Two - Page Two
and Symmetry continued
Transforming into Symmetry Order
how all patterns inevitably evolve from one kind of order to another allows a person to see the single underlying
process by which literally everything in the universe changes and evolves, including how we ourselves inevitably grow
and change as individuals and as a society. As a first step toward seeing this basic evolution of nature we must recognize that
disorder is a temporary stage between one order and the other. In the first four squares below we recognize a common
portrayal of order becoming disorder. Similar to an opened flask of gas, in the decay of grouping order a single dense
object breaks apart and begins to spread evenly. As with a gas, eventually the parts spread out randomly within the
volume of the square. The order of the single object has seemingly disintegrated into disorder. However, we can also see
below that in the overall spectrum of patterns the first four stages have been moving in the same direction toward the
objects being perfectly balanced within the space of the square. In the first four stages the patterns have not only
been evolving toward disorder, they have also been evolving toward symmetry order. Beyond that fourth stage exists the
extreme of the objects being evenly spaced, which exists beyond what we think of as disorder. In the fifth stage, beyond
the even spacing of objects, exists the extreme of a final stage, where the individual parts are diluted and spread
perfectly even. If a system continues in the direction of increasing symmetry order (balance) the objects become one
with the reference frame (the volume of the square). The range of possible patterns includes two types of order, with
extremes of each order on either end. This is true for the universe as well.
Figure 1: Symmetry
Order Exists Beyond Disorder. The typical way that we expect changes to occur involves order
disorder as shown in the first four stages, yet the extreme of even spacing (symmetry order) exists
in that same
direction, as shown in the fifth stage, then finally in that same direction exists the uniformity of perfect
purpose of this transition of patterns above is to show that even if disorder seems to increase, the evolution of
patterns in that direction are invariably moving toward another kind of order. Disorder is recognized here only to be a stage in the
overall transition between two orders. To understand why this temporary stage of disorder occurs, in the next step we
will reduce the disorder to a minimum.
any fundamental study of patterns we must recognize that all patterns exist trapped between the two kinds of order, and
every pattern exhibits measures of grouping and symmetry. Said more precisely, each pattern exhibits a measure of
cooperation between each order which varies in intensity. If the intensity of both orders is high, then the pattern
exhibits a high measure of both grouping and symmetry, which we call orderliness. The entire transition of patterns below displays very high
intensity between the two orders so it is very orderly. That high intensity decreases the amount of irregularity
(disorder) allowed in the transformation, making each stage appear ordered.
|Grouping Order extending into the future
reaching into the past|
Figure 2: In this very
simple transition between grouping and symmetry the tension between the two orders is high,
so there is no
irregularity. Each stage begins grouped, then breaks up, then spreads evenly. Once the objects are
evenly they are forced to undergo a phase transition by dividing apart, this being necessary if the pattern
is to continue toward symmetry.
Notice that at each
stage, between the extremes on each end, there is a high measure of both grouping and symmetry. Above we are seeing the
same transition as shown in figure 1, except throughout the transition in fig. 2 the influence of each order is intense,
causing the objects to remain grouped but evenly spaced. This maintains the objects in a lattice pattern. In looking at
these patterns we can imagine the cooperation of each individual type of order intensely competing against one another.
Notice the influence of each side is apparent throughout the transition, as if the invisible influence from the
extreme order on each side is reaching all the way across to the other side. Below we see these
same two transitions shown together, showing nature has two options when evolving from grouping to symmetry, one where
the intensity of each order is very low and another where the intensity is high.
Figure 3: The entire library of the patterns in between the two extremes
grouping and symmetry portray high and low measures of cooperation.
The more orderly patterns in nature are the product
of the two orders competing or cooperating with one another. Orderliness is created when two orders strongly cooperate or compete,
while disorder occurs when the two orders weakly cooperate or compete. In the images below, a field of grass forms a
large group of that plant and yet the even distribution of the grass in the field is symmetry order. An orchard or a
grove is a group of trees while the trees are spread evenly, extremely even in an orchard, and less intensely even in a
natural grove of trees where the competition between both orders is at a natural level.
Thus far we have only considered the transformation
of grouping to symmetry of a single element or one color. The same transformation using two colors is unique in that it
requires a much more pronounced stage of irregularity. The patterns below portray two groups transforming into a single
pattern of symmetry order. In order for balance to increase the two groups blend together, like the beginning moves of a
chess game. This two color transition applies importantly to the small world of atoms since ordinary matter is created
from positive and negative particles. With blue and red representing positive and negative, the end result of blending
together is the neutrality of empty space, since oppositely charged particles annihilate one another. In the final stage
the parts have enfolded into the perfect symmetry of space. They have become one with their reference frame.
5: With two or more colors the transformation has to pass through a more pronounced stage of disorder,
when the two
groups begin to mix together. In the end, positives and negatives become neutral.
always use a checkerboard pattern to represent symmetry order however that pattern is actually a limited measure of
symmetry order, since each square or circle in the lattice pattern represents a measure of grouping order, meaning that
we can divide up each square of our checkerboard pattern into smaller, finer squares and then mix them back together
again as a finer checkered pattern. Each square is unavoidably a grouping of smaller squares. Notice that once the
transition above reaches a stage where the objects are spread evenly, they must then divide apart or dilute in some way,
necessarily so if the pattern is to continue in the direction of increasing symmetry order or balance. In science this
would be called a phase transition.
note also in the two images to the right how an even distribution of the dots spread throughout the entire frame of
reference (the square), has much greater symmetry order than a tight group of dots. The pattern on the left has
greater grouping order, but the pattern on the right has greater symmetry order. The reason is because the even
distribution within the reference frame is a more balanced pattern. Surprisingly, contrary to our ordinary sense of increasing order,
symmetry order increases as parts are spaced or spread evenly throughout the entire reference frame. As we push
the checkerboard pattern toward the ultimate extreme of its order the colors unify with the space itself, which
exemplifies what always results from extreme symmetry order, a oneness of all objects and properties. Many
different qualities or properties become one property. The final state is a unification of many things into a oneness
that we ordinarily recognize as nothing at all, a perfect uniformity scientists sometimes refer to as a singularity.
Figure 7: Grouping and Symmetry Order with increasing color dimensions.
figure 7 above we see simple examples of rows, rings, and spiral, in this case portraying colors of light projected on
a screen, forming patterns in which we easily see both grouping and symmetry. The first image of each example shows a
grouping extreme while the last image shows the light combined together, resulting in a total lack of differentiation
and form, yet each is the extreme of symmetry order for these patterns. Of
course subjectively one's instinct abhors the notion of loss of form, the thought is almost horrifying to our
identification with form, even if the separate forms are becoming the oneness we otherwise sometimes idealize. In
reality we are more apt to see oneness as nothing. More objectively one's intuition might recognize that what is
generally occurring in these transformations is that imbalances are combining together to become a balanced whole.
There are many dualities in nature that balance out to zero, just as there are triads that balance out, and so on.
Colors of light are an ideal example, in how the infinity of colors all sum to white light.
Figure 8: We observe simple grouping order and symmetry order in both galactic structure
and atomic orbitals.
|Figure 8: A large mass ornamented with
symmetries. Orderliness is the product of two orders strongly cooperating. |
we know that all identifiable material things are non-zero imbalances. They are made of positives and negatives. And of
course the ultimate balance point is always a zero balance. In science we describe the grouping of matter, stars,
galaxies, planets, gases, as order, yet each represents an imbalance in nature. Here we are discovering that the
balance of zero has to be considered a type of order also. Balance isn't a nothing, at least not in the sense of not
existing. Real nothings are simply balances and uniformities. The absolute zero of physics is the ultimate
balance, it is a combination of all times and places and things that collectively form a oneness, making the uniform
result appear to be empty of things. A really amazing fact about the universe is that empty space, and the result
of combining everything together into a unified whole, have the same exact qualities. So how then do we
distinguish between the ultimate everything of symmetry order, and the nothingness of empty space? Actually there is no
distinction. Even the ordinary empty space that surrounds us is far from empty. It is full. The world of things we exist
within is not more than a primordial nothingness, but rather all we know is less than a timeless everything.
order is the unifying force in nature. It is the great attractor, the great point of balance toward which all
change naturally progresses. Symmetry order is the invisible backdrop, the blank canvas, the board on which the
game is played. But acknowledging symmetry order is far more involved than simply recognizing that balance leads
to a smooth uniform pattern. The direction of symmetry order is not merely toward a balance between the objects we
see in our universe. Such is simply what exists at the surface of symmetry order, like waves on an ocean.
True symmetry order involves unification of the world we see with the complete world, the infinity of other worlds, of
other times, and other lives, all of which must be in balance in order to not be a part of our world, because our world,
the things of our world, are created from imbalances. Parts are removed from what we experience, anti-matter for
example. For us to have form, our identical opposite anti-matter selves have to exist somewhere else, creating the
imbalances we see as the finite world. And naturally imbalances tend toward balancing out. That is a universal
principle we all recognize. And of course the final product of balance is the native state of the collective
Universe, the timeless whole, the basic nature of existence, the default of being. In the direction of increasing
symmetry, the form of objects of this world are fusing and combining together with the underlying balance of the
timeless infinite whole. The physicist David Bohm called this process
surprising number of others in the past have constructed similar models of two orders, including Henri Bergson and
William Yeats in the early 1900's, but the most recent and most notable was Bohm. Many of these same ideas were introduced by Bohm to modern science in the 1960's. In an interview with Omni
magazine conducted by F. David Peat and John Briggs, David Bohm explained his concept of enfoldment:
"Everybody has seen an image of enfoldment: You fold up a sheet of paper, turn
it into a small packet, make cuts in it, and then unfold it into a pattern. The parts that were close in the cuts unfold
to be far away. This is like what happens in a hologram. Enfoldment is really very common in our experience. All the
light in this room comes in so that the entire room is in effect folded into each part. If your eye looks, the light
will be then unfolded by your eye and brain. As you look through a telescope or a camera, the whole universe of space
and time is enfolded into each part, and that is unfolded to the eye. With an old-fashioned television set that's not
adjusted properly, the image enfolds into the screen and then can be unfolded by adjustment."
did mean for implicate and explicate orders to replace order and disorder, unfortunately, the mainstream of other
scientists didn't catch on to his vision, and Bohm struggled with despair and depression at not being able to convince
the scientific community of the scientific value of his discoveries, a struggle I indirectly inherited and share
frustration in. After independently discovering two orders in my own way, and learning to present my own system of
seeing the same thing, the same principles, the same process in nature, and then discovering and studying Bohm's work in
greater detail, I now believe the only reason Bohm's ideas were kept from having greater impact is that he was
led more to challenge how quantum mechanics was being interpreted in his day rather than led to directly challenge the
second law's usage of the terms order and disorder. Although judging from my own experiences I am sure it would
have taken years for the challenge to sink in to the often dull collective mind of science.
a practiced theorist I am personally aware of how developing ideas have a rhythm of their own, a way of emerging in
various forms, and unfolding. The way they introduce themselves determines the direction they develop.
Having discovered two orders as I did, as an exploration of the structure of possibilities, one of the most important
lessons I convey perhaps uniquely, is that properties of balance and symmetry are derived from an entirely separate component
of the patterns we find in nature, distinctly different than grouping, and that an evolution of explicate order becoming
implicate order is taking
place right in front of us. After learning to recognize grouping and balance as different orders we can observe
any pattern and recognize the two separate components contributing to the order of the pattern. Since we don't yet
recognize that increasing balance or symmetry order is the product of a special form of order, we incorrectly recognize
for example the spiral features below as being properties somehow associated with grouping order, we see them as a
product of the past, when such properties actually are related to the balance of the future. Eventually I shall
explain that symmetry order is an order in our own distant future continually influencing the present.
are not accustomed to recognizing the simplicity of uniformity and sameness as being properties of an underlying
easily recognize the balance and symmetry in the pattern of a snowflake as being highly ordered. Yet the same
qualities of symmetry and balance pushed to extreme leads to an indistinct sameness that we have
no respect or appreciation for because of our identification with finite form. The funny thing is that when
many things become one thing, we see nothing. We are so attuned to recognizing the organizational properties of
grouping order, or the pattern complexity that results of patterns which utilize both grouping and symmetry, that the
uniformity of symmetry order in extreme, the order of oneness and wholeness, doesn't seem like anything at all.
all know that if we mix two or more things together to extreme they become one thing, but when that one thing is
everywhere and everything, it looks like nothing at all, so it is difficult to rationalize that the original parts that
went into creating the uniform pattern are still there in the uniformity. There is a similar uniformity and
sameness in grouping order when we combine all of one kind of thing into a single object, like many atoms of gold
together form a larger body of gold. But the combinational sum of like things creates a larger object with
increasingly distinct and pronounced qualities relative to other things. In
contrast, when all things combine together into one thing everywhere there isn't anything else to relate the sum of
all to, so symmetry order is ever less pronounced as various qualities merge together. Of course this is
not how we expect the world to add up. In math when we add up things the sum gets ever larger
and pronounced, not increasingly
seems of course that mixing different things together creates disorganization, at least in respect to the order we are
so much more accustomed to. Causing the physical structure of things to disintegrate is not commonly seen as an
alternative method of creating greater order. Disorder seems an end on to itself. Disorder
seems like a general type of pattern with its own extreme measure, when in fact all disorder is a product of the two
orders. Disorder is just an irregular combination of the two orders, small measures of grouping contrasted with small
measures of evenness, arranged irregularly. The
extreme of chaos can be understood as having a negative tension between the two
orders. In other words, it takes work or effort to create high irregularity, which is why we observe so much order and
only mild irregularity in our environment
Symmetry in Art and Nature
move forward to map
The Space of All Possibilities
essay last updated July 7th, 2007