exclusively to the longitudinal bonding of opposing edges of any ZI topology to each other as they increase in complexity while the gravitational force (as well as physical mass) is brought about by the lateral curvature ‘naturally’ created by the two faces of a single ZMS and/or ZKB expressing higher complexity. To put it another way: gravity (and stable mass) express the particular shape of space-time and the other three forces are expressions of what is keeping that particular expression of complexity together over time.

In contrast to this, the most widely accepted models (in the natural sciences) explain gravity and mass as being brought about via carrier particles (the graviton and Higgs Boson, respectively). The author of the paper is under no illusions that he is capable of disproving such ideas, but rather is suggesting that mass and gravity seem to be able to be modeled in ZI as part of a single topological characteristic that provides an alternative framework within which the four fundamental forces might be able to be logically represented.
Equating the topological distinctions of second-order ZMS with a corresponding mass and gravity also suggests a possible explanation for the difficult question of why the mass between different types of fermions can vary so much. For example, the mass of an electron is very light relative to a muon. But, if we simply posit that the greater the latitudinal curvature of any second-order ZMS, the greater the mass (i.e. energy) of the corresponding particle then two different second-order ZMSs can have the same overall width (i.e. basic complexity), but much different masses depending on the degree of latitudinal curvature for each. Thus, when we observe high-energy second- order complexities (e.g. muons) their mass (i.e. degree of curvature) dramatically exceeds that of lower-energy expressions but when that degree of curvature cannot be sustained it naturally devolves into a simpler (i.e. less-curved) expressions with the extra energy being expelled as simpler first or second-order complexities of various stripe.
Although they can only exist at one place at the one time, both first-order and (some) second-order particles can be understood through ZT as sometimes being able to travel backwards in time. That is, when some particle polarizes as white and the cosmos as black (let’s call it a white-face particle), it must then unify with the cosmos (it's binary opposite) at grey however sometimes rather than switching and continuing along the second half of its journey as a black-face particle (into its future) there is some probability that it will polarize back onto the white face again ...back into its own past thus forcing it to travel again “through” the conditional space-time it had previously related to the moment before. Should our time-regressed "positron" meet up with a white-faced (i.e. normally oriented) electron...boom! The "temporal orientations" (one to black, the other to white) of the opposing particles cancel each other out and we end up with a lot of simpler first/second-order particles.

Another important characteristic of the second-order complexity worth mentioning is that because of the latitudinal curve of second-order ZMSs, each must be fundamentally oriented convexly or concavely towards either black or white (the topological orientation of black, white, and grey represent the cycle of change within the ZT model and do not vary over time for the second-order ZMS. Rather, it is the relationship between the cycling pair of opposites that "changes" as time). This might suggest a simple way to explain the possibility of both matter and antimatter existing in the universe and also why we almost exclusively find matter as opposed to more equal amounts of both matter and antimatter. That is, the almost perfectly uniform “orientation” of all the stuff in the universe towards "matter" (as opposed to antimatter) might be a simple reflection of the state of the entire universe as it "switches" its own defining orientation (between black and white) as part of some Great ZT cycle. Such a switch (via the grey point of perfect unification, i.e. the Big Bang) would signify the end of an anti-matter oriented universe and the birth of a (positive) matter universe. This suggests that over time, alternating, successive universes produce second-order pairs oriented (almost exclusively) to a white- convex (i.e. a matter-based) universe and the next oriented to a white-concave (i.e. an anti-matter based) universe. The ZT topology expressing such a universal "switching" would be similar to the way third-order complexities switch their own orientations (See below Figs. 5 & 6): a way that is not present in first or second-order complexities. Furthermore, through using such a topology, the Arrow of Time (i.e. the growing entropy of the universe) also becomes perfectly understandable as the natural progression of the birth and decay of each (either matter or antimatter based) universe returning to their respective states of perfect uniformity (Unification II, Fig. 2a) before giving rise to the next oppositely oriented universe (see addendum "**").

2.4 Third-Order Complexity - Collapse of the Wave-function, Inanimate Space, and Gravity II
Finally, due to a continued increase in complexity (via the connection between first and second-order complexities) of a binary pair, the lateral curve along the entire length of the corresponding ZMS becomes completely closed and a ZT version of the Klein bottle shape is realized. This is illustrated in the ZT topological model as a Zen Klein bottle (ZKB, see Fig. 5) and defines another full-order of complexity within the ZT topological model.

This third-order of complexity models the first truly quasi-independant state of equilibrium from the entirety of the cosmos for any pair of conditional inverses and finalizes the most basic ZT explanation for the "collapse" of the freely moving wave-function (i.e. the full cosmos-particle relationship). That is, with the creation of any third-order complexity a stable set of sub-binary opposites comes into being that is primarily defined as “imbedded within” rather than as “polarizing with” the cosmos as a whole. Another way to think about this would be that the resulting configuration is finally definable by its own relative set of polarized opposites functioning in pseudo- independence from the rest of the cosmos. Thus, atoms and molecules and the entire (more complex) macro-level of existence can come into being via the creation of binary relationships ultimately made up of more simple expressions (first/second-order complexities) that of course share the exact same ZT cycle. For the third-order of complexity, we can say that the ZMS cycle of change between black, white, and grey is now expressible as a brand new state characterized by having a true relatively stable (we can call it “form” in the general sense) characterized by some local inside and outside as well as an temporal history independent from it's greater environment.
Adding extra topological dimensions to a standard Mobius strip forms a Klein bottle (Fig. 4a), but to illustrate a ZKB we need to add some further topological asymmetries reflecting the specific parameters of the fourth-order ZT cycle. If we initially let the outside of the resulting ZKB be black and the inside be white, the point of greatest polarity between inside and outside (black and white) happens somewhere along the midpoint of the circumference of the “bulb” of the ZKB (see Fig. 5). The point of perfect unity (i.e. gray) happens where inside and outside contract (as the “handle” of the ZKB) to an exact point of convergence. At this exact point of unity, inside and outside actually pass through each other and switch faces with respect to each other. This 3D topological inversion is unique to third (and fourth)-order complexities and expresses a level of topological sophistication that doesn't exist for any first/second-order ZMSs. What it indicates is a definitive and relative “beginning” and “end” to each historical event in a way that's fundamentally different than (most) first or second-order complexities. It is this new level of sophistication that changes the emphasis from the entire 720º "wave-function" to one emphasizing the historical creation and ultimate decay of each particular "form" produced by the event phase of the ZT cycle.
At its most basic level, the evolution into a third-order complexity corresponds to collapse of the wave-function however, this configuration is not necessarily permanent. Furthermore, each switch creates a kind of “moving wave" of the "now" (limited by the speed of light) reflecting the relative change (for any set period of time) that must progress along the entire length, (see top of Fig. 5) eventually “transforming” the entire historical aspect of the ZKB to a historical orientation that is a new historical event over time (see Fig. 2, historical event). One way this progress of the switching outer orientation from a black to a white (and vice-versa) can be thought of is as reflecting the relationship that any historical event within time and space has with its own past and future as “temporal states” being experientially “behind” and “ahead” of it within some larger, set period of time. That is, there is some ZKB that reflects one hour of a rock’s existence. Of course, that hour has its own beginning middle and end for the rock involved. The length of the period of time can vary according to nearly any limit. This also models our human experience (although human experience actually belongs to the next order of complexity) of being able to remember our historical past (the area formed “behind” switching and advancing “wave-front” of our lives) but being unable to directly experience it. For the future, we experience the exact opposite: we can’t remember it, but we will directly experience it. The “past” history of any “existing” historical expression stretches back to the point of its own creation (just after grey/Unification I) and its “future” history will extend (at least) to some expression of its own destruction (also at grey/ Unification II) of itself as a particular historical event. Thus the speed of the switching wave of any ZKB reflects the "first-person" reality of time for any third-order object (although no actual sentience is possible at this order of complexity).
If the above model holds, then there should be a discrete topological tipping- point where a free floating, second-order particle(s) transitions from a wave-function (that's engaged with the cosmos-as-a-whole) to a sustained third-order state that is no longer chiefly defined by that characteristic. Such a test has indeed recently been found and often repeated as a particular version of the Double-slit experiment. As stated above, one of the hallmarks of binary polarities involving the entire cosmos is that the particle involved is able to divide into an entangled state (see Sec. 2.2), it’s been shown that even a relatively large bits of matter made up of large molecules (or even scattered atoms) can still, under certain circumstances manifest as second-order configurations and exhibit such a state of entanglement. One example is achieved by cooling a particle. By cooling a particle(s), the complexity of its connection to the surroundings is reduced to the point where it exists in polarity only with the cosmos-as-a-whole thus artificially inducing second-order ZMS behavior. But, once a certain amount of energy is added (e.g. it is heated up), it loses the second-order ability to be chiefly defined by its singular relationship to the cosmos-as-whole and once again creates more local connections that "collapse" it into a sustained third-order complexity. This huge and pivotal increase in the complexity between the molecule and its local environment form a new binary pairing that destroys its second-order configuration and “collapses” it into a third-order "blob" of matter. Thus, this (or any) wave-function collapse merely reflects an increase in local complexity. Although hyper-cooling was used as an example above, any binary pair of sufficient simplicity should be expected to behave in a similar way. In all cases, Zen Theory topologically maps this transformation as increasing the width (i.e. complexity) of a second-order ZMS (by the added energy) beyond the critical point where its opposite edges meet and form a stable third-order Zen Klein bottle.
First, second and third-order complexities all combine with each other to give rise to the raw “stuff” of the cosmos. First-order increases in complexity (i.e. massless) reflect a uniform broadening of a first-order ZMS. At some critical point, a lateral curve in the ZMS begins and the second-order of complexity is created. As stated above, this lateral curve is expressed in the real world as gravity and mass. However, there are number of ways that second-order complexities can progress. One way would involve the addition of first or (the most simple) second-order ZMSs to an existing second-order expression that would simply and directly enlarge a particular second-order ZMS. Another would involve a combination where the edges of both would join together to form a ZKB (however special cases could be possible where, under certain circumstances the longitudinal width is not completely closed).    Obviously, this bond would necessarily run the entire longitudinal widths (as the space-time) of the ZMSs involved. This type of bonding seems to fit as a topological representation of the nuclear forces between particles. At the third-order we can see in Fig. 5 that the character of any ZKB alternates between polar orientations and so it’s not illogical to suggest that ZKB’s of contrasting polar orientations combine in ways that reflect what we observe in the electro-magnetic force.  In contrast to both of these, (as mentioned in Section 2.3) we can consider the lateral curve of the resulting combined ZMSs as representing the real world phenomena of gravity and mass. The mass being the characteristic reflected by the particular particle(s) involved in some complex state (second/third-order) and the gravity being the resulting character of the surrounding space-time of that complex state.
Gravity is unique among the four fundamental forces because; a) at the smallest scales it is incredibly weak compared to the other forces, and b) it is the only force that can “distort” a light-cone, which is the same thing as saying that it actually affects the “shape” i.e. character of space-time itself. How and why should gravity exhibit such peculiar properties? In the ZT model, these properties are clearly identifiable.
With respect to gravity’s relative weakness compared to the other forces; in the ZT model, the nuclear and electromagnetic forces relate exclusively to the longitudinal bonding of opposing edges of other ZMS/ZKB to each other, while the gravitational force (as well as physical mass) expresses the much simpler relationship between the two faces of a single ZMS or between the faces of a ZKB to each face as well as to the surrounding space-time moment.

In this way, the vast difference in strength between gravity and the other forces (at the smallest of scales) is explainable because they are shown by the model to be fundamentally different aspects of the overall space-time topology for the elements involved. Gravity (and mass) being an expression of the particular topology of space-time and the other three forces being expressions of what is keeping that shape together over time. It also suggests why gravity becomes so powerful and important at larger scales because as any ZKBs increase in mass, the size of the space-time impacted by them (the area wherein the ZKB is embedded) also increases in a proportional way, whereas the forces that compound ZMSs/ZKBs into larger and larger bits of complex matter (masses) being made up of various smaller ZMSs/ZKBS fused together (longitudinally), don't impact or interact with the surrounding space wherein the ZKB is embedded.
Regardless of the exact (and incredibly complex) details of their interactions, the first three complexities might sequentially be compared with filaments (first-order) combining to make thread (second-order), and these threads combining to make fabric (third-order). Thus, each ZT-order of complexity can be understood as having its own unique “reality” of the universe yet, by the nature of everything's participation in the shared universal cycle, also simultaneously function within greater, new, and more complex expressions of the same reality. One of our stated goals was to show that a common basic algorithm exists within all systems that ultimately accounts for some form of "individualization” in every frame of reference at both the animate and inanimate levels. It can now be seen how a “first-order universe" (i.e. a universe as light), a “second-order universe" (i.e. a universe of physical distinction between “this and that”), as well as a “third-order universe” (i.e. a universe of form), can all "decohere" into their own individual realities yet also exist simultaneously as the merged and various functions of a single great universe.

Furthermore, just like a pre-determined pattern is used to transform a mass of fabric into a particular style of clothing, the higher orders of complexities express their evolving "form" as mass and gravity. In contrast to this, the most widely accepted models (in the natural sciences) explain gravity and mass as being brought about via carrier particles (the graviton and Higgs Boson, respectively). The author of the paper is under no illusions that he is capable of discounting such ideas, but rather is suggesting that mass and gravity can be modeled as expressions of certain levels of complexity inherent within the nature and shape of space-time itself.

2.5 Fourth-Order Complexities - The Animate Object
Third-order complexities are inanimate objects (including computers) and have clear limits regarding their relative spatial and temporal boundaries within the cosmos. One thing they cannot do is to actively participate in maintaining their own state of equilibrium (i.e. being) through the interactions of their inner and outer conditions. That is to say, as part of their specific reality, computers for example have no need or ability to internally generate influence over the manner through which their insides and outsides will reconnect moment after moment in order to continue their existence...although they may accomplish a staggering number of computations in the blink of an eye.
By contrast, animate things are characterized by their dependence upon and use of both their inner and outer surroundings in order to directly influence particular connections (i.e. decays) necessary for their own survival. Inanimate objects are incapable of any such dependency and can only express an exclusively mechanistic way to decay through time because they have no ability or need to synthesize (or benefit from) alternative behaviors beyond the single cyclical process that gives rise to and defines their physical being. That is, even the most complex computers cannot generate even the most vague of alternatives for how to behave in a way that actually extends both their own material and functional existence.  And so, rocks, stars and computers, all continue to exist without any ability to influence, by way of the product of their founding conditional inverses, what they are doing or how they are doing it (beyond their gross and completely deterministic physical durability) until their “forms” naturally decay and are transformed into something else.

This is topologically expressed by their representative ZKBs having only one “handle” through which connection (decay and unification) can possibly take place. Simply put, no matter how complicated their defining binary pair is, they can only “do” one thing. That is, for the third-order expression, every moment of its existence is brought about solely as the mechanistic outcome of their inner and outer surroundings crossing and uncrossing, around and around, in a stable condition of equilibrium until such time as their defining binary relationship is itself "externally" transformed or is destroyed. For example, even the most complex computers cannot generate even the most vague of alternatives for how they (the actual materials that make up the computer) will behave in order to extend both their own material and functional existence. Rocks, stars and computers, all continue to exist without any ability to “personally” influence what they are doing or how they are doing it (beyond their physical, third-order durability) until their “forms” naturally decay and are transformed into something else. Although, in the case of some of the largest (most complex) third-order expressions (such as giant suns), their post-“death” expressions don’t just dissolve or disperse, rather, their “switch” can transform them into third-order inversions of their previous state (i.e. they become black holes) which, of course, corresponds to just massively "switched" expressions of the same third-order ZKB. This behavior of extreme expressions of third-order complexities becomes important when contemplating the fate of the most complex fourth- order complexities as well (i.e. the fate of humans after death).

The fourth-order of complexity (Fig. 6) reflects the ZT model for the animate object (which ultimately includes the conscious being).  Animate object is used here in the broadest possible sense: as any historical event that expresses itself as a specific yet evolving region of dynamic homeostasis formed through the interpenetration 

of some inner and outer surroundings (binary opposites). Wikipedia defines dynamic homeostasis as: "the property of a system in which variables are regulated so that internal conditions remain stable and relatively constant". However, ZT holds that the unique fourth-order dynamic homeostasis is better described as some stabilized product ofbothinner and outer surroundings that’s capable of actively participating in the perpetuation of its own historical existence. Thus, fourth-order complexities uniquely exhibit some level of first-person "life" that somehow actively participates from within its own ZT cycle to extend or replicate its existence over time (consecutive ZT cycles). Another term for the action of "life over time" might be biological evolution. As stated above, the distinction between third and fourth-order complexities can be made positing that fourth-order complexities always involve the internal generation of alternatives and these, in turn, can be described as the necessity and ability to transform one's inner and outer surroundings into some set of tools for accomplishing the purpose of bringing about some form of continuation.
Tools, in this sense refers to any part of either the inner or outer surroundings (i.e. the binary opposites that gave rise to and ultimately sustain that historically produced space) that is able to be used by a historical event in such a way as to facilitate some form of its own, first-person continuation beyond its next connection at unification II in its ZT cycle. Needless to say, any tool must itself exist as part of the total content of any fourth- order complexity. This is a vitally important point. The numbers of ways in which the simplest organisms are able to use their surroundings as tools is very limited (relative to our own). But, any ability to do so still creates alternatives for how something's inside and outside might or might not connect in order to nurture, or in some way replicate the homeostatic relationship between inside and outside that defines that thing i.e. its life. For example, perhaps some primitive membrane structure allows the simplest expression of chemical based, self-replication to occur through a dynamic relationship with its surroundings. The alternative here is simple; either that dynamic homeostasis of structure continues...or not, depending on whether the integrity of the membrane is maintained and the necessary connections between what's inside and outside of that membrane take place. Should that membrane somehow loose its ability to maintain its integrity between it's inner and outer state i.e. “use” its surroundings in such a way that somehow continues the relationship between what's inside of and outside of that membrane, it fails and the utterly unique inner-outer relationship that that complete state of dynamic homeostasis brought into being "dies". This clearly differentiates all fourth-order complexities from any third-order complexities, which have no means (or need) to internally influence (in a historical, first-person-like way) how their inner and outer surroundings reconnect. That is, since third-order complexities have no quality of "life" as complex as exhibited by fourth-order complexities, they also cannot experience "death".
Thus it can be generalized that fourth-order complexities bring about a completely new way for lower-order complexities to be organized. These new organizations are characterized by having the ability to evolve by acquiring the ability to use more and more of the binary opposites from which they are composed (and upon which they are completely dependent) as tools for their own "personal" perpetuation. That is, as they evolve, their inner and outer surroundings also evolve into more and more complex tools that in turn can be used to help regenerate themselves (or some future generations) which in turn are the product of these more and more complex binary relationships. For example, men and women are “evolved” into father and mother upon the birth of their child. “Mother” and “father” are tools, used by the child to facilitate its own growth (and decay). Simultaneously, the child is used as a tool by the "parental units" (SNL anyone?) in order to continue some version of their own state of dynamic homeostasis...i.e. by passing on their genes and social influence (i.e. inner and outer realities) to a new generation. Thus, although both the amoeba and the human both exist as living beings, the human far exceeds the amoeba by way of huge increase in the complexity of their defining binary opposites (and more importantly, in their ability to divide those opposites into alternatives: tools) that give rise to each distinct, biological life form.
Expressing any alternative ways that fourth-order complexities might connect inside and outside can be shown in our ZKB topology (Fig. 6) by adding extra "handles" through which inside and outside can potentially connect for any particular unification (unification II in the ZT cycle). Adding only one extra handle means that for whatever historical evolution is being represented, the possibility exists for the binary opposites to unify in two different ways; perhaps most basically, continuation and cessation. Thus, every life forms experiences its own fourth-order universe of alternatives by being created from and creating pair after pair of opposing contrasts within it. Which alternative of any pair becomes the actual future connection is “chosen” by the "child" (i.e. historical being) the instant after the historical maturation (Polarity II), just at the point where some particular “decay” begins and culminates via some form of unification (at Unification II). This is not to say that a completely new set of alternatives couldn't (and indeed must) be made an instant later...before that unification is fully realized. Thus, for the human being, every decision to follow any particular alternative entails a continuous commitment of ones insides and outsides to form some historical decay resulting in some particular expression of unification (Fig 2, Unification II/I).
That is, every connection can be thought of as a form of death (for any historically present third-order complexity) and through that death, (Fig. 2, Unification I/II) extinguishes the utterly unique distinctions (Polarity II) of that moment. Thus, every execution of every fourth-order alternative ultimately entails a hurling of ones self into some petit mort, i.e. an ultimately unknowable future. This natural (hopefully momentary) loss of distinctions through the self 's ability to "choose" the manner to connect his/her inner surroundings is the fourth-order equivalent of quantum indeterminacy that can be used to describe the ZT explanation of free will. For example, we know if there are no cars on the street, we know we can usually cross it without getting hit by one but ultimately, crossing that empty street still holds a plethora of unknowable risks (both internal and external) to our survival which we must abandon ourselves to whenever we "choose" to cross it.
At the extreme of fourth-order complexity is the entire human world: both body and surroundings (our ultimate binary opposites). ZT posits that every bit of both can be thought of as an extraordinary set of tools generated in order to create more and better behavioral alternatives for the resulting, fourth-order complexity that ultimately can be used by that complexity to bring about the nourishing and perpetuation of its own, historical and/or individual (or collective) selves. Therefore, just as the third-order complexities (as expressed in the third-order ZKB), bring the “reality” of form (i.e. collapsed wave-function) into the cosmos, the fourth-order, by generating more and greater alternatives (i.e. tools) creates a completely new level of reality: a reality of "separate" objects, events, personal thoughts and experiences...or qualia which are all characteristics (oriented to some particular historical expression) that come into being (and decay) as the internally contrasted aspects of the binary relationship forming that fourth-order configuration. Thus the generation of alternatives creates a brand new dimension within-and-as the cosmos that can be described as the fabric of consciousness itself. It represents the universe expressed in-and-as "consciousness" in the uniquely fourth-order way. This fabric is always defined by the inclusion of some “centralized” or historical frame of reference "sandwiched" between a relative past and future in space- time that ultimately (as in truly sentient beings) can result in expressions of consciousness sophisticated enough to clearly objectify their own inner and outer surroundings and their personal "existence" in relationship to those surroundings. Thus, the observer is born together with its inner and outer surroundings.
Therefore, as introduced in Sec. 1.8, personal experiences of phenomena, or qualia, are brought about when both the inner and outer surroundings are fully internalized (at Polarity II) by-and-as the limits of that qualia-laden event (i.e. self). For example, when we have caught a red ball, the unification aspect of the ball meeting our hand gives rise to an internalized experience made up of a self realizing the fact that his or her body has caught a red ball together with many other, momentarily subordinated, inner and outer circumstances that also helped to bring that experience about. Thus we can proclaim, “I have caught a red ball!” However, rather than being constrained to throwing the ball back in the same direction from whence it originated, the catcher can re-arrange all of the (now fully internalized) opposites that make up her own (inner and outer) content, and synthesize many, many alternative directions that she can freely “choose” to throw the ball; ultimately unifying her inside and outside once more through the chosen alternative.
To reiterate what was mentioned above, this is not to say that the actual existence of lower orders of complexity depends on any fourth-order expression. Each order of complexity "experiences" in its own version of the one, shared universe. However, the fourth-order’s ability to transform inner and outer surroundings into tools, as a function of its own unique ZT cycle can potentially incorporate lower-order expressions (first, second, or third-order) of the "universe" into fourth-order expressions. Thus, first, second, and third order universes are all necessary to express the fourth-order universe, which, in turn has the capacity to further “weave” those realities into unique fourth-order alternatives that collectively form a new, tangible and measurable, order of “reality”. Thus, history, art, culture, good tasting food, and brick sidewalks all can come into being. It is this action, inherent at any level of biological life (although vastly differing in degree of complexity) that ZT defines as the phenomenon of "consciousness".
This completes the basic, ZT model for understanding how unconscious and conscious expressions of space-time are each are formed, interpenetrate, and are related. The model will now be applied to the Double-Slit Experiment.
2.6 The Double-slit Experiment
The Double-Slit Experiment usually involves a single, quantum level particle engaged in a wave-function being shot towards two parallel slits, after which it travels onward to a photosensitive detector screen set up at some distance beyond the slits. The first mystery exemplified by the Double-slit experiment is that, rather than forming a pattern that indicates the particle having gone through one of the two slits (as is the case when only a single slit is present) and acting in a macro-level particle-like manner, the single particle goes through both slits at the same time by evolving into two separate and entangled wave-fronts. The dual wave-fronts produced by this split then proceed to interfere with each other in such a way that when the entangled sub-particles finally arrive at the detector screen, they “collapse” again (via the third-order screen) into discrete, single particle that appears only in one of the reinforced wave-crests of the interfering fronts.
Why doesn’t a single particle (ZT polarity) just go through one slit or the other? To answer this according to ZT, we must assume that the third-order complexity of the double-slits does indeed present something that requires a response by the particle/cosmos polarity i.e. can interact with but ultimately cannot disengage the photon from its pre-existing first-order complexity. As a first/second-order complexity, as soon as the single photon is shot from the “gun”, it exists in a particle/cosmos polarity (i.e. wave-function) with an equal probability to interact with both slits. However, as described in Sec. 2.1 and 2.2, first/second-order complexities lack both the ability to either "internally" generate any binary polarity that is independent from the cosmos as a whole (third-order complexity i.e. collapse of the wave-function) or to generate any "decisive" alternative choices of behavior (fourth-order). Thus, the photon cannot “go through” one slit or the other but rather, responds to the connection (i.e. unifies and “switches”) with the double-slit screen by giving rise to two new and entangled "sub- polarities" that (from its own perspective) still maintain their integrity as a single first/second-order complexity with the entirety of the cosmos i.e. wave-function (see Sec. 2.2). That is, by entangling with itself, the particle/cosmos pair does indeed create a “switched” historical event (i.e. polarity II) with the double-slits but the character of that interaction is not sufficient to disrupt its existing first/second-order complexity.
The second mystery of the Double-Slit Experiment is; when an attempt is made to observe which of the two slits the particle goes through by placing a detector at one of the slits, the potential for the particle/cosmos to split into an entangled state is immediately destroyed and a single particle-like pattern (as opposed to the previous interference pattern) registers on the final detector screen as if the particle suddenly became a macro-level particle. How is it that the first/second-order complexities seem to “know” whenever it is being watched? According to Zen Theory any freely moving particle(s) sharing a binary relationship with the cosmos as a whole (as a wave-function) cannot be physically integrated into some other stabilized third/fourth-order complexity and still retain its original relationship with the cosmos. It is thus being suggested that in the case of the Double-slit experiment, by adding a new way (via some set of tools) for our scientist (the ultimate fourth-order agent) to “detect/observer” which slit the particle goes through, an actual physical re-ordering takes place whereby the “particle” is definitively wrested from its first/second-order state and transformed into part of a fourth- order alternative i.e. tool oriented to observing scientist(s). The ZT assertion is that it is this fourth-order re-ordering that physically redefines the particle as part of a fourth-order complexity and in so doing collapses the wave-function of the first/second-order particle thus rendering it observable as separate from the cosmos as a whole. This is indicated on the final detector screen by it registering the particle as exhibiting only a particle-like pattern of “hits” after some yes or no alternative has been detected at one of the double slits. That is, after the photon goes through one or the other slits, the wave-function of the first/second-order particle/cosmos polarity immediately re-forms but in a way that is not entangled with itself and thus yields a “particle-like” pattern on the third-order detector screen consistent with quantum probability for an un-entangled particle (i.e. two areas of frequent “hits” coinciding with each of the two slits).
The third mystery of the Double-slit experiment is that when the detector remains at the slit but is turned off, the entangled wave-like behavior returns. This observation now becomes perfectly logical because once the possibility for an observer to transform the particle/cosmos complexity into either a yes-or-no fourth-order alternative is removed, the first/second-order complexity remains outside the scope of any potentially transforming fourth-order influence and its first/second order state is naturally maintained. The turned-off detector (i.e. disconnected from any fourth-order agent) by itself is simply a mechanistic third-order complexity and as such is utterly incapable of influencing the particle/wave in any significant way (unless set directly in the physical path of the photon/cosmos polarity). Of course in all set-ups, the final detector screen will always bring about a mechanistic third-order wave-function collapse due to its physical location directly in the path of the photon/cosmos pair.

It should be stated that the ZT explanation for the double-slit experiment also allows for the particle/wave-function to be collapsed by something (e.g. a stray particle of sufficient energy that is independent from either the double slits, detector, or the detection screen) intervening from outside of the experiment so long as the intervening complexity is able to physically influence the first/second-order particle/wave to a sufficient degree. But, it is only a fourth-order complexity that can collapse the wave-function through conscious inference alone (i.e. conclude that because the particle didn’t go through one of the slits it had to go through the other).

2.8 In Conclusion
In conclusion, we have shown that by suggesting that everything as divisible into sets of binary opposites engaged in a specific cyclical change and organized through discrete orders of topological complexities, clear relationships between heretofore disparate features of the natural world such as the speed of light, quantum gravity, the collapse of the wave-function, as well as the nature of consciousness can be identified. From the identification of these relationships, a simple and elegant explanation has been suggested for the Double-slit experiment. If this is true it would suggest that entire cosmos might accurately be described as a single, great, yet almost infinitely varied cyclical function and that the principle that ultimately gives rise to reflective consciousness arises and is present within this great cycle at its most fundamental level.
I have recently read an interesting book called “Our Mathematical Universe” by Max Tegmark. In it, Professor Tegmark posits that our universe, as well as any possible others, are able not only to be represented or described through mathematics, but that all possible universes actually ARE expressions of mathematics. This proclamation has emboldened me to give voice to my own, similarly radical suggestion about the ultimate conclusion of Zen Theory. Specifically, that Reality is best described as the evolution of relationships between binary opposites and that that relationship is universally characterized by the co-dependent and cyclical interplay between unity and polarity. That is, because the ZT cycle as well as the relationships between the different levels of organization brought about through that cycle are precisely the same as those expressed through any of our most intimate human examples of either parental, filial, fraternal, or romantic love, (namely, the relinquishment of egocentricity i.e. static polarity, through merger with some aspect of our surroundings) I will be bold enough to assert that Zen Theory concludes that all of time and space can just as accurately be described as nothing but the pure, unborn, undying, and infinitely varied action of Love itself. That is, ZT shows that the same principles which shape all expressions of human love (i.e. the human “self” defining itself through its relationships rather than as an independent object) are algorithmically identical to those that shape the interactions between everything else, from the smallest quantum-level particles to the ever-repeating, birth and death cycles of the entire universe.
* Schrödinger's Cat
Note that from the perspective of Zen Theory, the Double-slit Experiment is very different from the famous thought experiment of Schrödinger's Cat. In Schrödinger's experiment, a cat is hidden in a box and a poison pellet has a 50-50 chance of being released within that box. Schrodinger suggested that, just like the entangled split that happens to a single particle in the Double-slit experiment, the cat would similarly exist in a both an "alive" and "dead" super-position until some outside observer looked into the box. In the Zen Theory model there is a clear description for how and why quantum-level entangled states come about (as first and second-order complexities) and why they do not come about at the third-order (or fourth) of complexity (Sec. 2.2 and 2.3). Thus, from the ZT perspective, the entire system inside the box exists as a third/fourth-order complexity from the very beginning. Cats, boxes, and poisoned pellets (all third and/or fourth-order expressions) all have the capacity to transform any quantum-level indeterminacy introduced by a first or second-order wave-function (used to either release the poison or not) into higher-order complexities (ones not defined by their relationship to the universe as a whole) in a ways that do indeed have their own third/fourth-order expressions of indeterminacy but these form of indeterminacy are not dependent on any observer outside the box to decide their outcome. That is to say, in ZT, cats, via their own fourth-order complexity, have the innate ability to die from randomly dropped third-order poison pellets without any need to be externally observed. Thus, by no longer needing an outside observers to collapse the wave-function there is no longer any need to spawn parallel universes (where identical cats don’t live out the "other" alternative)’s all just a question of how complex a system is. Thus, ZT offers a solution to Schrödinger's Cat that suggests at least one reason to doubt Everett's Many-Worlds Interpretation (and all its variations) for explaining the nature or relationship of a super-position to either the quantum or macro level of reality.

**The Alternating, Fine-tuned, ZT Universe
Applying the ZT model to the universe as a whole yields some interesting and elegant results. Like everything else mentioned above, all expressions of reality can be described in ZT by first positing two, complementary opposites cycling from unified to polarized states. From this, if we try to create a ZKB reflecting the action of the whole universe, then the first thing that needs to be established is the defining set of binary opposites. In the case of the universe as a whole, the pair of opposites that might be construed as the most abstract and fundamental (even more abstract than the “relative” distinctions of “largest” and “smallest” i.e. first-order complexities) might be simply “positive” and “negative”.
As in all other examples based on a ZKB topology, the points of perfect unity (Fig. 2, Unification I and II) represent the opposites combining into a perfect state of homogeny. This homogeny is also corresponds to the most contracted point topologically possible. Although such a point temporarily unifies the binary pair, their momentum (i.e. capacity for change) is maintained. Thus, the opposing orientations are forced to “pass through" each other and invert (see Fig. 7). This initial switching would correspond to the “Big- bang” at the universal scale, and would result in the birth of a positive-on-outside- negative-on-inside (white on outside, black on inside) universe similar to a third/fourth- order ZKB model and producing either a matter or anti-matter based outcome (see Sec. 2.3).

This switching of opposites (similar to third and fourth-order complexities), creates a “moving wave" of the "now" (see top of Fig. 7) which would correspond to the inflation and continued expansion of the universe. According to the universal ZKB (Fig. 7) the “ripple” of the new, “existing” universe expands into its own future by the progressive “switch” with it’s own pre-big-bang-past along its entire length.

Perhaps this might suggest a simple way to explain the Dark Energy mystery (another phenomenon for which current scientific models offer no accepted explanation). That is, at the edge of the switching "ripple" of change, our space-time is literally "ripped" into existence by the crisscrossing of the universal, binary opposites. Thus, it is the primordial and fundamental version of the ZT cycle that naturally creates the energy responsible for the expansion of empty space otherwise known as Dark Energy.
Interestingly, the speed (i.e. expansion) of these universal switching opposites would not be limited by the speed of light (as are all relative historical events within the cosmos). Remember, ZT defines the speed of light as the fastest rate at which a single particle can unify and polarize with the entire cosmos (Sec. 2.2). The binary opposites that give rise to the entire universe are far more fundamental than this, thus the limit of the rate at which their “switching” occurs cannot be defined or limited in the same, relativistic way. Likewise, the curvature of the universal ZKB does not represent either mass or gravity as it does in the usual sense for all curved relative ZMSs or ZKBs embedded within the universe. Although the principle of evolving-through-curvature is identical with relativistic examples, the resulting gravity cannot be coordinated with any particulate expression of mass as is the case for all second/third/ and/or fourth-order complexities. Thus the expanding and contracting curvature of the Universal ZKB is not oriented towards relative mass i.e. it is non-contractive. Rather, this dark energy directly forms and expresses the shape of the universe as the two fundamental binary opposites are switching with their previous, inverted manifestation.
What is expressed is the birth, growth, and the inevitable drawing down of one universal cycle and the beginning of the next...or rather, a fundamental and gradual transfer of kinetic energy from one binary pair back to its own inverted expression. Therefore, whatever it is that "powers" the switching of primordial opposites and their polarizing inflation will be the same force that dissolves that polarized condition (aka. entropy) back to a perfect, shared state of homogeny. However, unlike a third-order ZKB, the universal ZKB has nothing (i.e. is not embedded with a larger set of binary opposites) externally dictating its form beyond the perfect synchronicity of its own, fundamental opposites.
Finally, (but perhaps most importantly) because the single, unified aspect of the universe is divisible into two perfectly equal binary opposites, the quality of the space-time that their overlap creates must express the same, unique and perfect balance inherent in the original, equal pair. Perhaps this initial, perfect balance between opposites is the reason why the extremely unlikely and precise conditions i.e. the “fine-tuning” that allowed for the formation of complex atoms and, finally, life itself, was able to be realized within our universe. If that is so, then ZT suggests that this fine-tuning will not only be inherent within this universe but will likewise be expressed, to the exact same degree of precision, in the next, anti-matter universe (that will be the ultimate outcome of the de-polarization i.e. entropy, of our own, matter-based universe) as well as in the endless stream of alternating universes to come.
Copyright © 2014 William M. Ekeson. All rights reserved under U.S. copyright.