Learning to See everythingforever.com
Learning to See the Timeless Infinite Universe

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So far on this planet we can't seem to grasp a full understanding of the Universe. We don't even understand how or why anything exists. Is the Universe comprehensible? Consider all that we have accomplished already. And yet something is wrong, but we can't see it to fix it. What is this problem we can't see?

"We think the world apart. What would it be like to think the world together?
Parker Palmer


From The Book:
Everything Forever:
Learning to See Timelessness





















"The underlying nature of grouping order involves dividing and separating things into individual groups. The best example, a sort of prototype idea to represent grouping order, is to imagine setting up a game of checkers or chess."



















"Without the concept of time, there is only the wholeness of nowness."
Stanley E. Sobottka




















"Where grouping order separates things apart into many groups, symmetry order mixes and combines things together ever more evenly."
























"In emptiness there are no metrics, no time, no locations, and no differences between a point and the whole."
Nick Fulford












"Symmetry is in principle generally ugly because it is associated with information loss or entropy increase."
Shu-Kun Lin  Chemist











"If it seeks to attach an idea to the word, it finds that disorder may indeed be the negation of order, but that this negation is then the implicit affirmation of the presence of the opposite order, which we shut our eyes to because it does not interest us, or which we evade by denying the second order in its turn-that is, at bottom, by re-establishing the first."
Henri Bergson
Nobel Laureate














Making the simple complicated is commonplace; making the complicated simple, awesomely simple, that's creativity."
Charles Mingus














"Opposition, distinction, pronunciation, conflict all result of dividing things apart, they are products of grouping order. Oppositely, unity, similarity, harmony, and symmetry results of blending things together evenly. These basic patterns actually represent the basic reality that we exist within."










The New York Times recently featured this image in an article about the multiverse.













Related Links

David Bohm and the Implicate Order

David Bohm Links

The chemist Dr. Shu-Kun Lin has recognized similar issues in regards to how we conceptualize order and symmetry. Lin has recognized the correlation between entropy and symmetry.



Discovering the
Two Opposing Types of Order

In the same way that the presence of a universe seems like a miracle, as if there should instead 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. Order is everywhere, and yet it seems like there should be chaos instead of such strict governing forces of nature, for we naturally imagine the infinity of less consistent, less trustworthy, and more chaotic worlds that might exist instead. But suppose for a moment a rarely considered idea, that this universe is not actually unordinary or improbable, and instead we ourselves are making some critical mistake in how we see the world, a mistake which if we could somehow see beyond, suddenly the order in the universe would seem exactly how things should be. 

Very simply stated, at present most everyone, even in science, believes order is generally definable with a single concept.  In most dictionaries order is defined as "a condition of logical or comprehensible arrangement among the separate elements of a group." If we translate our sense of order into an image, we would draw an axis, with greater order in one direction and disorder in the opposite direction.  Thus if the order of some system increases its disorder must decrease.

As an example, the second law of thermodynamics describes the universe as more ordered in the past and increasingly disordered in the future. The second law is one of the most fiercely defended laws in science, and yet many people have difficulty with this law and instead point out that in contrast to the uncomplicated order of an increasingly dense past there also exists a complex orderliness that has increased as the universe has evolved forward in time. Although the following is more developed than our existing vague definition of order, the basics of what I am about to explain aren't very complex or difficult to envision.  We all know a great deal more about this subject than we realize because of our immersion in nature and because of our participation in the ordered flow of time. 

Grouping Order

The kind of order we are most accustomed to recognizing is Grouping Order which can be understood as any class, or similar kind of thing grouped together, and located in a specific area or separate place usually apart from another group.  Grouping order is the precursor of things and responsible for the definition we know as the finite world.  It is very common and very easy to recognize.  When we go to a grocery store there are groups and sub-groups of different products.  There are apples and oranges and bananas grouped apart from each other. Also the whole store is divided apart into sections, a meat section, a dairy section, a bread section.  By nature, like things grouped together become more pronounced, they stand out. If all the fruit was displayed mixed together with all the vegetables only the largest individual items would stand out.  Yet separated each group is very pronounced.  This same grouping kind of order is found in every store, every business, and every city.  At home the dishes are grouped together in the cupboards, and the canned food is grouped in another cupboard.  A well organized bedroom has the socks, tee-shirts, and underclothes each in their own place in the dresser drawer.  Everywhere we humans go we group things together as opposed to the chaos of individual items being randomly located throughout a room or a space. 

Grouping is how we typically organize the world of objects, but also places and information.  Books are all grouped together in a library, where they are organized into sub-groups by subject or title, as this allows us to find the book we are looking for.  When we communicate with others, such as when we convey ideas in writing, we tend to discuss one topic at a time, and we prioritize our subjects.  There are places where people congregate together into groups, where we shop, where we eat, where we pray, where we play. People separate and group together by age, by sex, by race, by wealth, by appearance. People form teams and group apart in sporting events, we group apart in politics as parties, and geographically we divide ourselves and lands apart to form cities and states and countries. 

In astronomy simple examples of grouping include a star, which is a large group of particles, galaxies which are large groups of stars, then clusters and superclusters which are large groups of galaxies. In chemistry and physics the classic example of order given is a concentration of gas particles contained within a flask, as opposed to opening the flask and allowing the gas to spread out throughout a room.  Here we are defining that concentrated gas more specifically as an example of grouping order.

Figure 1: Generally Grouping Order is a type of cooperation between things. Many things rather 
than randomly spaced in some frame of reference form a group. In nature things mysteriously cooperate 
with one another in response to forces. Grouping order involves an increase in density, which 
finally results in a more pronounced single object, like a star.

The underlying nature of grouping order involves dividing and separating things into individual groups.  The best example, a sort of prototype idea to represent grouping order, is to imagine setting up a game of checkers or chess.  To begin the game we divide the colors apart and place pieces of one color on one side of the board and another color is set up on the opposite side of the board.  The pieces were previously mixed together randomly inside a box, so we would ordinarily say that they were mixed together irregularly, and so they were disordered, until we separated them by color into two distinct well organized groups. 

Symmetry Order

The other kind of order, the second type, is called Symmetry Order which if I 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 evenly throughout the whole frame of reference.  Where grouping order separates things apart into many groups, symmetry order mixes and combines things together ever more evenly. 

The perfect prototype example of symmetry order also is visible as part of the games of checkers and chess, that is, if we focus our attention on the checkerboard on which either game is played, and for a moment ignore the game pieces.  A checkerboard pattern is obviously ordered but we normally might not reflect upon it as a special type of order. The squares of the checkerboard are mixed together evenly, white, black, white black, then the next row is black, white, black, white. With very little effort we can recognize something very important. The pattern of the checkerboard is ordered oppositely to that of the game pieces separated into two groups.  The checkerboard mixes two colors together evenly, which is completely opposite of the process of separating the game pieces by color into two distinct groups.  In one process we divide things apart, in the other we mix things together. Grouping order produces difference and distinction. Symmetry order produces uniformity and sameness.

Suppose we take everything from a refrigerator, put it all in a big stove pot, add some water, and stir it all together.  After we cook it awhile our parts begin to blend together evenly into a soup.  If we keep cooking the ingredients for five or six hours, or even a day or two, eventually what before were separate things all unify into a single substance, a single medium.  Suppose we take two colors of paint and pour them together into a larger bucket, then stir them together.  Just a moment ago we had two separate and distinct colors, but now we just have one.  We try adding another color, and the distinction of that color disappears also. We can just keep adding more and more colors, and yet the distinction of each unifies into one single neutral color. 

Figure 2: Symmetry Order is also a type of cooperation between things, except in this case
things spread evenly in some frame of reference. Symmetry order involves a decrease in
object pronunciation which in extreme results in objects unifying with their reference frame.

This process of many things spreading out to unify with one another which then collectively form an entangled single whole throughout the overall space they exist within (frame of reference) portrays the direction of increasing symmetry order. Symmetry order is not "similar things" grouping into a distinct single object, it is many different things unifying together in a way that creates an indistinct single whole that is everywhere and everyplace, shown above as a single single color in the reference frame of the square. In mathematical terms, we can easily imagine summing together a -1 and a +1 which equals zero. A +2 and a -2 sum to zero, and so on, and so on. Classically we imagine that the positive and negative numbers are canceling, but in terms of symmetry order the two numbers are combining together into a single whole which we call zero. Explained in detail in a later section, this symmetry zero contains all numbers enfolded into it. This zero isn't zero unless it contains all other numbers. If you take any number away, such as +1, this zero becomes a -1. All numbers are in this zero! Zero is full. The same is true of the zero of physics, or what we imagine to be empty space. Everything exists within zero, rather than arisen above it.

Similarly the physicist David Bohm identified an enfolding type of order and called it Implicate Order In his book Wholeness and the Implicate Order Bohm writes:

This order is not to be understood solely in terms of a regular arrangement of objects (e.g., in rows) or as a regular arrangement of events (e.g.  in a series).  Rather, a total order is contained in some implicit sense, in each region of space and time.  Now the word 'implicit' is based on the verb 'to implicate'.  This means 'to fold inward' (as multiplication means 'folding many times').  So we may be led to explore the notion that in some sense each region contains a total structure 'enfolded' within it.

Bohm also recognized grouping order, calling it explicate order, but he generally described explicate order as the order of the physical universe, while implicate order was almost a metaphysical concept, an order existing behind the physical world. The more specific concepts of grouping order and symmetry order extend Bohm's work and establish a new system of understanding the two orders of nature. In extending Bohm's general concepts I found that explicate order and implicate order are plainly visible in our immediate surroundings. Both implicate and explicate orders exist in lesser measure than the extremes Bohm recognized. The extremes do exist also, they are found in our distant past and distant future. The infinitely dense singularity of the big bang is the extreme of explicate or grouping order. The absolute zero singularity plainly evident in the future of an accelerating universe is the extreme of implicate or symmetry order. But in between extremes, where we live, we can easily recognize lesser measures of both orders. We can recognize lesser measures of implicate order as patterns of balance, symmetry, and uniformity, as shown in the images below. Therefore, a lesser degree of implicate order, which I specify as symmetry order, is a measurable physical property in any pattern. In fact both orders are separate components of a pattern. Each order is a one type of cooperation which overlap in the patterns of our intermediary present.

We quickly recognize the grouping of a single land mass, a cloud, a drop of water, a tree, a brick, while measures of
symmetry, and balanced distributions, are also common in our environment, both those in nature and man-made.

The two methods of creating order, separating apart and mixing evenly, are both very fundamental and yet opposite, which is what necessarily defines them as two very different types of order.  It can be surprising to notice at first how contrasting the process of grouping apart the game pieces is, in comparison to the process of mixing differences together evenly.  Below we see how the result of grouping order creates an imbalance on each side of the board, a purely black side and a purely white side, so that each side exists in opposition to the other, as if one side is positive and the other negative. While at the opposite end where symmetry order is pushed to extreme, the sharpness and contrast of the individual parts breaks down. In blending together previously separate things create a balanced distribution, so the black and white squares of the checkerboard transform into a single unified gray. Typically we see this gray as nothing at all. We see symmetry order as emptiness. Symmetry order in extreme is boring and even ugly to us, because we identify with a world of separate objects, rather than with the world of unified objects. 

Figure 3: In one direction of order away from the checkered pattern the parts form two pure groups
of difference and opposition while in the other direction the parts merge into one.

Directions of Evolutionary Change

It can be seen that opposition, distinction, pronunciation, conflict all result of dividing things apart, they are products of grouping order. Oppositely, unity, similarity, harmony, and symmetry results of blending things together evenly. These basic patterns actually represent the basic reality that we exist within. We exist  caught between two great forces, the two opposing ways objects in a pattern can cooperate with one another. All patterns, such as the checkerboard shown above, are recognizably created from the two kinds of order combining together in some way. This combining together can create the distinct orderliness of the checkerboard, or it can create the disorderly chaos of a cloudy sky. But both patterns are created by the two kinds of order combined together.

Once the two orders are made visible in a static pattern, we can also identify a fundamental direction of change occurring in the general evolution of the universe, and recognize that one kind of order is evolving into the other. One form of cooperation is becoming another. We are privileged to be living in that evolution, caught in the struggle between both types of order, where the two orders compete and in ways cooperate with one another to create complexity. The universe we observe is essentially a physical struggle between the extreme of grouping order and the extreme of symmetry order, which is why the universe is not simply chaotic and disordered. In the process of moving from one type of order to the other, all the myriad of complex orderly patterns are created as grouping order and symmetry order combine. The orderly and complex world we know is made from the myriad of possible combinations of both orders.

It is a fundamental rule or principle of nature, of physical existence, that we can only either mix things together or separate them apart.  And it is not possible to increase both types of order simultaneously.  In any attempt to change a pattern, we have to make a decision, either we move toward separating things into separate groups, or we move toward mixing things together evenly throughout the frame of reference.  This exclusivity, this either/or decision is what clearly reveals the powerful unyielding difference between grouping order and symmetry order.  We can even say the two orders are in competition with one another, because in creating any pattern, as we combine the orders together they both can't be continually increased.

Figure 4: The same underlying theme hidden in the game of checkers or chess, is true 
of the universe in general.  The universal way that patterns change in nature 
involves a transformation of grouping order into symmetry order. 

Many Patterns All Made of Two Orders

We observe order in the universe and are amiss at why it exists over disorder.  However, a general disorder does not exist. All patterns are created from two orders. What we think of as disorder is merely a necessary stage in any transition of one order becoming the other.  Disorder is an irregular combination of two orders.  Indeed it is surprising that we don't already clearly understand there are two types of order.  In fact there are serious negative consequences of missing out on something this simple and basic to nature.  In modern times the second law has led science to generally view the universe as an evolution of increasing disorder, and consequently our human interpretation of reality has been dramatically misled.

The first step toward repairing our expectations involves discovering that literally ALL patterns are created by utilizing two different types of order, mainly because there isn't any other way in which to order things.  Any classification, any categorization that we use to identify something is invariably grouping order.  Any measure of balance in any pattern is a component of symmetry order. To begin to recognize this visually we start off with a few very simple patterns in which a combination of the two orders is easily recognized.  Each pattern in the figure below utilizes both grouping and symmetry order.  Notice that what we would ordinarily think to be simply an ordered pattern is shown to be two opposite types of order working together to create each of these unique patterns.

Figure 5: It is not difficult to learn to recognize how any pattern is composed of both grouping and symmetry order properties.  In the first example above, grouping is necessary to create the vertical rows, and mixing creates the horizontal symmetry.  In the ringed pattern, grouping creates each ring, while mixing creates oscillating rings.  In similar fashion a spiral is an elegant and attractive mix of grouping and symmetry. Note that we can replace the objects of either color with empty space and still recognize grouping apart from symmetry.

These basic patterns repeated at every level of our environment. The following images are meant to help identify grouping order and symmetry order separately. Notice the grouping necessary of each stripe of a flag, or tower in a city, or tree in a forest, but also recognize the even distribution of those objects throughout an area as opposed to a closer grouping in one place. The pronunciation of each object or color is grouping order, but the even distribution of objects throughout any volume of space is symmetry order.

Figure 6: Orderly Rows
Even spacing of rows and lines is an elementary way grouping and symmetry combine.

Example 1: The design of flags must
naturally utilize simple measures
of grouping and symmetry.

Example 2:
The volume of a tree is grouped in the line of the tree while the trees are generally spread out evenly through a forested area.

Example 3:
Rows of sunflowers growing in a field are complimented by an orderly row of bicycle riders. Rows are grouped things and yet the separate rows or the bicycles in the rows are spread out evenly in some area.

Example 4: A mass of buildings is pronounced grouping order, as is each separate building, yet they are also measurably spread even within the city.

Grouping is very common in our environment and grouping is the most fundamental way definitive form is expressed in nature. The largest pure example of grouping order in the universe is a star.  A star is a single dense group of matter particles.  Then at another level of grouping, our nearby star, the sun and its nearby planets, held together by gravity, form the group we call a solar system.  At another level still, the stars on the largest scale, are gravitationally grouped into galaxies, while galaxies themselves group into clusters and superclusters.  Gravity, the force that produces stars and galaxies, and super clusters, relates intimately to grouping order. 

 From its iron core to its diverse crust, even though the Earth is a single collected mass, there are also groups and sub-groups of materials, true of all the planets and the sun.  Amongst all the different ingredients of our planet, it is most fruitful to find particles of gold grouped together in large amounts.  In the microscopic world, when the individual chemical elements are grouped purely and not mixed they create pure gases, solids, and liquids. 

Figure 7: Rings and Layers

Observing both symmetry and grouping in concentric layers or circular rows.


Example 2: Both grouping and symmetry are easily recognized in round circular patterns commonly found in nature.

Example 1: The orbits of planets maintains a balance between the potential of further grouping (gravitational collapse) and the increased symmetry order (non-grouped uniformity) of escape.

Example 3: A few biological examples of concentric layers where we see two orders.

All such order and structure exists in stark contrast to another universe we might imagine void of grouping; a cosmic soup of all particles blended uniformly throughout space so that there are no stars or planets, just a vast uniform sea of particles. Further still, we can imagine even the absence of particles where the universe is just a smooth fluidic material plasma spread evenly throughout the whole of space.

Yet grouping is not the only way in which the universe is organized.  The universe also mixes different things together producing various patterns of increased symmetry order.  Various elements mix to form molecules.  The oceans, the soil, and atmosphere of the Earth are each compounds created from varied and unique materials.  Rock, glass, wood, soil, plastics, and metals such as bronze and steel are all mixtures of atomic materials.  And on the largest scale there is an even and isotropic distribution of galaxies and dark matter across the universe of space as far as our telescopes can see.

The world we observe is not generally more ordered than disordered, rather our present time exists trapped within a struggle between two great powers. In the play between extremes, with the influence and cooperation of each order at a nominal level, there exists a wide range of patterns in which both orders can be highly cooperative or oppositely they can be uncooperative, disorderly and chaotic, yet both orderly and chaotic patterns are produced only as the two orders combine. Even what we imagine to be disorder is produced by two orders.

The prototype of two orders cooperating is a spiral. A spiral is probably the best example of how the competition between two different methods of cooperation can work together to create complex orderliness. A spiral exemplifies a decrease of grouping giving way to the symmetry of the spiral. A spiral requires that grouping and symmetry orders cooperate simply to create the pattern.

Figure 8: Spirals
The rotation of a spiral is the most common pattern in nature where we see grouping order being manipulated toward increased symmetry order

Example 1: A variety of spirals and fractals.  The grouping and symmetry in each pattern can be recognized separately. The grouping in the pattern makes each spiral distinct and stand out while the spiral expresses an unraveling symmetry.

Example 2: Spiral galaxies are the universal shape in nature that vividly represents the opposition of grouping and symmetry.
Example 3:  Moisture in the air of a weather storm produced by the collision of varied temperatures, and air and moisture densities.
Example 4:  Waves curl into spirals as they crash upon the shore. The shoreline is a boundary between two large groups.

In the opposite direction away from grouping order toward increasing balance and symmetry, particles, objects, colors, shapes, can organize into lattice symmetries. In this direction of increasing order literally all that we define as form integrates and unifies with the reference frame of space, merging with the space they seemed to be arisen above. The many become one. Since we identify with form, we generally devalue how this final stage of symmetry order integrates parts and interpret it only as a destruction or loss of form. We interpret the product of increasing symmetry to be nothing at all, even though we easily identify and appreciate the magnificent beauty of lesser symmetries.

Figure 9: Beyond the cooperation of rows, rings, and spirals exists the crystalline lattice structures of matter, in which we easily recognize the balance and even spacing of increasing symmetry order. Where grouping order produces round shapes, symmetry order produces geometrical structures.   

Generally in our culture, we idealize the way grouping order divides the world apart into separate and pronounced things, since this results in the diversity of form. We ourselves are distinct forms, seemingly arisen above the uniformity, the sameness, the seeming nothingness, of the symmetry order extreme, which we refer to as empty space or absolute zero. The imbalances of matter are pronounced and create the definitive world. So it seems that things are defined by what they are. However, things can also be seen to be defined not by what they are, but rather by what they are not. Imbalances are definitive, distinctive, definite, pronounced, because they lack the indistinction of extreme balance.

The key to fully appreciating symmetry order involves recognizing that increasing symmetry or balance eventually causes a shift in the nature of the pattern, because ultimately, when pushed toward the extreme of symmetry order, in the direction of balance, previously separate things transform into a single unified whole, just as colors of paint become one. When we combine parts together into a whole, everything we started with exists within the final product, in the same way all colors exist in white light, or mathematical values combine into a sum.

Figure 10: Within the Evolution of Grouping Order becoming Symmetry Order exists the systematic orderliness and complexity possible of both orders cooperating. In understanding two orders and viewing this spectrum the emergence of complexity and life no longer appear to be a product of an ordered past becoming disorder. 

In summary, within the great expanse of cosmological space, extreme grouping order by nature typically produces a pronounced round object, like a single star, the most common feature of the universe, and also round like the planets, which are also general examples of grouping order.  The very definition of an object is that it is isolated and distinct from other things.  However, in the opposite direction, things can also organize into symmetries and lattice structures. In this direction the parts of an environment increasingly entangle and merge into the uniformity of space.  As all things mix into one, the form of objects is given to the larger form of the whole.  All physical properties exist at the surface of an infinitely complex underlying order of balance and wholeness, which Bohm called implicate order. 

In part two of this essay we will begin to clearly understand exactly how patterns evolve in nature from one order to another, from grouping order to symmetry order. 


Page Two:  Grouping Transforming into Symmetry

Page Three:  Two Orders in Art and Nature

Page Four:  The absence of one order creates the other

This essay last updated July 7th, 2007

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