How to Begin

A Casual Observer’s Thought Experiments on Simplified Cosmological Models

J.K. Holman

Introduction to

We live in an age when amazing insights into our Universe and its mechanisms have been revealed by science, from the mysterious and sometimes counterintuitive realm of the microscopic to the awe inspiring power and majesty of the cosmos. It is not so surprising in such an age, where science has undeniably demonstrated its capacities for revealing the nature of existence, that a conviction that we only need look to science for explanations should become all pervasive. Science has certainly earned such a conviction, by making actual, through technique, that which society previously would have described as the magical. Nevertheless, perhaps a complimentary examination may contribute in some small measure to the search for deeper explanations. Thus what follows will take an alternative approach to cosmological inquiry based on a sequential progression through a “primordial” evolutionary logic of sorts as we endeavour to discover not just what is, but precisely why the Universe necessarily is as it is.

A few quick comments before getting started, this paper is long, though this was not the original intent, and it is rather a commitment on the part of the reader to stay till the conclusion. In appreciation of this the author has strived diligently to produce as original a work as is possible that will be worth the reader’s time, and that will be hopefully transformational in effect. It is rather informal and the style may be found to be a bit unorthodox due in part to the deliberate absence of an outline and the development of most of the included concepts during a process of discovery based on a consequential analysis of one simple principle. However, it is intended to be reasonably approachable for most readers for whom the subject matter would hold any interest, so if a term or concept comes up with which the reader is having any difficulty then please be patient as nearly every concept will be expressed several ways to aid absorption. Two things will most certainly become rather evident regarding this paper, first of these is the unabashedly ambitious nature of the effort, and the second is that the author is probably wholly unqualified to attempt such an undertaking. With regard to the latter a potential response would be that perhaps there are none entirely fitted to the task, and it may be argued that having a nature compelled to explore such topics is the singular qualification. It is hoped that the reader will overlook any perceived limitations of the presenter and focus instead on the fundamental concepts contained within as they may be found to have merit, perhaps encountering a few surprises, or perhaps more, along the way.

Conceptions regarding infinity will feature prominently in the commentary and for those readers having difficulty with the idea of the infinite it is suggested that they instead substitute for it with the idea of the “All” or the entirety of that which is. The terms system or “one system” will be used interchangeably with Universe, primarily so as not to abuse the reader with excessive repetitions of the same term. Forces or interactions will refer to electromagnetism and the nuclear weak (electroweak) and “strong forces” and their residuals coupled into a single force (particularly as the author began this paper not considering the strong force as particularly all that separate a force in any regard). Particles will be used frequently and will refer to unspecified spin ½ particles (singular matter particles), because for much of

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what follows “temperatures” would be far too hot for composites and the masses of particles would not be consistent with anything in everyday experience (it would seem). Where other types of particles are mentioned they will be referred to specifically. And of course the term particle itself is a convenience and an approximate term at best, academics will need no further explanation and others will hopefully be satisfied as we progress. Two types of observers will be used in this “paper”, real and hypothetical. Real observers will be elementary “particles” or composites of particles existing within the Universe. Hypothetical observers will be cognitive agents existing in an extra-universal domain of unspecified nature or (absolutely) non-interacting agents within the Universe injected into the commentary to facilitate explanation of various propositions. It should be apparent immediately that the latter agent is in some logical sense indistinguishable from the extra-universal observer. Excluded from that which follows will be any lengthy consideration of the effect of external systems on the Universe or laws of nature propagating from a “multi-verse” or other extra-universal system into the Universe. This paper will take the initial position that such potential external effects should be disregarded for discussions specific to the internal mechanisms of the early state systems being examined. Some of the propositions put forth later should make readily apparent the types of supporting arguments that could be formulated to support such a position.

A final comment before It Begins, please keep in mind that despite appearances this is not a paper on physics or cosmology so much as an introductory one on philosophy. The primary end is to gain a perspective on a long standing question and offer a definitive philosophical resolution.

The Beginning of

In the beginning there was “nothing”… or was there. Wikipedia describes the Big Bang as “the Universe was once in an extremely hot and dense state that expanded rapidly”. A casual discussion regarding this might lead to one participant uttering the phrase “but what came before the Big Bang?” possibly leading to the opinion in others that the speaker may not have spent a great deal of time contemplating the subject. So then what meaningful statements may be sensibly made regarding the first moments in time and the initial state of a, or the, Universe?

In order to investigate this further, one time honoured means will be to take a reductionist approach to the problem. This brings us to our first and most simplified model, a Universe containing apparently “zero” particles, effectively a null Universe. The first “observation” put forth is that we need to be careful to describe such a state in terms that would have some definition within the frame of reference of the system being described. Therefore, while it is correct to declare that such a system contains no particles or interactions and thus has zero mass, this system may also be described as being collapsed to a point and thus exhibits the maximum possible curvature of space and this is consistent with a singularity having infinite mass. This may now be getting ahead of things in some sense as the concepts titled curvature or space would appear to be without a rigorous definition within this system, but this does serve to somewhat illustrate the indeterminate rather than zero state of the system.

This Universe would also not be characterized as possessing a fixed finite amount of energy due to the absence of a temporal definition. That is to say, time is a measure of the duration (and dimension) of events, therefore in the absence of any events with duration, time itself will be undefined and such measures as milliseconds, months or millennia are undifferentiated. Were this a more formal document it would perhaps then be noted that the system is not classically time-invariant and thus energy is not

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conserved and the system should thus be viewed as possessing an indeterminate amount of energy. In simpler terms, measures of energy or potential energy are a function of the relative ability of components or subsystems of the system to do work on other parts of the system, as compared to the potential to do work possessed by other components of the system. However, by definition, at this stage there are no differentiated components so there can be no rigorous comparative measures of energy for the Universe as a whole or in part. For purposes of this discussion, an alternate way of stating this is that in describing the state of this system it is equivalent to declare that all probabilities for internal events can be considered to exist as a potential (infinite energy), or that no probabilities for internal events are expressed in the system state (zero energy).

At this point it may be helpful to clarify this operative viewpoint regarding the term “energy” when describing hypothetical systems which do not contain energetic events as are commonly understood. Generally, as noted previously, energy is regarded as the capacity of a physical system to perform work on other systems, as system in this discussion refers to a Universal system, the substitution of subsystems or components of a system was necessary. However, an alternate view of energy is the capacity for change in a system, or system component, that possesses some capacity to resist change. The prior statement can be further refined by expressing energy as a probability condition, that is, increasing energy will increase the probability that a potential event, having a certain resistance or improbability, will be found to have occurred in a subsequent state. It is suggested these alternate interpretations apply in the transition of a null state to a subsequent condition.

A null or empty Universe, as is obvious, has no events which could define the parameters of later events, therefore the system must initiate as a temporally collapsed transition from a null state to a non-null state that will effectively be the progenitor of probabilistic spontaneous creation events. Paradoxically, as there are no finite parameters available that would provide the codependent relationships that are necessary to define other finite parameters it may be observed that the only values that have relevance to this transition would be infinite, or reciprocally, true zero values (there is a subsequent section on the particulars of zero and infinity in an evolving mathematical system). Furthermore, as there are no phenomena to differentiate states having zero versus infinite conditions they must be considered to be coequal representations of the state of the one system, essentially a superposition of two states. This conception is notable in that it is representative of a characteristic that will ever after remain a ubiquitous trait of the one system, specifically, principles or properties of the Universe will be found to have decoupled from the relation between zero and/or infinite potentials and upon doing so pair off in co-dependant (neither is definable or real without the other) duality with counter-principles. This is an important point to note as the lack of appreciation of this concept and it’s derivative implications has been the cause of some protracted debates in the development of explanations, case in point, the long standing argument over the nature of light as being either a particle or a wave. It is in our natures to desire understanding in terms of absolutes and we are often resistant to the obvious nature that the Universe presents to us. That is to say, it is a system which embodies many paradoxical considerations in which a thing may be described as possessing one nature and an apparently opposing one that by some reasoning shall not coexist, yet the two opposing natures together form the complete description we seek.

In summary, it is proposed that true zero states in null systems are conceptually valid, are synonymous with infinite states and are highly unstable as they may be observed, hypothetically, to coequally express absence of potentiality for change, or infinite inertia, and infinite potentiality for change, or energy.

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This instability is otherwise describable as an aspect of quantum uncertainty and after succeeding decoupling transitions will be synonymous with uncertainty as is described in developed universal states. It is also proposed that energy is the product of, and once expressed resolves, the infinite relation from which it has condensed, and is henceforth observed in nature as the potentiality for overcoming “improbability” (doing work). It is suggested that as a fundamental property such as energy becomes defined the Universe will undergo a transition and the property will henceforth retain this essential definition as the infinite states necessary for reformulation are necessarily normalized in later states. As the initial state of the system is in a sense a condensed “probabilistic” state, then by the same logic, the nature of the one system as a probability driven mechanism will ever after be maintained.

One Universe,

The next model to consider is a Universe consisting of a single particle. The first question that may be asked is “by what mechanism does such a first particle come into existence”? One approach to this question is to postulate that the improbability of a single particle having unspecified properties being found to exist in a subsequent state of an initial null state is infinite. However, as has been discussed, the null state does not exhibit conservation of energy and may be considered to have the requisite, or infinite energy (thus temporally collapsed infinite probability), required to overcome an infinite improbability and result in the certainty that the hypothetical particle is realized.

A more systematic approach to an argument for certain creation of the new particle perhaps may be formulated by considering the properties that it might possess, such as mass energy, which is actually just an alternate measure of the probability / improbability relation. Continuing, it may be postulated that possible, and the only possible, first particle realizations would be a spontaneous creation event with a resultant particle possessing either zero mass, infinite mass or the product of zero and infinite mass. It follows that a null state possessing only zero potential would be expected to produce a particle of zero mass, which in the absence of any other particle properties translates to no particle at all and leaves us in the original null state. It also follows that an infinite state possessing only infinite potential would be expected to have the necessary energy to overcome the improbability of producing a particle of infinite mass. This also may be considered to translate to the original null state, though perhaps somewhat less obviously, (the reader should find themselves equipped to explain this as we progress). However a null state has been postulated that is coequally described as possessing zero and infinite energy and this may be regarded as resulting in a particle having the product of zero and infinite mass energy, and given that there are no other factors to modify the product, therefore a mass of 1. Another way of expressing this is to say that the value one describes and is described by the superposition of a true (absolute) zero by true infinite state. As this may be contentious it will be stated yet again as “Since zero and infinite expectations co-exist in the null system they must be in a state of relation, one to the other, in order to co-exist, and for a system that does not possess any other normalizing factors to consider then that relation is described by the value one”.

At this point a bit of explanation regarding the last statements is in order. Regardless of what finite value we might suppose this single particle possessed, its mass energy (or just mass for convenience) would always correctly be regarded as having a value of one. For the point of argument lets say we were to suggest a mass of ~1e53 kg for this hypothetical first particle. Then the next inquiry to be expected must be “what exactly is the standard of comparison that establishes the value of a kilogram in such a system”? The answer to this is that there is no valid reference here for the kilogram or any other

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presently used unit of mass. The only reference unit of comparison is the mass of the only existing particle, and the only existing particle, such that it exists, has one times that unit mass.

So what of the other properties of this singular particle? Are there definitive finite values for the angular momentum (spin), charge and velocity? The answer to this is (almost) certainly no, these are all undefined as independent properties. Each of these properties must necessarily require at least one other reference external to our singular particle in order to establish a definition, so regarding angular momentum what reference confers a finite value for this when no event transpires to be altered by this property, likewise the particle may be said to possess any charge whatsoever and the system will be unaffected and the number of possible configurations will remain unchanged. Perhaps the most visually accessible example is to discuss the motion of this particle. Where would it go and how fast is it getting there when everywhere that exists is where it is already?

There is one interesting additional observation, this quasi-particle contains all of the mass in the Universe and as there is no reference, the intrinsic spin “may be considered from a certain perspective” to have a value of 0, that is to say the infinite mass potentiality is coupled with all available zero potentialities and one of these is the spin zero potential. Lest there be objection to the bias of a “certain perspective” we should note that “all aspects of existence not specifically forbidden will be found to be true though perhaps partial descriptions of reality” for the early one system. The particle so described here may turn out to be of some interest with respect to certain present day research efforts.

Summarizing the single particle system, it is observed that this Universe is essentially symmetrical to a null state Universe. Neither possesses constituents having a definable charge or angular momentum, nor events by which time might be measured. There is no motion within either system (yet), the null system has no objects that are able to evidence movement as the single particle has “nowhere to go and no time to get there”. The only remaining difference is the mass of the single particle system which is really just a restatement of the energy state of the null system, which is further still no more than a declaration that a subsequent state will be found to have occurred that is not symmetrical in all respects with the initial state. As the two models are indistinguishable, it may then be declared that a null system is identical to and describable as a single constituent particle system and vice versa. This demonstrates paradoxically, that “nothing” as such ever exists, since null systems are intrinsically energetic and unstable systems that may be regarded as containing a single entity possessing the entire mass energy of a Universe.

Questioning What Is,

The next system to be examined is a one plus one particle system model which should be realizing many changes relative to the null/single particle system. Apologies are offered in advance for the occasional (read as frequent) digressions that occur within that examination as there are some necessary inclusions in order to develop the proper conceptual framework.

The first change noted is change itself, in order that this state has any sort of differential definition from the prior state there must be some measure of change and this will then represent the first tick of the clock. The system was in one state (time 0), and then was found to be in a subsequent state (time 1) in which the Universe contains one plus one particles (almost). Note that there would not be a gradual transition from State 0 to State 1, as there is not an intermediate stage that would have a distinct definition. For instance, were we to declare that there was an intermediate stage with 1.5 particles, say

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by mass, then how would this differentiate from the null/single particle system? As discussed previously, the mass necessarily is unchanged in such an instance and further, any and all “changes” that would create a second identity, no matter the measure, are equivalent. In other words, there is no meaning in declaring a finite distance of separation between the particles in the one plus one particle system such as 2.72 microns or .5 meters. As the only unit of distance in this 0 “spatial” dimensional system engaged in decoupling to 1+ dimensions is the separation between the particles, then they are necessarily separated by a distance of 1 or not separated at all, in which case we have “returned” to State 0. One effect of this discrete “instantaneous” transition from an initial state to a subsequent state is that this is essentially defining the first tick of the universal clock as a quantized event. Naturally, given that the first event is a discrete, quantized one it would be expected that all subsequent events and states within the system would also exhibit quantized behaviours, and as these are all necessarily a function of time, there is the suggestion of a broader explanation for many phenomenon, some of which will be addressed as we progress.

Digressing for a moment, what is actually to be said of a system in which we have subsequently regressed and returned to State 0 from State 1? One possible opinion is that the system has gone into a temporal loop of sorts and that State 1 has come full circle and is like State 0. It should be apparent however that this is not the most correct interpretation, for if two states are truly identical then they are completely undifferentiated. All states that are “like” our State 0 are of the same only possible configuration and are in fact synonymous with the singular condition that is the null/single particle system. Therefore a history such as 0,1,0,1,0,1… is identical to simply 0,1 unless witnessed by our hypothetical external observer. Extending this logically, then all Universal histories are as has been described here and share the same common State 0, and in the absence of a super-temporal dimension to create differentiation in a multi-verse framework then any and all alternate Universes arising from the above described decoupling of “possibility” also propagate from this common singular State 0 connection. For those who would wish to propagate a concept to its broader implications this suggests that any state that is an exact duplicate of the data values of a prior historic state will result in a temporal bridge to the prior state. The entropy of the developed one system makes this an overall impossibility at the Universal scale, however it is suggested that some measure of temporal replications may be commonplace at the quantum scale and may be a significant causal principle in various phenomena that exhibit cyclical and/or durable characteristics, for example, the stability of electron orbitals within the atom and the extension of the neutron mean lifetime within the nucleus of atoms. It is offered that these sub-systems would be in a superposition of a fixed set of quantum states, a temporal loop, in terms of the relations between the elements of the subsystem, while exhibiting a cyclical pattern that advances forward in time with respect to other elements of the Universe that are not likewise in a condition of temporal replication with respect to the elements of this same sub-system.

Previously the State 1 system was described as a one plus one particle system, the reason for this was to highlight the development of mathematical relations and representations that occur as time progresses in the early Universe. For our State 0 system there was no relevance to the value 2 since no aspect of that system is described by such a value definitively. To be clear, what is being declared here for State 0 is that the very concept of the number 2 is undefined and effectively does not exist as a value within that context, therefore, when the State 0 system progresses to State 1 it necessarily “invents” (decouples from the initial infinite potential) the number two, as well as the reciprocal value 0.5, due to the pre-existing identity 1 and the relation of 2 to this prior identity. The “primordial” logic here is that there was a state in which there existed 1 of something possessing what may be described as identity.

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Subsequently there was found to be another instance of something and thus there was now an identity and another identity thereby defining the successor function and establishing what it means to say there is two of something. This position may lead to a challenge of the initial proposed zero by infinite state as not having met the same burden of definition as the definition of the number two.

The response to such a challenge is with what might be described as a sort of fundamental theorem of knowledge (though the term may have been in favour previously in an alternate context). In the absence of all that may provide that which may be described, such as is the case with our “null” system, then what may be stated regarding such a system which has any relevance? It is suggested that for such a system it may be described, and only described thus, “It is nothing, it is everything, it is something”. In other words, it has Zero history, Infinite possibility and one unified identity. And thus, Zero, Infinity and one find definitions as representing the full embodiment of first knowledge. It is proposed further that this also represents the ontological limit of a priori knowledge and all further knowledge, including all of mathematics and its axioms, is derivative from these primary declarations that represent the most that may be declared regarding the least that may be.

An Identity,

Returning to the, now acknowledged to be, two particle system, what must necessarily be the case in order that the system may rigorously be described as having two particles? The answer is that each particle must exist in a state of relation to the other while possessing at least a measure of identity separate from the other. In other words, if a particle is found to be in a state in which it is not related to (affected by or affecting) any other particle then it will be degenerate to and synonymous with State 0. The reason for this is that it would then be describable as a single particle system in an eventless, timeless state with no references to define finite rather than Infinite or Zero conditions. As we are considering the nature of State 1 then by definition the two particles present must be in some state of relation one to the other. Thus, a mechanism must exist for establishing relations between entities and this must initiate at State 1 and thereafter remain continuously engaged to every “real” particle within the Universe.

To clarify, what is being declared here is “that which exists only exists beyond the 0 State because it possesses a robust definition that arises from relations with other entities that exist only because they likewise codependently possess defining relations”. Furthermore any entity only has properties, and those properties finite measures, as is established and maintained by those relations. Continuing, if an entity (particle) were to come into existence without establishing or otherwise fail to maintain defining relations it will be or become at least partially undefined (virtual) and lack the full measure of reality from the perspective of observers in developed universal states (not probable for entities having effective duration in developed universal states of sufficient interactive density such as is our present experience). And thus, it is suggested by extension, that existence is not an absolute discrete certainty and differentiated measures of existence across frames of reference may be valid. This measure of existence then is a product of the collective “intensity” of identity defining relations with which the particle being examined is engaged. Continuing, it is reiterated that a consequence of this may be that matter and, to a lesser extent, energy particles that are engaged in a significantly reduced number of defining relations (as may be the case where densities are very low) may be observed to be even less interactive with other entities than their dispersed condition would otherwise suggest and be less “real” or appear as “dark” entities to non-local observers. Yet another way of stating this is that the linked

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chain of collapsed and expanding wave functions connecting the observer to the dark entity is extended in this case. Finally, it is hypothesized that perhaps it is ultimately the case in mature universal states undergoing “heat death” that such a one system may fraction reality and dissociate and certain conservation laws that are currently absolute may not be maintained. Exploration of this latter possibility is probably best left for a more developed subsequent consideration.

Identity as a fundamental universal concept engenders certain paradoxical considerations that warrant mention. Most noteworthy of these is that the establishment of individual identity for particles is a function of the relation between what is differentiated versus what is identical between entities being examined, and not just the differentiation. Expanding on this, consider a Universe in which there was a multitude of entities but the one system did not possess extension in time and space. In such a case, the charge and intrinsic spins, of a charge and spin neutral system, such as ours appears to be, cancel out as they are co-located in time and space. Mass and energy sum up but there is no mechanism to differentiate the contributions of individual entities and thus it should become immediately apparent that this system is degenerate to State 0. Conversely, consider a one system in which entities are distributed in time and space but share no common properties whatsoever. In actuality such a one system as this is also degenerate to State 0 or at the very least one of the primordial states. The reason for this is that all of the entities in this system have failed to engage in sufficient defining relations with other entities and thus have no measure of existence and each individually are synonymous with and thus at State 0. We cannot argue that one indeterminate particle transmits an indeterminate force carrier (or engages in a field phenomenon) that is received by another particle to establish a relation without first confessing the two particles are identical with respect to, in some measure at least, being affected by and affecting the indeterminate force and thus the particles in question are not completely differentiated.

Which Spins,

Thus it should be evident, that for a one system to have space and time and contain distributed matter / energy such as is expressed by galaxies and living things then a strict framework must exist for establishing the differentiated and also the undifferentiated properties of constituent entities. Previously it was observed that the relations or interactions between particles would condense finite definitions for properties of those particles from the inherent Zero by Infinite conditions that would otherwise be the case. Returning to our two particle system, we may be led to inquire as to what types of properties might exist, the nature of such properties and the basis for their resolution from an infinite potentiality. Earlier it was declared that the 0 State, as a single particle system, possessed no definable spin as a property. However, we do know that intrinsic spin subsequently is a fundamental property of real particles and thus was an inherent potentiality in the 0 State so what then may be said of particle spin as it pertains to this initial condition? Returning to our “primordial” logic we would rephrase this question as “what is the most that may be said of the least example of angular momentum or spin”. One way to approach this is to regard the spin state of the single “particle” of State 0 as being an aspect of the unobserved and uncollapsed wave function of that particle and thus in an unknown state. However this then is yet again a Zero by Infinite condition and in the absence of any competing reference such conditions will be regarded as resolving to a value of one as previously explained. Another perspective on this may be found by consideration of a hypothetical model in which the 0 State is viewed as a string of 0,0,0… states by an external observer using an external time measure. Our hypothetical observer would note that the particle may be regarded as having a spin value of Zero and Infinity within its frame of reference and thus one by the same reasoning as above and that the particle may thus be considered to

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have completed one full rotation on an arbitrary axis and thus every axis, albeit by rotating in opposite directions simultaneously as neither would be preferential, in each subsequent 0 state by extension of the same reasoning and then also note that in each subsequent state the particle would appear to be unchanged. Therefore, in an abstract sense, still undefined in the reference frame of the system itself at State 0, the particle may be regarded as having possessed an absolute expectation potential of spin 1 with a condensed (summed) value of 0 from the point of view of subsequent states. Furthermore, it will be noted that spin 1 will be then defined as the value for that property that when subjected to one full “rotation” (360 degrees?) will render the particle indistinguishable from itself prior to the rotation, as would necessarily be the case using reasoning previously explained. Several additional comments, first it will be necessary to return to the term rotation used above and provide additional comments. Secondly, spin is a measure that will become an element of establishing identity, and the initial particle may be regarded as intrinsically possessing a self-canceling spin 1 (it is in a state of existence co-located with non-existence), and spin 1 will not produce a differentiation or “sign swap” on a rotation of 1. However, the initial particle certainly fails to rigorously establish identity due to spin alone due to the lack of a relation to another particle and the resultant condensation of arbitrary spin characteristics into definitives. And finally, if questions remain about the assignation of unit one values to “potential” aspects of spin in State 0, recall that mathematically one is the only finite value that has any sort of definition in State 0 as all other (non-zero, non-infinite) values are fully undefined.

Admittedly, the development in the above paragraph may be regarded by many as a bit ad hoc, however it hopefully serves to reinforce in the reader the idea that conventional viewpoints regarding number and relation break down at the beginning of time and that finite properties of real entities as we understand them to be are progressively decoupled from the undefined potentialities of prior states. Progressing on with at least some sort of conceptual framework established regarding spin (more will follow) we return to the two particle system. Interestingly, all matter particles may be considered as having decayed from the combined initial particle pair and residual field of State 1, in a cascade and not from one component or another. This consideration is due to the observation that as the total mass energy distribution of this state would be considered to be contained in the “unobserved” particle wave functions of its constituents, this event would be indistinguishable from a process in which some or all of the energy of this state, regarded as not being contained within the two initial particles, was the genesis of the cascade. Continuing then, subsequently realized particles will be able to “observe” the original pair, as indeed they must if co-self-realization is to be maintained and expansion of the system is to continue, and in so doing “discover” the spin state of the initial pair.

If the single particle system as represented by State 0 may be regarded as possessing the intrinsic potentiality of spin 1 then what will be the expectation of the particles with regard to spin for the two particle system that is essentially the decay product of the initial entity? It is suggested that of the two initial virtual particles, which decoupled from the singular state, one will be discovered to have assumed one orientation of spin and the other the opposite. As they possess identity only in as much as they have a relation to each other the intrinsic spin identity of each component is ½ in order that the entangled identity state has an identity spin magnitude of 1, and also a sum value of 0, this latter value being a product of conservation of spin. However, other as yet undiscussed particle phenomena would need to be considered and, more importantly, we are looking for deeper explanations and thus will need to answer the question “what is spin and why it is that it should be conserved?” To answer the first part we must recall what it is that may be definitively said with regard to State 0, specifically, that it possesses one unified identity and that this is the only “real” finite property of State 0. Thus it is that when we

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consider the decay of our single particle system to a two particle system what we are otherwise describing is a system in which identity as a property having a proper value of 1 in State 0 is split in State 1 to two entities that have a combined absolute identity value, or in other words spin, of 1. As stated above, this results in the “invention” of the values 2 and 0.5 and we thus have 2 particles with .5 or ½ spin (identity). However, it should be apparent that the correct perspective is to view each of the particles in the initial pair as part of a conjoined subsystem, regardless of the apparent distance of separation, possessing a combined absolute spin (identity) of 1 and that this relationship and its products must be pervasive for these and subsequently all matter particles (individually possessing spin ½). Another way of stating this is that if spin is to be the embodiment of a concept described as identity, which may otherwise be described as discreteness, then it will need to retain discrete unit values. Therefore it is impossible for a separate particle to exist with a spin of ½ or any other fractional value, thus matter particles are never truly independent, a restatement of the prior observed necessity of maintaining a constant state of relation with other particles. As a critique, it will be considered that the assignation of the value ½ to matter particle spin is merely convention and that alternatively spin value 1 might have been assigned, yet it will be arguable in response that the various considerations presented do in fact give support to the ½ value representation. As to the conservation of spin, this is actually defined as the conservation of the Zero, reciprocal of the Infinite, precipitating precondition from which all existence derives, which if the very concept of existence is to have any meaning whatsoever and remain applicable must necessarily be conserved if the system is to proceed forward in time. Finally, it should be noted that at State 1 of the Universe “spin”, or rather the precursor to spin, has decoupled (been formulated) and no later reformulation of this as being a specific property is possible.

One interesting observation is, as previously stated, that the initial particle / anti-particle pair that engaged in subsequent interactions, and thus may be regarded as having decayed into the family of particles known as matter, would have their wave functions necessarily collapsed by observation into only one of two possible paired spin states. As these initial particles are then linked universally in a chain of entanglements with all subsequent matter (particularly since these initial particle realizations still exist as an aspect of reality in the present), this is perhaps then suggestive of an explanation for certain pervasive asymmetries in what later becomes realized as the nuclear weak force. Also it is suggested, that there is an operational pairing of differentiating intrinsic properties of fundamental particles with each aspect of the one fundamental interaction (always there is duality) and for the nuclear weak force aspect it would appear to be intrinsic spin.

In summary, by the first principle of unity, the collocated universal potentiality, is derived the concept of identity. For reasons explained previously the unified identity is unstable and decays into two partial identities, thereby forcing the definition of new values 2 and ½ as representing the measure of partial identity which paradoxically is the actual embodiment of identity. Thereafter particles which decay from these initial entangled entities will exhibit this same nature and possess value ½ in this 0 to 1 dimensional space (more regarding this to follow) which will appear in developed states to be the intrinsic spin. However these values of partial identity arise from two equivalent yet opposite entities as there is also the principle of symmetry to consider. Symmetry arises from the equivalent but opposite relation between the “unrealizable” values Zero and Infinity. Their unity is then described by the concept and value one. Each of these values however embodies elements of and serves to describe the others, therefore if there is a reciprocal of Zero about 1 of Infinity then there should be reciprocals of one about Zero and Infinity that would share an absolute value with 1 but which are not one but rather its opposite, a value that is one but not 1 is -1. And thus the concept of opposite or negative values is a

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necessary consequence of the initial state 0 (as we contemplate that the number “line” may be a limiting perspective). As our identity is now split (or is it, more to follow) between two equivalent but opposite entities then necessarily the values of identity are of symmetrical, or opposite, sign and thus ½ and -½, though each particle lays equal claim to being either the ½ or the -½. And finally these particles will have a dual relation and their behaviour explained by the sum of their values to Zero which “partially” separates and differentiates them. And also the absolute sum of their possible sub-state values to 1 which unifies and binds them to a first principle.

And Charges Forward,

As is abundantly evident at this point, this paper has taken as a fundamental precept a notion of duality, which is seen as the nature by which all things find their definition in other things which reciprocally are defined by them, which is itself naturally a restatement of the first principle relation between Zero and the Infinite. So we are led to ask with respect to intrinsic spin or angular momentum, what is it exactly that engages in this? It is suggested that this is particle charge, which is therefore another component of the unifying aspect of identity, our decoupling first principle in this case. Before going further several observations are in order, first is that only spin ½ particles exhibit charge, the apparent W particle exception is suggested as being no exception at all as will be explained later. And though seemingly fractioned by thirds instead of halves, as is the case for spin, the fractioned states are likewise bound into entangled sub-states. It will be noted also, with a paraphrase, that “nature abhors a fractional charge”, that is to say, particles of fractional charge are not found to exhibit the property of temporal differentiation that we view as spatial separation, beyond a certain quantum realm distance. Finally it is observed that at this early state of the one system it is probably not necessary to consider colour charge and the associated fundamental interaction and residual effect as a separate phenomenon due to the fractional charge exclusivity of this interaction. Rather it should be viewed as an aspect or particular behaviour of the one fundamental interaction when particle identity is insufficiently established, or rather, further subdivided.

Returning to the State 1 particle pair the question will naturally arise as to what charge these possess, or rather will be seen to have possessed when “observed” by subsequent interactions. It is suggested that the answer to this is that the answer has already been provided. Charge is spin is identity and for State 1 these are bound together as a singular property. We have established previously the relation of identity to Zero by the conservation of spin and the sum of identity to Zero. And have also established the relation to the concept of unity by the absolute sum of the possible particle sub-states or degrees of freedom to 1. However, the counter relation to Zero, the relation to the Infinite, is not in balance and thus the system remains in a condition driven by an unrealized Infinite potential. This imbalance is again, simply a restatement of the Infinite potential, or heat, embodied in the initial condition, a force that ultimately leads to the creation of multi-dimensional time space and the expansion of the Universe. And will be an imperative which also results in the decay of the initial conceptual identity into a near Infinite number of “distinct”, “separate” particle identities. It is observed that this latter conclusion may be correct but incomplete. Continuing, if it is the case that a property exists which has been described previously as identity, and also that this property should then be fractioned as a result of the creation of additional entities, then would not the multitude of particles further fraction that identity? It is suggested that the answer to this question, in a system which embodies the characteristic of duality, will be a paradox. It will be yes such that the property relations of each entity or proportionality to the absolute sum of all identifying properties will diminish as the population of entities increases. Conversely, with

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respect to the quanta or discrete value of identity that each entity possesses the answer will be no. As previously observed, once condensed from a Zero by Infinite condition a property requires no later reformulation with regard to being a specific property. However, remaining Infinite conditions may continue to apply a decoupling imperative and result in the further resolution of a property into sub-properties. Where this occurs there should remain some aspect or sub-property that retains the essential prior definition and thus continues to be a solution to the prior precipitating Infinite conditions, and another aspect or sub-property that acquires a new essential definition as a solution to the residual Infinities.

It is offered that the initial condition will inherently impart an Infinite property (charge) potential on entities as they may be declared to exist. That is to say, if the Infinite expression is to be realized there must be a property in each entity that approaches a maximum non-zero value and possesses the capacity to induce change in the system, recalling that change is the measure of time which is itself an expression of, and necessary characteristic of, an Infinite potential. In a developed Universal system, this Infinite expression unopposed would produce a runaway effect sufficient to overwhelm all other phenomena. As such expressions are in each case a product of the inherent time like nature of an Infinite condition this runaway effect results in the instantaneous realization of all temporal states and the system is thus at State Infinity, at the end of all history. Arguably, State Infinity is symmetric with respect to state 0 and indistinguishable, and there will be more regarding this further on. Continuing, if there is to be any sort of rational existence, all Infinite expressions must be balanced with zeroing potentials so we are left to inquire as to a possible expression of this zeroing effect. It should be apparent that this Zero expression would be well realized by an invariable Zero condition of the property in question, however the Infinite expression would then not be realized. The Universal solution to this, yet again, will be a paradox that is a superposition of Zero and Infinity, the result being coincident Infinite positive and negative potentials that cancel each other to Zero, in other words intrinsic charge.

A response to this conclusion may be that these potentials are negated by their relation so then of what significance is this. Hopefully the reader has engaged sufficiently such that a series of counter responses is immediately evident. For instance, keeping in mind that Universal reality is the actualization of all that has not been specifically forbidden, it may be observed that neither the negative or positive potential would lay absolute claim to being either negative or positive as the system evolves implying that positive may become negative and vice versa. This then will be the precipitating principle behind cyclical or oscillating functions that are at once of a nature and then are subsequently of an equivalent and opposite nature if for no other reason than this will not be forbidden due to a lack of absolute references. If we grant that there is some phenomenon we may describe as charge which exhibits charge reversal, still are we not left with a self-canceling phenomenon? There are additional considerations, the charge potentials described in each case are Infinite, so we are led to ask what would remain expressed as charge potential should the opposition of the two canceling Infinite charges be other than perfectly realized. As this is a process that necessarily occurs at the decoupling of State 0 the only finite definition available is 1 and this would apply no matter the hypothesized measure of phase misalignment. This may invite an additional response, “by what logic is it necessary that this phase decoupling occur”. To answer this it is necessary that we yet again revisit the Zero by Infinite relation and consider how this would apply to the neutral phase realization of the opposing potentials. They may be perfectly opposed as an expression of a Zero defined condition and the charges would be absolutely neutralized. Or they may be perfectly misaligned as an expression of a condition defined as an Infinity, and thus the inherent Infinite charges would be fully realized, would utterly overpower the system at all

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points in Universal history and the system would be degenerate and “eternally” bound to State 0 or State Infinity. Therefore in keeping with the usual principle of a superposition of a Zero by Infinite relation the result is a finite value and in the absence of influences of other resolved finite definitions the reference initial finite value for the residual potential will be one. In a further development it is therefore proposed that what is defined here is the fundamental concept of charge, and the relation to the phase decoupling process that realizes it is declared to be the previously described intrinsic spin. However, the full realization of the relation between, and the development of, these properties will await the evolution of the one system to the State 2 and later realizations.

Summarizing the Two Particle or State 1 system, it is observed that such a system possesses a fundamental conceptual property which has been described as identity, which is no more than a restatement of the unity aspect of the initial condition. Likewise, all particles that come into existence are bound to this initial condition through the propagation of identifying sub-properties which are necessarily divided into sub-properties that are either unifying or differentiating in nature. It is suggested that the first order and second order unifying properties are thus intrinsic spin and charge. It is implied that the paired differentiating properties are time and space, the latter of which await the State 2 system for a proper definition. Extending the logic, it is therefore implied that particle spin is synonymous with the ticking of the system clock and is the basic Universal meter of time. It is noted that although the State 1 system is described as possessing two equivalent but opposite entities, these particles are actually virtual, that is to say, they have no observer other than their entangled partner particle. A consequence of this is that distribution of energy within the system may be regarded as discrete yet retains marked uncertainties. In other words, the system is symmetrical and will “appear” undifferentiated with respect to varying energy distribution between the two particles and the energy field which is the residual of the initial condition. Elaborating, were one particle regarded as possessing the vast preponderance or all of the system energy over the other, no third particle reference is available to measure and provide robust definition for the energy and momentum differences between the particle pair.

There is one particularly noteworthy observation before proceeding. By reasoning previously explained, it is noted that this process of decoupling of the initial condition of State 0 to the particle pair creation of State 1, as the initial imperative of the one system, will ever after be a defining characteristic of the Universe. Therefore it is to be expected that the earliest phenomena to be expressed will be found to be among the most fundamental and persistent aspects of nature and that we should see continued evidence of these phenomena in the evolved Universe. It will also be proposed in this paper that Universal present time be regarded as simply the current data state image of the totality of a continuum of interactions (relations) between its myriad constituent entities. Therefore, any point in physical space examined for progressively smaller intervals will be observed to be engaged in fewer and perhaps less rigorous temporal frame defining relations. At some infinitesimal least interval therefore, the “present time” as a concept would be expected to break down and the sub-system under examination should revert to a primordial State 0 and / or State 1 condition. Thus it would appear that Zero point fluctuations and every particle pair creation event are in actuality a window back through time to the initial creation or Big Bang event. To be clear, this is not a declaration that such spontaneous particle creation events are like the initial event, rather it is a declaration that these events are the same singular creation event that is the beginning of time. It is posited that were these event instances to occur outside the context of the present or another Universal framework that will redefine these creation events as

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having limited energy then all that has been described as being the behaviour of the one system would also be an applicable description for these synonymous events.

While Multiplying,

The final system to be examined is a many particle system model which should be realizing many changes relative to the one plus particle system. Apologies are offered in advance for the occasional (read as very frequent) digressions that occur within that examination as there are some necessary inclusions in order to develop the proper conceptual framework. It will immediately be apparent that the preceding statements, while being similar to previous statements, have some measure of differentiation and therefore we are in fact progressing forward in “time”.

Perhaps the best starting point for an examination of the many particle, or State 2 or 2+ system, is to review that which has and more specifically that which has not been rigorously defined under the prior State 1 system and then examine the means by which the undefined will be resolved or evolve in State 2. Previously it was observed that the State 1 system consisted of two particles that may be regarded, with the residual field, as collectively possessing the mass energy of an entire Universe, however the actual mass energy distribution within the system is not fully defined due to the lack of a reference observer (third particle) entity from which measurements may be taken. Therefore evolutionary pressure remains as the system is still dominated by Infinite conditions that remain unresolved from the initial condition. This evolutionary pressure is equivalent to the primordial heat of the Universe that classically would lead to large relative velocities between constituent entities. However the State 1 system does not behave classically and the two constituent entities have velocities relative to each other within that context that are a Zero by Infinite relation as they can be regarded as having taken an arbitrarily short time to go an arbitrarily long distance and vice versa. By reasoning previously employed their relative velocity is therefore 1. As the first velocity manifested in the one system this would necessarily become the benchmark reference for the system ever after and should be evident as a fundamental value in the developed Universe. The only apparent candidate is of course “c”, the natural speed of later massless particles, accepting the caveat that it increasingly appears as though there may not actually be any particles possessing Zero rest mass in developed universal states (rest being a term that should be used with restraint generally).

Relatively Speaking.

As noted previously, our State 1 system consisted of two spin ½ particle identities, and also a spin 1 (energy) phenomenon or aspect that has yet to be discussed in detail. From the perspective of later frames of reference these particles may be regarded as having possessed an Infinite combined mass at a speed of separation of “c”. It would necessarily be “c” as any lesser speed, in other words 0, would result in the collapse of the system to State 0. Dimensionality as it is understood in the developed one system is essentially undefined at State 1, however some meaningful statements may still be made regarding spatial relations. It is observed that if State 1 were instead viewed as a sequence of repeating State 1 conditions, such as may be observed by our hypothetical external observer, then each of the two particles may be regarded as possessing a potentiality to send and receive information to only one other destination, their anti-particle. It would be noted by our external observer that these two entities are necessarily identity differentiated which translates to them being in different temporal and/or spatial locations. It would be further noted that all directions from each entity in which information may

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propagate are the same one direction that leads inevitably to the “other” entity as there is simply no “anywhere” that is not where one of the two entities reside. In other words space is collapsed upon itself and does not express a three dimensional structure as we are accustomed to. Alternatively stretching this concept to its limits, from this persisting external perspective, it might be noted that if the degenerate dimensionality under consideration were regarded as a collapsed three dimensional space then in the frame of reference of particle “A” it may appear to be completely enclosed by particle “B” in State 1, however particle “B” also “observes” itself to have been surrounded by particle “A”. From a perhaps more relevant perspective, it would be noted that each particle would be without a rigorous measure of its identity being unique from its partner and they may be regarded as swapping identities and associated measures of identity, and therefore when a particle observes its partner it is in some sense observing itself in a continuum that exhibits a maximal spatial curvature. It is suggested that this may offer an insight into an essential element of the nature of fundamental forces, which is to say, an operational imperative by which entities possessing partial identities in a particular space time location are always drawn toward unity with the balance of their partial identity at another space time location. It also becomes the basis for the interchangeability of particles in the quantum realm which has been observed in prior works. At this point an argument against the relevance of much of the preceding could be made, that the external observer is a convenience for arguments sake and not a component of Universal reality. A response to this is to note that the State 1 system, from within the frame of reference of the one system, while not a continuum of similar states, is at the beginning of an evolutionary sequence of related states and the external observer viewpoint conveniently aids in the understanding of conditions that may have existed for the first of these states which then becomes fully realized in later states. It is to be noted again that generally speaking this is the type of function for which our external observer is called upon repeatedly within this commentary.

Some of the principles of relativity with regard to extreme conditions should be readily apparent at this point. That is to say, matter particles traveling at speed c will be observed to approach Infinite mass, particles approaching Infinite mass then will be observed to “cause” an Infinite curvature of space time resulting in the Universe being in a collapsed physical state with essentially Infinite time dilation. Lest there remain question regarding the extent to which the one system is time dilated, it must be remembered that it exists at this point in a Zero by Infinite condition. The spatially collapsed condition is a reflection of the Zero component and the time dilated condition may therefore be observed to represent the Infinite component. Remembering that all perspectives are true unless specifically forbidden, it will be noted from the Infinite perspective that the particle components are at the first moment in time and yet have achieved an arbitrarily large distance of separation, that is to say they are on opposite “ends” of the Universe and arrived there in an arbitrarily short time interval.

It has been generally accepted in prior commentary that the Universe began as a system that was extremely small and then expanded in size over time, however, this is not necessarily the most accurate description of Universal extent past to present. It is at least as accurate to describe the one system as having always been the size of a complete Universe. It would take a hypothetical external observer to settle the issue with certainty, relative to an external unit of measure of course, and it would by no means be certain that such an observer would not report the size of our Universe as having remained unchanged or actually having decreased as the system evolved. This observer would however report that within the frame of reference of our system light pulses are taking much longer to transit distances in our present than externally equivalent distances in our past. A more correct interpretation of phenomena therefore would be that relations between constituents of the Universe are undergoing

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change such that the apparent size of individual entities is decreasing and the distances between them relative to the overall size and scale of the entire system is thus increasing, giving the “appearance” of universal expansion with respect to an internal observer, no more than this is certain. If the argument were to require additional reinforcement it is again noted, that for every spatial point in the present theoretically expansive Universe examined at sufficiently fine an interval we may observe the present time to be co-located in space with the one system at State 0 and 1 (commonly referred to as the Big Bang). One conclusion that must be drawn is that speed “c”, or the speed of light, is almost certainly not an absolute constant throughout the history of the Universe in all contexts, in fact it becomes difficult to formulate a robust argument for an absolute reference speed c when it is so evidently codependent on the developing existence of entities that are able to express spatial translations.

It will also be apparent that the maximal relativistic condition of the State 1 system must decay for there to be a State 2/2+, that is to say, for things to progress matter particles must never again be observed to be traveling at speed c (though a caveat must apply) or have Infinite mass or be seemingly infinitely time dilated. Furthermore these therefore decreased properties will have to be defined and some means will need to come into existence for variable gradation of these properties. This means will be the finite numbers and the rapidly evolving mathematical constructs and relations that define them.

There are a number of consequences that arise from a relativistic viewpoint and these are very well documented elsewhere. The additional commentary to be offered here is that, on reflection, many of these are not conceptually or even mathematically complex and are logically evident from a single fact, that being that light propagates at a common “fixed” maximum (in an ideal vacuum) speed relative to different observers. Thus a pen and a piece of paper are all that is needed to deduce and explain, for example, the non-relativity of simultaneity, time-dilation, relative determination of electric versus magnetic field effects and the relativity of observed rotation and orientation. So a question is proffered, “Why is it the case that a lone individual of singular insight was required in order for an essentially self evident set of consequences developed of a simple idea to become generally understood?” Perhaps this is indicative that, when considering the collective human intellectual mechanism wherein we are each of us possessed of a belief that we function essentially as individual independent free thinking beings, it is arguably the case instead that we function generally as parallel processing sub-systems more or less conforming to customary avenues of thought as accommodates the common means of interaction, thus language, in a distributed human network. Not so surprising then to find that the quantum shifts in scientific understanding and development have generally been the products of truly independent and rebellious thinkers of which there have been relatively few. Thus it is that much of the intellectual advancement of our kind has been other than a democratic enterprise, as it is often the case that the viewpoint of the majority, and on occasion all of us, is exceeded by the awareness of a lone maverick thinker, one better attuned, or rather less resistant, to a Universe constructed and apparently committed to the self evident revelation of its one nature.

One additional point of observation before proceeding, there has been a somewhat protracted discussion in other commentary regarding the incompatibility of relativistic and quantum theory at the initial moments in time. Apparently this incompatibility is made evident by solutions that seemingly produce Infinite results when the two theories are then converged. The position that is offered here is that equations producing Infinite results are exactly what would be predicted when attempting to reconcile the two theories in the early Universe, and does not at all indicate the theories are irreconciled. It has been a certain proposition in this paper that all phenomena and the equations that describe them will

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produce Infinite (or Zero) results when examined back to the very first moments in time. Therefore it is proposed that relativistic and quantum theory are already unified by a present understanding and the supposed incompatibility is in actuality illusory.

The Point Being

Much has been proposed above regarding a particle description of existence without an explanation of the counter principle and why it is necessary that there be a counter principle. To address the latter inquiry it is important to reestablish the necessity for change in order that there be a defined existence, rather, anything that is describable as existence. No particle, complex composite object or physical manifestation will exist that is not in a state of constant change. Using an electron for example, absence of change would imply that the particle is not in a state of relation with other entities for if it were then those entities must necessarily interact by affecting change upon the particle in question, that is to say, it was in a particular state described by certain parameters and then an effect was experienced from another entity resulting in a changed set of descriptors for it. Absence of change within a system or partial scenario may be viewed as a sequence of moments that have precisely the same values for all degrees of freedom, are thus undifferentiated, and are one and the same. Such undefined states are then time collapsed conditions in which advanced time frames (experienced or elapsed time) will not propagate, have no defined parameters and are synonymous with and revert to the primordial conditions (State 0, 1, 2, …), which function to establish the very time defining relations that were absent.

A consequence of the aforementioned is that a classical point particle description for the smallest constituents of the Universe could never be a complete and accurate description of what things actually are. One reason for this is that point particles are by definition of Zero size with no extension in three dimensional space. Therefore were an experiment conducted in which two particles were directed toward one another in order to realize an interaction they would always manage to avoid interaction by passing at some infinitesimal distance of separation, for example 1e-33 meters, which is nevertheless not Zero and therefore does not result in physical contact between them. An argument may be put forth that below a certain minimum length differences in position are indistinguishable, however this is in a sense the same as stating that there is a minimum size that is the size at least of fundamental particles. Regardless, at the least length scale it would seem improbable that interactions would be experienced with the frequency observed, though the definitive solution of this requires a mathematical approach that is beyond the scope of this work.

Another argument against the point particle model that holds even for the adjusted notion of a minimum possible size is the previously made arguments regarding the maintenance of relations and necessity for measurable change within all frames of reference if those frames of reference are to remain in temporally evolved states and not degenerate to primordial states. It is difficult to reconcile the need to maintain a constant state of relation, even if given as a condition a minimum possible temporal unit of measure, with a point particle conception for the most basic of entities. Admittedly this latter argument is subject to a response declaring that the “Zero point” field and virtual particles may provide the defining relations needed however this would then be potentially challenged by the prior argument that these quantum fluctuations are a relation to the primordial states and do not define or maintain evolved states. It is proposed therefore that substantive and continual relations to “real” entities is necessary for the continuance and development of evolved frames of reference, which is to say relations with entities

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that are actively engaged within the entangled Universal network, the progressive collective data state of which defines the particular “age” of the one system.

That a point of 0 size without a wave function could not be an accurate description of a fundamental entity such as an electron or photon in the context of developed later frames of reference would appear to be self-evident regardless of several observed phenomena that are best explained by this expectation. However for the sake of argument let us proceed with the development of just such a particle concept. As previously mentioned the notion of Zero size for a particle will need to be adjusted to the smallest possible and definable size, particularly as Zero size has applicability to the State 0 condition and is a problematic value to assign thereafter. Therefore we have at the simplest a “stationary” particle of minimum size. However the term stationary will also have to be regarded approximately, as absolute lack of motion is a condition that likewise only exists as a partial description for State 0, for in developed systems every single constituent entity will be found to exist in a state of relative motion with respect to at least one other entity (actually at small enough intervals, all entities). Then if we may now describe our prototypical “stationary” entity as actually a minimally sized particle exhibiting minimal motion, what may be declared regarding this minimal motion? One aspect of this would be that any motion contemplated must necessarily be with respect to some reference entity, the issue here being that there is no absolute preferential entity for this role. It may be offered that we are referencing the position of an electron to a neighboring one yet it must then be acknowledged that the reference itself is in motion and subject to a separate history that may involve its departure at some point from a proximate frame of reference. Likewise the reference object is reciprocally in a position that is in part being defined by the target entity itself and in part by other entities.

The point here is that all motion is relative, as is commonly understood, meaning there is no absolute motion and thus no regular transition from one position to the next for fundamental entities at the quantum level due to fluctuations in all aspects of any frames of reference selected as a basis for observation. The minimal motions of quantum particles should not be regarded as proceeding smoothly from one position to another with respect to a fixed reference and are instead necessarily defined by a host of relations each of which has a continually variable contribution to the overall measure. This implies that the motion of our “stationary” entity, if we are to regard it as effectively stationary, will have to be distributed non-linearly in some fashion about an approximate center or focus. It would also follow logically that on each occasion that the entity travels away from the focus it must at some point and in some sense reverse its direction and travel towards the focus in some frame, otherwise the entity would not be at “rest” in any frame of reference. This suggests a reciprocating or cyclical component to the statistically distributed “motion”. Previously it was observed that a Zero size point particle model was not consistent with advanced Universal time frames suggesting there may be a minimum size for fundamental entities. This may be conceptualized as the decoupling and projection of a dimensionally neutral entity into one or more extended dimensions.

Arguments have been put forth strongly against the Zero size point particle description for fundamental entities yet it will now be proposed that all fundamental particles are in fact Zero size point particles. The reason for this is that all fundamental entities are eternally gravitationally bound to, and projections of, the State 0 identity from which all existence arises and for which Zero size is an applicable description. All entities likewise have their 0 State identity temporally and dimensionally extended and tied to the condition that is the State 1 identity that imparts spin within a tightly compacted closed Universal frame of reference, in effect a temporal loop or string. Matter particles additionally have their

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State 1 identities further defined as to charge differentiation in their State 2 and later realizations which also establish the developed, though gravitationally compacted, dimensionality of space time, and which also sufficiently define the nature of relations between entities to allow the development of the later Universe into a distributed system of entity projections. To be clear, it is being declared that all electrons for example are one and the same thing, and likewise all quarks, and all unit spin entities, in fact all particles are proposed to be but one, instanced and projected as a multitude by the Infinite potential of the initial condition, differentiated by the closed loop geometries of the State 1,2,3 identities as to type, and differentiated as to location in time and space and thus made real only by entangled relation into a chain of universal causally connected data states that is the elapsed history of the one system.

The actualization of an ideal point particle is in effect a cyclical, statistically distributed multi-dimensional complex that involves a progressive derivation from decoupling first principles. Once again, the very events that define particle identities and establish the relations that are the phenomenon that is Universal elapsed time are also persistent and omnipresent connections back to the very first moments in time when the Universe was governed by a collection of limited and mathematically simple relations, all of which ultimately trace back to the singular identity of the initial state. It is further proposed therefore, that all entities and events are linked to one common set of primordial references which is the basis and explanation for the universality and applicability of one set of natural laws that spans across the far reaches of the cosmos and to the ends of time. Were this primordial connection absent, given the great turbulence of the quantum realm which is largely the realization of developing local influences, it would not be logical to expect the physical laws to remain so constant everywhere. And the Universe would have long since degenerated into an incomprehensible fractured system of separate domains having no common governance.

That Energy

It was previously indicated that the initial condition may be described as possessing Zero “expressed” energy (there is hesitation to use the term kinetic energy for lack of a rigorous defining framework) and also Infinite potential energy. The Zero energy representation is simply then the observation that no defined energetic events have yet transpired. And as there are no events to cause other events that might lead to change, based on this condition alone it is incapable of development into an evolved system. A Universe as we understand it to be, it would seem, is impossible.

The Infinite potential energy is a bit more interesting to consider. It is suggested that this is accomplished by a single identity possessing Infinite energy, or perhaps an Infinite number of identities possessing other than Zero, which is to say, still Infinite energy. It should be apparent that an Infinite number of undifferentiated entities is indistinguishable from and synonymous with a single entity. An argument regarding differing “measures” of Infinity will likewise not apply to the initial condition, in a State 0 system these are indistinguishable due to the absence of all but a single comparative reference, the primordial Zero condition. Proceeding, regardless of the measure of Infinity selected the result must necessarily be the realization of all possible energy expressions, thus all events not specifically forbidden will occur simultaneously. As there are no natural laws or criteria that may establish limits this translates into “all events that are conceivable, or perhaps inconceivable, will occur at once”. Thus the creation of a Universe with an instantaneous history is, apparently, inevitable.

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What cannot be overemphasized is the indefatigable raw power essential of either of these two initial conditions. At risk of being trite, what follows is in a sense the answer to the age old question “What happens when an unstoppable force meets an immovable object?” The question is brought up as it is a reminder that our viewpoints are often prejudiced by our limited experience of the Universe, and we may not offer an otherwise obvious reply such as “the unstoppable force is unimpeded and the immovable object remains at rest and they pass one through the other”. It is in the nature of real things that such seemingly impossible to resolve paradoxes always find resolution and this is true also for a Universal possibility that will both never exist and that must have always existed. It will no doubt be noted by some that this last statement is a contradiction of the classical Law of Non-Contradiction, as well as the Law of the Excluded Middle, both of which have been challenged elsewhere. There is no desire here for unnecessary controversy for the sake of nothing other than, rather the engaged purpose is to follow a line of reasoning wherever that may lead. And if certain prior beliefs are somewhat adjusted as a consequence then the intent is to suspend any and all pre-conceptions as may be necessary for a logical development. Regardless, the laws named above, and the Law of Identity, are not at this point being declared as untrue in all circumstance, they are self-evidently true in some measure for common experience. That these do not hold under certain extraordinary conditions at the beginning of time is simply the acknowledgement that these conditions are, just as described, extraordinary.

It is generally regarded that energy in developed systems is the measure or quantity of capacity for change in a system or sub-system, as such it is not so much a thing in itself as it is a quantifiable representation of the relations between elements of systems such that some or all of those same relations will tend toward differing quantities over time. None of this is new, the only additional consideration to be offered would be a perspective on the interdependency of the various measures of existence as a response to declarations elsewhere regarding the primacy of any one of these versus the others. The only absolutely necessary requirement for evolved Universal realities is change itself, thus the most fundamental quantities are simply those that are required in order that there is definable change within a system. Of Time, Space, Matter and Energy it is then necessarily the case that any system exhibit all of these quantities or it will exhibit none of them. Otherwise how is change to be realized if all events are simultaneous or co-located or there are no entities to act upon or transmitted forces between them? Extending this it should be apparent that intrinsic spin and charge are necessary pre-requisites for differentiating matter from force carrier particle and matter entities from themselves just as wave phenomena are necessary that fundamental forces be proportionable and propagate between entities. It would be pointless to say that one of these various aspects of existence is “real” and the others illusory, they are each and all interdependent co-defining elements of an evolved Universal mechanism without which the system would be ever limited to a primordial condition.

Travels In Waves

In the preceding developments for the concepts of a point particle and charge, complimentary arguments were offered regarding the necessary decoupling of wave like phenomena, no apologies are offered for the repetitiveness, the reader was forewarned. The point was to establish that certain evolutionary progressions are an inevitable consequence of initial conditions and therefore different lines of reasoning tend to reach the same conclusions. Continuing, it is proposed that, aside from the inevitable decoupling of wave behaviour and wave functions as a necessary consequence of the initial condition, they represent a Universal solution to an ontological mandate (for which it is hoped sufficient argument has been made) that in order to demonstrate existence “real” entities must evidence change in some measure.

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As an example of this we might consider the nature of the most notable of wave phenomena, light and the electromagnetic interaction. It is of course commonly understood that electromagnetic radiation propagates as a dual transverse wave phenomenon consisting of an electric and a magnetic component. This is the nature of light and all E-M phenomena in free space as effects near an interaction are more complex and involve multiple less correlated effects. Explanations based on the approaches developed in this this paper would potentially take the position that any of these local effects would be an expected consequence of the greater dominance of primordial state conditions in expressed phenomena examined at reduced measures of time and space. However as phenomena that require a more systematic mathematical approach for explanations, these local effects are outside the scope of this effort.

Setting aside for the time being 19th century observations that a changing electric field will produce a changing magnetic field and vice versa, why should it be conceptually necessary that light and other forms of radiation propagate as combined electric and magnetic effects and not just one or the other? Is it not arguable that some mechanism is conceivable for the propagation of information from point to point with a phenomenon that does not possess this dual nature? It is suggested that the reason for this is as has already been proposed for other aspects of existence. Though all entities theoretically derive some element of existence from their State 0 relation to themselves, the self-defining nature of the first relation is one bound to necessarily undefined parameters that would not allow for variable finite frequencies or energies. It is therefore necessary for the propagation of a non-infinite electric field effect through space that it have a continuous relation to a defining paired relation, and this is the orthogonally related magnetic field effect which describes the change in the electric field over time. And naturally expressing a dual nature, the preceding applies reciprocally in the case of propagation of any non-infinite magnetic wave. It should also be apparent for developed systems that the two propagating field potentials necessarily will take the form of a wave continuously expressing a perfectly smooth transition from a Zero potentiality in the net Zero charge of the propagating E-M wave or photon to the co-equally necessary unified defined value in the peak amplitude of the waveform while exhibiting an Infinite potential in the unbound open waveform that will propagate as long and as far as is necessary to encounter a terminating interaction. Thus it is that in order to exist as finite potentials beyond the range of the relations to the source phenomena that initiate them, electromagnetic waves exhibit the characteristics as would necessarily be expected in order to maintain and establish a semi-independent existence.

E-M propagation through space as a phenomenon that does not exhibit sinusoidal wave characteristics is not being completely discounted. In fact, adhering to the first principle “that which is not forbidden in nature is necessarily an aspect of nature”, we may declare that such phenomena are necessarily present as a potentiality. However we should observe that a non-varying field effect is synonymous with a wave function having any amplitude with an Infinite wavelength and Zero frequency and thus Zero energy, therefore a Zero probability of interacting with any particle. As these Zero frequency waves are completely non-interacting they may be disregarded for real systems. An additional qualification is in order regarding E-M waves, specifically the sinusoidal continuously variable geometry of the familiar wave shape known to all. It is not consistent with other commentary in this paper to regard waveforms in the State 0 and 1 systems as being sinusoidal. Particularly in the State 0 condition there are no graduated measures of existence, conceptually therefore, variable measures of existence progress from is or is not; to positive existence, neutral existence, negative existence; to discrete measures of positive and negative existence; to continuously infinitesimally incremented variable measures as the Universe develops. Thus the earliest wave expressions are more or less to be likened to square waves though this

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statement may be a bit conceptually deficient as a visualization tool. The point is that there can be no realization of the trigonometrically defined sine wave in the 0 dimensional space of the initial State 0, in which trigonometric relations as a developed conceptual framework necessarily requiring two “real” dimensions, are themselves undefined and effectively non-existent.

Having established not “what is the nature of E-M waves”, this has been exhaustively documented elsewhere, but hopefully rather why they are, we are next led to ask “what exactly is the nature of these fields which are being acted upon?” Recalling the preceding development of the concept of charge an additional declaration regarding the realization of this property is as follows, “charge exists as a phenomenon because it acquires a robust definition before the Universe develops any condition that would have the capacity to forbid the actualization of charge.” Thus it was a potential unexpressed in the State 0 condition. In keeping with previous logic, it would be equivalent to say then that all of the measure and effect of elementary charge which so dominates our experience in the developed one system at present, existed as an unrealized potential in the Universe at State 0, however, their co-location in time and space resulted in a net Zero summation. A consequence of this is that all points in the developed universal system (still bound to State 0) may be considered to possess an Infinite charge potential which will become progressively more evident as we probe the system at ever more minute scales within the quantum realm. They are also bound to the other primordial states that act to give finite measure and variability to such Infinite potentials. This is best understood by contemplating a phenomenon wherein all possible wave functions for fundamental interactions exist simultaneously with their, more or less, neutralizing inverse wave functions at every point in space time. This will be an underlying principle for field phenomena in this commentary.

Restating, given that the entirety of space time should be viewed as fields infinitely and minutely populated with all possible wave functions at every allowed frequency for any and all fundamental interactions (all “particles” actually), as well as their equivalent and opposite neutralizing wave functions, then what would be the expectation regarding the nature of interaction with an entity that is both affected by and affects aspects of these fundamental interactions? It must follow that for the declaration that these entities have affects on, for instance, the electric and magnetic fields, then the net Zero neutralized E-M field potential must experience change and this it cannot do and remain at a net Zero potential. This creates a paradox, the one system must maintain a Zero charge potential in order that charge be a conserved quantity which it has been argued previously is necessarily the case. And yet it must not exhibit a Zero potential if charge is to have an expression through modifying relations that define and express charge as even being a real phenomenon at all. The solution again is obvious, both must occur, which is to say, the overall charge neutral condition of higher sub-systems or the system as a whole is maintained while local imbalances may result in the expression of charge as an affecting local potential.

With respect to the frame dependant electrostatic and magnetostatic phenomena, these are being viewed as an effect in which an entity possessing elementary charge such as an electron, in order to satisfy the zeroing potential of the initial condition, is drawn towards unity with opposite charges and away from unity with like charges. This has the effect of decoupling proportionately to the electron or other entity charge the in phase relationship of the otherwise equivalent and opposite E-M wave functions that always exist as a potential at all points in space, which will now evidence a charge potential which will then likewise progressively create an extended phenomenon by exercising the same basic principle, though with diminishing effect, on adjacent space extending in all dimensions. It should be noted that

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the effect described must diminish with distance necessarily and the mathematical relations describing this are well known. The reason this must be the case is that if such effects did not diminish with distance then all particles would create fields that extend through all of space at full strength regardless of distance, as the system as a whole is charge neutral then this zeroing potential would be fully realized at every point in space, there could be no local imbalances, and charge would ever after remain unrealized as an aspect of reality.

Previously E-M waves were described as propagating “open” wave phenomena and so perhaps an explanation is in order. Open in this case means that that the wave propagation is of a linear form that travels in a “straight line” through space directly away from a source (towards a destination?), accepting that the space through which it travels may be, and in fact always is, curved. This is hardly a new concept, what follows that may be of some interest is a particular viewpoint regarding the relation of open to closed waves. What is being declared is that all entities may exist either as an open or closed propagating wave and that the open form is the wave representation as has been described for light and other E-M phenomena, and which also applies to entities not typically thought of as waves such as leptons and quarks. And it is further declared that the closed waveform is actually a mode of the same wave phenomena in a closed loop geometry (string) which is what we typically regard as the particle form of an entity. It should be noted at once that in a sense these are one and the same thing. That is to say, the closed loop wave is in actuality an open linear wave function in a tightly wound space time geometry, in other words the type of radically curved gravitationally collapsed dimensionality that exists in the primordial states. Continuing, it is proposed then that the particle expression of an entity, regardless of spin identity, is in effect a consequence of the interaction of elements of the temporally evolved extended wave expression of an entity with the extended expression of another entity within a frame of reference, resulting in the localization of the identities within the evolved space time frame. It is suggested, this instantaneous localization, effectively a partial zeroing (time negating) effect, necessarily results in a collapse of elements of the temporally evolved definition creating a temporal bridge to the defining primordial states, and while observed to be particles these entities will then necessarily exhibit the fundamental quantized properties defined in those states. Furthermore it is noted, as has been observed elsewhere in a different context, that increasing mass energy of entities will increase the probability of and contribution from the primordial condition expression (particle like nature) of the entity and decreasing mass energy will result in the open extended wave function providing a greater overall contribution to the expression of the entity. The reason for this is that increasing energy in a particular entity is equivalent to saying that an entity has a greater improbability of continuing to exist in the current condition while instantaneously possessing sufficient probability (energy) to exist in that condition. This is manifest as a higher natural frequency, an expression of an increased rate of change due to self-interaction or interaction with a paired potential that is a necessary consequence, and which also results in an increased probability of change with respect to other entities resulting in a wave function collapse to a particle condition.

A possibly controversial declaration is that from a certain perspective it is impossible for the photon to act as the carrier of the E-M interaction. How should it be that an entity that does not possess electric charge is affected by or affects electromagnetic phenomena that are the very mechanism by which charged particles interact? Yet it is also certainly the case that the observed nature of such phenomena are very different than what would be observed if photons possessed elementary charge as such, thus there is yet another paradox to consider, photons must be charged entities and must also not possess charge. Fortunately this is readily resolved along the lines of prior solutions, the open wave expression

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of a photon is the previously described decoupling of the in phase relation of the normally mutually cancelling paired charge potentials that permeate all space thus exhibiting a distributed non-zero charge realization. And yet due to having an intrinsic spin of 1, the closed wave expression of the photon exhibits 0 charge as the same paired charge potentials are coincident and in phase with respect to being mutually cancelling in this case, this being necessarily an element of the definition of integer spin in this commentary.

Given the apparent wavelike negative and positive oscillation about Zero nature of many aspects and properties of fundamental entities it is interesting to note the apparent electric monopole nature of elemental charge, that is to say there are entities possessing either a positive or negative electric charge but not both, and these charges exist “independently” of the opposing charge. It becomes even more interesting given the apparent absence of magnetic monopoles, entities possessing independent north or south magnetic poles. Is this monopole nature of electric charge an exception to a rule, perhaps it is, yet given the ½ integer spin of charged particles a suggestion arises as to a deeper explanation of just what is meant by ½ integer spin. It is suggested therefore that the entirety of all ½ spin entity expressions in the developed one system, all bound to the synchronizing identities of the primordial states, may be regarded as switching polarity on each and every ½ half cycle, electrons become positrons, positive fields become negative fields and vice versa but the charge relations and proportionality remains unchanged due to the synchronization inherent in a unified primordial charge defining process and thus the system behaviour is unaffected and we are none the wiser. By extension it will be seen that this also offers an explanation for the apparent inequality of matter and anti-matter in the one system, that is to say the total amount of matter and anti-matter in the Universe, when a ½ cycle and the following ½ cycle are taken as a complete cycle, will be necessarily exactly equal. In closing it should be noted that the proposed Universal electric charge oscillation may be a certain aspect of reality, if for no other reason than the observation that this proposition may not be disprovable.

Through Dimensions

At last it is time to examine the State 2 and 2+ system, the protracted review of the preceding primordial states being more or less complete. The reason this final state sequence to be examined in detail is described as 2 and 2+ is that the developments that are described next are of a similar conceptual nature and could arguably be the product of a single state transition. Notwithstanding, the opinion offered is that the following occurs during a two interval transition while accepting that the reader may then draw their own conclusions. Regardless, there will be some commentary on the subsequent states to develop following the primordial states and this would to some extent satisfy the suggested extended description.

Previously the State 1 development suggested an explanation for the concept that is fundamental charge but did not elaborate on the causal mechanism underlying charge differentiation, specifically the theoretical fractional charge nature of quarks, commentary thus follows to hopefully demonstrate that our “primordial logic” may lead to a deeper understanding of this. In describing the system states thus far it should be apparent that the State 0 was a 0 dimensional system and State 1 is 1 dimensional (though not exhibiting the full range of mathematical expression). One might ask is a developed system possible in which a one dimensional nature does not progress into a 1+n dimensional system but nevertheless evolves as a complex developed reality. It is suggested that the logical answer to this is self-evidently no, in fact the system at State 1 is arguably already the full embodiment of a 1 dimensional reality. Consider that in such a reality there are at most two directions propagating from

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any frame of reference (entity). Necessarily the “line of sight” for each of these will terminate upon reaching any entity as the 0 width of space precludes “seeing” around the outside of any entity towards more distant ones. Therefore in the frame of reference of all entities there will be at most two other particles in the Universe and as such the system will have no differentiated expression for evolved temporal states. Another way of stating this is that every entity would have the potential, and only the potential, of observing 0, 1, or 2 entities. Immediately it should be apparent that an entity observing 0 entities is degenerate to State 0. It should also be evident, though somewhat less obviously, that observation of either 1 or 2 entities may be regarded as synonymous with State 1. Where one other entity is observed the entity may be described as either viewing itself as a temporal displacement in a closed spatial context (the ½ cycle future or past of itself) or viewing another entity in a terminated one directional (still closed) context. As neither case is preferential then both are true representations, thus the system remains partially undefined and evolutionary “pressure” remains in the system. It will be apparent that the observation of two other entities does not greatly alter the situation, the system will still be degenerate to a primordial state in a compact closed spatial domain, as absent more definitive relations, the entity observes either itself twice (temporally displaced) via the nascent process of interaction, or itself and one other particle that in turn, observes itself and the original entity. Or it observes two separate identities which in the frame of reference of the original entity are then observing each other. This latter instance may be regarded as the residual potentiality of State 0 within State 1, by means of the temporal loop mechanism previously described, observing the first particle pair and thus all conceivable relations are degenerate to State 0 or 1. Concluding, the one system necessarily must exhibit dimensionality greater than 1 in order to possess sufficient defining relations to evolve to a later state, thus a two dimensional reality will follow.

Having determined that a second dimension of space must develop then the question naturally follows as to the nature of this extended reality. It should be evident that in order to be defined as having existence then something must occupy this extended dimensionality, as the space in which to contain that which exists is not itself defined if there is in fact nothing to be contained within. The existing entities in our State 1 system will be insufficient to accomplish this as two entities and a prior temporal reference by definition will not rigorously describe a two dimensional reality. Therefore the Universe will need to contain additional entities and these will need to have differentiated measures of existence. Previously it was proposed that spin as a unifying aspect of identity was resolved to multiples of ½ and that intrinsic spin is the primary identity defining mechanism, that is to say, all “real” particles possess spin and particles without spin are not “real” in the normal sense beyond State 0. As spin is a resolved property at State 1 then further pairing of a unifying principle to the differentiation of entities falls to the secondary mechanism of elementary charge (a consequence of spin realization). Thus it is to be expected that new particles created to occupy the extended domain of a 2 dimensional reality will possess differential position and charge (position in this case is charge). At this point a contradiction may come to mind and the question may arise “As a unifying principle would not charge remain the same for any new particles created?” The answer to this is that it cannot remain the same. We must realize that the Universal realities being described in this paper are very different from the world of everyday experience. The one system is governed by an incomplete mathematical framework and all potential interactions and relations are in degenerate modes. If there were to exist a particle of identical spin and charge to another in these primordial states, then in all frames of reference, including those of the matched particles themselves, these particles would be “seen” to be one and the same as there is simply not a sufficiently developed mechanism for identifying them as separate. For the states in question, in order that locations in what may only approximately be described as space are defined as

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differing and not coincident, these locations must be “occupied” by a differential identity. So then what may be expected of charge as a property under these conditions, the proposed response is that it will fraction/multiply as did spin previously.

Recall that intrinsic spin is that property which decouples the otherwise mutually canceling charge oscillations of the Zero field and makes evident the elementary charges of “real” particles. And continuing this line of reasoning, these elementary charges then are a manifestation of that which were it to have evolved in a developed system would potentially be a statistical distribution, that is instead necessarily quantized in the mathematically simple (non-discrete numerical relations are non-existent) framework of the primordial states and which we may then describe as a closed simple “wave” oscillation. Continuing, it becomes apparent that there is a straightforward conceptual model for the decoupling of charge in State 2, that is, if we view charge as an oscillating field potential in an n-dimensional space then the possible values of charge will be a function of the dimensionality of space itself. It is suggested that in the case of a 1 dimensional space where charge, such that it exists, must be in relation to the potentials of another reference charge, then the elementary charge realized for any particle we examine may exhibit a value of 1 (a charge potential exists between the entity and the reference), or 0 (no charge potential exists) or -1 (an opposite charge potential exists). Progressing to a 2 dimensional system such as is proposed for State 2 we would then expect as possible values for charge, 1, ½, 0, -½ and -1. These particle values may be conceptualized as a ½, 0 or -½ contribution possibility for each of the two possible dimensions of the total unit charge potential of the combined dimensionality. Thus two “perpendicular” constructive “realized” charges result in a total unit charge of 1 or -1, a realized charge in one dimension results in a ½ or -½ value and a 0 dimensional, or two destructive (opposite and thus canceling) charges, produce a 0 value. It is interesting to note in the preceding that a particle with 0 total net charge may arise as the product of a “neutral imbalance” of charges. Of course this charged particle or ½ spin entity that does not exhibit elementary charge in developed states would be consistent with a neutrino definition and is also suggestive of a possible mechanism for the nuclear weak force, more to follow. Finally, given the prior development that all of the initial conditions and primordial states represent perpetuating potentialities in developed Universal systems, discerning readers will have noted the implied prediction of the existence of “semi-electrons” and “semi-positrons” and this will require additional commentary as well.

The entire commentary thus far has been focused on the necessary elements in order that a Universe may progress such that matter entities, as these are understood to be constituted, will be fully realized in developed one systems. It should be apparent that a complete and alternative development is possible in which the primordial states are consequences of the minimum requirements necessary for fundamental interactions (unit spin entities) to occur and exhibit the behaviours we are familiar with. Again, it should be expected that in the early history of the Universe things are as they are from more than just a single perspective. Continuing the development of a two into a three dimensional “spatial” system using the approach taken up until this point, certain supporting arguments could be formulated regarding unconfined fractional charge and the inconsistencies inherent in the implication of nucleons (composite particles such as protons and neutrons) with unit spin, suggesting the formation of that which we experience as ordinary matter being instead a mix of entities both obeying and not obeying the exclusion principle. This would preclude the development of complex material structures as we understand these to be. As an alternative argument, the limited degrees of freedom and small number of potential configurations of a quantized two dimensional reality would in and of itself be expected to result in the decoupling of a third spatial dimension from the two existing ones in order to create the means to

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increase the number of potential configurations and satisfy the extreme inflationary pressures exerted by the Infinite initial condition. A word of caution at this point, there are perhaps certain known mathematical arguments that may suggest the inevitability of decoupling a three dimensional spatial reality out of that which existed previously, however, we must be careful to regard as applicable only those arguments which use logical or mathematical operators and relations that are shown to be necessarily realized within the Universal states in question.

One visually accessible approach to the question at hand is to return to the previously offered development on E-M interactions and their propagation. Recalling that E-M radiation may be regarded as a transverse wave propagating through free space, one dimension will be the direction of propagation, the first dimension and a second will define and be defined by the plane of the electric field oscillation, and finally the first and third will constitute the plane of the magnetic field oscillation. This is consistent with well demonstrated equations developed in the 19th Century from which the observed speed of light was a necessary consequence and is consistent with the far less authoritative preceding developments in this paper. It should be noted that the existence of less commonly considered circular or elliptically polarized E-M waves does not alter any of the conclusions above. The last point to be offered regards the possible argument that a two dimensional system may develop, perhaps through some version of holographic principles, an equivalent configurational extent and data content as a fully developed three dimensional system. The response to this would be that though this may be the case for two dimensional spatial domains that are fully expressed mathematically, this is again not the case for the quantized two dimensional domain in question where it is proposed that the only defined points that exist are those with unique identities.

Having hopefully established the necessary development of a three dimensional spatial framework (State 3) from prior states it is time to consider the implications. In the development of State 2 there was a declaration regarding expected possible values for elemental charge, for State 3 the possible values are 1, 1/3, 2/3, 0, -1/3, -2/3 and -1, these values being of course commonly recognized as the known ratios of charged fundamental particles. And using the same logic as was declared for the 2 dimensional system, these particle values may be conceptualized as a 1/3 contribution possibility for each of the three “perpendicular” charge dimensions though there are obviously more combinations possible for the fractional values and the neutrino solution acquires additional aspects as well. Several interesting implications may be noted, first is that somewhat of an explanation has been implied for the scalar quantity nature of charge. That is, due to the quantized nature of the primordial states there are no graduated measures for time, distance or rotation. This latter inclusion necessarily is the case since any partial rotation may be expected to define a completely new particle possibility with new potential values for spin-charge. If as is the case in the geometry of temporally evolved states, there were an Infinite number of potential angles between 0 and 90 degrees then we should realize a Universe with an Infinite variety of fundamental particles, it would be hard to imagine a more chaotic reality than this would produce. As charge and rotation are both quantized at this state then the summation of orthogonal charges in a particle with multi-dimensional charge must be a simple addition of each of the three symmetric (exhibiting the same behaviours) dimensions of charge contributing equally. If there were inequality then the natural laws of the Universe would not be expected to exhibit symmetry with respect to spatial rotations of physical systems leading to some rather unfamiliar physics, or alternatively there would be no charge contribution at all and the system would not develop.

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An additional implication to note is that there is potentially a significant difference in the nature of fractional charge identities versus particles with 1, 0 or -1 charge. This is because the fractional charges are not dimensionally symmetric, that is, undifferentiated in all three dimensions. So whereas the electron (-1) is symmetric with respect to charge in the “x, y and z” directions, the quarks (particles having fractional charge) all have two symmetric and one asymmetric charge dimension regardless of dimensional construction. If we regard State 3 as essentially a definition of a single quantum state, in which every entity must have a unique definition, then quarks will have this additional mechanism for establishing identity. Therefore, a single quantum state which may contain only a single electron with positive spin and another with negative spin, may contain x, y and z aligned quarks in both spin directions for a total of six quarks of each fractional charge value, an arrangement that is perhaps reminiscent of atomic orbitals.

Given the potential superposition of temporal relations in the primordial states it may not be correct to regard the summing of dimensional charges as always summing from 0. For example it is suggested to be the case that the positron, which may be regarded as an entity possessing a 0, +1/3, +1/3, +1/3 charge representation, may also be regarded as a prior state defined +1, with a State 3 of +0, +0, +0 representation. If we are to continue logic developed previously then it should be the case that all possibilities are realized. It may seem then that the possibility is being suggested for the existence of fundamental particles possessing charge with an absolute value greater than 1. While the possibility is not being dismissed out of hand, it will be tempered with a declaration that the simple addition of values as we understand these to be, necessarily are adjusted in the context of primordial states and values we regard as simple integers, which nevertheless represent the largest value for a property that may be realized for a given temporal state, may take on aspects of the Infinite / Zero potentiality. Thus it may be the case that the summation of a charge of either sign to a +1 or -1 intrinsic charge may result in the intrinsic charge summing towards 0. As an additional favouring argument, this adjusted view of the summation of intrinsic charges does serve to remedy certain asymmetrical aspects of the potential configurations of 1/3 and 2/3 charges and should result in these differentiated values having similar behavior with respect to forming composite particles. Additionally, it is suggestive of certain characteristics of the neutrino, that is, due to the consideration of a neutrino expression of net 0 charge due to symmetric charge neutralization of a charge 1 reference, the neutrino should be free to propagate through evolved three dimensional states unhindered. Yet, since it embodies aspects of charge and some charge characterizations should exhibit asymmetrical charge distribution there should be a non-zero probability of encountering a neutrino with a statistical instantaneous charge realization that should then permit some probability for the occurrence of interactions with other charged entities.

Recapping, some additional insights may be realized by attempting to visualize the structure of time and space so far presented. In so doing we would of course be cautious in applying constraints on our expectations that are the product of everyday experience. The State 3 system may express three spatial dimensions but these elements of a quantized system would certainly not be spatial extents as we understand these to be. It should be expected that time would also exhibit an unfamiliar nature within the primordial states, specifically, it is suggested that rather than viewing history as progressing from one point in time to a subsequent point in time, the sequence of states in question should be viewed as progressing from each point in time to an extended definition which includes the contributions of each prior point in time. As the particle expressions or instances of later evolved states are bound to this identity defining phase then there should be continuing evidence of this temporally superimposed nature. It is offered that this is an underlying principle leading to the prior proposition that all entities are in

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some sense of one nature and expressions of a single conceptual identity and are thus bound to a unified and persistent collection of inter-related Universal “laws”.

Of Time and Space,

When this paper was begun the intent was to demonstrate a logical and possibly necessary Universal evolution up to the creation of the quark identities. Having hopefully achieved this goal in some measure, additional commentary, some perhaps speculative, is offered on the further development of our, or perhaps any Universe. There is a phenomenon that should be increasingly apparent to the reader at this point, that is, from a small number of additional parameters may arise a considerable additional conceptual development and each progressive state becomes increasing more complex to formulate. This was to be expected and is basically the beginnings of emergent complexity in which the exponential growth in the number of possible permutations of a system populated by a handful of different entity types rapidly approaches a seemingly Infinite value. It has the effect also of limiting the extent to which the type of philosophical approach to cosmology applied in this effort will be effective. Necessarily the system, all systems, which begin as conceptual ideal mechanisms that translate into and develop a mathematical structure soon become primarily mathematical mechanisms with a conceptual or axiomatic basis. Therefore if there has been value in this effort and insight has been gained from an essentially non-mathematical approach, then it should be appreciated that this is only possible for the states in question because they are mathematically undeveloped. Once particle instancing begins and the Universe establishes a true history this approach will no longer be the method of advantage, a formal mathematically rigorous approach must be followed.

With the decoupling of a third spatial dimension the propagation of E-M waves as they are understood to be constituted becomes possible. This allows for the transmittal and reception of identity defining relations beyond the primordial states described and thus permits the instancing of the primordial states as many times as is necessary to relieve the remaining, though still extreme, inflationary pressure of the Infinite initial condition. It is suggested that this alternate mechanism for dissipating energy will effectively preempt the formation of any additional extended spatial dimensions. If this is correct then all Universes in any Multiverse system will also have just three extended spatial dimensions. The suggested mechanism for Universal evolution is then, the incremental increase in the extent of, and reduction in the curvature of, the closed three dimensional structure of the primordial states due to establishment of a multitude of temporally related identities which by evolution in the values of those relations collectively define extended spatial fields while obeying a set of logically necessary conservation laws. Several implications come to mind, one of these being that certain theories in which a Universal definition requires a number of additional tightly “curled” dimensions becomes much simplified as the quantum variables so explained are now explained as the primordial function of the same dimensionality as the familiar extended dimensionality of space and time that is our everyday experience. Additionally, as has been already noted, spin and charge are simplified to a single phenomenon, which are also coupled with time and space as aspects of the same phenomenon thus there actually is just a single underlying, though multi-faceted, identity defining process. There may be some reluctance to accept the immediately preceding equating explanation so a brief thought experiment is offered. All that is necessary to clarify this is for any of us as observers to pause and consider the spatial environment we presently occupy as not possessing charge or any consequence of charge. Instantly all colour would be removed from experience, indeed all light, radio, microwave or any other E-M wave propagations as all charged particles would now be at charge 0 and will no longer affect or be affected

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by electromagnetism. Additionally, all quarks will have the same value for charge and be undifferentiated so their composites such as protons and neutrons will also be undifferentiated. Regardless this would be compounded by the fact that now chargeless electrons have become synonymous with neutrinos. As such they are no longer electrically bound into atoms and thus all chemical bonds would be instantly broken resulting in materials such as water and DNA being immediately disrupted thereby destroying all living things. If we contemplated this effect Universe wide then the entire system would cease to function, all stars would collapse immediately as there would be no outward radiation pressure to prevent their collapse due to gravity. Furthermore, the W and Z particles of the nuclear weak force will now be identical and the phenomenon of quark flavor changing will Universally fail due to the loss of quark charge, thus the weak force collapses and stellar nuclear fusion would cease. Of the remaining fundamental forces, gravity and the strong force (which this paper regards as an aspect of charge), there is only attraction on a universal scale and no means for any particle to establish a frame of reference in which it has relations to particles beyond the quantum scale. Thus special relativity itself fails, temporal definitions cease to exist and the full force of the great zeroing effect that is gravity is utterly unopposed. All of existence collapses to a singularity, a primordial state with no more information than a Zero by Infinite initial condition. It is most definitely the case that charge and space are aspects of a single phenomenon as are their precipitating predecessors, spin and time. Remove charge from the Universal mechanism, and there will be no space.

Which brings us to the pairing of time and space, it is generally held that there are three dimensions of space and one of time. It will be offered here that all dimensionality is fundamentally realizations of the same underlying potentials and from a perspective as valid as any other there is equivalence and thus the three spatial dimensions are in effect three dimensions of time. That there is a maximum possible speed at which information may be conveyed has been long understood. Perhaps less understood is the implication that the speed of light in a vacuum (assuming a rest mass of 0 for photons), being the maximum known speed that anything may travel and which is the same in all inertial frames of reference irrespective of the motion of any light source, effectively equates time and distance. In other words, measures of distance using meters, feet or any other unit of length may be equated to and replaced with a length in time for “light” to transit the distance in question. So for example the distance around the Earth at the equator, within a frame of reference at rest with respect to the Earth, is approximately 134 milliseconds and the moon is ~1.3 seconds from Earth which is ~8.3 minutes from the sun. What may be less intuitively evident is that measures of size may be regarded in this manner as well, the actuality being that size and distance function identically. Our perception of objects as having absolute sizes is in reality an evaluative process of analysis and identification in which information that is gathered by our senses is interpreted as indicating that certain groupings of materials we observe may be regarded as distinct entities having particular extended sizes. Continuing the proposition, a person that might normally be described as being 1.83 meters in height we may now describe as being 6.1 nanoseconds tall. It is of course the case that all macroscopic objects are composed entirely of fundamental particles and forces that are only more or less associated in particular configurations for some non-zero period of time. Thus in a sense the “objects” of everyday experience do not have absolute identities at all but instead are collections of data currently describing these configurations of relative position and momentum for the only “real” objects, that is, the elementary particles. Extending the logic further, once we acknowledge that the sizes of composite objects are a product of the positions of, thus distances separating, leptons, quarks and other particles, then the only actual objects of size are these microscopic particles. However, the only sizes applicable to these quantum scale entities is their

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spin-charge extents (string oscillations) in the primitive dimensionality of the primordial states, remembering that spin and time are aspects of the same phenomenon.

The foregoing does lead to some counterintuitive results, specifically, equations describing motion may now be expressed as units of time per unit of time. It should be noted that motion is still described consistently if we appreciate that what has been described is the change from one temporal frame to another during a specific advancement or state progression of a specific temporal frame. In order to avoid confusion then we can accept conventional units of linear length as representing the measure of temporal shift from one frame of reference characterized by a particular set of defining relations, to another having a greater relational differentiation the greater the distance. This leads to our next declaration, if the spatial organization and configuration of entities is necessarily a function of time then the reciprocal statement must also be true, that is “that a condition is defined by a property is at least in part a definition of the property itself”. Thus it must be the case that present time itself is in some sense synonymous with and defined by a particular configuration of “real” particles having particular defining relationships, and absent those relations time as an advanced temporal phenomenon will not be sufficiently resolved and effectively does not exist.

Having provided a conceptual framework for time as a later continuum of evolving states describing a Universe of entangled relations, there are a number of developments related to fractional particle charge effects subsequent to the primordial states that become relevant to the evolution of systems. The first of these is an extension of the fractional charge consideration and is the proposition that the dimensionality of charge is synonymous with that which has been described as colour charge elsewhere. Though instead of the three “colours” red, blue and green producing neutral white baryons (composite particles composed of three quarks), we have three particles having asymmetry in one dimension combining into and confined to a bound closed relation in order that the extended developed Universal system is shielded from the fractional charge asymmetry that would otherwise be the case. As quark charge asymmetry is effectively spatial asymmetry, unconfined quarks would potentially violate conservation laws for linear and angular momentum while the partially undefined dimensionality would evidence into the developed system, no doubt catastrophically, the unresolved Zero by Infinite condition of State 0. As such the fundamental force phenomenon mediating fractional charge confinement would necessarily be exceptionally strong, actually creating a finite value relation as strong as is necessary to remedy any fractional charge imbalance by new particle instancing. From another perspective, this may be viewed as an imperative that actually initiates particle instancing. As a product of the State 0 condition it would also not be surprising to find the resultant force does not diminish with distance beyond the effective range of the effects of primordial states, this being an expected consequence of distance as a concept being undefined for State 0 and only partially defined in the early subsequent states. It is also by definition omnipresent, and the asymmetric axis may be regarded as being at these states in a partially undefined, thus Zero by Infinite condition. It is also not surprising to find quarks forming various groupings of threes as both 1/3 and 2/3 charge quarks are identical with respect to exhibiting dimensional asymmetry that will be negated in composite entities structured of three entities. An additional consideration relates to effects on baryon (a particle composed of three quarks) formation that are described as arising due to the existence of certain symmetry groups. A possible explanation arises from the observation that charge is a function of spin and as such spin can translate one direction of charge to another without changing the magnitude of the charge, this being essentially the mechanism of conservation of angular momentum. Therefore while spin aligned quarks within a baryon will be expected to maintain a particular charge dimension arrangement such that their asymmetrical charge

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axes are continuously unaligned, spin unaligned quarks must be considered to be potentially swapping their asymmetrical charge axes such that these are potentially aligned “1/3 of the time”. Since this is a primordial state and temporal potentials are superimposed this translates to quarks of identical total charge would be effectively aligned and undifferentiated (the same particle) with respect to asymmetrical charge axes and thus the charge axes mechanism would not be available to permit baryon formation for charge identical quarks, only spin differentiation would remain.

It was previously offered that State 2 should define particle identities possessing ½ and -½ charges. This paper has proposed that there would necessarily be residual phenomena from each of the primordial states, however, we may be inclined to dismiss State 2 and consider instead a Universal progression from State 1 directly to State 3 in order to avoid the obvious implications. Nevertheless, this effort is intended to be an exercise in which the imperative is to allow conceptual developments to lead where they may so an exploration of the potential consequences of State 2 will follow. As noted previously, it would seem that “nature abhors a fractional charge” and it should be expected to be all the more so for ½ value charges as they require pairing with other ½ charges that are also instantaneously in a transitional state. In other words, ½ value particles would be expected to exhibit the phenomenon of confinement which mandates that the extended system definition is populated only with instanced entities possessing integer values of charge. And they will have to achieve this pairing with particles that are likewise improbable in that they are instantaneously non-expressive of their State 3 identities. Therefore, if the State 3 fractional charges result in the creation of composite particles (hadrons) having charge magnitudes of 0, 1 or 2 (at least), then these State 2 fractional charges should result in hypothetical composite particles having charge magnitudes of 0 or 1. As the spin magnitudes must result in an integer spin value these hypothetical particles will be spin independent and not subject to fractional spin exclusion, as opposed to ½ integer spin particles which engage in spin pairing with other ½ spin particles to achieve integer spin. As they are constituted of identities possessing realized charge they will have mass, as mass realization necessarily is a function of reality defining relations. Considering that fractional charge entities are able to engage in defining relations to a greater degree than integer charge entities (charge 0 or 1) then these constituents combined with the energy associated with confinement should be expected to have significant mass.

Obvious potential candidate particles for these composite particles containing State 2 specific entities would be the W+, W- and Z particles. If there is any validity to this proposition then an immediate question arises, given the enormous amount of test data gathered from high energy collisions in accelerator experiments, how could a composite nature for these particles let alone the proposed ½ charge magnitude constituents have been missed? As the author is not a physicist and does not have access to the resources to investigate further then it could be presumed that this has already been ruled out as a possibility. However, this hypothetical construction of the carriers of the weak force is perhaps masked from ready detection by certain possible considerations. Due to their significant masses the bosons in question are extremely short lived and perhaps this places constraints on the designs of experiments to detect the ½ charge constituents, described earlier as semi-electrons and semi-positrons (collectively semi-leptons perhaps). There is another consideration of perhaps greater significance, the ½ charge values of the hypothetical entities may be regarded in a different context, specifically they are the product of a transitional State 2 definition that will find a redefinition in State 3. It is suggested that the correct way to view this is that the “semi-leptons” are unresolved super-positions of all of the charge potentialities of State 3, so for instance, if the semi-positron is envisaged as a persisting entity then it

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may be regarded as, cycling between or the co-realization of, an up quark and an anti-down quark, or a positron and a neutrino. In either case it should be apparent that conservation of charge is maintained.

It would have been a simple matter to have omitted these hypothetical State 2 charge effects from this effort were it not for the rather straightforward explanations that follow for several phenomena. The first of these is the apparent indeterminacy of particle charge identity when examined at sufficiently small scales, that is to say for example, electrons may appear to be neutrinos and neutrinos may appear to be electrons. This is readily explained as representing the insufficiency of relations for an examined entity to resolve a State 3 identity from the State 1 or 2 identity resulting in the aforementioned superposition of charge identities. Admittedly there are other effective mechanisms to explain particle charge oscillation and indeterminacy. The more interesting development concerns the weak force and quark flavour transformation as a function of charge only, the process whereby an up type quark may decay to a down type quark or the reverse process may occur. This is explained as a quark of a particular flavour, interacting with the W particle of opposite charge of a virtual W+ and W- particle pair resulting in resolution due to interaction of this W particle from a State 2 to 3 condition whereby the original quark will annihilate with its antiquark. This leaves as a decay product a quark of opposite type and the remaining W particle which is no longer virtual as it no longer has a partner with which to annihilate. Initially this surviving W particle will exist due to the ½ charge identities having no realizable separable identity in evolved states. However as the W particle translates through the extended dimensionality of an evolved temporal definition this must soon resolve to a coupling of State 3 defined entities, specifically a lepton pair which may propagate freely and separately through space due to having the integer charge identities that permit this. Depending on the particular transaction presumably energy will be liberated due to the lower total mass of the resultants, however this is well explained elsewhere. In fact the entire process of flavour transformation is well explained elsewhere, with a mathematical formalism that is thorough and verified by experiment. The contribution that is being offered here is an explanation that envisages a necessary and logical development from the simplest first principles conceivable to yet again declare why things are as they are and not just an explanation of how elements of the system interact.

And so we reach the end of the primordial state consideration without having discussed the specific mass relations of fundamental particles. This is because it is intended to be demonstrated in the following developments examining evolutionary mathematics that these values are a product of evolved Universal states and are not realized fully in the primordial states.

Counting Out

In much of the preceding a discerning reader will have noted that many of the concepts proposed do not necessarily require extensive reformulation of the mathematics presently employed in studying the topics in question. This will almost certainly be the case for any viable alternative conception of the nature of the early Universe, current theories regarding quantum mechanics and relativity being the most tested and experimentally verified in the history of science. However, just as a philosophical re-examination of the physics of the early Universe may lead to a more unified understanding without a complete reformulation, the same may be said for aspects of the mathematics of the beginning of time. In the preceding commentary there have been propositions for which the author is quite certain of a truth value and there have been others for which it is believed there are strong favouring logical arguments.

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Regarding the commentary on mathematical evolution only those philosophical arguments that meet the more stringent expectations of logical certainty will be presented, at the very least this is the intent.

In 1905 a landmark paper changed the way we view the nature of time and space. Since then the intervening years have witnessed physics, arguably first amongst sciences, demonstrate continuing success in developing a consistent, logical and experimentally verified model of our Universe as a vast mechanism of innumerable microscopic elements obeying a unified, rational collection of natural laws. The basis and means of specification for much of this model has been and will continue to be a formal system of rules and methods employing rigorously defined symbolic representations and operations for numeric and logical relations developed and constructed from and upon a limited set of axiomatic first principles of unquestioned truth value, in other words, mathematics. In fact, the relationship between the physical sciences, physics in particular, and mathematics has been so interdependent that in many instances the equations describing some particular aspect of reality have preceded the actual discovery of, or even contemplation of, the predicted aspect in nature. Given such a climate of success it is easy to understand why we may now habitually seek mathematically derived explanations for phenomena that prior generations would have attributed to the mystical actions of various gods, spirits or other “unexplainable” forces. It would possibly not be an overstatement to declare in fact that the prevalence of a viewpoint in which the Universe is seen as predictable, quantifiable and mechanistic is one primary differentiation separating the modern era from the prior ages in which the majority viewed the world as governed by the “transcendent unfathomable”. Some may argue now that we held to such prior beliefs for far too long, for it would seem that we are prone still to accept without question certain transcendent beliefs even within the very systems which challenge our prior “non-scientific” explanations on the nature of existence. Thus what will follow will be a philosophical examination of certain aspects of the mathematical ideal with a view to uncovering remaining transcendent unfathomables.

Within commentary elsewhere it is generally not stated, yet by a lack of counter argument and by inference it would seem commonly accepted without contest, that mathematics itself as a relational system was realized in the fullness of expression at the instant of creation (or perhaps preceded creation). It is declared here that such a belief is not a rational scientific one, in actuality, this imparts onto the mathematical ideal aspects of the divine. For to believe that a thing has unqualified and fully realized existence without consequence, verification or measure of that existence is not science, it is instead mythology or metaphysics. A potential response to this is to declare mathematics to be an abstraction, not even a science at all, and thus not subject to logical considerations of what is required of a thing in order that it be considered “real”. Yet it will be countered that math and number are no less real than material objects that do not exist without a measure of energy, which does not exist without measured space, which does not exist without a measure of time, which does not exist without material objects that may experience measurable change. All of these measures have in common that they may be expressed as numerical representations, thus it is declared here to be the singular common trait that identifies these as measures. And to the extent that a considered system contained no measurable existents it would be meaningless to discuss the existence of number itself within such a system. So, whereas the author may choose to offer arguments for the divinity of number in a subsequent work, pre-existence of a fully realized Universal system of relations, in the absence of the elements that would be described by these relations, is not the basis on which such a declaration should be founded. Extending this, it is being declared that number and numerical relations are a product of the primordial logic of the initial condition. To be clear, what is being declared is that the only axiomatic precondition that must be accepted is that there is a logical imperative that is the certain nature of the ever present initial condition

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itself, all other rules and relations are not axiomatic and must be demonstrated as necessarily consequential. Therefore, numerical relations, often regarded as abstract representations of the state and behavior of real systems, are declared to be a necessary intrinsic component of reality and co-evolve with the aspects of the system that they describe. For most of the sciences it should be noted that there is little practical consequence or effect due to this, however, theoretical physics is seeking to apply the complex evolved mathematical rules and relations of a fully realized Universal mechanism to events ever further back toward the beginning of time. A successful completion of this effort would thus appear destined to be ultimately unrealizable. That being stated, it should be clarified that number and numerical relation logically must be expected to develop explosively in the early one system, it is only at the very earliest moments in time that the mathematical ideal is found to be in a primordial form. This latter point should be unsurprising as this entire paper could certainly be rewritten as a treatise on how the Universe as a system governed by natural laws necessarily evolves from an initial condition of mathematical axioms rapidly into a fully expressed mathematical description. And just as was the case for the entity-charge argument that was employed instead, the early Universe necessarily engages early on exclusively in decoupling the relational parameters, mathematical and otherwise, that permit the definition of succeeding temporal states, else the system could not evolve and we are not here to debate such things.

Earlier in this paper there were some references to the creation of number and relations at various stages. What was being declared is that a mathematical ideal develops concurrently with that which may express its development. The operator that is multiplication is evidently an intrinsic aspect of the initial condition in the Zero by Infinite relation that is unity. Division as a “real” mathematical operation certainly must exist consequentially as well and unquestionably describes the transition from State 0 to 1. Interestingly, it is arguable that addition and subtraction do not really exist as independent operators at the primordial states (the author may argue for and against such a proposition). Instead, with regard to measures of real systems at least, these latter operators may be seen as simply a method and means of representing mathematically the reconfiguration of arrangements of real entities from the perspective of intelligent observers. In other words, is anything ever actually added to or subtracted from the system as a whole, identity which is everything is divided and multiplied of aspects of the initial condition? Likewise, it may be declared that particle instancing is a decoupling of possibility from the Infinite aspect of the initial condition wherein nothing has been added or subtracted to the system as a whole, just redistributed from a pre-existing potential. With regard to exponentiation it would appear that this has at best, if any relevance, a limited applicability to the primordial states, though clearly must become critically important for the instancing of representations of those same states into a coherent extended spatial expression of existence subsequently. More complex mathematical relations than these naturally evolve subsequently as the developing system is able to realize expressions of these relations.

As previously noted, the number 2 exists once there are two of something that exist, which reciprocally occurs once there is an ideal “twoness” as an aspect of reality. Similarly, a long recognized theorem relating the lengths of the sides of a right triangle requires the existence of triangular relationships at least in order to have relevance and constitute a meaningful element of a defined existence. This leads to some rather surprising follow up declarations, for example, by this logic it cannot be the case that either the constants e or pi exist as meaningful descriptions of reality and have specific values at the initial condition, in fact the values we recognize for these constants are not even possible as definitive at that time. Rather it should be expected instead that their specific valuations are a consequence of the necessary development of a trigonometric ideal that must be realized if particle instancing in three

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dimensional space is to occur, thus immediately following the primordial states discussed. The reason that this must occur then is that the orthogonal limitations of the primordial states are fully populated at State 3. Additional particles will be expressions of the same particles in a geometric reality in which each of three spatial dimensions operate effectively as was described for a bounded 1 dimensional system in which particles are not able to “see past” next particles to particles in an extended spatial reality thus an extended spatial reality does not exist from the frame of reference of any particle without a non-discrete mathematically evolved contextual framework.

Returning to the constant e we are left with the burden of at least providing a conceptual framework for how this “irrational” number that is so fundamental to the Universal mechanism comes to have the numerical value that is known and will need to do so without resorting to the identity often described as “remarkable for its mathematical beauty”. Recalling that the primordial states are populated with entities that do not possess finite values for properties so much as they have measured relations to other entities which they co-define, it should be apparent that the reality of number is in reality the measure or ratios of properties of one entity to another. And this then is the key, the Universal state and its long history is no more than the evolving proportionalities or ratios of its myriad constituents. The system is not just number, rather it is the rationality of constituents that is both defined by and defines number. So now we have the necessary components for solving at least in part the ontological paradox of e, the Universe as a mathematical ideal is primarily a rational system, meaning in this case that it is composed of constituents whose measures are ratios, and it is driven by an Infinite (time expressing) potential which also expresses reciprocality with the zeroing potential as a fundamental aspect of the State 0 condition. As it has been argued then that the one system advances from axiomatic simplicity to ever more developed mathematical formulation then if there is a solution to why the constant e has the “transcendental” and “irrational” value that it has, we should expect this to be manifested of that which is integral to the nature of the system states from which it emerges, specifically, an infinitely iterative series of reciprocal ratios exhibiting simple regularity of pattern in a logical and mathematically primitive relation. In fact such a description for e does exist and has been known to mathematicians for some time, it is none other than the regular continued fraction representation of e, which is 2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10,… and so on.

Exploring the conceptual implications of continued fractions further reveals that there are in fact a great many significant irrational values for which the decimal representations exhibit no discernible regular pattern that nevertheless have regular simple patterns when expressed as continued fractions. Notably this is the case for all square roots and thus the entirety of trigonometric expression which defines and measures spatial relations can be seen as a logically consistent progression from a single generalized mathematical development. Even the ubiquitous value pi is a development of a known continued fraction representation exhibiting a simple progressive pattern of squares, unsurprising and perhaps somewhat suggestive of the logical mechanism of its development.

Summarizing, it would appear that the concept of the continued fraction is a key to understanding the process by which the one system evolves complex seemingly irrational number and arguably represents a more “natural” representation of number itself (a point noted in other commentary). Developing this further, given the broad applicability of continued fraction representations in demonstrating fundamental underlying patterns and relations amongst the most significant of irrational and transcendental numbers, it is proposed that this is in fact indicative of a ubiquitous trait for all Universal systems. Specifically, it will be the expectation that every mathematical constant, such that it is constant over time, will be

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definable as a continued fraction or other continuing representation (for example, Egyptian product) which exhibits a simple repeating or progressing pattern. And thus by inference all seeming “constants” that do not exhibit these simple patterns are proposed to be not constants at all but rather necessarily are the relational solution for some combination of instantaneous Universal parameters. It is beyond the scope of this effort to investigate the logical rationale and necessity of the certain and various patterns revealed in the specific continued fraction representations of the significant constants, perhaps pursuit of this will be of interest to others. The author does however find the pattern in the arrangements of all square root representations suggestive of a direction for further logical development.

A Number Of

Having proposed an evolutionary view of number and a mathematical ideal we will now address another aspect of number, specifically, the operative understanding of what is meant by the terms Zero and Infinity. As all that has been presented in this paper arises naturally from an attempt to better understand Zero and the Infinite it would certainly be imperative to clarify definitions. In our daily experience situations frequently arise that may have quantifiable parameters or particulars for which we may assign a value of Zero. Our familiarity with and common use of the term may lead however to an under appreciation of certain aspects of the Zero identity, so in order to proceed it will be first necessary to differentiate the contexts in which the term may be used. The first of these is the just described judgment as to whether a measure sufficiently and effectively satisfies more or less subjective criteria for being close enough to Zero to be so described. It should be noted at once that we are describing Zero here as an abstract representation and not an absolute and in this context a null result is quite literally in the mind or minds of the beholder(s). The second is as an empirical difference or measure of some quantifiable aspect of a real system, in this context it will be shown that the applicability of true Zero value assignments will be subject to an extraordinary burden of demonstration.

The equations 1+1=2 and 2-1=1 would be almost “universally” accepted as representing absolutely true statements in all circumstance to most observers without question. While the truth value is obvious in each case some insights may be forthcoming if we suspend acceptance of this and endeavour to determine the limits of applicability of these relations. The application of such seemingly straightforward evaluations to real systems are in some measure a reflection of the commonality of symbolic representations regarding experience that are necessary for the development of language, and not necessarily an absolutely objective appreciation of reality. We may be led to inquire when tasked with an assessment regarding the absolute truth of the first equation for all circumstance, for instance the existence of a set of physical objects, as to whether the second identity is expected to be an exact equivalence of the former. That two entities of size should ever be perfect representations of one another is a virtual impossibility given the rigorous requirement of a perfectly realized ideal versus the massively data rich descriptions that even trivial everyday objects possess. It must certainly be the case for any two objects much larger than the scale of the quantum realm that a declared equivalence of absolute value for any measurable properties of the two is subjective and fails to satisfy the strictest of definitions. Employing a variant of the paradox of the heap, we should understand that if we have an apple in hand for example and are given another and all parties agree, then we are each of us making an evaluative assessment that the first apple is for practical purposes equivalent to the second so that all may declare there to be two of what is described as apples. Suppose however that a small piece was taken from one of the two, would our consensus amongst observers still remain that we are holding two apples or will some now say we have one, and another that it is something less or something else? The

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important point here is that as we remove more and more of the defining characteristics of any object there will necessarily be disagreement amongst observers at various points as to whether we have a sufficient entity to still constitute an object of a certain type such as an apple, or if it now represents a Zero quantity of the original object type and an increase in the quantity of some other object type such as an apple core. Some observers may in fact argue that even microscopic remaining portions of an object not directly observed, may still constitute some non-zero amount of the object. This process of evaluation wherein a social consensus is reached regarding the sufficiency of identity claims for objects of consideration is not being critiqued as unjustified for it serves well as a means for individuals in a society to interact and conduct their daily affairs. Objection is however offered when the habitual allowances we grant for the sake of uniform classification and organization of a common experience become so ingrained into our perspective that we continue to apply the same allowances for evaluating conditions for which such approximate solutions are inappropriate.

For the example presented above and related examples there is arguably always the potentiality at least of an observer perspective that two of any objects of a type are never equivalent (particularly if the author is present) and thus the sum may be declared to always be some approximate value that includes a non-zero statistical differential or tolerance. The key term in the preceding statement is non-zero, which is to say that for all macroscopic objects the comparison between any two always results in a non-zero value and a true Zero differential relationship is never realized. As implied previously, the only identical object to another object would be one in which all degrees of freedom for all constituent subcomponents are measurably identical in the strictest terms to another object. This can only occur above the quantum realm when comparing an object to itself, and given that no macroscopic object will remain identical from one moment to the next due to the ceaseless and complex interactions that are unavoidable within and with the environment, then all complex objects fail to represent a Zero difference even with respect to themselves at a different point in time. This should be readily apparent since an absence of change in the data state of an entity, or collection of entities in an object, by definition (at least the definition in this paper) means that the entity or object has experienced no passage of time.

Having established that Zero as a measure indicating complete absence of a differential between two objects is an ideal that typically cannot be achieved in practice, Zero as a measure of object properties will be considered. As all complex objects of size are in actuality composed of fundamental entities which express the essential properties of that which exists, then in order for composite objects of size to exhibit a Zero measure for a “real” property all of its constituents must either possess a Zero measure of this or instantaneously and continuously sum to a Zero measure of this property. The problem with this is that we have already established that fundamental entities have properties, and those properties measures established, due to dynamic relations with other entities, thus there is a statistical nature to the differentiating aspects of identity. With respect to position and momentum of each and every entity within an object these must never exhibit Zero or unchanging values in all frames of reference within an object for to do so would imply the Universal mechanism and temporal progression within have stopped completely, thus all objects must contain entities which have non-zero momentum components in their description and an aggregated Zero summation must exhibit a statistical nature that will exhibit a non-zero instantaneous value at sufficiently small intervals. Adjusting the counter argument, an obvious particle property that could be declared as exhibiting a Zero value would be charge in the case of the neutrino. However it has already been explained that at intervals that are extremely short the identity defining relational mechanisms break down and a neutrino will statistically exhibit a non-zero charge, in

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other words it will oscillate through and behave as other charge realizing identities such as electrons. This is in actuality a restatement of the scientifically well established uncertainty principle that limits the possible accuracy of all measurements, which is in turn a specific example of a broader proposition here that declares “for all real systems with measurable characteristics, all such characteristics will be non-zero values provided there are no paired characteristics that may be observed with Infinite values”. This leads naturally to an alternative viewpoint of the mechanism of the uncertainty principle as being simply the natural resistance to evidence Zero measures of conditions that is intrinsic to all real systems as doing so would require the realization of Infinite conditions. That there are some measures that may be correctly declared as having Zero measure is granted, however, it will be declared that such measures are more typically, though perhaps not obviously, of an abstract nature as constructs of social processes that integrate consensus definitions into language.

It should be apparent at this point that even the seemingly straightforward declaration that a Zero quantity of a particular object is observed to be present in an observed situation is not without qualifying considerations. As has been noted, macroscopic objects are best regarded not as singular entities but rather as groupings of interacting entities that exhibit some degree of configurational persistence. So yet again the only real entities in some sense are the fundamental particles, all of which may and do instantaneously appear and disappear randomly as virtual particles, thus exhibiting even a changing quantity, for exceedingly short intervals at every point in the Universe, consequentially each point in space theoretically possesses a non-zero quantity for each fundamental entity. It should also be considered that an apparently singular particle demonstrating “oneness” may also be regarded as a projection of a primordial state entity into present space time which is representing the sum total of all particles of a type or even of all entities further distorting the notion of individuality or singularity for particles. Summarizing, what is being declared is that the ideal Zero representation is extraordinary for any aspect of real systems and is rarely if ever fully realized. And that the subjective assessments we frequently engage in wherein insignificant yet non-zero parameters are regarded as being irrelevant and thus “effectively” Zero is so ingrained in our collective process that it obstructs a thorough appreciation of the implications of an ideal Zero condition. And finally, it is proposed that paired Zero conditions for real systems are extraordinary relations that in evolved temporal states are difficult to observe in the ideal as the system will exhibit ever more energetic and unpredictable behaviours when probed to Zero measures in order that the corresponding Infinities are equivalently realized. That being said, there are interesting examples of the nature of Zero like conditions being observed in present day experimentation, notably, in superconductivity and the behaviours of fluids as temperatures approach absolute Zero and these should be viewed as providing valuable insight into the true nature and power of the Zero ideal.

The next topic is the nature and effect of the concept of Infinity itself upon the behavior of the one system. If it is being suggested that misconceptions may exist regarding the common understanding of the function of the Zero relation in real systems, then such a suggestion regarding the function of Infinite relations must certainly follow and require further suspension of prevailing interpretations. When contemplating early conditions there are many counterintuitive indications if we pursue a logical approach free of these prior expectations, for example, it is arguable that at the beginning of time 1-1=1. For, if a first instance universal expression exists and then the entire system is subtracted from itself by a negative temporal displacement through State 0 then the system will by previous argument still be at State 0 and there is no net change. Continuing it could then be similarly argued that at the beginning of time 0+0=1, as perhaps yet another instance of a conceptual ideal demonstrating Universal inevitability.

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There are other aspects of that which is being described here as primordial logic to consider, contemplate the applicability and relevance of any typical extended finite value within the frame of reference of the 0 State. For instance what is the meaning and significance of the value 197 in such a context, or 1/12, or 3.14159. It is offered that in the 0 State these values are all undefined relations and that since 197 is a greater value than the measure and quantity of all that exists then it is effectively synonymous with Infinity at this temporal state. An alternate perspective on the Infinite is suggested by which we view this as representing the “all” or entirety of possibility for any consideration under examination. It will be noted that the relation of Infinity to certain initial finite values is not without debatable considerations. Specifically for example, it could be argued that two and Infinity are synonymous at State 0, or instead that two and three are established by the existence of three identity elements and it is four that is first synonymous with Infinity. This can be logically extended no doubt, however this paradoxical condition should not be regarded as an intractable problem to be solved but rather an indication of the dynamic potential of the Infinite condition in which all possibility, even of logic itself, is coincident. The implications are obvious, the Infinite potential of the initial condition is not fully realized at State 0 as the system has no complexity by which this coincident potential may be expressed by proliferation of finite relations. In order then that this potential is to have meaning in a Universal context the system must experience change that realizes some measure of an Infinite possibility, and if there is change then we will have measures of time. Thus it is that Infinity intrinsically embodies a time like potentiality just as Zero embodies anti-time and thus gravity, the ultimate zeroing potential of the cosmos.

In the commentary regarding Zero there was a distinction offered between the real world operational implications of that value versus our conceptualizations of the value that are the product of our intellectual architecture interacting within a social network of common understanding. While the latter is not completely invalid in a social context, it should be the natural law of Zero that provides a correct framework when evaluating systems constructed according to the natural laws. Of course the same must apply to our understanding of the Infinite and a proper understanding of this term should also emphasize an interpretation that is based on effective nature. Considering this, another perspective is to consider the means by which an Infinite measure might be observed, specifically, by what means would we declare that a measure of a natural system is an Infinite one. It is suggested that in order to establish such a declaration as factual a measurement or observation will need to occur. For the sake of argument let us accept that when we are measuring parameters that have fixed finite values that the concept of an instantaneous comparative measurement value has an absolute meaning, such as simultaneous arrival of a light beam from both of the ends of a metre stick at a sensory apparatus. Then by what mechanism is it to be expected that we may establish an instantaneous observation of an Infinite value? It is arguable at least that there are no such instantaneous means and any declaration of an Infinite condition implies not a measurement but a series of measurements in which each succeeding attempt to find a progressively greater finite value is exceeded by the measured parameter, in other words not an instantaneous realization of a value but rather a continuing process over time in which the Infinite parameter is always “ahead” of all attempts to fix an absolute finite measure. This then is simply another restatement of the time-like nature and potentiality of Infinity, and suggests to us that all that is, the entire history of the Universe, is in a sense an exercise in determining the true measure of Infinity.

An interesting conjecture develops from consideration of the State 0 conditions of Zero, One and Infinity if we regard these as mathematical identities, and it is declared that we should. From this perspective Zero is generally seen as the identity for the operation of addition in which N+0=N. The

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number one is then generally understood to be the multiplicative identity for which N*1=N. So then if we are to extend the symmetry there should be an operation and its inverse that finds definition, as do the above noted operations and their inverses, during the primordial state sequence such that N©∞=N, where “©” represents a new mathematical operation previously not considered that has Infinity as the identity. It would seem that a proper development of this concept, if in fact there proves to be anything to develop, is best left to proper mathematicians but several indications will be noted. First is that as N-N=0 and N/N=1 then N by the inverse Infinite operator from N will be ∞. The second is that such an operation and its inverse would be expected to have applications and potentially lead to new insights where Infinite series or developments are involved. Thirdly, as addition and subtraction in some respects bridge the definitions of the finite numbers and Zero, a more intuitive understanding of Infinity should emerge.

Early in this paper a declaration was made regarding the natural development of a Universe of relations from the initial Zero by Infinite condition. Expanding this, just as the number 1 was observed to be the product of the relation between a primordial Zero and Infinity, all finite values of measure are declared to be either directly, or vastly more often indirectly, the resolution of relations or ratios between Infinite conditions and are a reflection of the relative magnitude of those Infinite (and/or Zero) conditions. It is certainly to be expected that such a declaration will be met with some skepticism so somewhat of an example of this is offered. Consider the case of a spacecraft launched from a planet to a satellite destination 384,400 kilometres away scheduled to arrive 100 hours after departure. We would easily be able to compute a finite average travel speed of 3,844 km/h. However, at the halfway point of the trip both the planet and destination mysteriously disappear due to some unknown force. What then will be the finite speed of the spacecraft? It certainly will no longer be 3,844 km/h relative to anything meaningful as the two physical references that defined both the start and the end point of the journey on which the initial calculation was based are absent. Of course conservation of momentum will still be maintained and the laws of physics are unaffected, thus the crew of the craft would see no transient inconsistency in their motion relative to other celestial bodies that remained. They could elect to consider their finite speed relative to a new destination and this will certainly be a different value, say 50,000 km/h. Consider that the crew adjust course for this second destination only to witness this body plus the entirety of the star system mass disappear due to the same mysterious force. Undaunted the crew calculates their speed relative to the nearest stars whereupon the entire galaxy disappears followed by nearly all the visible galaxies in turn until the only remaining matter is at the farthest reaches of the cosmos, all the while calculating their speed relative to what remains at ever increasing values. At this point this same craft that set off at 3,844 km/h must be said to be travelling at a large fraction of the speed of light relative to the next closest material object, lesser speeds simply have no reference or relevance. Then what should be declared as the speed of the craft when the last visible matter in the Universe has disappeared? Is it now travelling at Infinite speed or instantaneously decelerated to Zero speed, is there a difference? What is certain is that any declaration of a finite speed for the craft as an absolute is meaningless, it was only the relations to other objects each of which would also be travelling at Infinite or Zero speeds in isolation that made a finite speed declaration possible.

In fact there is no true independent finite measure of anything, say for instance, the author’s age or body mass, these are Infinite and unfortunately becoming more so all the time. There are ratios of comparison to other references to be sure, with the age of the earth or weight of some great elephantine beast for example, however these are all without an absolute independent finite measure themselves. As in a prior example, it may be helpful to visualize an object in question as suddenly having the Universe around it

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blink out of existence. What is the measure then of time’s passage, what is the one remaining objects mass and where is it going? The only remaining comparisons now will be to the constituents within the object, and if it is an indivisible elementary particle and possesses none then what will we offer for comparison? The answer of course is nothing at all and, yet again, we will have returned to the very first instant of time.

Different Sets

It is certainly appreciated that readers may struggle with conceptions regarding the Infinite as expressed here. To better understand resolved variable measures of Infinity which are omnipresent in developed states it is important to consider the time like aspect inherently implied. Another approach is to simply regard all measures of physical properties as inherently being at all times Infinite with the finite part of the term or expression representing the ratio to other Infinities. For example, instead of a single spacecraft in the previous scenario there will now be two, both of which will be launched into deep space side by side without a destination. Temporarily we will suspend consideration of all extraneous factors such as space-time curvature, boundaries of the Universe and interception by other objects or their gravitational effects. After the launch craft #1 is found to be travelling away from the origination at 10,000 km/h and craft #2 is travelling away at 5,000 km/h. After 10 hours of flight time it will be clear that craft #2 has travelled 50,000 km and craft #1 has travelled twice as far. The interesting aspect of this is that after an Infinite passage of time craft #2 will be an Infinite distance away from home yet craft #1 will have travelled twice as far and be at least an Infinite distance from home and also be infinitely far out in front of craft #2. If this is not the case then at some point during the journey the laws of physics as they apply to the two spacecraft differed from the laws in the rest of the Universe, or at least so it would seem. Regardless, when would such an adjustment to make it otherwise occur, and if craft #1 is not infinitely far in front is it now alongside craft #2 at an equal Infinite distance from home? It is suggested that the answer is that craft #2 has gone one Infinity of distance and craft #1 has gone two Infinities. This may be critiqued by statements such as “What (on Earth) does it mean to say that one craft has travelled twice the Infinite distance as the other?” The response to this is to note that the distance travelled by craft #1 is a certain ratio to a particular reference unit of length just as every other distance in the Universe is, it just happens to be that the unit of length in this case is the distance travelled by craft #2. The important point to note is that all units of measure are in some sense arbitrary and the significant aspect here is simply the ratio of that which is being measured to something that serves as a reference. In this case since an Infinite amount of time must have elapsed the appropriate unit of measurement will be one that is an Infinite reference. Also being declared is that differing measures of Infinity are valid and subject to the same mathematical rules and operations as finite values. It is of course acknowledged that equations containing both finite and non-finite values may have solutions that contain both finite and non-finite values and that Zero may in some cases correctly be regarded as finite and in other cases non-finite, more to follow regarding this.

The just prior conclusions are perhaps not so exceptional or even novel, yet there are deeper implications and a more complete understanding if we inquire further along the same lines of reasoning. Returning to the twin spacecraft thought experiment, some additional particulars will be necessary. Now, instead of travelling in a straight line the two craft will do equal parallel orbits in the same direction beginning from a common starting marker fixed relative to the body being orbited with each travelling at the same relative speeds as in the prior example. Onboard spacecraft #1 a log is maintained and on every orbit on passing the starting mark the total number of orbits it has completed is recorded.

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Interested to compare themselves to the progress of their twin, in a second log the crew of craft #1 also record the orbit they are just completing each time they overtake craft #2. After 1000 orbits the #1 crew examine the logs and note that the last value entered in each log is 1000. However examining the number of entries in their own log they discover there is a set of 1000 while the log for craft #2 has a set of only 500 entries, thus orbits completed. On receiving news of this the crew of craft #2, desirous of completing a number of orbits of equivalent size as their compatriots, consults their onboard mathematician for a solution to the problem. After a moment of contemplation comes the observation that the set of all entries in the log of craft #1 is a subset of the positive integers and that the set of all entries in the log of craft #2 is a subset of just the even positive integers. Recalling 19th century developments in set theory our math whiz declares a solution. All that is necessary is to convince the crew of craft #1 to accept a proposal to continue orbiting and recording forever. As according to set theory then and since, the result will be a countably Infinite natural number of orbits for craft #1 in one to one correspondence with the Infinite even only natural number of orbits for their craft which it is theorized results in a tie.

From the example given and the no doubt countless equivalent ones that could be formulated it should be apparent that conventional set theory size equivalence based on cardinality of Infinite sets, as currently formulated, is not applicable to real systems or their constituents. However, for the sake of argument we will consider some possible responses to the proposal by the hypothetical philosopher captain of craft #1. Firstly, it is by no means certain and there are many indicators as to the theoretical impossibility and thus irrelevance of the proposal, which is to say that it requires the craft orbit an Infinite number of times. As each orbit must be some “finite” measure of time then this will require an eternity or Infinite amount of time in total, yet it is highly questionable that the entirety of any Universal history will be Infinite in length. Secondly, all observers stationary with respect to the marker able to witness any single orbit of the Infinite sequence will observe that craft #1 completes orbits at twice the rate of craft #2. Conversely, none of these observers will witness any period of any length of time during the entire Infinite sequence in which craft #2 completed the same or a greater number of orbits than craft #1.

Thirdly, the response could address the issue of cardinality of sets. In the case of some Infinite sets of elements, for instance the set of all drops in an Infinite ocean as compared to the set of all thoughts in an Infinite mind, there may be some argument that a one to one correspondence is logically correct. Such a position could be based on the fact that there is no means of demonstrating other than a one to one correspondence thus the two Infinite sets must be of equivalent cardinality. It could then be “proven” by declaring that each drop is countable and the set of all drops is countably Infinite and that the same could be said for the set of all thoughts. Therefore a bijection or mapping of each and every element of the first set exists to an exclusively paired element of the second and vice versa, and a one to one correspondence exists between these two sets of thus equivalent Infinite cardinality. In even this case it is arguable that the relation is ambiguous and such a pairing does not necessarily exist. However it will be argued more specifically that in the case of the two spacecraft, and thus also with respect to the cardinality of the set of all natural numbers as compared to the set of all even natural numbers, that instead a two to one correspondence exists. In the case of the two spacecraft the relation between orbits completed by the first craft to orbits of the second craft is not arbitrary, it is known, and the set that best describes this relation and what is actually observed contains an Infinite sequence of two orbits of craft #1 paired with one orbit of craft #2. Likewise, there is a commonly recognized pre-existing relation between the set #1 of natural numbers and the set #2 of even natural numbers that is best described by an

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Infinite solution set containing pairings of two elements of the first set with one of the second. Notably in this case all the elements of set #2 are also elements of set #1 yet the reverse is not true. In other terms, the cardinality of the set of all elements that are in set #1 but not in set #2 is Infinite while the cardinality of the set of all elements that are in set #2 but not in set #1 is Zero, thus demonstrating the inequality. The point being, we should not find ourselves on the one hand appreciating the two to one correspondence when regarding the counterintuitiveness of the relation between these sets as having equivalent cardinality, as is frequently noted elsewhere, while simultaneously disregarding the two to one relation when actually attempting to determine the comparative cardinality of the two sets. It is certainly an imperative that there should be consistency in representations within mathematics if it is to function as a means of communicating a common numerical and relational understanding of that which is governed by a common collection of Universal laws. That we recognize an intrinsic two to one relation in any capacity then argues for that same relation in all contexts. Otherwise, we may invent all manner of hypothetical mathematical relation and, by the employment of prejudiced inconsistent logic, devise as suits the occasion any number of proofs to substantiate these. This may provide engagement of the mental faculties in a lengthy discourse, but it will have nothing to do with a Universally applicable body of symbolic representations and methods used to quantify and describe real physical systems, which it is declared exemplifies the ideal construction of that which is mathematics.

It may appear to some readers that the topic in question is being belaboured, that the point has been made and it is intuitively obvious that there are differing finite measures of the relations between Infinite quantities. The reason for this extended discussion is that it is expected that there will be resistance in some circles to alternate conceptions regarding the relations between Infinite sets. Some critiques may have as their basis a perceived failure to appreciate a proper understanding of the Infinite within this effort. The response to this would be that yes, ideas expressed here are not consistent with current understanding, rather it has been the intent to establish a new conceptual framework. To that end it has repeatedly been asserted that the Infinite not typically be regarded as a static instantaneously realized or realizable identity as so often seems to be the case elsewhere. Instead it is asserted that due to the time like nature inherent in Infinities that such values should be generally regarded as a dynamic progression through an Infinite numerical space.

Possessing Infinite Possibilities

Returning to the set of all natural numbers, it is suggested that this set contains elements that do not and have not ever existed as an active measure of anything. What is meant by this is that there are unrealized elements of the set as no entity has contemplated, calculated or communicated these values, and they are greater than the maximal measure of the system. That is, they represent a relation that exceeds the value necessary to describe the present data state of the Universe. Thus a new concept is proposed for classifying the numerical elements of sets wherein the realized status of values is recognized as a potential, though in practice somewhat hypothetical, consideration. That is, numerical elements of a set may be realized, unrealized or unrealizable at least. Realized values are ones that are known to have relevance in the present data state of the Universe. Examples of these are 197, 1/12, or 3.14159 and other “everyday” numerical relations known and commonly recognized as applicable to real systems, though as previously noted these values may not always have been “realized”. The unrealized are extremely large values or ones of great precision which may not presently have applicability to real systems or for which the certainty of realization is questionable. The unrealizable are values so extreme that it would not be expected that these values will have relevance to real systems

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within the entire history of the Universe. Such values for example may require greater than the present information content of the one system in order to just approximate their description. It is arguably the case that these unrealizable values are mathematical unicorns and in fact not numerical at all, instead being fictional ideals that are never used in the computational dynamic that is the actual workings of the Universe(s). Several aspects to the classification of values according to their applicability to real systems should be apparent. First, as noted, the boundaries between these classifications will always be ambiguous. Second, as time and the history of the Universe is in some sense no more than a continually expanding definition, thus realization, of the initial Infinite potential, there is an implied Universality of realization of Infinities for which any relation is established. In other words, when the one system “discovered”, that is decoupled from the initial Infinite potential, for example “eightness” once there was eight of something, the possibility of some aspect of the Universe being described by the value eight became at once and ever after a potentiality throughout the system. All these factors together combine to support an alternate perspective when considering the comparison of two or more Infinite sets, which is to regard each set as engaged in a paired maximum value realizing progression, with every other set with which there are any logical or mathematical relations, into the future or extent of an Infinite numerical dimension. Therefore the fallacy in the one to one correspondence of the set #1 of all natural numbers to the set #2 of all even natural numbers is in not recognizing that this requires comparing the cardinality of set #2 at an implied Infinite realization that is the unrealized future of and twice the corresponding progression of the “concurrent” cardinality of set #1. It is therefore suggested that the correct view is to regard each set as having equivalent hypothetical greatest instantaneous realized values, thus concurrent though non-specific progressions through a numerical space that is temporally extended, in which case the cardinality of set #1 is always twice that of set #2.

Previously, and repeatedly, it was declared that a clarifying perspective may be achieved by regarding the measures of a physical system as the ratios of Infinite particulars. Elaborating, all measures may be considered to be functions of Infinity, or rather orders or powers of Infinity. Thus everyday values such as 12 metres or 7 years are then “shorthand” for expressions 12 × ∞^0 metres and 7 × ∞^0 years respectively. An example that may better illustrate this develops from consideration of a Universe containing initially no objects other than a single particle that we specify as being of one unit charge or negative one unit charge. We may suppose that this is an electron and has a mass approximating 0.511 MeV. However, it is just as correct to say it is a muon or tau particle with a substantially higher mass in either case, because in that state of existence those particles are undifferentiated from the electron. In fact by prior example the particle in question is degenerate to State 0, possesses the entire mass of a Universe and is none of these from a certain perspective. Exceeding this, if we contemplate the previously declared connection of all possible Universes to a common State 0 this supposed lepton may be regarded as the embodiment of the entire mass of an Infinite Multi-verse system from an expanded perspective. For each of these possibilities it should be clear that specific applied measures of mass are arbitrary and there are just relations to the totality of all that exists. If we were to contemplate a second particle being added to the example Universe, neither of the two existing particles will have an absolute mass and we are left to debate whether each is half the total mass or some indistinguishable unequal distribution. As in the prior development the question of specific values of properties is dependent on an observer or third party frame of reference that can measure the relative behaviour of any two examined entities and still then all that will be known is differing ratios of each relative to the others and to the totality.

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Continuing the development of orders of Infinity, it is apparent that the set of all natural numbers would be an example of a first order Infinity, in other words it has one Infinite degree of freedom or dimension, a suggested value being 1 × ∞^1. One critique of this might be as follows, “how is it that we know the quantification of all natural numbers (positive integers) to be 1 × ∞^1 and not 2 times or 0.5 times or some other value?”. The answer to this is that in absolute terms we don’t, what we may know is simply the comparison or ratio to another reference just as was the case for Zero order values. So if we collectively agree that the basis for the cardinality of all number will be a declaration that the set of all non-zero natural numbers contains 1 × ∞^1 elements then we have established a reference no more or less “real” than the metre or second. Continuing, within the framework being described here it will be apparent that there is a complementary solution to that which has been described elsewhere for the “size” of the set of all real numbers, specifically this would be declared to be a second order Infinity as there is in this case one Infinite degree of freedom or dimension in the expansion of the sequence and another for the Infinite decimal representations between any two specific selected values. However, were the reference proposed as a “standard” above to be adopted then it should be noted that the set of all real numbers would be declared to contain 2 × ∞^2 elements. Naturally there would be the understanding that “Infinite decimal representations” presumes there is any relevance to real systems for an Infinity of intervals or subdivisions between any two values. Based on present quantum mechanical understanding, it would appear that there may be no real aspect of the Universe that can be subdivided without limit in a meaningful way and thus such limitless decimal representations will contain values that are unrealizable. None of the immediately preceding is particularly exceptional, of more interest however is the application of these considerations to all that has been previously stated regarding the initial Infinite condition. Previously it was stated that this Infinite state embodies all possibility instantaneously realized. As all possibility includes all of the dimensionality of the Universe, or all Universes, then this is arguably Infinite degrees of freedom, instantaneously realizable. This is suggested to be the value 1 × ∞^∞, the realization of which would allow for the decoupling of as many first order Infinities, such as the dimensions of space and time (and number?) of an individual Universe, as are necessary to express an ideal Infinite realization. Conceptually, an interesting development arises from consideration that greater values than a highest order Infinity are not possible. Specifically, based on the reciprocality of the Infinite and Zero, it is declared that beyond the primordial Infinity of state 0 are the progressively decreasing negative Infinities. As previously suggested, when we are discussing all numerical possibility perhaps a “number line” or complex plane are limiting perspectives, and a concept for this is contemplated though a thorough discussion that would fully integrate the imaginary and complex numbers is beyond the scope of this effort.

Zeroing In,

It should be apparent that the initial Infinite condition represents a potentiality so irresistible that only an equivalent and opposite irresistible influence could forestall an instantaneous realization of all possibility. This instantaneously experienced super history would effectively leave no events yet undone which in a sense would be the annihilation of any and all future possibility. The annihilation of any and all future possibility may otherwise be described as the irresistible Zero condition of State 0. Thus it is apparent that Zero and the Infinite are related opposite aspects of the same potential, the influence that constrains the initial Infinity is the Zero aspect of that same Infinity. And the influence that overcomes the initial Zero condition is the Infinite aspect of that same Zero condition. Once again, there is paradox and symmetry in the nature of real systems. If we consider Zero and Infinity to be reciprocally interchangeable representations coequal in nature, and it is being declared that we should,

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then all that has been declared regarding Infinite sets and orders of Infinity will also be true for Zero and orders of Zero. Therefore if the Infinite energy (positive time) potential of the one system at State 0 is declared to be described by a particular Infinite measure then we must acknowledge that theoretically this must be opposed by an equivalent Zero measure and thus there would always be a zeroing (negative time or gravity) potential opposing any Infinite potential. Conceptually it should be noted that this Zero measure is not being regarded specifically as an infinitesimal under a hyperreal or surreal number system as is presently understood elsewhere, this is instead a system of zeroing influences that are all 1/∞ reciprocals of Infinities for which the ∞ may be any of the Infinite considerations previously mentioned. Concluding, if there is a set of all real numbers “n” that may be represented as n × ∞^0, and a set of all Infinities possessing a theoretically equivalent cardinality that may be represented by n × ∞^1, then logical consistency requires that there be a set of all values represented as n × ∞^-1. This latter set logically (in a simple sense) has equivalent cardinality to the two sets prior and will contain all the reciprocal pairings to the members of the set of all first order Infinities. Thus it is that there is a set that might elsewhere be described as infinitesimals that here will be described as the set of all zeroing values. We will return to this presently.

To date, when considering the set of all reals as a “number line” the chosen form is one for which a common finite length representation is used for equivalent numerical intervals, usually integer intervals, and the line is regarded as extending to Infinity in the positive and negative directions from a “Zero” reference. It should be apparent that an alternative approach for which an Infinite reference is substituted for the Zero reference is possible. Continuing to mark integer intervals, the “number line” will in this case mark off ∞+1, ∞+2, ∞+3 and so on in the positive direction and ∞-1, ∞-2, ∞-3, continuing in the negative direction. At first glance it would appear that these two number line approaches cannot be reconciled, that is, a point on the 0 symmetric line cannot be equated to one on the Infinity symmetric line. However, when considering the simple configurations of the primordial states it becomes apparent that reconciliation is possible. That is, for these states the Infinite potential is in the preliminary stages of decoupling into an expressed reality and the result is that values that are differentiated for developed states may be synonymous with the Infinite condition. For example, at State 0 it is arguably the case that there are no other operative existing values than Zero, one and Infinity (and from a perspective also negative one). Therefore the entire extent of the open number line is 0, 1, ∞ and the closed number line (circle) would be 0, 1, ∞, -1 and then back to 0. It may in fact remain the case that even in developed states that these relations of finite number to non-finite number are not broken but are instead merely extended as an expression of an ever developing Infinite potential, arguably this is the operative mechanism driving Universal history. That we are not able to establish the specific relations between what we characterize as finite and non-finite values then may simply be regarded as an epistemological consequence of the limits of our ability to measure the numerical extent of the system for any particular parameter of interest. It is declared here that the Universal whole as a coherent interrelated mechanism will not be so limited and in fact the nature of Universal dynamics is a continuing expression of, and solution to, the evolving finite to non-finite relation.

There are additional aspects of the relation of number to itself to consider. Returning to the traditional number line representation the question is proffered “is it necessary that the number line representation be viewed as extending to Infinity”? Arguably, a number line may be envisaged which is represented as being of a finite overall length for which equivalent numerical differences are represented by progressively smaller length representations. For instance, contemplate a number line such that the left extent is bounded by the value 0 and the right extent is bounded by 1. It should be immediately apparent

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that the Infinity of all real numbers from 0 to 1 may be regarded as infinitely many points along such a line having absolute finite or non-finite decimal representations as to position. However, as has been made evident here and elsewhere, the Universe should not be regarded as a system governed by absolute values, rather the expressed data state of the one system at any point in history should be considered as an expression of the many and complex present state of relations of its constituents. Therefore, rather than regard the points on our 0 to 1 number line as decimal values they will be regarded as the relation between 0 and 1, that is, ratios or fractions of the numerical distance from 0 to 1, such as ½ or 1/1000007 or 999/1000, noting that each and every point with a decimal representation on the line could be so described. None of this is new, in fact what has been described is simply a segment of the traditional number line from 0 to 1, which is then analogous to the interval between any two sequential integers, viewed from an unremarkable perspective. Continuing, if we regard the set of all values between 0 and 1 as representing one of the two Infinite degrees of freedom of the set of all real numbers, as in there may be Infinite digits to the right of a decimal point, then the cardinality of this set may be described as 1 × ∞^1 per the reference previously proposed. It should be apparent that for decimal representations there may be Infinite digits to the left of the decimal point as well and that this will then be the second Infinite degree of freedom for the positive real numbers and will have the same cardinality, barring considerations of Universal extents, as the set of all values from 0 to 1. Therefore if the cardinality of all real numbers from 0 to 1 equals the cardinality of integers from 1 to Infinity, then returning to our 0 to 1 number line we can envision symmetry with respect to unity and a number line twice as long that describes the cardinality of all positive real numbers. The length equivalence of the number line from 0 to 1 as compared to from 1 to ∞ is most evident when considering the reciprocality with respect to unity of the values to the left of 1 versus those to the right of 1. That is, if we regard the value 2 as being midway between 1 and ∞ and the number 4 as being midway between 2 and Infinity and every further successive power of 2 being successively half the remaining distance to ∞, then there will be a reciprocal value of 1/n for each of these values n that will be equidistant from unity, that is 1, on our proposed number line. Furthermore, as we approach 0 in this representation it will be evident that we will be describing points at ever smaller intervals of 1/n, thus larger values for n, such that no finite value for n will solve for precisely 0. Thus it should be evident that for every extremely large finite value n progressively closer but never reaching ∞ on our hypothetical number line there will be a correspondingly small reciprocal finite value that approaches but never reaches 0. In fact (presuming convention) the position that is exactly equidistant on the right side from center as 0 is on the left is occupied by the value ∞. Of course the representation being offered is still in some sense of Infinite extents due to the certain understanding that the number line proposed here may be regarded as a projection onto the number line (x axis) of a planar curve with equivalent distances represented for equivalent intervals and rapidly increasing measures of y as the numbers represented approach ∞. What this demonstrates is nothing new mathematically, it is more an exercise in visualization of the dynamic reciprocality of 0 and ∞ and to reinforce that these mathematical ideals are aspects of the same universal ideal and wherever and whenever one may encounter a 0 value it may, exponentiation aside for the time being, be substituted with an equivalent 1/∞ value. A critique is envisaged with respect to the cardinality of the right side of our hypothetical number line being actually greater than the left side since the right side, in order to be a complete representation of all real values, must include values that are not just integers but also those that are between any two integers and include a decimal representation. The response to this should be obvious at this point, the primary relation of the values on the right to the values on the left is their symmetry about unity (reciprocality). It would make no sense to declare that a value exists, such as for instance 1.618034, without acknowledging the potentiality at least of 1/1.618034. In fact any logical means employed to extend the cardinality of the right side of our

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hypothetical positive real number line must necessarily imply a corresponding extension of the left side and the two sets will retain equivalent cardinality. (Note that the balance of the real numbers is the obvious symmetric representation about 0 that requires no additional explanation.)

Some additional comments are indicated regarding the nature of the 0 and ∞ points on the proposed number line or circle representation for the set of all real numbers. Specifically these were regarded as ideal 0 and ∞, that is they were considered as being dimensionless in order to simplify the discussion. It has been argued elsewhere in this paper that this is not the proper context in which to regard these non-finite conditions. In order to satisfy any arguments regarding conceptual consistency that may arise, it will be acknowledged that the set of all real numbers is the set that was previously described as satisfying n × ∞^0, and that 0 and ∞ in fact should be viewed as zeroing and Infinite number sets of the same Infinite cardinality as the set of all real numbers n. That being the case it will be apparent that the prototypical number “line” as it has been constructed here for the finite will be a model for the Infinite and zeroing numbers as well. The logical next step of course would be to try and integrate the orders of Infinity into a common representation as an open or closed number line encompassing the full range of finite and non-finite numbers. The difficulty in this is that the dimensionless 0 and ∞ also delineated the ideal Zero width boundaries of the prototypical finite number line. If we are to be consistent with regards to representations and methods then neither of these boundaries should continue to be considered dimensionless for such a logical progression. A consequence of this is that it would not be logical to consider that the ideal delineation, of for instance the Infinite limit or asymptote of the finite number line, will then become synonymous with the 1 × ∞^1 numeric value. Instead it will be synonymous with the limit or boundary at which the greatest finite and least Infinite measures approach convergence. Compounding this is that the finite and Infinite approach to this limit of convergence is best described using Infinite representations that may then recursively be subject to the same logical imperative for dimensionality of the Infinite. Adding further complicating factors, it must not be forgotten that the Universe is essentially a process that from a perspective is no more than a resolution of Infinite possibility into finite realization, therefore in a natural mathematical system, an evolutionary redefinition of the differentiation and relation of finite number to non-finite number. And there is still the issue of incorporation and integration of the natural representation of number that is the continuing fraction. One final comment before proceeding, it is suggested that the utilization of lines and planes and their developments are not necessarily the best geometric analogs for the relation of number to itself. A more natural geometric representation, one that may lead to deeper insights, may take the form of a circle that expresses the inherent trigonometric nature of a developed space time, or a helix through orders of Infinity, or perhaps a toroidal helix that demonstrates a profound symmetry in the grand equation that is our mathematical Universe, or perhaps something as yet uncontemplated.

Based on the preceding commentary, it would appear that the development of an appropriate model for the relation of every number to the entirety of numerical possibility is a topic of considerable complexity in its own right and worthy of a separate effort. Pursuant to this, it may be discovered that some aspects of mathematical understanding, such as discovering the hypothetical relations that would allow for translation and conversion of the finite to the non-finite and vice versa, will forever be beyond the reach of human capacities. Perhaps such challenges will be the occupation of engineered intelligence here or elsewhere. Fortunately notable insights may be achieved with a simplified understanding that foregoes in part the need to resolve all questions of Universal mathematical truth.

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For example, awareness that there is a simple reciprocal symmetry between 0 and ∞ in and of itself leads to an expanded understanding. It is generally considered to be the case mathematically that the expression n/0 has a solution that is undefined. However, from a certain perspective this is one of the first equations the Universe had to solve in order to exist so such a position is untenable for the mathematics of real systems, otherwise we might expect the system to halt on a divide by Zero error. Of course this does not happen as it is in the nature of the one system to solve by physical expression all valid mathematical operations on any and all mathematically valid terms. With the certain knowledge that we may substitute 1/∞ wherever we encounter a 0 term then it will be evident that n/0 is equivalent to n∞ and is not undefined in any context. Likewise, the equation n × 0 = 0 is in fact demonstrably not a general solution for real number values of “n” solving to non-finite Zero values. When considering measures of real systems, the correct solution is that n × 0 = n0, as a finite number multiplied by a non-finite number is not reducible to a simpler result without knowledge of the specific finite to Infinite relationship for a particular parameter at a particular time. Since the result as shown falsely appears to simply multiply n × 10, the solution is more clearly expressed by the equivalent n/∞ result. There may be an inclination to regard increasing multiples of Zero as indicating increasing potentiality for zeroing opposition to other potentials, thus a clarifying argument is in order. Just as Infinity as a concept is inseparable from change and time, the same may be said for Zero. Therefore a perspective on zeroing potentials is to regard these as measures with a finite rate of advancement or progression through a numerical space that expands in measure at an Infinite rate. Therefore a simple Zero value quadrupled, should be interpreted as 4 times the rate of progression of a 1 × 0 progression through a numerical space that will nevertheless be concurrently expanding outward at an Infinite rate.

Continuing, the following basic mathematical relations are proposed to further this development, therefore with unless otherwise specified, 0 and ∞ representing ∞^-1 and ∞^1 respectively and n representing a member of the set of finite real numbers;

∞ × ∞ = ∞^2; 0 × 0 = ∞^-2; 0 × ∞ = 1;∞ / ∞ = 1; 0 / 0 = 1; 0 / ∞ = ∞^-2; ∞ / 0 = ∞^2;n × ∞ = n∞; n × 0 = n/∞;n / ∞ = n/∞; n / 0 = n∞; ∞ / n = ∞/n; 0 / n = 1/n∞

As should be expected, addition and subtraction of non-finite values does not provide a means for normalization of these values and for typical applications will not produce a simplified result;

∞ + ∞ = 2∞; 0 + 0 = 2*∞^-1; 0 + ∞ = ∞^-1 + ∞∞ - ∞ = ∞^-1; ∞ - 0 = ∞ - ∞^-1; 0 - ∞ = ∞^-1 - ∞

For 0 - 0 there is a conceptual complication, the obvious solution is 0 - 0 = 0 which is 0 - 0 = ∞^-1. However, theoretically there is an argument for resolution to 0 - 0 = ∞^-2. This latter result does appear to raise concerns regarding mathematical consistency, perhaps this is a topic requiring additional exploration as to implication and the conditions of applicability. It also should be noted that the actual numerical measure of a zeroing value increases as the zeroing potential that opposes an Infinite potential decreases. Continuing, as was the case for non-finite values, addition and subtraction of non-finite values with Infinite values does not produce simplified results. The situation involves additional considerations for addition and subtraction of non-finite values with Zero or zeroing values.

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Specifically, the status of 0 as a finite or non-finite representation becomes critical. One general rule may be to regard 0 as finite when measures involve abstractions, such as the balance owing on an account or the number of goals scored in a football match. There are other situations involving tangible things that likewise will indicate usage of a finite or ideal Zero due to their being defined by consensus as having a particular ideal discrete character. In such a case this is implied in the use of language, which is an abstract means for representation of a common reality which we ourselves have established with such implication and application as we collectively agree upon. Thus when one person declares that all of their family members have left the house leaving 0 remaining, there will be little sense in another declaring that based on microscopic forensic evidence some vanishingly small portion of their family remains there still. Regarding that which our common use of language has not defined as having a discrete character, it is still certain that for the majority of questions of measure that we encounter in our daily lives, extraordinary precision in these measures of things is simply not relevant to our furthered interests. However, when the subject involves derivation of precise mathematical models or measures of the nature and behaviour of our Universe and its subordinate mechanisms then certainly there are arguments for employing the non-finite usage of 0 as the default approach.

What then is actually represented by 0 in such “precise” mathematical models or measures of real systems? Again we should defer to nature for an explanation and this will be as has been repeatedly declared, it is simply the reciprocal of that aspect of the initial State 0 condition that is an imperative to realize the full expression of an Infinite ideal. Therefore, if an Infinite potential is an imperative to increasing data complexity by decoupling a near Infinite complex of interactions amongst a multitude of identities, then a zeroing potential opposes this by simultaneous negation of true independent measures of identity through a perpetual connection to the common definitions that are the Universal laws of nature as established at the primordial conditions. If the Infinite potential leads to an energetic expansion of Universal realization that overcomes the Infinite gravity of the initial condition then the zeroing potential is none other than this gravitational force itself. This gravitational force is manifest as a mathematical bias in the dynamics thus equations of all later events (a similar concept presently is in circulation elsewhere) in order that such events should trend towards that which is most in keeping with the conditions at State 0, in other words, a singular, condensed identity in a collapsed spatial and temporal framework. Therefore, celestial singularities such as black holes are simply manifestations of a locally realized zeroing mathematical ideal. Furthermore, the differing mass and associated gravitational field bias are consequential to the actual non-finite measures of Zero that describes each of these physical objects, measures that are made finite in relation to the totality of the one system. Another aspect of the Zero condition as an ideal is a suspension of the individual variable measures of existence as possessed by an individual identity such as is represented by fundamental particles. Thus it is that the zeroing potential of the many and various particles is a reflection of the extent to which their measures of existence approach an ideal Zero value which is never realized. For example, an electron represents an intrinsically zeroing potential that is closer to the ideal than a tau particle and this is reflected in the lesser relative mass of the electron. A critique of that which has been declared here may take the form of a challenge to all of these examples cited as being subject to finite measures and representative of finite definitions. The response to this will be yes, that is precisely the point that is being emphasized. In other words, as State 0 represents the ultimate realization of a Zero condition and non-realization of an Infinite condition, and in order that the Infinite condition will exist as such, then the Universe must progress towards realization of the Infinite condition and non-realization of the Zero. And since this process of an evolving Universal history is modeled on the simple Zero by Infinite condition that defines the first finite relation of State 0, then all finite conditions subsequent are, again,

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normalized Zero by Infinite relations that in our frames of reference may be perceived as finite or absolute. That we do not typically observe realized Zero or Infinite conditions as measures of our common experience is then no more than an expected consequence of our definitions being present at a highly developed state in the overall course of Universal history.

Returning to a conceptual appreciation of that which is the Universal zeroing potential it should be expected that this zeroing effect will oppose the Infinite realizing potential that is represented by change. In other words there should be an aspect of reality that opposes change and is a product of the same mechanism that is gravity. This is certainly none other than inertia, the natural tendency of an entity to resist a change in its relative motion, state of rest will be excluded as such a condition is an ideal that never exists as an absolute. Thus it is that all physical objects will be subject to inertia and also gravity, both of which are the influences of a common conceptual ideal. It should come as no surprise then that we find ourselves in a Universe which exhibits a notable symmetry in the nature and measure of their complementary influence on real systems.

Another aspect of the great zeroing potential will be observed as an operative imperative within that which is commonly described as the uncertainty principle. It should be evident that the progression in science toward theories of ever greater explanatory power will require observations and information gathering experiments to examine subjects at ever finer resolutions. As is well known, there is inevitably always a point at which the minimum energy required for an effective measurement interaction will itself result in a significant disturbance to the motion or condition of a measured subject. Therefore it is not possible to achieve arbitrarily fine precision simultaneously for all measurable parameters of any entity of the system, particularly when investigating quantum scale events. The Universe thus has an effective limit of minimum resolvability as is explained through various mechanisms of present quantum mechanical theory which has been previously explained here as a natural consequence of the relation between Zero and the Infinite. In other words the mechanisms of the one system such that these are functions of a developed state, by definition oppose denormalization of resolved Zero by Infinite conditions in order that there will be a developed state at all. Attempts to measure the system at ever finer resolution will in effect result in partial negation of the extended entangled relations of the developed state locally in the experimental domain and therefore the reemergence of Zero by Infinite, therefore by definition, indeterminate and probabilistic conditions. It is from consideration of this that certain concepts regarding the necessary existence of negative identities arise. Specifically, positive zeroing potentials, such that these are developments of a Zero ideal, necessarily as they more closely approach that ideal become progressively less differentiated from relatively equivalent hypothetical negative zeroing potentials. As the Zero ideal is in fact an aspect of the initial condition that is perfectly and thus symmetrically realized at State 0, and as all positive zeroing values may still be regarded as positive thus non-symmetric finite progressions through an infinitely expanding numerical space, then the existence of symmetric negative zeroing potentials operating likewise, and thus negative measures generally, is implied and specifically not forbidden.

It may be noted as a critique of this preceding explanation regarding the Zero concept that logically much of the suggested irresolvability to a perfect ideal is extensible to all finite number and not just Zero and we are thus left with no absolute values as results in any mathematical examination of real systems. The response to this would be to say that theoretically this is correct and is a point that has been reiterated. It would be granted that for practical matters, for instance when we are adding or subtracting finite values to achieve non-zero results, we are somewhat justified in disregarding the uncertainty or

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zeroing potential component of the result as by definition this must be extraordinarily insignificant for all finite values above the scale of the infinitesimal. However, when 0 presents as a separate term, or intermediate or final result in an equation without a corresponding finite significant and all that remains is the zeroing potential that is represented by the symbol 0, then this Zero term should not be disregarded for all circumstance, specifically, where a differential outcome or relevance will result. Otherwise, where is the logic and mathematical consistency in even presenting an expression or term containing 0 if it is absolutely non-relevant and the result we are seeking is undifferentiated? For example, when we ask “what is the meaning and measure of an expression such as 7 × 0 ?”, then the implication is that there is at least the possibility of some differential understanding versus simply stating “0”, else there is no logical purpose served by the former expression stated as is. So it may be asked how all of this understanding should be practically applied? The answer it is suggested is quite simple, treat Zero and Infinite values in expressions as simple algebraic terms, provided the proper consideration has been given to the question of concurrency of these non-finite values. And then if residual Zero or Infinite values remain in the solution then evaluate and make a determination as to the applicability and relevancy of these to the utility and purpose of the mathematical inquiry in question.

As an alternative development along similar lines as the concepts expressed above, it should also be considered that all values or measures of real systems may potentially consist of a nominal value term and a specified or implied variance or tolerance which it is suggested in many cases may be considered synonymous with uncertainty. In the case of non-zero real values the typically far greater magnitude nominal value term may be regarded as the significant primary component and the comparatively small tolerance will generally be insignificant and thus we may be well justified to disregard the tolerance or variance altogether. However, where the nominal value is Zero the tolerance by definition will be the only significant component and by default should be considered when solving equations containing Zero value terms. Otherwise, we are on the one hand stating that we are concerned with absolute differences by the very inclusion of a Zero term, or expression that solves to a Zero term, while on the other hand then regarding the Zero variance component as immaterial. Again, there should be consistency in mathematical approaches and methods if such methods are intended to describe the behaviours of real systems.

At this point hopefully a deeper understanding of the nature of number in the early Universe has been realized. Previously it was suggested, that when impossibility is countered by the Infinite potentiality then the result is necessarily something in between. It is neither a Zero realizing emptiness nor a split second realization of that which is as great as the totality of all ideas, constructions, relations and events that the sum of all intelligence may contemplate, instead it is simply a beginning.

Logically Speaking,

Paradoxically, it was not part of the original intent of this effort to address the relevance of formal or classical logic to a Universal mechanism that arises as a consequence of the Zero by Infinite initial condition. All projects must have some limits as to their scope and breadth if they are to achieve a timely completion and it should be clear that a complete development of a system of formal logic from Universal first principles would be a massive undertaking. However, there are certain implications that require clarification for the sake of a consistent overall argument.

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A logical paradox was significantly conceived in 1901 that demonstrated contradictions in the then understood theory of numerical sets. To paraphrase the paradox as stated by the Stanford Encyclopedia of Philosophy; if R is the set of all sets that are not members of themselves, then such a set is not a member of itself only if it is a member of itself. As a demonstration of the explanative utility and completeness of the certain and many propositions developed in this effort, it will now be argued that the paradox in question, rather than being a true paradox at all, solves immediately and elegantly in a manner that implies the nature and character of all existence. Continuing, it should be inescapably apparent that the primordial ideal Infinity is in fact synonymous with the perfect set of all sets, in other words,, the identity that embodies the potentiality that realizes all possible configurations or sets of all possible elements that may ever exist. Ironically, it is noted that the set of all thoughts in the minds of inquisitive beings in the Universe(s) that may contemplate set theory, also arises as a consequence of potentialities that are some subset of, or are elements of, the initial Infinite potentiality. However the initial condition is not described simply by an Infinite potentiality, as a reciprocal and inseparable aspect of this potentiality is embodied that is the set of all configurations of that which must not or will not ever exist. Continuing, as the Infinite potentiality which is the progenitor of the full continuum that is Universal histories, the initial condition (set of all sets) of State 0 contains as its first element the initial Zero state representation of the one system (another description of the initial condition) in which no possibility has been realized as well as the potentiality of all later Universal states (also a description of the initial condition). As such the initial condition may be regarded as the set of all sets that contain themselves as members.

Yet as the reciprocal Zero aspect of that same Infinite potentiality it does not contain the Infinite potential that is the full realization of all Universal history, it is instead the equivalent antithesis or that which prevents instantaneous realization of all possibility. Therefore in this sense the initial condition, which by definition contains the potentiality of all sets of any kind, has as an element the Zero aspect of itself which is the progenitor of the set of all later state zeroing potentials which oppose Infinite potentials by negation as has been previously explained. Continuing, the set that is all such zeroing potentials, which is of an opposing nature to the set of all Infinite potentials, is synonymous with the set of all sets that are of an opposing nature and thus must not contain themselves as members. By the fullness of these arguments it is apparent that the initial condition is synonymous with the set of all sets that in their Infinite potentials contain their Zero aspects, that in their Zero aspects do not contain their Infinite potentials. Additionally, there is the consideration that all finite relations of any kind, such as will be used to describe all typical sets and the properties of their constituents, are derived from Zero by Infinite relations or the products thereof. Therefore, when contemplating all perspectives of the State 0 condition then it is by definition simply the set of all sets that are not members of themselves while being members of themselves!

It is at this point that many traditional logical approaches will declare for the preceding to be an absurdity and an unsolved contradiction. Yet to even exist the Universe must solve a seemingly impossible related paradoxical argument, that is, in order to not exist the Universe must exist in so far as the definition of non-existence will require a reference to the potentiality of something existing. Stated another way, in the absence of potentiality, such as that which may create Universes, then there is no mechanism for resolving and defining an absence of potentiality. And yet by existing a definition for non-existence will be found that describes the initial condition from which it must proceed. It was in appreciation of these seemingly irreconcilable paradoxical considerations at State 0 that it was previously declared that the classical Law of Non-Contradiction must not hold at the beginning of time.

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It should be evident that the Law of Non-Contradiction is by its self-limited definition not an absolute law governing all truth relations if a single violation can be demonstrated, unfortunately such a violation was immediate and complete at State 0 as such a violation is a precondition of existence. Some attempt at salvage may be developed along the lines of stating that the impossibility of the statements “A is B” and “A is not B” being simultaneously true, while violated in some “sense” at the beginning of time, is not violated in that there is another perspective in which the exclusivity holds true. The problem with this defense is that it presumes that there is the possibility of a coincident interpretive process at the beginning of time that could formulate multiple perspectives. It should be evident that the realization of any process, including intellectual and logical developments requires an extended temporal frame that is unrealized at State 0. That which has been described in this paper as aspects or perspectives on existence at the beginning of time has been for the purpose of argument and explanation, with the understanding that such perspectives only find definitions relative to the information processes of later developed states. For instance, the evolved temporal frame developed of the Infinite initial potential that we presently find ourselves in. By definition at the beginning of time all ideas, thoughts, contemplations and rationalizations are but one absolute contradictory ideal.

In a Universal system born of a contradictory condition and expressive of an intrinsically paradoxical entanglement of identity realizations perhaps merely the title “Law of Non-Contradiction” speaks to a limited appreciation of the interconnectedness and complexity of existence. Therefore, in contrast to a preceding comment, and in appreciation that the examples given are representative of many instances of inapplicability, it is suggested that this “law” be regarded as not relevant when considering the significant mechanisms of Universal systems.

Returning to our 1901 paradox, if the Zero by Infinite initial condition is effectively the set of all sets that are not members of themselves, that is not a member of itself only if it is a member of itself, then what are the further implications beyond the noted non-universality of the Law of Non-Contradiction? It is proposed that a second implication is that a fully expressed resolution of the paradox in question implies a time-like consideration. The reason for this is that the resolution, in order that it be fully defined by relations, is demonstrably not a static truth condition, it is instead a dynamic one. Put another way, as a fixed unchanging (static) truth at State 0 it is certain that there is no unambiguous logical resolution of the paradox, however the paradox does resolve in that a Universe of entity arrangements and configurations having contradictory natures does exist, therefore the paradox must be representative of a non-static truth. If we then proceed to develop a further explanation of this, it will take the form of a sequence of paired opposing truth states for which the realization of one state implies the other state. Demonstrating, if it is realized that the set of all sets that are not members of themselves does not contain itself as a member, then such realization denies the truth value of itself and implies the opposite truth state, thus it will now be realized that the set of all sets that are not members of themselves does contain itself as a member. This latter realization then denies itself and implies the first realization and so on as an Infinite sequence of repeating states of the relation between contradictory elements of an argument. What is important to note is that such a state sequence is not completely realized in the State 0 condition, it requires temporal extension such that there is a data state and then a subsequent data state, this is change, change is time, the Universe must become temporally extended and evolve in order to resolve the paradox.

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There is an additional implication, the preceding may be restated as, the instantaneous truth value that is the resolution of the paradox is a superposition of one state and an equivalent and opposite state. This necessitates that existence will include the potentiality of an equivalent yet not equal existence such as may allow negation of existence.

Restating the preceding arguments again, the truth value (data state) of the resolution, in order that the superposition of contradictory states is resolved, cycles between equivalent and opposite values and this must occur in time (have a frequency); restating again, the resolution of the 1901 paradox is a wave function; and once more, the logical paradox regarding the set of all sets which, by definition contains and embodies all possibility including all instanced particle representations resolves to a wave function. Therefore all entities in the consequent Universe must be representative of the initial logical imperative from which they derive, the imperative is a wave function of equivalent and opposite states and thus they will all be found to possess this same cyclical nature. In summation, the 1901 paradox is something else altogether, rather than being unsolvable, it is a dynamic imperative that mandates an extended Universal realization of a multitude of instanced entity representations (members of the set of all sets) that each necessarily possess a cyclical wave nature. There are no doubt many further implications of the paradox that have not been addressed here, for example the theoretical implication that the Universe must develop intelligent process that may contemplate and thus realize the full resolution thereof. Perhaps, this will be a focus of a subsequent effort.

In addition to the Law of Non-Contradiction, also known as the Law of Contradiction, there are two other laws or first principles in classical thought on logic that warrant mention. Of the Law of the Excluded Middle which declares that with regard to a proposition and its negation one and only one of these is true, all that will be said of this law is that it patently does not hold for real systems. It is violated necessarily by quantum mechanical processes and has been sufficiently critiqued elsewhere and dismissed here by the fullness of implication. Regardless, certain arguments regarding the Law of Identity which follows will necessarily apply to or further qualify this law as well.

The Law of Identity is so foundational and apparent that it may appear to many that it is not subject to critique or qualification. Discerning readers may appreciate that this nevertheless has already occurred within this effort as regards real systems. This law which has been stated in various ways over centuries declares simply that a thing is identical to itself, or in other terms, an existent is that it is and is as it is. The exception being taken is that an absolute independent nature or identity is implied for existents, which has already been demonstrated to be not the case with regards to real entities. There simply is no independent definition of existence for anything except a Universal totality. Therefore in an absolute sense the only entity type for which the law holds is a Universe itself. It is proposed that the Law of Identity would be of far greater applicability to subcomponents of real systems if it were restated as “A is as A, that it is as A and not as B, from the point of view of C”. It should also be remembered that argument has been previously given that “A is as A” only at a single temporal definition. In subsequent states “A is as A was” must include the allowance for some necessary measure of change having differentiated the two states of “A”, otherwise if “A” is unchanging then it is not in a state of relation and then “A is not A” it is instead nothing at all.

A critique to much of the preceding commentary may focus on a perceived preoccupation shown by the particular focus directed at classical syllogistic logical ideals. Arguably it has been the limitations of pre-modern logical development that has actually led to the present diversity in modern thought such as

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is represented by fuzzy logic, paraconsistent logic and other theory. Without getting into a protracted commentary, a response to the critique would be acknowledgement, and, an expression of concern that elements of the reasoning employed subsequently do appear from a layperson perspective to demonstrate an intellectual heritage from classical thought on the subject that may harbour certain biases. It is suggested that to the extent that current logic theory and methods do not provide for the possibility of dynamic or cyclic truth states or dual truth contradictions (dialetheia) then such theory and methods may be limited in terms of their applicability to questions regarding the behaviour of real physical existents, particularly those of a quantum mechanical nature.

Obviously the potential implications from the foregoing review of logic suggest a need for potentially substantive reformalization. For this reason the author is and has been hesitant to employ existing principles of logic in this exercise, the concern being that these may not in fact be axiomatic and hold true for all circumstance. For instance, the Principle of Bivalence that argues for a two-valued true or false exclusive logic instead of a many valued logic cannot by similar argument as has already been given be a general principle applicable to the logical considerations of Universal systems. It is declared that even the argument form reductio ad absurdum, which declares true any statement for which the denial results in a contradiction, is subject to qualifying consideration. Specifically what is meant by the term contradiction and what are the types and consequence of various contradictory relations? Certainly the cyclically dual natured existents that are the constituent particles of the Universe are contradictory, they are particles, they are waves; as waves they are of a nature and then an exactly opposite nature; as particles they are of 0 size and they span the breadth of the Universe; they are real, solid, tangible and illusory, ghostly reflections of primordial entities that exist solely as abstract relations to other abstract relations; and finally they have properties and existence in the present and other properties and an existence bound to the beginning of time. Interestingly, another logical principle, The Principle of Explosion which declares “from a contradiction, anything follows”, adopts a surprising implication in the context of arguments offered here. Specifically, it will be acknowledged that from a contradiction, the initial Zero by Infinite condition, anything follows, as in a Universe of near limitless possibility.

One additional example of the alternate logical perspective that this effort suggests is as follows. Consider the example of a simple single phase AC waveform and the truth table for the electric potential that we may wish to resolve wherein “A” will represent a positive, and “B” a negative potential exists. If the actual “instantaneous” potential measured in a tested circuit is positive then it is realized that “A” is true and “B” is false. If the potential measured again is negative then the result is “A” is false and “B” is true. If however the potential is at ~0 which necessarily occurs periodically then the result will be that “A” is false and “B” is false. Now it could obviously be noted that this is all well enough granted but the point is that these differing truth table outcomes are for different points in time so there is no logical inconsistency. Whereupon a counter argument may be offered that accepts this if it is acknowledged that each of these results taken singly do not adequately describe the true and complete nature of the test subject. For instance the knowledge that at a point in time the system had an “A” nature and not a “B” one does not in and of itself lead to a thorough understanding of the existent. In fact in the absence of any one aspect of the nature of this phenomena then it is undefined and there are no aspects of its nature. Therefore, if we then insist upon a singular truth state for an existent which has a temporally extended truth by nature then we are electing to consider the temporal extension to be collapsed else it will have a partial and thus no “real” definition. This implies that the resultant condensed truth state must then be a superposition of all truth statements regarding the existent that are valid at any point in time. Thus we find in this case that all of the following results (A=1, B=0) (A=0, B=1) (A=0, B=0) and (A=1, B=1),

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where 1 is true and 0 false, are all applicable to the existent in question. Even so it must be evident that what is known solely from a simple true false assessment of a dynamic truth is a limiting perspective. Arguably the “truth” of the existent as a waveform is only properly understood when truth is expressed as a waveform.

Lest there be a perception that a distributed relational truth gives support to a form of moral relativism, it is declared that in fact there is only one single real truth moral or otherwise, that is the absolute which is represented by the present complete data state (description) of the Universe in its entirety. That an impractical omniscience is thus required in order to possess absolute truth beyond question is acknowledged, no apologies given. A critique of such an intractable epistemology may receive the reply “if it is so, it is so, and does not require our acceptance”, a search for truth is by definition a quest that will last so long as the stars yet shine. The point is that all truth, let alone ultimate truth, is elusive, complex, intertwined and to some extent inseparable from the context in which it finds a definition. After all, the only full and complete description of a thing, anything, is the thing itself in the Universal context which defines its existence.

On One Uncertain Future

All that remains before concluding is to address a few remaining scattered implications that prior comments suggest and inject some commentary on our present and future, presuming that we have the latter of course.

A lengthy development was previously offered as to the necessary nature of Fermions (spin ½ particles) and Bosons (integer spin particles). There was no equivalent commentary specifically offered regarding their organization into families or the present proliferation of a host of hypothetical particles. With regard to the families of Fermions each of which contains a particle of 0/3, 1/3, 2/3 and 3/3 charge for which each succeeding family is populated with progressively heavier mass versions, the following is offered. That the masses of fundamental particles and the relations between masses of related particles such as electrons, muons and tau particles do not appear to be discrete or have discrete relations argues that these (actually statistical) mass values are not a direct consequence of the primordial state development herein described. That there appears to be just three particle families of differing mass raises suspicions of a counterargument in consideration of the three dimensional spatial system of our Universe. A possible theoretical explanation could be built along the lines of considering that the ultimate realization of all the potential charge identities await the primordial state development of three dimensions. However, the mass is a function directly of the primordial condition and propagates and is distributed therefore through the primordial states. Thus while the three dimensional imperative that must be strictly maintained for particles in the subsequent extended temporal states binds their charge definitions to the three dimensional primordial state, their masses are not given to the same restriction. Thus it is theorized that they can be bound to the progressively reduced mass definitions of State 1, 2 or 3 (State 0 of course being associated with the Higgs identity). It should be apparent that the familial masses as initially established would not appear from our perspective to be equal to the masses of the same definitions in a present context. The relational masses of particle instances are after all necessarily a function of just how many total instances there are in a state of relation at any point in Universal history.

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With regard to the proliferation of hypothetical particles, additional curled up dimensions and complex primordial geometries that are being proposed elsewhere the author has no specific expertise by which these could be evaluated. What will be offered in response is the observation and challenge that every new aspect of the Universe required for a consistent overall model of what the Universe is, requires a complementary explanative mechanism for why such an aspect must be and the manner in which it propagates from an initial imperative. At some point of regression each of these aspects, including mathematical and geometric ideals, must recouple and become synonymous with a precipitating simplified principle. Realized complexity is emergent or we are left to explain how a Universe must come to initiate with a partially evolved dynamic. This is not out of the question as a potentiality, it will be noted however that now science will have entered the realm of the metaphysical. The author does not find this objectionable, the question is whether science will be satisfied at having proven that there are in fact unfathomables forever beyond the reach of science. It should be appreciated that even theories regarding a cyclic repeating Universal possibility do not completely remove these unfathomables.

The realization that the 1901 paradox, published several years later by Bertrand Russell, essentially solves for the Universe as it exists under a particular logical approach was not an expected outcome of this endeavour. Interestingly, while constructing arguments supporting an alternative resolution it became apparent that an extension of the same logical approach may provide insight into a mathematical development where previously there was no expectation of a clarifying explanation. With an understanding that reality contains entities and measures of entities that are of one truth value and paradoxically also of an opposite truth value, a more intuitive understanding of the conceptual dynamic of the imaginary and complex numbers is achievable, and in contrast to a preceding indication, will be addressed specifically.

Though the mathematical formalism and methods with which imaginary and complex numbers are currently understood may or may not remain unchanged, it is not unreasonable to consider that from a conceptual basis at least there is a solution to the square root of -1 that is not a static solution but is instead the dynamic relation between 1 and -1, yet another example of a superposition of truth states. Therefore in a similar fashion to the solution for Russell’s Paradox, when it is declared that the square root of -1 equals 1 then such an answer denies itself and implies a solution of -1. In now familiar fashion, realization of -1 as the solution denies the truth of itself, whereupon it is 1 again and so on. Thus the imaginary unit i which is the basis for the imaginary and the complex numbers may be regarded as a state wave or cycle alternating between coincident truth states 1 and -1 that are a product of a Zero relation yet demonstrably not synonymous with 0. The symmetry is obvious and apparent between such an explanation and the primordial state propagation of identity and equivalent and opposite negative identity that was the basis for all wave functions such as is later represented in electromagnetic phenomenon. And once again it will be necessary that there be temporal extension in order that such a relation between identity and negative identity is differentiated and defined thus mandating a continuing Universal progression. In retrospect symmetries such as these between physics, mathematics and logic as it relates to set theory should be expected as these disciplines are aspects of a single explanatory mechanism for all Universal behaviour. There is a temptation to consider that one of these developments propagates into the others, however, in keeping with prior arguments it is proposed that all are codependent aspects of a single development. Thus it would seem logical that the imaginary numbers are a consequence of the wave nature of existence which is a consequence of the necessary dynamic of the truth state of the imaginary numbers. Once again, there is nothing that exists that does not prove the existence of something else and by so doing defines its own existence.

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Regarding the many and varied mysteries of quantum entanglement it is apparent that these supposedly counterintuitive propositions regarding quantum subsystems may be logically deduced from simple realizations. The observation that in the initial and continuing debates regarding entanglement the potentiality of these realizations was missed is exemplified in the assumptions made in critical responses to these “counterintuitive” propositions. Interestingly, statements such as “spooky action at a distance” raised as objections to the entanglement and relatedness of for instance, the possibility of paired spin states between entities at seemingly great physical distances, were actually suggestive of straightforward self-solving conceptual resolutions for these arguments against entanglement. That is, if it is a logical impossibility that the spin direction of a particle light years distant may be suddenly and instantaneously “discovered” by detection of the opposite spin direction of an entangled partner particle then it may be inferred that regardless of the considerable apparent spatial distance between the two entities this is not necessarily indicative of equivalent separation with respect to all aspects of relatedness. It is declared here that in fact these particles are always adjacent as long as they are entangled with respect at least to their primordial definitions from which the concept of spin finds definition and resolution. An equivalence to this was declared certainly by John Bell in his papers of 1964 and 1966. It must be kept in mind that separation in space beyond the primordial state definitions is in a sense illusory and is simply a manifestation of the vast interlinked chain of entangled relations between entity instances. To the extent that such phenomena fail to establish a rigorous spatial differentiation then spatial separation will not be realized.

Regardless we do not even need to consider even such a mechanism as this to come to terms with entanglement. As a critique, a response to the obvious and intuitive expectation of entanglement as an aspect of existence may take the form of declaring that it is neither obvious nor intuitive. A counter response then may be formulated that states “why should spin or any of the less readily measured properties of entities be chosen for consideration?”. Instead let us consider the charges of particles and their anti-particles and their identities as such. Therefore we create an experiment in which a particle and its anti-particle are created, for instance an electron and a positron. The experiment is designed such that one unspecified particle will exit the apparatus via one of many possible trajectories that go into orbit around the Earth and the other will exit in an opposite direction and travel off into space without the experiment recording or indicating which of the paired possible directions each of the two particles followed. We can now declare the two particles to be in a superposition of states, either could be and both in some sense are the electron and the positron, there is no issue to be had with this. After some number of years we send up a probe and check on our particle in orbit and determine that it is a positron in one specific orbit and thus we suddenly are able to determine that the other particle now some number of light years distant is an electron having travelled in a now known specific direction. Is this mysterious, counterintuitive, unexpected in any way? How else should this or could this work? Now a critique of this may take issue that the behaviour of the two particles will be different within a magnetic field and that will reveal the identities of the particles at once, or that the particle in orbit if a positron may annihilate with ordinary matter revealing itself early. The response to this in either case is that we then certainly did not design our experiment correctly such that an early determination of particle identities would be prevented. Any interaction whatsoever whether intentional or not is still an interaction thus an experiment. If an electron interacts with the positron in orbit then from a Universal perspective another observer has just run an experiment in the course of the duration of ours potentially invalidating our results, we are not in a special class of observers. To say that we are is not science. From this it should be evident that in part the mystery of entanglement is more specifically a topic of

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interest from a design of experiments standpoint and a commentary on the relative ease with which some properties of entities can be measured or determined as compared to other properties. It is suggested that in our grand and mysterious Universe that there is little difference between what is known or what is possible ultimately to be known about an existent and the full and complete reality of an existent itself.

What seems to be commonly missing from many commentaries regarding quantum entanglement is a declared awareness that at all points, preceding, during and after the execution of such experiments that it is not just the target entities that are subject to quantum mechanical considerations. In fact the entire experimental apparatus plus the observer / experimenter are also statistical realizations of complex entity relations. That a property of an entity has a definition at all is a function of that property being in a state of definition due to observation by other entities in a propagating information cascade. Beyond the influence of the informational “wave front” of this cascade the entity property in question will be expected to exist as a superposition. Thus it is that an experiment that completely or partially “blocks” the propagation of “awareness” of a resolved entity property will then maintain a superposition of states for the entity from the perspective of all frames of reference that are in the blocked region. Note that in a sense it is the “awareness” of the information as to the state of an entity that collapses a superposition of possibilities into a singular condition. Clearly this implies an extensibility of indeterminacy due to the limits of information propagation as being applicable to larger subsystems to include macroscopic objects. Unsurprisingly, recent developments seem to support this conclusion.

It should be evident that this paper expresses a very broad definition of entanglement in which all entities are engaged in relations that may be so characterized. Typically, entangled relations discussed elsewhere tend to focus on the pairing of states of a particle with one or two or a few other particles or objects. It is suggested that initial “simple” entanglements may, through additional interactions, become distributed complex relations between collections or groupings of entities that mask the initial relationship from direct observation without negating the reality establishing influences of these initial relations. It is further proposed that the totality of identity establishing relations in the fullness of expression is in fact the entirety of the history of existence and a thorough understanding of the extraordinary complexity so realized will reveal a true and complete natural science. Certainly there will be an expectation that ever more complex experiments and theory regarding quantum entanglement will lead to a more complete explanation of developed Universal dynamics. Experiments in which the actual experimental apparatus and detectors operate in entangled or limited related states or entangled states exist across multiple experiments are suggested. It will also be noted that due to all of reality being fully and completely a consequence of a Universal complex of such interactions that all phenomena must be an element of these interactions. Thus it is that gravity itself must necessarily be an element of all interactions and entangled relations, whether simple or distributed, and must be expressed as a natural mathematical bias in the consequent apparent distances between entities that is manifest over apparent time, that is itself a consequence of these same interactions.

Arguably, one of the most recognizable examples of the “counterintuitive” nature of the quantum realm arises due to aspects of the double slit experiment in which electrons or other particles directed at a screen with two slits will be seen to create an interference pattern due to their having a wave nature. This may be revealed as a pattern of successive dark and light bands on an opaque barrier that is caused by the peaks and troughs of waves proceeding from each of the two slits interfering with each other either constructively or destructively. The counterintuitiveness is supposed to be revealed when these patterns of interference build up over time even when electrons are sent one at a time implying that each

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electron interferes with itself. But this is what the nature of a wave identity would naturally imply, an entity that has an extended physicality defined by a distributed wave function and which cannot be described as having a specific instantaneous position. Were the electron to pass through one slot or the other and not interfere with itself would imply it possesses a persistent independent particle identity in the absence of an interaction or resolving interaction, a condition which has been demonstrated to be logically inconsistent. It is as if we are on the one hand acknowledging that these wave natures exist while simultaneously clinging to expectations of an underlying coincident true particle nature. The reality is of course that the extended wave expression of an entity and the particle expression are the same phenomenon, it is just that the particle expression is a more or less localized and thus a non-extended wave expression from an observer perspective due to the effects of or interactions with other extended or non-extended wave expressions having eliminated the extended potentiality. Such a collapse is seen to occur instantaneously precisely because the entity has a distributed physicality from the observer perspective that from the perspective of the entity itself is local. There should also be no expectation that these particle and wave forms are of an entirely antithetical nature and that a marked transformation occurs from one to the other. Rather it is suggested that these forms are differentiated in measure only and an entity may be regarded as progressing smoothly from one to the other.

As an example of the manner in which the propagation of primary influences may form the contextual basis for complex developed phenomena, one additional digression far afield is offered before proceeding. It is interesting to note the similarities between the concept of money as the medium of exchange in a socio-economic system, and energy as a medium of exchange in a Universal system. This suggests that “claims on units of energy” could arguably be the basis for, and the reserve currency of choice for, a Universal Theory of Energy Economics. In other words, economic viewpoints that fundamentally equate energy as money may be the model for decision making regarding the critical energy allocations of advanced civilizations. In a sense, even the stars themselves are subject to an energy denominated economic reality.

Much of what has been elaborated on within these pages would no doubt seem far removed from the everyday concerns of most. Thus when during the course of working on this paper a realization occurred that hypothetically could be of benefit generally then it was of course essential to include this. Previously it was declared that the progression we experience as elapsed time, rather than being an inexorable locally uniform phenomenon, should be regarded locally (at the quantum scale) as an entangled intricately interconnected progression of particle instance relations to other particle instances that may be discontinuous, cyclical and irregular. The overall appearance of a smooth gradually transitional or invariant temporal progression at the macroscopic scale is then a consequence of the statistical aggregation of a near innumerable profusion of these quantum scale events. It was suggested that at the scale of such events it is likely that particles may actually engage in temporal loops in which a tightly bound cyclical relationship with another entity by definition does not define a normal temporal progression. Of course these particles will be engaged in relations with other particles as well for which such temporal loops are not maintained. These additional energetic transactions, though establishing new temporal references, are not in and of themselves synonymous with a progression to a later historical state. Rather it is the tendency of persistent configurations of entities to gradually progress to less ordered configurations of entities due to these ceaseless interactions having an entropic bias that gives the appearance of an inexorable continuum of states that progresses forward in time.

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Deterministic transitions of ordered configurations to less ordered configurations may exhibit varying modes and rates of progression. Of additional significance is that transitions of order to disorder can themselves be more or less ordered as at some point the onset of chaotic behaviour may occur. So the question should now be asked “how is this of any benefit to any of us individually”? The answer is that the human body is itself an ordered configuration of particulate entities. And the process of aging is in a manner of speaking more or less an entropic process whereby the ordered configuration that is each of us experiences reorganization that is progressively more conducive to further reorganization. This naturally enough at some point in time exceeds the limits of controls and leads to a runaway deterioration in critical structures and death.

Therefore, if repeating patterns at a quantum level forestall the progression of time then the question at hand is to what degree the establishment of cyclic patterns and regular behaviour, such as carefully regulated respiration, can engender a limited realization of some small measure of a related effect at the scale of living things. Certainly there seems to be anecdotal references at least to the health benefits of regular meal and rest times, perhaps there is a mathematical or physics basis and not just biology behind this. And there appears to be many examples of nature employing cyclicality within the critical processes of organisms in order to forestall the onset of chaotic reorganization within living things. There are of course many reasons for conservatism in regarding such a potential, it would not be expected for instance that regular pattern establishment for normal human behaviour and micro behaviour would lead to measurable time dilation at the quantum level. Effects generally propagate from microscopic to macroscopic and not the other way around. However it is conjectured that some small reduction in the rate of cellular aging and deterioration may be achievable due to the relatedness of macroscopic processes to their microscopic basis. Of course moderation in the use of such techniques is indicated, an absolutely inflexible lifestyle of ritualistic behaviour is not being advocated here, there must be at least some elements of changed expectation or adventure in our lives or we are at risk of other modes of systemic deterioration. The final point is this, though time ultimately is inexorable and forward progression must continue, time itself is not entirely immutable, it also is subject to laws and driving influences and, though wildly speculative, perhaps therein lays an opportunity for extended healthier lives for those who can master certain techniques.

There have been frequent references to paradox within these pages. It should be apparent that many of these are not in fact paradoxical, and those that truly are, typically necessarily are. There are exceptions to this of course, the Fermi Paradox comes to mind. Other sometimes considered paradoxical scenarios such as Schrodinger’s Cat have obvious resolutions, in this case, once we realize that a superposition of states is relative to the observer and that the term “observer” refers to any and all observers such that a single particle can satisfy the definition thereof. In other words the cat knows if it is dead or alive, we as human beings are not among some ideal class of observers so much as we may think (best to avoid the dead cat does not know it is dead argument, a proper response is expected to be lengthy).

The great mystery for the author is none of these, rather it is our persistent prejudice in favouring an instantaneous and infinitely divisible truth possessing an absolute independent definition as being the nature and mechanism of reality. It is an interesting idea, unfortunately it is an idea that the actual observed nature and character of the one system argues to have limited relevance to the Universal reality in which we actually exist.

We Reach A Conclusion.

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This paper has been an interesting challenge to undertake. The author has attempted to express a consistent logical model of existence in the best manner achievable while desiring to maintain an approachable and somewhat visceral character to the effort. It will be the judgment of others that will be the arbiter as to the degree to which this has been successful. There are more formal modes of presentation that might have been employed certainly, as initially noted the structure itself is a bit unorthodox, and by intent it will remain unfinished in some degree. There will of course be those that will not accept that some of the ideas expressed were independently developed regardless of the author’s assurances. Suffice it to say that there have been many instances wherein the author as may have been granted some insight was given to both disappointment as well as validation upon discovering that a concept has been fully expressed elsewhere. Yet, this is to be expected, ideas as they are elements of an evolving explanative body of knowledge will tend to progress in a logical fashion at their own pace according to the development of a collective human intellectual process that is greater than each of us. Within this process we are all in some sense no more than processing nodes in a global information network. In other words, when the time is right for a new understanding then a vehicle, one or more of us, will be found to serve as advocates. Strange it is in some sense that as humans we are real physical manifestations, measurable, tangible yet impermanent and fleeting. Whereas it is the ideas and thoughts that have found accommodations in the minds and spirits of women and men, though ephemeral and intangible, that are possessed of a transcendental nature that reaches across time and space. For all we know, children of distant stars past, “present” and future are taught variants of the Pythagorean Theorem, Euler’s Identity, Maxwell’s equations, though the names will be changed the underlying concepts given unto them will be as we have received them.

If there are in fact contributions that increase understanding first disclosed here then this will beg for an answer to a question, if such as has been examined here is so readily apparent why then has it taken so long for such ideas to be presented, and why not by others certainly more qualified? The response is that this is then one paradoxical consideration that the author does find somewhat unfathomable. Without a protracted commentary on societal influences that may constrain the evolution of a body of human understanding regarding the nature of existence the question will be proffered “are humans naturally suited to philosophy”, and is it even necessary that we be so predisposed? Perhaps the Human organism is equipped with analytical capacities that are optimized to other more operational requirements instead. That is, in order that humans survive to reproduce so that humans will continue to exist, and contemplate existence, they must individually take actions as necessary to prevent the occurrence of critically reconfigurational events to their existing physical configurations. To facilitate this are we not designed to quickly process a variety of sensory inputs in order to narrow down a very large number of possible next actions into a single decisive best next action? An action calculated to give the highest probability of maintenance of our physical being. While ideal for survival in a dangerous world these same mental proclivities for simplification of a complex dynamic down to singular black and white absolutes may not always be ideally suited to a deeper philosophical understanding of such complex dynamics. This contrasts with our apparent design for intelligence that allows creative problem solving to improve long term probability of survival in scenarios that do not involve immediate hazards to survival. In these conditions we are more analytical, appreciative of detail and less intuitive. The concern is that when faced with a problem or question of a philosophical nature that requires resolution we may make quick intuitive decisions as to the most critical aspects and best course of “action” and then follow up this initial perhaps limited assessment with extensive and protracted detail development. Thus perhaps we are always at risk of building vast intellectual

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constructions on questionable foundations. If this is perceived as a criticism of the particular disciplines most identifiable with this endeavour then it would be replied that this is not the primary intent. The sciences in particular are subject to such introspection as has been made inescapable as a consequence of the rapid advancement of science itself, present truths are expected to be replaced or supplemented by later developments. That societal modes and models for economics, politics and other social disciplines should exhibit the same progressive self-examination is in the opinion of the author a hope yet unrealized. Certainly within the political and legal spheres there is little apparent appreciation and accommodation for the cyclical nature and periodicity of existence. This is not a gentle admonishment, everything we have been, are or may be is now at risk due to our stubborn adherence to outdated social mechanisms and general disinterest in a rigorous philosophical discourse aimed at establishing achievable goals and an overall direction for our kind. If all is lost due to our often short sighted preoccupation with the meaningless over the meaningful then we are surely cursed for all eternity by those who preceded us in vain and those who would have followed us in greatness but were denied existence. The very Universe itself will scoff and deride us as the projections of our last days travel outward at the speed of light across the cosmos as a warning to all of the ignominious fates given unto fools. Certainly it would be the very measure of hubris to expect to be granted forgiveness for such a callous disregard for posterity and utter rejection of our Universal obligations.

In closing, it may be said that the human mind may never be able to properly witness the true nature of the quantum realm or comprehend the vastness of the Universe. Perhaps this is so, yet by the efforts of so many before us, and with us, we have seen much by daring to believe otherwise. We are after all, each of us, born of an Infinite possibility. The author hopes the reader has enjoyed the journey so far, and found within these pages some small spark that may light the path forward on their own journey of discovery. At the very least it is hoped that you were unexpectedly entertained by this my first paper on philosophy and Universal principles.

Thank U for your time,

J.K. Holman© Copyright 2012, this document may be reprinted whole or in part for non-commercial purposes without prior approval provided there is attribution to the author.

Acknowledgements;

My Loving Wife who has indulged my frequent and untimely philosophical monologues with great patience, my brother for a particular insight into the Infinite that he provided, and also the local philosophical discussion group where I have had the good fortune to participate in many a lively debate on all manner of topics.

A collection of read and partially read physics and cosmology books by the following authors amongst others: Amir D. Aczel , James Gleick, Stephen Hawking, Ray Kurzweil, Michael Talbot

The many contributors to the search for understanding many of whose works were referred to indirectly in this paper that live on as fleeting images bound for the stars; John Stewart Bell, Niels Bohr, Satyendra Nath Bose, Louis de Broglie, Georg Cantor, Albert Einstein, Leonhard Euler, Enrico Fermi, Friedrich

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Gottlob Frege, Werner Heisenberg, Georges Lemaitre, Edward Lorenz, James Clerk Maxwell, John von Neumann, Emmy Noether, Wolfgang Pauli, Max Planck, Bertrand Russell, to mention a few. Previously they remained unnamed not to deny their great importance but rather to avoid unearned merit by association. And also as an element of a response to certain proclivities in the formal structured expression of fundamental inquiry of a distinctly human character that may on occasion inhibit a creative approach in the development of alternative explanations. Additionally, we should commemorate the meritorious efforts of so many more whose names and contributions have nonetheless gone unheralded, and to the no doubt many lives dedicated to inquiry which have been lost forever to arguably the greatest human tragedy, the catastrophically massive data loss that is individual human history unrecorded.

Various titles on CD-ROM and DVD from The Great Courses series, by The Teaching Company.

The Internet, compliments of the incipient Technological Singularity.

There are other acknowledgements that unfortunately cannot be given to named individuals and apologies are offered for this. This is a consequence of the philosophical approach taken on this effort, specifically, once the project was conceived as possible and shortly thereafter begun, minimal additional research of significance was conducted other than the definitions of terms. As was indicated in the term “primordial logic” in the introduction, it was always the intent to have the concepts evolve of their own accord from an initial realization with minimal external input, to the extent that this is ever possible. Thus while the preponderance of this work is original, it was inevitably the case that certain concepts expressed here overlap or are similar to those presented elsewhere that were known to the author prior to commencement of this effort without specific notation having been made at the time as to the sources from which these were first encountered. Regardless, the author acknowledges that all that has been presented here that is of merit is not so much a product of the author as it is a product of an extended human enterprise endeavouring to better understand the far greater Universe in which it lives. After all, none of us may claim independent ownership of a Universal truth, it is its own master, and we are each of us individually and collectively its subjects.

“That the Stars may Live, as One, of Many, a Neutral Imbalance was Created, of God,

The End.”

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