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On Modeling the Macrocosmic Structure of State Space

II: Defining the Two Opposing Types of Order

Devin Harris
February 5, 2001


This specific comprehension of order identifies two opposing directions of increasing order, leading to the recognition that the order in one direction is simultaneously a disorder of the opposing type. In study of this phenomenon it can be realized that it is inaccurate to consider any pattern as exhibiting a general disorder, but rather all patterns are produced from a combination or synthesis of two separate types of order, the only exception being the two extremes or highest order of each type. Note that this comprehension of order is both congruent and evidentiary of the proposed three radical extremes of possibility previously identified, and also the proposed contrast gradient existent adjacent an average density gradient representation of all possible states.

1. Redefining order

At present order has a complex yet singular meaning. Order is most commonly defined as a grouping of separate elements or a regular arrangement of objects, colors, events in time. Although the following is a more accurate and fully developed comprehension of order, what follows is by no means complex or difficult to envision. 

There are two principle classifications of order in nature, not merely a single order opposing disorder. Two orders blend to produce all the diverse shapes and patterns that are observed. Each has its own distinct direction of increasing order and an individual increase in either type produces opposite results. The first type to be identified will be referred to as Grouping Order which can be understood as any class, or similar kind of thing grouped together, and thus located in a specific area, or separate place apart from another group. The second type of order is identified as Symmetry Order, which if we simplify its definition to extreme, is an even and regular pattern or arrangement in which all different types of things are combined together and distributed uniformly throughout a frame of reference. In extreme this type of order produces a perfectly smooth and uniform pattern. The perhaps unexpected element involved is the opposition of these two types. I shall show that each deserves to be classified as a unique type of order and even that each type is disorder to the other.

By far the most lucid exposure of this contrast between orders is seen in the way in which a chess or checker game is set up. Even if the example initially feels mundane, let me reinforce the fact that this example in its simplicity reveals the distinctiveness of each type of order, and illustrates the opposition well enough to act as a lasting template to identify the separate orders in nature.

To prepare for a game of checkers, black and white game pieces are separated and grouped together. Each color is grouped and set in a location at opposite positions upon a board. In fact we commonly divide apart and group a number of objects by classification into a set, ordinary examples being: smaller parts grouped apart from large parts, round objects apart from square objects, or things of a positive nature apart from things of a negative nature. This order requires only that one group be established in dense form apart from another class, or the group is merely distinct apart from a neutral background.

However, if we change our focus and consider the checkerboard, which is in this case serves as a moderately neutral background, we observe a uniquely ordered pattern, unique in that its arrangement is an admixture of colored squares, spaced evenly in alternating rows. The most evident property of this archetypal pattern is its overall conformity and balance represented by the symmetrical placement of squares. Note that this conformity and balance is in stark contrast to the set pattern of game pieces which are divided purely into two separate groups.

Using these two patterns it will be possible now to reveal two opposite directions of increasing order, at first focusing directly on the checkerboard pattern. Since we will transform the checkered pattern it helps to assume a flexible or liquid quality to the shapes.

If we first imagine the direction toward grouping order, we imagine the individual squares of the same color gravitate together. Enclosed within the square frame of reference, this motion simultaneously forces the opposite color to group as well. The extreme result is two uniquely colored rectangles at opposite ends of the board. The black color is now fully separate from the white color. The only way to push this pattern further in the direction of increased grouping order would be to increase the density of the individual points of color which would deflate the frame of reference, and the red and white squares would shrink toward becoming the extreme of two infinitely small points.

Now if we reverse this same process, starting from these two points, we inflate the frame of reference, and begin to mix the two colors, although not evenly. We maintain a measure of grouping order dividing the red and black areas into squares which are then mixed to recreate the original checkered pattern. Now the pattern is transforming in the direction of increasing symmetry order.

To continue in this direction toward the extreme of symmetry order we further subdivide the checkered pattern, and then evenly distribute the more miniature squares, which causes the pattern to become increasingly variegated. Continuing to subdivide, the checkered pattern can become ever more finer in its distribution until we are unable to detect the fine squares and visually only observe the smooth result of this perfectly symmetrical spacing. Our observations reflect how the pattern is transforming ever nearer to an extreme where two distinct colors are blended into one single color, this being the ultimate extreme in this direction of increasing symmetry order.

Like two liquids blended together, this direction of increase produces an order of a nature precisely opposite to grouping. Rather than two pure and separated groups, this fully opposite direction of order produces a singular result, a uniformity, neutralized of difference and form, yet not truly absent of form. The contrast of black and white becomes the balance of gray. Shapes and form become formless and neutral. Balance, uniformity, neutrality, combination, in extreme becomes formless, yet ordered, and thus not dissimilar to absolute flat space (AFS).

The gradient increasing from a checkered pattern to the extreme of a uniform pattern exposes the relationship between evenly distributed patterns (EDP) such as the original checkerboard and an absolute uniform pattern which will here be recognized as an extreme form of order of a symmetrical nature, identified here as symmetry order. I shall consider AFS as the physical reification of symmetry order.

The same gradient increasing along the axis in the opposite direction exemplifies the more common type of order of grouping where parts or classes are densified and consequently increasingly pronounced or definitive. It is this type or order that is ordinarily recognized as general order while the direction toward symmetry order is associated with high entropy and even disorder. Where AFS relates to symmetry order, an infinitely dense and hot singularity relates to grouping order. In fact I shall argue that the big bang singularity is the reification of extreme grouping order, an inseparable positive and negative duality, which on a macrocosmic scale, verifiably results in two directions of time, not simply the one containing matter which we observe.

Note that the directions we have just encountered do also establish more clearly the contrast gradient previously explained in the first essay, but much more significantly they demonstrate the major proposition of this paper, the replacement of the order-disorder axis with a grouping-symmetry order axis.

2. From an ordered to an ordered state

The second law of thermodynamics describes the mixing of materials and the increasing entropy of a system as an increase in disorder. That an evolution is taking place of increasing entropy is not in doubt, however, we must recognize in principle that the material within an area of any pattern can only either separate or integrate, and its topology can only expand or contract. I submit that what we perceive at present to be a trend toward disorder is instead an evolution that begins from grouping order and ends at symmetry order.

As the most simple example, gases that dissipate from a condensed grouping, and spread evenly throughout a room, or any frame of reference in which it escapes from confinement, until it reaches a state of equilibrium, is not a general increase in disorder but rather an increase in the balanced distribution of a gas throughout its reference frame and therefore constitutes an increase in symmetry order. The immediate or short term settlement into an equilibrium state can be associated with the basin of attraction within the contrast gradient (CG), as determined by the system's position along the average density gradient (ADG). On a much greater time scale the system is moving toward a radical equilibrium, toward perfect symmetry order or AFS, due to spatial expansion toward flatness and cooling toward absolute zero. While the contrast gradient recognizably influences the system toward an equilibrium state along the density gradient, the total evolution of any system is relative to macrocosmic state space (MSS) and thus we recognize the general direction of time toward the balance and formlessness of AFS.

Increasing symmetry order has been mistaken for disorder because the observable history of space-time most evidently records the divergent evolution from the most extreme state of grouping order to an intermediary transitional phase (ITP) between both orders. The ITP in any transition from grouping to symmetry order can be viewed plainly if we imagine setting up a checkerboard game and move the game pieces out of their initial grouping order positions toward a pattern which identically matches the symmetry order of the board of squares. As we randomly choose one game piece for each move, at any point in time along this procedure until it is completed there exists what we normally consider to be a general measure of disorder. In actually each area of the board can be seen to be retarded toward grouping order or advanced toward symmetry order. Note that in the middle of this process the transition appears to have no objective. As a whole the pattern appears to be moving toward disorder when in fact we are observing a transformation from one type of order to another.

The intermediate patterns seem disordered yet each is simply part of the vast majority of possibilities produced by uneven mixtures of grouping and symmetry order, patterns which must be utilized in the transition. In respect to this new model of order it becomes necessary to abandon the general meaning of disorder since no area of a pattern is without order of either type, and since the order of one type is necessarily the disorder of the other.

While the future convergence from ITP states to the single extreme state of perfect symmetry is not observable at this point in history there is a great deal of evidence to support the transformations and changes suggested and later predicted by this model. The transition from grouping to symmetry is visible in everything from red hot flowing materials that solidify into rock or steel, to droplets of water which crystallize into a snowflake. At ultra cold temperatures, order is less complex than a snowflake and consequently expresses the simplicity of the archetypal checkerboard pattern. At temperatures near absolute zero, materials such as cesium gas particles organize into orderly columns and rows. Less than a millionth degree away from zero the definition of the particle itself is lost as atoms blend into a unified condensate. And finally, hidden in the symmetry of space, virtual particles leap out and back, for an instant form emerges spontaneously from formlessness until the balance of symmetry order returns.

This notion of the one order being the disorder of the other is more acceptable when considering an AFS as the most disordered state of the more commonly recognized grouping order, and less acceptable when considering an increasingly dense state as the disorder of symmetry order. However, the central issue is in differentiating between the two unique directions of order, as well as observance that either direction involves the necessary increase of order for one type, to decrease the order of the other.

It can be recognized that the breakdown of each type of order is required, in any transition toward the other. We recognize the breaking of either order without difficulty, if we imagine a mis-printed checkerboard where two red squares were accidentally placed together. If the placement of squares is uneven in the slightest measure, the order of the pattern is lessened. The balanced symmetry of the board would be visibly decreased yet the grouping of red squares is increased in that displaced area. Likewise, if we consider we mistakenly displace one red checker with one black checker in setting up the board, a mistake in sorting, has made the two separated groups less pure and less ordered yet this has also initiated the necessary mixing of any transition toward symmetry. Again I will mention and so reinforce the principle that the material within a space can only either separate or integrate, and its overall topology can only expand or contract. It is in recognizing the extremes of separation and integration, or expansion and contraction, that we discover the inevitable transition between extremes.

3. Synopsis

There is in our thinking minds an expectation about the universe, and then there is the natural world, or our experience of the real world. Much in the same way our very existence seems like a miracle to us, as if there should be nothing at all, so also are we perplexed at the order that is such an elementary part of the universe in which we live. There should instead be chaos, it seems much more evident to us, for we naturally consider the infinity of less consistent universes that could exist in place of the one ordered and systematic universe that is present. Yet suppose here for a moment that our universe is not unordinary or an exception to the absolute chaos possibility, but rather we make a mistake in how we model order. I hope the reader can sense here that when we fully understood order we find that there is nothing extraordinary about an ordered universe even in comparison to the whole of possibilities. In fact it is our notion of disorder that is an anamoly and unreal.

Before ending this article we should consider how commonly and automatically we group things. In a well organized home, books are placed on a shelf, dishes in the cupboard, canned food in its own location. The vegetables and the fruits are kept in separate groups. The bedroom has a separate drawer for shirts, pants, and underwear. At the store there is a meat section, a bread section, a dairy section. An at the library books are organized alphabetically or by subject. If instead all that is mentioned here were all mixed together the result would be a world in disarray, something we might expect after an earthquake.

In this same way we can also consider the basic elements of the material world and fortunately the universe isn't just a cosmic soup of particles randomly in motion. Grouping of elementary particles produces pure chemical elements, gases, metals. Our planet is a grouped mass of materials, as is each stellar body, while the sun and planets form a group. There are cluster and supercluster groups of galaxies. Amassed groups of elementary particles represent the most basic expression of grouping order as opposed to an easily imaginable admixture of all subatomic particles.

Yet as groups of elements and solar masses give the universe its definition and bring about order as we know it, this grouping type of order is not alone in creating the universe that we observe. The universe also requires uniformity and balance. The moderate combination of elements creates for us our oceans, the soil, and the air that we breath. The materials most common to us are medleys, such as composites of rock, glass, wood, soil, plastics, metals such as bronze or steel, or gases such as petroleum and propane.

At the macrocosmic scale, the even distribution of galaxies reflects the even distribution of lumpiness in the early universe and the initial smoothness of inflation and expansion. At the microcosmic scale any closed system settles into an equilibrium state. And finally, perhaps the most important expression of symmetry order is the measured neutrality and formlessness of outer space.

There is a stark and dramatic difference between the nature of these two orders, an opposition that is responsible for all the complexity and the beauty of ordered patterns in nature. One nature involves division, separation, distinction, individuality, density, pronouncedness, opposition, and conflict, while the other expresses combination, uniformity, homogeneity, singularity, formlessness, balance, symmetry, and unity. The contrast and struggle between two orders is why existence itself is comprehensible, and why spacetime is complex in its systemization and orderliness.

III: On the problem of multispace

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Copyright © 2001 by Devin Harris