Part Two - Page Three
and Symmetry (From
- Natural Order)
Orders in Art and Nature
Life is acutely tuned to
the discovery of order. It is our nature to develop structures and organize, categorize and store. It is also our nature
to strive for beauty. We gravitate toward the arts, judging the complexities of music and painting, sometimes not
knowing anything more than how it makes us feel. The artist tunes into the open world of possibilities searching for
ways of combining patterns and colors that triggers interest in the mind of the observer. We can recognize now that it
is some complex combination of grouping and symmetry which we are attracted to in art, architecture, and the artistry of
In the wide range of human-made visual art there are compositions more toward the nature of grouping order
that emphasize the order of definition and form, by being realistic, distinct, and bold, from artists such as
Michelangelo, Picasso, or Salvador Dali. And there are compositions in which distinctiveness and boldness is traded for
showing the connectedness and commonality between things, where objects flow together, where a unity is felt, as found
in paintings from Vincent Van Gogh or Winslow Homer.
1: Comparing the bold pronounced work of Rembrandt with the flowing low-contrast unity of Van Gogh. The
composition of a painting can be more variegated and distinct or it can be more uniform and flowing. Colors of a
painting can blend smoothly or they can stay pure and sharp in contrast.
Works toward the nature
of symmetry order are often low contrast with blended colors and wide brush strokes. Generally speaking, the overall
expression of a painting can either be more uniform and flowing or it can be more variegated and distinct. Paint colors
can blend smoothly or they can stay pure and sharp in contrast. Each of the different mediums in art, such as watercolor
or inks, express either the unity of the world or the distinction of things. Watercolor paintings overlap and flow
together while ink pen drawings are contrastive with sharp lines and distinct shapes. This range of possibilities we are
comparing is the two directions of order governing both materials and composition.
There are artists who in
exploring composition have learned to recognize and utilize two orders at an intuitional level years ahead of science.
Some art work seems to capture the rules of the unseen underlying orders, especially visible in the woodcut prints of
Charles Beck. In Beck’s art we see a rigid combination of grouping and symmetry. Generally in Beck’s work, distinct
subjects are spread almost perfectly even in the painting, like rhythm in music, sometimes with the only asymmetric
element being a trace of human activity taking place among the combining of grouping and symmetry. In his art Beck often
seems to convey an intuited awareness of our place in nature between the two orders.
Charles Beck Maplelag & Poplars
2: Woodcut Prints of Charles Beck visually reveal the two orders cooperating.
In Beck’s prints,
objects or things are portrayed evenly and symmetrically and although the evenness of the trees and the buildings might
be increased to an even greater extreme, they would then appear so orderly that they would not convey the message. They
would not relate in a mysterious way to similar patterns we see in nature. In nature we commonly see things combined
together evenly although the evenness is less rigid and distinct than what artists often portray. Artists often add-in
or choose a point of view that frames greater symmetry, since we all enjoy symmetry. Beck’s landscape compositions
above compared to those below communicate that we are constantly witnessing balance and symmetry in nature, it is just a
less rigorous and exacting symmetry.
3: Similar scenes in nature show a less tense combination of two
orders although the two orders are
cooperating in every real life setting.
The Axis of Orderliness to Chaos
the difference between the beauty we see in nature and the artistic beauty we see in man-made creations?
The difference between common patterns in nature apart from those patterns that are constructed
intelligently by humans as seen in art
and architecture is understandable as a variable of the tension between the two orders. A carefully planned
intelligent design can increase this tension until the two orders begin to cooperate to create orderliness and
to cooperation there is randomness. Normally the definition of randomness means to have no specific pattern or
objective, and randomness creates disorder, chaos, and disorganization, however, randomness is understandable as a measure of freedom
that only exists between the two orders. The extremes of grouping and symmetry orders are very strict. Each part
cooperates with other parts to create a whole pattern that is highly ordered. A random pattern is the opposite case
where the parts of a pattern do not cooperate with one another.
The ordinary patterns we experience in nature are always created only by two
orders, but most patterns in nature are less intensely symmetrical or less intensely grouped than man-made patterns, so
there is a randomness or freedom in the pattern, which is still the two orders working together, but not as intensely or
synchronically as is possible. In comparison, man-made creations can fuse the two orders together in a way that
eliminates randomness. A checkered pattern for example includes both grouping and symmetry in a very strict way.
Such a pattern is possible only if each order is intensely cooperating, while the two orders are also combined together
and so competing against one another. A calico pattern shows a less intense measure of competition between both orders,
yet we still can see the cooperation of each order, with grouping order creating distinct round objects, and symmetry
order spreading those objects evenly.
Figure 4: In the transition from grouping to symmetry order
group things and spread them evenly but not as rigidly
even as is
possible if the pattern is of man-made design (checkered pattern).
the checkered lattice pattern above we can easily recognize orderliness and complexity where in the calico pattern we are
seeing more freedom and irregularity. Such patterns portray the spectrum from order to disorder that we normally imagine
applies to all patterns, however, this spectrum is only one of three fundamental axes. The first axis runs between the
Alpha state of the big bang and absolute zero or Omega. The second axis exists adjacent the first and spans between
extreme contrast and zero contrast. Then adjacent the second axis there exists a third axis spanning from extreme
orderliness (such as the checkered lattice shown above) to the calico pattern, then further to extreme disorder and
chaos. The three fundamental axes are presented more fully and displayed graphically in part three.
Two Orders in All Patterns
speaking the conditions of our
own universe could travel toward extremes, but that is not what we observe. The expansion of the universe is moving conditions away from
Alpha and ever nearer to absolute zero in a very steady and consistent manner.
The universe stays very balanced between the extremes of lumpy and smooth, and we
observe a mild level of orderliness throughout the cosmos as opposed to extremely high orderliness or extreme chaos.
Figure 5: Above the universe over 13 billion years ago as represented
by the microwave background radiation measured by the WMAP Satellite revealing regional lumpiness in the
early universe before galaxies had formed (images from NASA), and below, a small sampling of the distant galaxies
that early lumpiness became (HST Abell
is an increased orderliness in patterns at low temperatures, first seen in things such as window frost or a snow flake, but
in warmer climates we commonly observe a measure of freedom or irregularity, which is essentially a measurable weakness
in the influence of the two orders, in contrast to a man-made fractal which displays an extremely intense combination of
6: The uniformity of water vapor in clouds and in the air and symmetry in the chemical structure of water translates
into the complex symmetry of a snowflake. Fractals exhibit intense symmetry.
we draw a line between patterns in nature and patterns that are man-made, as if man isn’t natural, but the only real
difference is the combined intensity of each order. Intense competition creates a level of cooperation in what can be
called an order game, or some way in which the two orders are intelligently made to work together. Human beings play all
sorts of order games where the two orders directly compete against one another, most plainly in sports, card and board
games (especially checkers), but also in social situations, business, politics, and conflicts such as war.
It doesn’t take long before a person is able to recognize grouping and symmetry in all patterns, both natural and
we analyze the images below as an exercise of finding cooperation between two orders, in the first photo, clouds of fog
float through a recognizably even distribution of trees in a forest. A cloud of fog is a group of particles, although
there is an obvious symmetry in the distribution of the particles within the cloud. Also this photo displays an
"S" curve to the fog, well known to be an attractive pattern in art and photography because it has symmetry,
true also of spirals. To the right, the growth of a plant exhibits obvious symmetry while the rain drops are grouped on
particular leaves. Next, even in this irregular growth of trees there is a measure of evenness in the distribution of
the trees and branches, difficult to appreciate as order, yet there is symmetry order in this image, although it is more
evident in the even distribution of fallen leaves. Below left, grooves carve up the earth evenly and seedling plants
sprout along each row evenly, forming the group of each row, and here we easily appreciate the symmetry of the
collective rows. Mountains in this satellite image of the Himalayas each represents grouping order, particularly
Everest, but from afar we see the collective uniformity of the mountains.
To focus more
clearly on what we perceive as beauty we can turn to the less temporary art of architecture. We most commonly find an intense competition between grouping and symmetry in man-made designs of governmental
and religious architecture. The pronounced grouping of materials contrasting the even distributions of windows and
columns are easily recognized in these buildings, as well as the general bilateral symmetries. All these symmetries are
components of a balance showing little sign of the innate conflict with the grouping order nature of the buildings
themselves. Yet take away the symmetries and we would have a simple pile of matter. Obviously it is pronounced masses
ornamented with symmetries that we find to be beautiful in architecture, likewise true of sculpture, music, art and
States Capitol Building
of Peterhof St. Petersburg Russia
Chapel in Rome Italy
Kaaba Shrine in Makkah Saudi Arabia
Searching for Photographer!
8: These great landmarks show the human preference for both orders combined together intensely competing and yet
course we forget sometimes that literally everything that exists is of the natural world. All that human beings create
is part of the universe and so nature. The only imaginable distinction between nature and the human world is that we
humans can intelligently make the two orders cooperate in ways that nature cannot accomplish without our help. This does
not mean however that there isn’t an equal measure of cooperation occurring generally in nature.
might even ask, when we consider patterns in general, is there a greater measure of cooperation in human-made patterns
over natural patterns? Note that most human-made patterns are not as rigidly perfect as the architectural examples
shown, while many plants and animals rival our creations with exquisite orderliness. There are likely consistent
measures of chaos and cooperation at all levels everywhere in the universe, even at the human level, almost as if we
accomplish exactly what nature has designed into us.
Two Orders in Sound and Music
Near the turn of the century the
art philosopher George Lansing Raymond struggled to understand the common underlying structure of order as it exists in
art, music, and poetry as equally as it exists in nature. In The Genesis of Art Form Raymond writes:
the child first observes the world, every-thing is a maze; but, anon, out of this maze, objects emerge which he
contrasts with other objects and distinguishes from them. After a little, he sees that two or three of these objects,
thus distinguished, are alike; and pursuing a process of comparison he is able, by himself or with the help of others,
to unite and to classify them, and to give to each class a name. . . . All his knowledge, and not only this, but his
understanding and application of the laws of botany, mineralogy, psychology, or theology will depend on the degree in
which he learns to separate from others, and thus to unite and classify and name certain plants, rocks, mental
activities, or religious dogmas. Why should not the same principle apply in the arts? It undoubtedly does…
enables one to conceive of many different things—birds or beasts, larks or geese, dogs or sheep, as the case may be—as
one. Classification is, therefore, an effort in the direction of unity. It is hardly necessary to add that the same is
true of art-composition. Its object is to unite many different features in a single form. Unity being the aim of
classification, it is evident that the most natural way of attaining this aim is that of putting, so far as possible,
like with like…
Grouping and symmetry provides a
simple way of understanding the common order of all patterns in nature including art and music. In separating grouping
and balance into two components the complexities of art and the harmonies of music are perhaps more fundamentally
comprehensible than with any other method of description. The first level of grouping order in music is just a single
note breaking silence, like a particle in space, or a star in the sky. Then in the rhythm of music we find the evenness
and balance of symmetry order. Often in a song several different notes are played simultaneously with one instrument to
create a chord, which is somewhat like cooking various vegetables into a soup. A careful selection of certain like notes
create harmonious chords, just as many different instruments create songs.
In the same way that we can define
a frame of reference in space, we can define a frame of reference in time, which in music is called a measure. A musical
example we can pick apart which most everyone is familiar with would be the first notes of Beethoven's fifth symphony.
Three sudden notes are followed by a drawn out fourth note. A series of pronounced individual notes played close
together as opposed to further apart in time is of course intense grouping order, although the even rhythm is symmetry
order. A steady rhythm is perhaps the most important ingredient of music. Rhythm is what distinguishes music apart from
all other sound. But we also find symmetry in a lasting note duration, which is like a smooth dense space in which
matter is spread evenly.
The complex ordering of many
musical instruments can be interesting, pleasant, saddening, spirited and exciting, able to compliment and enhance every
human emotion, perhaps suggesting a connection. Musical instruments create either more pronounced blunt sounds akin to
grouping order, as with percussion instruments such as drums. Other instruments play sustained notes and chords more
evenly across a measure of time, such as a violin or a flute, representing symmetry order. Music genres like rock and
roll or rap that are pronounced with a strong beat are more of the nature of grouping order, while the smooth and drawn
out rhythms sometimes produced by a symphony are more toward the nature of symmetry order. Regardless, a beautiful
musical composition resonates with both the distinction of notes and instruments, and the limited harmonizing of those
notes and instruments.
Multi-tracks of regular sounds.
Raymond, who was a professor of
aesthetics at Princeton, also considered how two very basic but very different elements contribute to the beauty of art
and music. Raymond initially focuses on the role of “likeness”.
[likeness] to art-composition, and looking, first, at music, we find that the chief characteristic of its form is a
series of phrases of like lengths, divided into like numbers of measures, all sounded in like time, through the use of
notes that move upward or downward in the scale at like intervals, with like recurrences of melody and harmony. So with
poetry. The chief characteristics of its form are lines of like lengths, divided into like numbers of feet, each uttered
in like time, to which are sometimes added alliteration, resonance, and rhyme, produced by the recurrence of like sounds
in either consonants, vowels, or both. In painting, sculpture, and architecture, no matter of what "style, "
the same is true. The most superficial inspection of any product of these arts, if it be of established reputation, will
convince one that it is composed in the main by putting together forms that are alike in such things as color, shape,
size, posture, and proportion…
The likenesses mentioned of lyrics
and poetry are most apparent in very simple poems such as, “Mary had a little lamb, its fleece was white as snow. And
everywhere that Mary went, the lamb was sure to go.” But specifically what does Raymond mean by likeness. How many
different ways can things be alike? Are there perhaps opposing directions that things can be alike? For example, each
letter in the alphabet is different, yet some letters form a group called vowels, which are alike in ways but different
than the group of consonants. And yet all are alike in simply being letters, so letters are simultaneously different and
alike. Where letters are expressions of distinct form and thus grouping order they are different, and where letters are
a general type of forms they are alike, and as a whole create a uniformity. It can be a surprise to realize that all the
letters in this book, or every book that has ever
been written in any language, exist within any tiny black square.
It is said that someone asked
Michelangelo how he had created such a perfect image of David out of stone, to which he replied that David was there in
the stone all along, and just needed a little help in getting out. In being so focused upon likenesses that establish
the differences we notice between things, which make classification possible, we easily forget that everything is of a
single existence and thus is ultimately just one thing. Ultimately all difference is an illusion. All things are
Is the beauty of music and poetry
and art determined by a mix of these two opposite directions of likeness? Having considered likeness, Raymond then
focuses on variety and contrast:
mind is confronted by that which classification is intended to overcome, by that which is the opposite of unity—namely,
variety. If there were none of this in nature, all things would appear to be alike, and classification would be
unnecessary. As a fact, however, no two things are alike in all regards; and the mind must content itself with putting
together those that are alike in some regards. This is the same as to say that classification involves, occasionally,
putting the like with the unlike and necessitates contrast as well as comparison. A similar fact is observable in
products of art. One of the most charming effects in music and poetry is that it is produced when more or less
unlikeness is blended with the likeness in rhythm, tone, and movement which, a moment ago, was said to constitute the
chief element of artistic form. In painting and sculpture one of the most invariable characteristics of that which is
inartistic is a lack of sufficient diversity, colors too similar, outlines too uniform.
In how likeness in one way makes
things different and classifiable, and in another way makes all things the same, we can see distinctly why there are two
different and incompatible kinds of order in nature. In one direction of being alike things are different and unlike
other things. Birds of a feather flock together. This classification creates contrast and unlikeness. Unlikeness is even
required of diversity. In another direction of being alike things are more general or similar to other things. All birds
are mammals. All mammals are animals. All animals are life forms. All forms are matter. All matter is part of one great
existence. In combining like with like we create the distinctions and definitive form of grouping order, yet in
combining that same unlikeness we somehow further the unity of symmetry order. We bring all things together into a
We are all attracted to symmetries
and balance in music and art, yet unlikeness and imbalances are a critical ingredient of the aesthetics of all art and
music. Too much symmetry, too much harmony, too much balance, and we end up with silence. No matter how intense, a
synchronized positive wave and a negative wave turn each other into silence. And to us, silence, like the white canvas,
When two sounds are perfectly out of phase they combine into silence.
The more the notes and chords are
drawn out, the more the music is indistinct and unified over its measure of time, and here again the extreme moves
toward a single sound that cannot be heard. Sound is fundamentally an oscillation. Without oscillation, sound is
silence. Sound, like both energy and matter, is an oscillation of waves, and when we stretch that wave flat it becomes
silence. Flat sound, flat energy, flat matter, is like the color white, our senses perceive it as a nothing even though
all possible sounds combined together have the same consequence.
All music is created from limited
measures of imbalance and balance. In music, in art, in poetry, we want to experience imbalances and balances eloquently
woven together. We want the imbalances of grouped likenesses combined with the sameness and balance of symmetry. We want
to see and hear the complexities possible in the myriad of ways of combining grouping and symmetry. We are attuned to
those complex combinations possible of both orders. It isn’t simply order out of chaos that gives art and music its
pleasurable qualities, it is the cooperation of each order in strict competition with one another.
A wave stretched flat looses energy.
distinction between the two kinds of order, between dividing things apart and mixing things together, initially seems
too simple to be of any great importance. Certainly, the important simple principles have all been discovered long ago.
It is after all something a child could understand. How can something so simple dramatically change how a person sees
the complex world? Indeed the distinction between the two orders is simple, but our existing definition of order is even
simpler than what is being explained. Consequently the concepts of order and disorder only vaguely describe the patterns
we experience, which actually makes the universe seem more complex and perplexing than it is.
learning to recognize two orders virtually everywhere we look, we can try to return to the basic concepts of order and
disorder, except an increase in symmetry order now means that grouping order is lost, and an increase in grouping order
requires that symmetry order is decreased. This completely contradicts the commonly held belief shared by most that
order decays into disorder and it contradicts the belief in science that there is high order in the direction of our
past which is decaying in the direction of our future. The exclusivity of two orders necessarily replaces the
commonplace concepts of order and disorder, showing that neither concept can be generally applied to nature. In essence,
we have to start over.
more Advanced Page on Two Orders:
Absence of One Order Creates the Other
Or move forward to map all possible universes.
Part Three : The Space of All
last updated Mar 7th, 2007