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The Omega Zero of Accelerating Expansion

Part Three: Symmetry Mathematics


Gevin Giorbran
January 24, 2004

I. Zero as the Whole of All Numbers

Most of us expect there to be some direct relationship between mathematics and reality, but what single number in ordinary math symbolizes the everything of numbers? We all are accustomed to using words such as Universe, existence, or being, and meaning them to symbolize the whole of all that exists. Why then, if it is so easy to refer to the universe as a whole, why is it impossible for a number to represent the whole of all numbers? What is so different about the nature of mathematics which makes all numbers impossible to represent as a whole?

We might conclude radically, that words such as Universe or being in fact have no meaningful application to nature, or perhaps it is more accurate to say that modern mathematics only represents the finite side of reality, and thus only partially represents reality. In the same way that the physical process of time could quite easily be secondary to a greater physical reality of timelessness, like a story in a book compared to the book itself, it is also possible that mathematics and even much of science conceptually models a sub-system of the primary whole.

There is actually a way to combine together or sum all real numbers into a single whole number. If we sum all positive numbers with all negative numbers, then the total combination of all in question would sum to zero, as shown below. 

(1 + (-1)) + (2 + (-2)) + (3 + (-3)) +... = 0 + 0 + 0 + ... = 0

Except mathematicians recognize there is a problem in the consistency of the result of such equations. In fact several different equations sum all real numbers yet each yields a different product:

0 + 1 + (2 + (-1)) + (3 + (-2)) + (4 + (-3)) + ...  =  1 + 1 + 1 + ...


0 + (-1) + ((-2) + 1) + ((-3) + 2) + ((-4) + 3) + ...  =  (-1) + (-1) + (-1) + ... 

So we conclude in math that the sum of all real numbers is undefined, which solidly makes sense because if the sum of all numbers did indeed equal zero then we would be faced with the most complete of logical contradictions, since zero would simultaneously represent nothing and everything in the same system. Instead, zero represents nothing and there is no ultimate number that represents all numbers, and the logical consistency of mathematics is preserved.

However, one rather significant issue has obviously been overlooked here. It is said that the sum of all real numbers is undefined, but logicians and mathematicians must have made a mistake when investigating the simple idea that all real numbers sum to zero. They failed to consider switching the value of zero away from nothing. They failed to consider the option of assigning zero the value of everything, a value equal to the combination and whole of all numbers, and then considering the consequences.

In essence we have in the past tested the hypothesis that all numbers might sum to zero, against a mathematical system where the value of zero is already pre-set to be nothing. In ordinary math, all values are relative to zero as nothing, so of course we would discover that all real numbers do not sum to zero. If it were not so, the logical consistency of mathematics would be destroyed. Yet we can as an alternative allow zero to transform into the sum and whole of all numbers, it just can't be done half way. As the saying goes, it's all or nothing. The proper test of zero as the sum of all numbers requires that we allow the value of zero to transform into a value greater than all other numbers. At first this seems nonsensical, because we are switching into an entirely different set of axioms.

If zero contains all other numbers, and becomes the largest value in a mathematical system, what then is the value of number one, or two? Which is greater, one or two, if zero is greater than both? If zero is the largest value, the sum of all numbers, the only way there can be lesser values is if we remove some measure of value from the whole of zero. For example, suppose that we take away a (-1) from zero. What remains? Zero is suddenly no longer an absolute value containing all other numbers. Something has been removed from it. But what value does the zero whole transform into to show that loss? The answer is simply that a now slightly downsized zero transforms into the value 1, which in this value system contains all numbers, except (-1). The principle here is simply that if we remove a negative one from the whole the value of zero records that loss by becoming a positive one. And likewise, as shown below, the number two is the sum of all numbers except (-2) is removed, and so on, and so on.

Figure 10. The value of 2 can be drawn on a number line as shown below:


Just for the sake of clarity, switching to the negative, the number (-1) is a combination of all numbers except that a positive 1 is removed. In removing a positive two the whole shows that loss by becoming the number (-2), and so on, and so on. The larger the number, the more is removed and set apart, and thus larger numbers have ever smaller values. Of course this feels odd to anyone at first exposure, and to a mathematician who is learned and naturally entrenched in the extensive field of mathematics, all this likely seems absurd and perhaps useless. Hopefully everyone is interested in and fascinated by logical consistency, and maybe wise enough to not expect to immediately see how a logically consistent set of ideas can be applied for some practical purpose.

All we are really doing is considering a system of values where positive and negative values combine rather than cancel. But because values on either side of zero in such a system decrease rather than increase, as we count into ever larger numerics, the numerical value diminishes. So the value of ever larger numbers moves toward becoming infinitesimally small in both directions away from zero. In fact the values of this system converge toward two points of infinitesimal value, an infinitely small positive value, and an infinitely small negative value, which we can denote as �numbers�. Indeed this is a very different mathematical system.

What makes this system relevant and easily related to the SOAPS model presented, is that the content and subsequent value of numbers decreases as we count toward greater numerics. In what I shall refer to as Symmetry Math, there are three extreme values, or three ultimate numbers. First there is zero, the sum of all numbers, which I refer to as the number Omega. Then in the same way the number one in ordinary math bounds the infinite decimals that exist between zero and one, there is a value of positive infinity in this system which I refer to as the number Proto, and a value of negative infinity which I refer to as the number Eleat.

In symmetry math, zero and the entire spectrum of values are infinite and yet entirely definitive. Infinity in this system is not merely a series or a process. As we remove a part from the whole, we can only create other values which are themselves infinite and definitive as well. We still have a logically consistent system of values, but unlike the finite system of values embedded in this system, all values in symmetry math are infinite, because every positive value contains all positive numbers, and every negative value contains all negative numbers. For example, a positive one contains all the positive numbers and also all the negative numbers except a (-1). The number one million contains all positive numbers, it merely contains fewer of the negative numbers than does the near zero and so nearly whole �positive one�.

The absolute smallest positive value that is possible in this system is produced by removing all negative numbers from zero, by grouping separately the positive from the negative (the extreme of grouping order). In removing all the negative numbers all the positive numbers remain. This is the smallest possible value in symmetry math. Nothing more can be removed. One of the more elegant features of this system is that although the two smallest numbers are points of infinitesimal value, Proto and Eleat are themselves each half of the whole.

+ + (-) =    =  Ω  =  0


I. The General Probabilities of State Space

The astronomer Allan Sandage once remarked, �The expansion of the entire universe is the most important single hard scientific fact of cosmology�. We might then consider how the discovery of accelerating expansion might reveal the deep future in equal measure to how the deep past was revealed by Hubble�s discovery of red-shifted nebulae. We now begin to study the general probabilistic features of the proposed SOAPS model to consider how all identifiable sets would influence temporality, perhaps establishing the partition of a many-worlds universe. Utilizing here exactly the same rational as it has been held that a greater number of disordered states influences the entropy and temporal direction of a system, we are attempting to understand the why of cosmological expansion, gravity, electromagnetism, the strong and weak forces, in the same way we understand the why of entropy, by viewing the probabilities of all conceivable states.

Boltzmann�s order-disorder gradient, or the wedge model, allowed only an indeterminate estimate of probability influence on cosmological time from an ambiguous body of disordered states. This new model, in that the measure of states is bounded, leads to a new field of probabilistic study only here introduced. Improving the specificity of the wedge allows us to clearly recognize the influence of four distinct groups of states, allowing us to compare the percentage of probability influence between the four conditional directions of freedom in state space, expansion versus contraction, and lumpiness versus smoothness.

The diagram below considers the evolving location of a single system in the SOAPS model. Set A or the Alpha set includes all states which are more positive than the present state of the system, and represents an always growing counter influence of states related to the past. The larger set B includes all states which are less positive than the present state of the system, which we will refer to as the Beta set, and being the dominant attractor, relates to the future. Set C includes the two groups adjacent the position S of the system, the two groups more smooth and more lumpy than the state, which also includes those states which are near the average density and are thus more immediately available to the system.

Figure 11: Probability Groups


If we consider probabilities from the position of the positive alpha state, at no time is the probability to travel toward zero greater, since from that position in state space the beta set includes the total of all states minus alpha, while set A is empty. We would expect then an unconflicted probability without needing to escalate would drive or attract conditions (all spatial directions) toward becoming more negative, which inevitably involves expansion and the creation of a positive volume (matter space-time).

It is easily recognized that as a temporal system changes its location in an initially divergent state space environment, moving nearer to the position shown in figure 11, the rate of transformation relative to the superstructure of state space would decelerate at an ever decreasing rate in alignment with zero, gradually slowing as the measure of states in the alpha set increases, and the measure of states in the beta set decreases. The countering influence of the past-like conditions of set A, which are not normally considered due to our present failure to include an absolute zero boundary state in our modern conception of all states, are here recognized as having considerable influence upon the probabilistic flow of time, especially as a system approaches absolute zero where the competing sets approach equalization. The simple proposal is that the influence of past-like conditions in the alpha set can be equated with gravitation and the influence of the beta set can be equated with Hubble expansion (excluding late-time acceleration).

Generally, the measure and probabilistic influence of set A is always the lesser compared to the Beta set, with the influence of set A growing until the two sets become equalized as the system approaches zero. However it should be noted that as the system travels away from the alpha state the momentum of time would also be moderately influenced and so initially slowed by a growing measure of pos�sible states adjacent to the contrast gradient's basin of attraction, specifically those states equal or near the average density of the system in set C, which naturally compete with the much broader axis of states along the density gradient. In fact the probabilities become increasingly more complex and predictive as we consider the grouping order of alpha in competition with the symmetry order of omega.

Once a space-time system enters the Period of Convergence, where the measure of states in group C begins to decrease, all previously divergent pathways of time crossover into a far different environment where the volume of state space narrows, so that all available temporal directions invariably become aligned into radial trajectories toward the single omega state of zero. During convergence the inevitable future begins to more directly influence the past. The specific destination of time also shapes the past or our present. In a very real sense a zero future being the neutral balance of all positives and negatives necessarily prepares the past in order to actualize itself. Convergence reaches deeply into the past, forcing temporal systems to become systematic and orderly in preparation for the collision of all temporal systems with zero.


An analogy we might consider of Omega�s forceful ability to influence the past is if we deem some future event probabilistically inevitable in the life of a human being. Let�s imagine a person living in the American continent who will inevitably be at the top of the Eiffel tower exactly at noon in one week�s time. This single future state then dramatically changes the potential events in this persons life, limiting the probability of more distant travel, eliminating the possibility of remote travel that would make the journey to the tower impossible, and dramatically increasing the probability of a method of travel toward the future goal of events. As the date of the event approaches faster modes of travel become ever more probable until finally some particular course toward the tower becomes inevitable. The inevitable future state does not dictate a specific means or specific time of travel, it maintains degrees of freedom although all have a common conclusion. We can imagine all the possible methods, and times, of how this person might travel to the tower, imagine this as a cloud of potential (each realized in the many worlds scenario), and beyond that cloud we can imagine seemingly normal events which are made impossible.

The oddity for us is of course that in our reference of time, the effect occurs before its cause, however, there is already an interpretation of quantum theory in place, the Transactional Interpretation[30] developed by John Cramer, which recognizes the influence of the future. Based upon absorber theory originated by Wheeler and Feynman and time symmetric Lorentz-Dirac electrodynamics, the Transactional interpretation describes all quantum events as a �handshake� executed through an exchange between future (advanced waves) and past (retarded waves), therein causing the collapse of both wave forms. As Cramer writes: �The absorber theory description, unconventional though it is, leads to exactly the same observations as conventional electrodynamics. But it differs in that there has been a two-way exchange, a �handshake� across space-time which led to the transfer of energy from emitter to absorber.�

In convergence we discover the reason for the distinctiveness of the wave functions which shape space-time and the entire partition of Many Worlds. In that our inevitable zero future requires all space (beyond the collapsing event horizon) to stretch perfectly flat simultaneously, such a future necessarily reaches into its past (our present) and dictates particle structure (protons and electrons) as well as particle relationships or configurations necessary for that balance to occur, in the time allotted between the present state and omega. From our perspective within the product of past and future influences, we merely observe the retarded wave, but as Cramer states, �The transaction is explicitly nonlocal because the future is, in a limited way, affecting the past�When we stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been traveling for a hundred years to reach our eyes, but the advanced waves generated by absorption processes within our eyes have reached a hundred years into the past, completing the transaction that permitted the star to shine in our direction.�

It is possible to recognize even at an intuitional level, that a zero future would influence matter in the specific ways that we observe forces presently influencing space-time. An increasingly neutral future would force like particles to repel and opposite particles to attract in order to balance the distribution of particles evenly, this force acting in opposition to the counter influence of the past toward grouping matter into dense bodies, first at the level of gravity slowing expansion, trying to re-collapse the universe, then at the level of the gravitational collapse of particle matter into galaxies and stars, and finally at the particle level where the strong force bonds positive protons. We can recognize an ever more stringent necessity of positive and negative pairs built into a distant past.

A zero future would necessarily force complex particles to eventually decay into single particles, hydrogen atoms that can be distributed into orderly columns and rows, a symmetrical chequered pattern. This is the hidden role of the weak force, to counter the grouping order actions of the strong force, eventually forcing all complex particles to decay in preparation of distributing all particles evenly through space during a late-time Einstein-Bose condensation phase near absolute zero (note that the strong force appears here to be unifiable with gravitation over the electroweak interaction). So the general proposal then is that the why of electromagnetism and the weak force is the product of increasing symmetry built into the gradient of states approaching perfect flatness. The why of gravity and the strong force is the counter influence of all past-like states cast in the role of conservation of the past, as well as maintaining a precise measure of grouping order and positive density relative to the density gradient. Note that the influence of a converging state space near zero is not considered in the big rip scenario but here we recognize that convergence requires a preparation process of increasing symmetry in the finality of time.

Eventually in this approach, in recognizing the struggle between the past and the future, between grouping and symmetry order, we depart altogether from a view of time as a dimension and recognize that time in our surrounding space travels in all available directions. In a complete quantum cosmology all forces of nature are probabilistic and the proposal here is that the superstructure of state space and an otherwise free flow of time actualizes all force in nature and all physical structure. In other words, what we think of as the direction of time is the sum of individual directions in space moving both forward and backward in state space, toward the past and toward the future[22]. The density of stars and galaxies, and also individual particles, are retarded time, while the cold and empty expanded space between the galaxies, and between particles, is advanced time. Gravity and the strong force are literally consequences of time moving backward while expansion, electromagnetism, and the weak force are time moving forward. The world around us is a tapestry of time directions.

Notably, this would seem to eliminate the possibility of temporal paradoxes. If an observer could somehow manage to intrude on a past-like state, all temporal evolution from the instant of the intrusion would proceed probabilistically free from the observer�s expectations of the future. Simply the presence of the traveler changes the overall dynamics of probabilities, similar to the butterfly effect. But since the process of time travel would require that any time traveling observer re-establish a past-like macrocosmic state in their own evolved dynamic, such intrusions are more likely members of the temporally impossible or imaginary realm.

II. Infinities in Cosmology

The idea of Many Worlds existing in whole infinite form was until recently almost always treated with skepticism, in large part due to our confusion of zero and non-existence. The integrity and definition of the infinite has long been an unresolved mystery in both physics and mathematics, although there are a few tolerated infinities, such as electrons and black holes. However, any hope of ever discovering that the cosmos is purely finite vanished with the return of MBR data from the Boomerang and Maxima balloon born telescopes[31][32], and more recently the Wilkinson microwave anisotropy probe[33][34] further verified that the geometry of deep space is flat, indicating profoundly that if we could observe galaxies at a common age the universe would extend infinitely in all directions without end. It follows logically, and most cosmologists agree, that if the geometry of the universe is flat, then the first moment of time, the alpha state, is necessarily also flat and infinitely extended.

We no longer need question whether the universe is infinite or not. Once we separate nothing and non-existence we can reasonably conclude that existence is fundamental and ultimately timeless because there is no alternative to existence. The case for a mode of timelessness [35][36][37][38][23][20][2] is no less compelling than the case for a many-worlds universe, and without question only the profound nature of both positions have delayed their inclusion into science.

So in this golden age of cosmology we have arrived at a question that seems less scientific or at least far more difficult to answer. How infinite is the Universe? Is the existence of universes bounded in some way? Evidence for an infinity of galaxies or space-time bubbles was not entirely unexpected, but what of the utter chaos of possibilities, all conceivable temporal universes and beyond, the majority being completely unlike our own. Are there any identifiable boundaries to what exists?

I would suggest, based on this work, that the physical existence of all possible states may be the extent to which existence is radically infinite, satisfying an existential requirement of nature that all possibilities exist. The success if this initial work in finding a relationship between the aggregate possible realm and the structure of space-time and the many worlds of quantum theory, suggests the SOAPS in serving as a timeless foundation, limits the dimensions of temporality to a macrocosmic system of space-time bubbles all similar to our own.

To understand the whole we must switch into a different mode. In symmetry math, and most intriguing, the values of the smallest numbers, Proto and Eleat are themselves infinite, which I suggest represent in mathematical form the positive and the negative alpha states. The alpha state in our past is a positive singularity, a body that is spatially flat and infinite, yet it is the smallest value possible in nature. Internally alpha is smooth and uniform, due to being all positive, and from our perspective is definable as a false vacuum innately in a constant state of inflation, yet because macrocosmically it contains merely half of the whole, it is the smallest value in our reference of values, a tiny point in our past, that expands only as negative values are added to it.

The science fiction writer and doctorate of chemistry Isaac Asimov, in an article, What is Beyond the Universe? wrote: "Where did the substance of the universe come from? . . If 0 equals ( + 1) + (-1), then something which is 0 might just as well become + 1 and -1. Perhaps in an infinite sea of nothingness, globs of positive and negative energy in equal-sized pairs are constantly forming, and after passing through evolutionary changes, combining once more and vanishing. We are in one of these globs between nothing and nothing and wondering about it."[39]

The process of transformation from the alpha state to zero is indeed similar to the phenomenon of virtual particles, if they are viewed as combining into a uniformity rather than canceling, and also there is no need of the creation phase. The alpha state itself, the first moment of time, like all other states, simply exists, and time is a product of directions away from that state. As Richard Feynman remarked, time is a direction in space[22], and in fact the progression of time can be understood as a fourth dimension of spatial directions that due to backward causality (zero being the great attractor) inevitably originate from either of the charged alpha states. This interaction between past and future is already described by the Transactional interpretation of quantum mechanics.

To complete the virtual particle scenario, we place ourselves within the positive virtual particle, while the identical negative particle (anti-spacetime) integrates slowly and invisibly from within, expanding our positive volume and moving us ever nearer toward neutrality. Of course the reverse process synchronically expands the negative volume of our parallel anti-spacetime. The two worlds manage definitive form only by being grouped separately, and seemingly annihilate one another in the cosmic evolution of grouping to symmetry order. The existence of separate positive and negative volumes can explain why negatively charged electrons are point particles, since the intrusion of negative density cannot exist spatially extended in a positive volume.

The evolution and expansion of our universe is equally analogous to counting from the number Proto to the number Omega, traveling probabilistically through the body of all possible states, initially diverging into an expanding state space, but finally converging in state space toward the omega state, which is also in a constant state of inflation relative to our position in space-time. In the same way the number Proto grows in value toward zero as negative numbers are added to it, the universe grows spatially because of a finely controlled influx of negative density into a positive density. The values of symmetry math also reflect our large-scale reference of space and volume, which is not the internal infinite volume of the alpha state, but rather our sense of volume is in reference to the space and form that is born of the growth of alpha due to the influx of negative density. The flat infinite extension of alpha is merely an infinitesimal point to us.

III. The Relativity of Space-time

In any study of space-time, it is self evident that time includes two distinct components, physical existence and change. Any physical system must primarily exist, and so the component of change could conceivably be a secondary component which is no less real than the first component, but merely relative. Assuming this secondary time is embedded in a four dimensional existence, we have two evident components also. One is the necessity of a linear string-like path extended across the permanent landscape. The path of a dynamic system, like a story in a book, could conceivably be solidly imprinted into a static existence. However, like any story in a book, there must be a sort of binding which fuses the multiplicity of pages. The momentary states of a system must be fused into linear form, that form being at very least our temporal experience. I shall refer to this as the linear component or as linear time.

Simultaneously, the time of change requires a transition through unique states or patterns. Differences must exist between points A and B necessarily lateral to the linear evolution of time. Each state must possess a distinct identity apart from others along the linear path. Without an independent identity there could not be the temporal experience of a singular present so there would not be for us the illusion that existence evolves, as is commonly assumed. We can make reference to the necessary transition from state to state as the lateral component of time. It should be noted that like the four dimensional existence itself, each quiescent state is without beginning or end, and is thus unable to contribute any measurable time duration, but rather only offers change. I shall refer to this as the lateral component or as lateral time.

In a universe viewed from a perspective of timelessness, it is not easy to reconcile how we so convincingly experience a distinct moment of now and clearly perceive change, be it illusion or not. One of the problems with the block universe view[18] or the existence of a multispatiality[41] has been concerned with how it is possible that many individual blocks of space which are necessarily distinct dimensional frames can simultaneously be spatially linked to form a fourth dimension of space which we refer to as time. Any fused series of distinct spaces form a whole space and thus would seem to forfeit the original separateness. If we then maintain each state as an individually distinct dimension, like a series of photographs, there is no indication of why we experience continuity and order between multiple frames of time.

The problem of trying to reconcile the two components and the problem of trying to reconcile our experience of time with a timeless existence is the same paradox faced in resolving the distinction between quantum theory and the general theory of relativity. At the macro-scale we observe objects to move along linear and continuous paths, and in knowing the position and momentum can predict the future or past. At the micro-scale it is not possible to decipher both position and momentum, and we conclude that particles travel as a wave from one position to the next without having a definite position between two definite points A and B[12].

My suggestion here is that the focus should not be upon how such spaces are linked, but instead how such spaces are maintained discretely in nature as individually distinct. If we assume a spatial holism and then ask what separates one state from another, the question is then not unlike other spatial issues regarding the relationship between two locations in space or different references of time. Note that there has never been an intuitive rejection to the integration of two dimensional slices of space into a three dimensional continuum, and likewise there is no reason to expect that three dimensional blocks would not be linked naturally to form a four dimensional spatial continuum.

The as a last conclusion from inducting absolute zero into the SOAPS, primarily based on the new construct of symmetry order, is that in addition to all the ordinary expected directions embedded within and constructing the continuity of a three dimensional block of space, there also exists directions in space which travel across or through the existing multiplicity of all possible states. The proposal here is that directions in the fourth dimension travel probabilistically and thus dominantly pass through particular configurations within the superstructure of all possible spaces (SOAPS), forming a four dimensional matrix which we refer to as many worlds. These directions in space are no less natural and inevitable than those which build a three dimensional continuity, except for the critical feature that each single direction contributing to four dimensional space probabilistically constructs the lateral component of its surrounding conditions relative to itself. In essence, each linear direction in four dimensional space constitutes a unique space-time bubble, and since each observer invariably surrounds a linear path in the four dimensional matrix, the lateral component is composed relative to each observer. This multi-spatial construction would explain why an observer in a four dimensional system simultaneously experiences quantum mechanical and relativistic properties, and in that such properties arise from the physics of space may indicate that such properties are not exclusive to observers.

The resulting four dimensional volumes are structured systematically in reference to configuration space, or a superspace[1], and each volume is unique from any contributing three dimensional volume and also unique from the matrix superstructure. Each linear path, rather than traveling freely instead encounters the inherent probabilities that exist within state space relative to its present state. Applying the model of configuration space proposed, each linear path inevitably begins confined by grouping order in a state denotable as positive or negative, and in escaping is probabilistically directed toward becoming neutral. As mentioned, the overall cosmology of this model predicts there are two opposing cosmological arrows of time[42], one producing positive volumes of space-time containing matter and the other producing negative volumes containing stable anti-matter, and of course each system is inseparably connected to the evolution of the other and the sum of the pair equals the greater whole zero.

This formula should be particularly enticing because if we can adequately describe space-time as a fourth dimension of space it would explain why we experience physical reality as we do, since this particular finely tuned universe we live in is the fourth spatial dimension. This would eliminate most multiverse scenarios with different constants that otherwise might exist, excepting the fifth, sixth, seventh spatial dimensions and so on. It would greatly lessen our reliance on the anthropic principle to explain why we experience this particular universe although questions concerning the relationship between consciousness and a view of omega as the sum of all life, thought, intelligence, concept, ideas, and complexity, may not allow us to eliminate anthropic principle influences altogether. A measure of systemization of physical space-time may be the result of what is required for life to exist, with the evolution of intelligence inevitably built into the gradient, also the result of backward causality. The profound suggestion being made, is that our intelligence and consciousness, our desire to understand and model reality, likely arises in relation to omega zero being a supreme state of intelligence and consciousness, the sum of all life, this scenario not totally dissimilar from Frank Tipler�s Omega Point theory.

IV. Fitting the pieces together

In ordinary math we count upward into an endless staircase of numbers, with no finality or boundary, and thus reality modeled by such a system has no ultimate or macrocosmic definition. In that ordinary math fundamentally counts things, there is naturally a number that represents nothing or no things, yet no number represents everything. If we instead switch into a mathematical mode that is able to represent the greater infinite universe as a whole, then naturally we find that the system represents reality in an entirely different way. We haven�t merely reversed values, we have changed the very nature of our system of understanding.

In symmetry math, infinity is no longer constrained to a never ending process, but rather the infinity of mathematical values is whole, bounded only by infinite extremes. Engulfing the finite, the entire symmetry mathematical plane is real, complete, and consequently quiescent and timeless. In symmetry math zero represents everything, and because the smallest values of this system still represent half of the whole, we no longer confuse the nothings in this system with non-existence. Nothings in this system are singularities.

In considering the new axioms of this system, we would not expect the values of the symmetry plane to be derived from an elementary first thing somehow emerging from nothing or an empty set. This world isn�t magically arisen above nothing. There is no axiom of nothing implying non-existence, from which we question the existence of the rest. From the timeless Proto and Eleat singularities we can derive the single positive one and negative one from which all finite values and numbers of an abstract finite math unfold, like binary numbers that multiply into virtual worlds.

Symmetry math, combination over cancellation, is as logically consistent and as valid as common math, perhaps of no use within the abstract world of individual definitive things, yet immeasurably valuable in cosmology where a mathematical value for the universe as a whole is of critical importance in any attempt to understand for example, the implications of the many worlds theory, or how to conceptualize the realm of all possible states, or how to appreciate the evolution of a geometrically flat universe.

In a purely philosophical study of the three fundamental states, Omega is of course denoted as everything while interestingly the positive and negative outer poles can be related to something and nothing; two singularities annotated the simplest of any two meanings. This particular case of nothing is the negative of form or anti-form, which is itself form, just as anti-matter is matter.

In exploring the nature of the alpha states, the most interesting application I have found is in psychology toward understanding fundamental attitudes (states of mind). We can imagine the natures of Proto and Eleat as the core of masculine and feminine states of self identity, �I am; you are not� and �I am not; you are� (the absent element being of relevance). It can be recognized that each person assumes and oscillates between such states, more pronouncedly in forming identity during youth, then usually maturing toward a more generally respectful attitude of �I am, you are�. Evolving from the necessity of establishing boundaries, distinction, identity, our tendency is to mature toward a more spiritual state of becoming one with others and the world, in states of �I am everything, you are everything�, or �I and the  universe are one� and so a dissolving of boundaries between self and the universe.

Obviously in this approach we more lucidly recognize the conceptual switch that has been emerging for centuries, particularly in eastern philosophy. The void is not a simple nothing or a non-existence. The nothing of zero, of empty space, is the whole of form and not the absence of form. It may even be reasonable to refer to this mode as primary and consider our ordinary perspective of thingness to be secondary, as long as we respect the validity of either reality. It is not held here that time, or the definite world, is an illusion as some claim in metaphysical philosophy. Instead we should respect the two fundamental natures of being, the definition and form of the past, versus the formlessness of the future.

There are two fundamental forces of nature, what we might call the Alpha Force of grouping order and the past, and the Omega Force of symmetry order and the future. The prototype of alpha force is of course gravity, which holds back the expansion of the universe, slowing the cosmic evolution. With the aim of recreating the past, the alpha force serves the role of maintaining the past in the present. Without that force of conservation, without the influence of the past pulling at time, the story of the temporal universe would be a short one, over in an inflationary instant. Instead, the gravitational pull of the past slows time and change, producing the expanses of time and the variety of many worlds.

Fundamentally speaking, grouping order involves division, separation, distinction, individuality, density, pronunciation, opposition, and conflict. Symmetry order involves balance, integration, combination, uniformity, homogeneity, singularity, formlessness, symmetry, and unity. The two orders reflect two natures, and also two directions of increase that are opposite to one another. We can easily find these two forces as conflicting influences in nature, in society, in psychology, in politics.

The past   


    The future

Grouping into parts


Balance of the whole



The Many




The individual     


The group

Any Group


The Whole



















Self Gain


Planetary Survival




Left brain


Right brain




Ideally we fully appreciate the value and necessity of both sides of each dichotomy, understanding the necessary balance between selfishness or identity and the greater sense of self that is human society, the Earth, and the Universe. If imbalanced, either force of past or future can detrimentally dominate a person's mentality. The cosmic struggle between the two forces is the most common human theme in both fiction and non-fiction. Of course the trick is balance. We can view the world both from the bottom-up and the top-down. We can avoid extremes of selfishness or selflessness, and rather nourish fullness, meaning that we fully develop our personalities or self, yet also develop our function and place as a member of a community, country, as human beings or simply life, and finally it is essential that we become aware of our ability to dissolve all boundaries, to know that we are ultimately one with the universe. Understanding both our individual distinctiveness and our unity with one another and the world, even our connection to the timeless whole, may be an essential ingredient of our future survival on this planet.

V. Accelerating Toward the End of Time

As if the beginning of time were being swallowed by a cold black hole, accelerating cosmological expansion and the great seeming void sucks the majority of galaxies beyond an outer event horizon. Erasing the rich history of the universe we are now so fortunate to enjoy, eventually the volume of space-time shrinks inward to the local group then collapses inward to the gravitational curvature of our own Milky Way galaxy.

As to the final fate of the Milky Way universe, as if the cosmos has a sense of humor, again we find ourselves stonewalled by a deciding critical density, with the universe riding the line between two dramatically different futures. In the equation-of-state parameter w =  p/ρ, the ratio of dark energy pressure p to energy density ρ required for acceleration is < -⅓ and has been generally assumed to be ≥ -1. Since the acceleration was discovered it has generally been maintained that gravity would hold off a final collapse to zero for an infinite period of time, in which case the galaxy would survive. Discussion on the dark energy density heated up this last year when Caldwell, Kamionkowski, and Weinberg introduced the Big Rip Scenario[7], where a dark energy density dubbed phantom energy[8] by Caldwell increases with time.

Even if w is only equal to -1 cosmic acceleration is exponential, however if w exceeds the critical value of �1, the future is no longer in question since neither gravity nor any other force will be able to restrain the collapse of the absolute cold event horizon. The density of ordinary matter and energy exponentially decreases with time, finally becoming zero in finite time.

As is presently thought, the source of accelerating expansion is a property of space itself and so not evident in the probabilities of state space. Some acceleration to expansion is built into the process of convergence occurring because the contrast gradient narrows. However, a fully independent acceleration force occurs more dominantly due to the nature of time itself.

Prior to the discovery of accelerating expansion, it was assumed that a state of absolute zero or a perfectly flat space, if entertained as being physically real, would initially be envisioned simply as a Euclidean space, a static three dimensional block of empty space in which ordinary properties such as distance have no meaning. As acceleration was integrated into this state space model it gradually became evident that we in this discovery are simply witnessing the most innate property of a four dimensional existence, meaning that the most innate property of zero from our perspective is an ever constant inflation. In fact that conclusion is inevitably made of the discovery itself. The conclusion that time ends in either infinite or finite time in an inflated state has been made for us.

Symmetry order further indicates absolute zero as an integration of all possible states, as well as all four dimensional directions in space, and thus the four dimensional whole, meaning the composite of all the many worlds predicted of quantum theory, and also the composite of all life within that expanse. With our universe converging toward, joining with, and becoming a part of that matrix, the expansion of the universe is required to accelerate by the expansive conditions which exist at the end of time.

With the direction of time following the basin of attraction within the density gradient we can expect a more complex scheme for the end of time than the Big Rip scenario. The dominant quantity of isotropic patterns near flat space require a gradual and increasingly uniform descent to zero more reminiscent of the beginning of time in reverse than a late-time shredding of whole galaxies. As space-time approaches absolute zero, stars and galaxies and all complex atoms will be systematically broken down into a supercooled condensate of protons and electrons stationed in orderly rows and columns.

In the final moments hyper-expansion stretches all remaining matter and energy flat. Not even virtual particles are able to compete with the inflation. Space-time collapses and in that instant our universe completes its integration with all other space-times including its inseparable parallel partner. The two opposite arrows of time become omni-directional and inflated, producing at time's end the ultimate singularity, a oneness of space and time and things, which is and always has been the native state of a timeless infinite Universe.

The question left then is to wonder at the influence of such a paradigm shift on society, give that such theories pass the test of time and are adapted to hard science. These theories were not developed from any spiritual belief system, and were always meant to conform to strict science, even experimentation. But the product of discovering symmetry order is obviously knowledge concerning a supreme state. How interesting if an advanced scientific cosmology without difficulty can be related to both religious and eastern philosophical cosmologies. At the heart of all scientific discipline is a devotion to truth, although it is sometimes a naive expectation of science. It is hoped that science will gracefully adjust, and not consider the profound and even spiritual nature of symmetry order a basis for rejection. I must agree with Huxley who declared wisely �Follow humbly into whatever abyss nature leads or you shall learn nothing�.


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