The Square Format - Example 2

THE SQUARE FORMAT


Cliff Dwellers - 1913
Artist: George Bellows (1882-1925)

This is the second post with an example of the square format used in a painting. The first example was a painting by Alfred Sisley titled The Rest by the Stream.
The square format of The Rest by the Stream, helps achieve a very calm, restful effect. In the painting shown above, by George Bellows, the square format helps achieve a stifling, compressed, claustrophobic, "no way out of this place" effect. (It makes me think of the trash compactor scene in Star Wars.)

WHAT IS GOING ON IN THIS SCENE

Obviously these are poor people who cannot stand the heat inside these brick buildings they live in (and I assume their apartments are small and crowded, adding even more pressure). Of course there was no air conditioning back then. They have to go outside in order to get any relief at all, though they can't go far - either onto their tiny balconies or onto the crowded street and sidewalks directly below. One gets the feeling that the people in this scene are trapped, unable to get any real relief before they'll have to go back inside. Although outside of their rooms, they are still virtually imprisoned between the high apartment walls.

Although I did not read about what was actually going on in this picture before I first saw it, I knew immediately that this was a crowded tenement scene in New York. Where else could it be? I knew of the Ashcan artists of New York and what their usual subjects were, and that George Bellows was associated with them (though I had only seen his boxing scenes). I was especially familiar with the tenement drawings of John Sloan, which I have spent a lot of time looking at and am still fascinated by. (See Sloan's drawing called Night Windows (1910), on the Phillips Collection website; also, there is an article on John Sloan on Wikipedia.)

However, I am assuming that even if I hadn't known anything about these artists or their typical subjects or about the living conditions of recent immigrants in New York City in the early years of the twentieth century, I would have had a strong inkling of what was happening here because of what the composition and the square format are "saying," and I'm pretty sure you would have come to the same conclusions.

But what if a stranger who had just arrived from another planet and had never before seen these types of buildings or human beings, nor knew what we know about the times, the place, and the local artists were to observe this picture. Might they be able to quickly figure out what this picture was about? The basic idea, I mean. It depends. If their home planet was large and dense and gravity was as important there as it is here (which would probably be the case), it seems likely to me that the stranger would at least be able to figure out the basics: these creatures have been forced outside, they can't go far, they are trapped. Also, the alien -- being some kind of intelligent creature (here alone, observing, and curious) -- might realize that the "people" were at least some kind of animal life, probably intelligent (they are not all doing the same thing, so one might guess they're self-guided), and so on -- but what I'm most interested in here are the basic forces and the forms and directions and such that reveal them.

THE SQUARE FORMAT AND GRAVITY

Although the square format has been much used since the early 20th century for abstract and semi-abstract pictures for the very purpose of eliminating the appearance of the effects of gravity (which are so much a part of "realistic" painting), Bellows obviously did not wish to disregard gravity and in fact the effects of gravity are very much taken into account by the artist, and used to help us understand what is going on. Just one example: The people, sapped of energy by the heat, seem to have spilled from their no doubt sizzling apartments downward toward the relief of a lower, comparatively cooler and airier, stratum, but now that they are there they appear to be weighted down and barely able to move (note that everyone at the bottom of the picture is sitting at or almost at ground level, or has both hands and knees on the ground, and they do not look like they're about to get up). Our intuitive understanding of how gravity works to pull and hold people down when they're weak or tired or injured or sick helps to suggest or reinforce the idea of these people's lack of energy and lack of ability to do anything about the situation.

THE SQUARE FORMAT'S CONTRIBUTION TO THE OPPRESSIVE LOOK OF THE SCENE

In this square format, all four sides seem to be pushing toward the center or at least holding it very firmly in their coordinated grip, giving a feeling of compression throughout the entire picture. Of course there is help in creating this squeezing effect from the vertical edges of the buildings which repeat the verticals of the inward-pushing sides of the square, plus there are the converging perspective lines which make it look as if we're peering into a brick box, at the far end of which is a lighter-colored building which appears to be marching forward right up the street toward the crowd of people ... who, as we know, cannot escape. (All I can say is, this picture must have been a lot of fun to think out).

WHAT IS IN THE CENTER OF THE PICTURE

In Sisley's square painting, The Rest by the Stream, there is nothing but a blur of leafy branches in the middle of the picture, but this central area of indistinct "leafiness" seems to be surrounded by a "circle," which transforms it into something like a pinwheel that seems to move around and around hypnotically, helping to give the effect of movement and breeziness that spreads to the edges of the picture. This is a very refreshing effect.

The center of Bellows' inner city scene is also virtually empty - There is nothing to focus on there. But just as is the case with The Rest by the Stream, the empty space is surrounded by a "circle." In this picture it is a virtually inert circle of people (in the foreground as well as at the windows and fire escapes) along with the clotheslines at the top (a weak link that makes the bottom of the circle seem heavier). A circle has somewhat of a mesmerizing effect; it holds your attention. The people are around the edges of it but they seem to be held to it, too. It seems that nothing is allowed to escape this confining circle, only to drop to the bottom of it.

Besides employing the tondo-like circle (Arnheim calls these "internal tondos" - see in The Power of the Center, p. 130, by Rudolf Arnheim) within the already confining square format, in order to, among other things, make us see the pattern of distribution of the people including those just outside their rooms, the artist has seen to it that no one is making a move toward the edges, not even at the bottom where most of the people are concentrated; the people seem held in place -- they have escaped the worst, but this is as far as they can go. They are "held to the center" by the artist's composition (including his choice of the shape of the canvas).

The verticals of the buildings, especially the one in dark shade, very effectively keep the "circle" from spinning (as the center does ever so slowly in The Rest by the Stream by Sisley), thus oppressively helping to keep the people weighted down at the bottom. Those verticals are reinforced by the nearby presence of the verticals of the edges of the picture. Also, the convergence of the buildings as they go into the background, where they meet even more buildings so that there is obviously no escape via that route, adds strongly to the effect of claustrophic confinement.


A Day in June - 1913
Artist: George Bellows (1882-1925)

A COMPARISON

In the above picture, painted by Bellows in the same summer that he painted the Cliff Dwellers, the effect is quite different. These are not the people who live in the tenements. These people can go to a park with cooling grass and shade trees and have a pleasant picnic when it's too warm in their homes. You will have noticed right away that the picture is not square - it is a horizontal rectangle. The horizontal rectangle allows the people the possibility of moving beyond where they are and accommodates well a feeling of peace and ease and conviviality. This rectangle is made even more peaceful and unstressful looking by its division into two shallower rectangles, the upper one a dark green mass that looks very deep and inviting.  Also, there are views beyond of the blue sky with clouds (including at both upper edges, so that the dark mass of trees doesn't seem to continue on forever as do the buildings in the inner-city picture), and people appear to be moving beyond the confines of the frame as well as into the dark, cool interior. In other words, there is a feeling of "escape from stress" present everywhere. It makes Cliff Dwellers look like a pizza oven in comparison.

ALSO READ: The Square Format - Part 1 (The Rest by the Stream by Alfred Sisley)

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Visiting Spirits - Where Are They Coming From?

When it comes to the entrance of spirits onto a scene, the main rule is this (as we all know): The exceptionally good ("holy") and powerful spirits come from above and the exceptionally bad (as in "they are coming from Hell") and powerful ones come from below -- while ghosts of ordinary dead people enter at ground level (unless they're raised from their grave six feet below the surface - but then they end up at ground level or just barely above).

Another "rule" seems to be that these visitors usually enter the scene to the left (i.e., the viewer's left) of the person or persons they've come to interact with. Of course there are exceptions, but it does seem that most of them enter from the left, especially if it's their idea (or the idea of their superior, who has given them orders) to make this contact with one or more living humans (and sometimes animals); on the other hand, it seems that in most cases if someone summons a spirit then the summoner is shown to the left of the spirit.

An Angel Appears to Balaam - 1866
Artist: Gustave Doré (1832–1883)
From Wikimedia, this picture is in the public domain

The angel, who at this point can only be seen by the donkey, has obviously entered the scene from the left (i.e., the viewer's left), and obviously from above, as we can see that she has wings of a size that would be awkward for regular use at ground level but very useful for flying purposes, plus of course it is common knowledge that angels live in Heaven (which is "above").

Gottvater mit Propheten und Sibyllen - 1497-1500
Artist: Pietro Perugino (1446-1524)

When God himself decides to communicate with people on earth, things are a little different. In pictures he very often seems to reveal himself from directly above - or very close to it - and doesn't come anywhere near ground level. He is often in something resembling a bubble, or large halo (aureola) when he is in this location. In addition to announcing his "holiness," these appear to seal him off from everything outside them. This appearance by God does not have to do with approaching humans at their level. This is not a "visit" so much as "vision," or some kind of a revelation, and is a one-way communication, apparently without any expectation of, nor desire for, immediate personal response from the human(s) below. The fact that he is near the top of the picture also makes it clear that this is a picture that is meant to imply a hierarchy wherein the person "on top" has power over those below even though they may not come into direct contact with them.*

* Please see other posts on this blog that have to do with gravity and how it influences our interpretation of what is going on in a picture. Not only does our understanding of gravity "tell us" that what is up higher has more weight (in a picture - not in real life) and thus (at least if it is not very close to or actually touching an edge of the picture) has power over what is below it, but also we are aware that something that is higher up can "observe" and perhaps understand better (and for that reason, too, have an advantage over) those who are below -- while those below, of course, for the same reasons are at a disadvantage.

 

Picture from a German church

From Wikimedia - Photo of this painting taken by Andreas Praefcke

I don't know the story behind the deathbed scene above, but this picture seems to me to be extremely easy to read, with its zigzag composition that includes all the characters, who are arranged in a way that tells us much more quickly than words what is going on here -- Without knowing anything about this, not even the title, it appears obvious to me that: the man is dying and receiving the last sacraments from a priest who is no doubt at that very moment pleading with Mary to intervene and ask that this man's soul be accepted in Heaven. Mary is placed between God (who is above, and not personally participating in the deathbed event) and earthly life, and she is (looking at and) begging God to have mercy on this man and either to let him live...because, as it also very obvious, the man has a wife and baby who will be left behind if he dies...or to let him into Heaven. Meanwhile the devil, rising from blackness below, and unseen by all, is surveying the whole scene and apparently waiting to take the man's soul down with him to Hell. The scene is pertinent to this essay because of the visitations of Mary (from above left) and the Devil (from below right) as well as the appearance of God to Mary, who has summoned him in order to make a request.

As mentioned earlier, whether the living person is purposely approaching or summoning the spirit, or the spirit is approaching the living human of his or her own volition, sometimes seems to make a difference with regard to which side of the picture they seem to have entered from. I have noticed that it is usually the one who has the idea of communicating who is at the (our) left. In the above picture the summoner is the priest on behalf of the man. The devil has taken it upon himself to enter the scene -- he was not summoned by anyone.

Magician raising a ghost

Illustration from Robert Cross Smith's The Astrologer of the Nineteenth Century (1825)
The image is based on an 1806 illustration by Ebenezer Sibly.

In the above picture, the idea of communicating was that of the magician, not the ghost, yet the ghost is shown to our left. But if you look at the illustration this picture was based on, below, you will see that the artist, Ebenezer Sibly, shows the magician and his friend on the left and the ghost on the right.

Edw[ar]d Kelly, a Magician. in the Act of invoking the Spirit of a Deceased Person
Engraved by Ames of Bristol (1806), original drawing by Ebenezer Sibly

Ghost of humans who, upon death, did not graduate to Heaven nor plunge directly into the depths of Hell (they seem to still be entirely preoccupied with earthly affairs and want to be handy so they can interfere in them easily), may approach people from any direction (except from skies above or from below, with the exception of rising from their own grave or from a lower floor or basement), but generally they approach at ground level or at times floating, upright, just a tad above the ground (no doubt due to their weightlessness - It's hard to keep your feet on the ground when you're a ghost, apparently).

Cap'n Goldsack, Pirate Ghost
Artist: Howard Pyle (1853 - 1911)

Although the pirate ghost in the above picture appears to be approaching the viewer "from above," that is because he has been placed near the top of the picture; he is not actually descending from above (from the sky), but, rather, seems to be approaching at ground level (with no sign of having flown or floated in) and appears to be stumbling down into an indentation in the ground.  His position at the top of the picture, in fact, (helped by the darkness of the head) gives him the "weight" that makes him appear to be stumbling heavily downward.

The Witch of Endor Raising The Spirit of Samuel.

c. 1800

Artist: Willliam Blake (1757 - 1827)

"The Witch of Endor, sometimes called the Medium of Endor, was a woman who called up the ghost of the recently deceased prophet Samuel, at the demand of King Saul of the Kingdom of Israel in the First Book of Samuel, chapter 28:3–25."

I am not sure which of these figures is the witch, but I'm assuming it's the person on the (our) right side of the picture, dressed in blue. "Her" arm is raised as if to "pull up" the spirit (yet the spirit seems to only have eyes for the fellow in orange, who must be King Saul, though I don't know). All I know about this story is what is quoted in the above paragraph, but the story the picture tells is what concerns me. We should be able to get the general idea of what's going on without knowing the story ahead of time.

The witch seems to have pulled up Samuel directly out of his grave. The relationship between the three, if we are to go by their positions in the picture seems to be that it is the man on the left who is the one who summoned the spirit, using the witch to do so, and that would fit the short description quoted in the last paragraph. In other words, the entity whose idea it was to make contact is to the left (i.e., our left) of the ghost (which tells us why the ghost is facing in that direction).

Brutus and the Ghost of Caesar - 1802
Copperplate engraving by Edward Scriven

(1775-1841) from a painting by Richard Westall (1765 - 1836). London, 1802

Brutus, visited by the ghost of Julius Caesar, whom he has helped to kill, is obviously feeling very worried here. The ghost is probably no taller than Brutus would be if he were standing, but still he seems quite threatening not only because of his gesture and his evil look, but because he (particularly his head - the center of his thoughts, which lead to actions) occupies quite a large area near the top of the picture and "above" Brutus who has been sitting in a casual fashion, not ready to run anywhere. Also, Brutus has been surprised from behind by the ghost and being penned in by the table (and apparently a wall or a drape to his left) is not prepared for a quick exit whether he can get his feet under him or not.

Nissaka Man Receiving Baby from his Wife's Ghost - 19th Century
Artist: Utagawa Kuniyoshi

Above: The description under this picture says that this man's murdered wife (the ghost) has just handed her baby to her husband, and that the woman's spirit lives in the rock that her blood flows from.

I don't know whether the man went to the rock to implore his dead wife to give him the baby, or if he was just there to visit her spirit as one normally visits a grave of a departed loved one and it was her idea to hand over the baby, or if perhaps he has just killed her himself, though I doubt the latter as it does say her spirit "lives" in the rock as if has been living there for some time.

She is looking toward her husband but there is some reason she has turned her back on him after handing him the infant. Perhaps he killed her some time earlier, and giving him the baby was her revenge - though if he had killed her, certainly he wouldn't want to visit the place where she was murdered as he'd probably be very worried about what her ghost might do to him.

The fact that she is "above" him in the picture, in the same area that Ceasar inhabits in the picture above, may tell us that she is the one whose idea it was to appear to her husband...that it was not his idea. I really don't know. I am not (at this time) able to "read" this picture clearly. Possibly if I had been raised in the Japanese culture it would be obvious.

The Approach of Doom - 1788
Artist: William Blake

When I first saw this picture I thought it was unfinished. Then I realized, or supposed, that it was not, that we finish it in our own minds, not with any "thing" that could be seen, but with a huge feeling of dread of the unknown.

Whatever it is, this "doom" that is approaching is coming from the left and it is filling the air over and under and around the people, nibbling away at them - dissolving them. They are backed up at the right as if they had gone in that direction to escape, but now have nowhere else to go as they have reached a dead end. Their legs are straight and their arms are entwined so they can be as close together and as far away from the dreadful thing as possible, and they are looking the only way there is to look, directly into whatever it is, which they can't see clearly but know means their certain death.

No monster could look as frightening as this cloud of "nothingness" that is enveloping them and that there is no escape from. The white tentacle-like shape at upper left that seems to be leaping toward the huddled group makes us realize that this is no innocent fog but something that contains a hellish element that seems to be throwing its light onto them, seeking them out in order to find and destroy them, very likely by dissolving them so that they become part of the cloud.

You may think I'm reading too much into this because I know the name of the picture ("The Approach of Doom"), but try to imagine this picture with a less morbid name, such as "A Lovely Summer Night's Walk in the Cooling Fog." You would probably then look at the picture and say to yourself: "I don't think so."

My hope is that this little essay will help the reader to realize that the placement of objects in pictures, in relation to each other and in relation to the perimeter of the picture, is very important to the viewer's understanding of what the picture is about.

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Verticality - Heaven is Up and Hell is Down

A vertical format strengthens the theme of the great desirability as well as difficulty of reaching Heaven and the ease of descending to Hell instead.

Why? Because Heaven is "up" and Hell is "down," and a vertical format, which so unmistakably shows who's on top and who's below (metaphorically speaking) is the best format in which to show a hierarchy, in this case the hierarchy that has Heaven at the top and Hell at the bottom.

But why is Heaven up and Hell down? It's gravity that gives us an up and a down, and it's the effects of gravity that make going "up" difficult and therefore admirable and "down" easy and therefore unworthy. Down is the direction in which gravity constantly pulls us toward the center of the earth. Up is the opposite direction ... toward the sky. Gravity holds us in place on the ground or...if we dare to try to defy gravity and move upward by some means...is ever capable of pulling us back to earth, in a most deadly fashion if we dare to attempt to go further than we safely can. For most of the time humans have noticed this they have not had airplanes nor were they able to go so far "up" that they escaped the pull of gravity, so when they imagined gods - beings superior to us - they imagined them like the clouds and stars and the sun and moon, apparently unaffected by this powerful force that we mere humans experience here on earth.

Lucifer - The Fallen Angel by James Donahue
For an angel who is no longer welcome in Heaven alas there is suddenly a very definite "down."
Source: Wikimedia

As for Hell, it is the opposite of Heaven and it is a place into which we "fall." Naturally it's "down." But it is not at ground level. It's even further down than that. We do not start out in Hell, after all, and so If we fall into it, it must be further down than the level at which we start out, even if we do not attempt to ascend to Heaven.

The Ladder of Divine Ascent - 1612
(The Heavenly Ladder of St. John Climacus)
Source: Wikimedia

According to an article in Wikipedia, St. John Climacus was "a 7th century Christian monk at the monastery on Mount Sinai." St. John's literary output included "The Heavy Ladder of Divine Ascent" in which he described the thirty "steps" one must take in order to reach Heaven.

One can see that it's a difficult climb to reach Heaven as there are many temptations by devilish types along the way which can lead one, no matter how high they have climbed to fall down further even than to the ground from which they began. It looks to me like a monster from below the ground has his mouth open ready to swallow up those who fall. In any case, obviously Heaven is Up (and a hard climb) and Hell is Down (and an easy fall), and a vertical format is very suitable to get this idea across.

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Centric Systems

I have no illusions about someone happening upon this post, seeing the title, and thinking "Oh! This sounds like a fun read!"

However, for someone who is just now trying to understand just what centric (or concentric) systems are, it might be a sight for sore eyes (okay, maybe I'm stretching things a little!). At any rate, it's not very long, there are several examples, and it's something artists need to know about.

The Introduction to The Power of the Center, by Rudolf Arnheim, begins with this sentence: "This book derives from a single idea, namely that our view of the world is based on the interaction of two spatial systems." Those two spatial systems are the centric system and the Cartesian grid system. They are both gravity-based systems, one (the centric system) natural and one (the Cartesian grid) constructed by humans.

Centric System

The Cartesian Grid

Combined Centric and Grid Systems

I've written about the Cartesian grid in a post called Art, Gravity, Life, and the Cartesian Grid. Also, in a post on Round Artworks I showed examples of how the two systems are used together in art. The post you're reading now is a (very) basic introduction to centric systems, but it should be kept in mind that the two systems work together (I will write more about that in the future).

DEFINITIONS In case you wish to refer to them as you read CARTESIAN GRID: A system of straight lines meeting at right angles, either on a two-dimensional surface or in three-dimensonal space. (The Power of the Center) CENTRIC: Having a center. (thefreedictionary.com) CENTRIC SYSTEM: A system organized around a center, either two-dimensionally or three-dimensionally. CONCENTRIC: Having a common center. (thefreedictionary.com) COSMIC: immeasurably extended in time and space; vast. (dictionary.com) GALAXY: A massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. (wikipedia.com) GRAVITY: The fundamental force of attraction that all objects with mass have for each other. (thefreedictionary.com) HIERARCHY: Any group of objects ranked so that every one but the topmost is subordinate to a specified one above it. (dictionary.net) PAROCHIAL: very limited or narrow in scope or outlook; provincial (dictionary.com) SYSTEM: An assemblage or combination of things or parts forming a complex or unitary whole: a mountain system; a railroad system. (dictionary.com)

I include the definitions above because the two systems are called so many different things by Arnheim. Centric systems are also called by Arnheim cosmic systems and concentric systems -- and at least once he refers to a centric system as a cosmic onion. (He also refers to the Cartesian grid as a parochial system.. .not to impress you with his extensive vocabulary, as there is a very good reason for calling it that and also for using the other terms rather than just one for each of the two systems ... but it can be confusing nonetheless to encounter all these names for just two spatial systems, and this is why for the most part I have only used the term "centric" to describe the one system that this post is about.)

TO BEGIN.....

Let's take just the most important definition out of the above table and look at it here. CENTRIC SYSTEM: A system organized around a center, either two-dimensionally or three-dimensionally.

And look at this simple diagram of a centric system again:

Centric (or Concentric) System

Holding that definition and the diagram in mind, read on.

OUR SOLAR SYSTEM - EXAMPLE OF A CENTRIC SYSTEM

Possibly the best example of a natural centric system, held together by gravity, in this case with the sun at the center, is our solar system (aka planetary system): Earth, Mars, Venus, etc., and the sun [star] they travel around).

"Our Solar System...showing the Sun, Inner Planets, Asteroid Belt, Outer Planets, the largest object in the Kuiper Belt - Pluto (originally classifed as a planet), and a comet."

A CENTRIC SYSTEM IS USUALLY (IN NATURE) AND OFTEN (WHEN HUMAN MADE) PART OF OTHER CENTRIC SYSTEMS (and sometimes has centric systems within itself)

Just as in our solar system there is the sun (a star) that is orbited by planets some of which are orbited by moons (all of which together make a centric system), in a galaxy there are an incredibly huge amount of stars, some of which are at the center of their own centric systems that include planets (some of which are orbited by moons). In other words, there are what seems to me at least (not being a scientist) probably a huge amount of solar systems (which are centric systems) within galaxies that are centric systems themselves. Centric systems within centric systems, that is. And so on...this not being a science blog nor I a scientist ... but the point is that centric systems often have smaller centric systems within them and, as well, they are often parts of other, larger, centric systems.

GRAVITY IS WHAT HOLDS A CENTRIC SYSTEM TOGETHER

Gravity (roughly defined as the attraction of a smaller mass by a larger mass) is what holds a natural cosmic (centric) system together. You will already know that moons are held in place by the gravitational pull of the planets they orbit, and the planets are held in orbit by the gravitational pull of a star that we call a sun (the center of a solar system), and so on.

A SOLAR SYSTEM IS PART OF A GALAXY, A LARGER CENTRIC SYSTEM

We call the galaxy that contains our own solar system (the solar system is also called a planetary system) the Milky Way. Galaxies do not all have the same shape, but they are all centric systems, even though the "center" of these systems may not be one object but a cluster of many very dense objects (a black hole, stars, dark matter...) all of which add up to an immense gravitational pull on everything further away in the galaxy.

The Sombrero Galaxy

The Sombrero galaxy is about the size of our Milky Way galaxy. It probably contains hundreds of billions of stars, many of which are probably orbited by planets. Not only is a galaxy a centric system, but any planetary systems it contains are also centric systems.

EFFECTS OF GRAVITY THAT WE CAN SEE HERE ON EARTH

We and everything around and under us is affected by gravity in many ways. One example of how gravity works is the quite observable (though probably seldom thought of) fact that the pull of gravity of our own planet is holding us to its surface thus preventing us from floating off into space (we feel the pull of gravity on our bodies as weight). The pull of gravity from the center of the earth is the reason it takes energy for us to rise from our beds, to lift our arms (especially when carrying something heavy), to walk uphill or even to walk downhill if the incline is steep as we must expend energy to keep from falling ("falling" means being pulled by gravity). It even causes our nose and ears to grow longer as we age (they sag toward the center of the earth).

Another example, which most of us probably do relate to gravity, as it is fairly common knowledge, is the moon's gravitational pull and (to a slightly lesser extent because it is so far away) the sun's gravitational pull which cause the tides here on our planet. "Tides are the rise and fall of sea levels caused by the combined effects of the rotation of the Earth and the gravitational forces exerted by the Moon and the Sun." (Wikipedia article on tides)


Mount Orgueil at low tide

CENTRIC SYSTEMS ARE HIERARCHICAL

A centric system is hierarchical and what's at the center is at the "top" of the hierarchy. As you move away from the center, objects are, generally speaking, less affected by the center, and eventually you get to a point where objects belong to another centric system. However, of course, all objects within a centric system are by definition a part of it and affected to some degree by its center no matter how far away they are.

THE SHAPE OF A CENTRIC SYSTEM IS NOT ALWAYS ROUND

"Centric" systems are not always round (natural centric systems are round, or at least symmetrical, only when there is enough space to achieve their ideal shape and when there is no interference by agents -- chemical, physical, or etc. -- that are able to deform them; and certainly centric systems are not usually round in works of art).

The "Network Tree Diagram," above, is a good example of a centric system that is not round, nor even symmetrical, yet is a hierarchical system like any centric system. It also shows how a centric system can be a part of other centric systems, as there are actually several centric systems within the large one here.

BIG THINGS, SMALL THINGS -- ALL ARE HELD TOGETHER IN THE SAME WAY

The same thing happens in nature even in systems that are much, much smaller than planetary systems, as all matter attracts other matter, the matter with more mass attracting with greater effect and from a greater distance. However, when it comes to very small objects (compared to planets and moons and stars) gravitational attraction is hardly if at all perceptible. Yet it is there. The pictures below show some examples of smaller centric systems in nature.

"Even in the crowded world of our direct experience, inorganic and organic matter occasionally has enough freedom to follow its inclination and form symmetrical structures -- flowers, snowflakes, floating and flying creatures, mammalian bodies -- shaped around a central point, a central axis, or at least a central plane. The human mind also invents centric shapes, and our bodies perform centric dances unless this basic tendency is modified by particular impulses and attractions." -- Rudolf Arnheim in the Introduction to The Power of the Center.

CIRCLE DANCES ALSO CONFORM TO A CENTRIC SYSTEM ARRANGEMENT


American Indian circle dance

"The circle is probably the oldest known dance formation." Wikipedia article on the circle dance

Bird's eye view of Avebury, in Wiltshire, England.
(Image from fromoldbooks.org)

Avebury is about 5,000 years old, even older than Stonehenge. You can easily see the centric systems involved in these man-made structures.

WHY DO WE NEED TO KNOW ABOUT CENTRIC SYSTEMS?

Knowledge of how centric systems work in nature (along with knowledge of how the Cartesian grid system that we have imposed upon centric systems in order to organize and understand what we see works) is essential for artists, and often is understood intuitively, if unconsciously. It is likely that we already "know" much of how these spatial systems work just from what we have observed in the world around us and what we have learned from school and books and so on -- and in the case of the centric system, we may even have been born with a tendency to arrange things hierarchically in circles and possibly even to find round or spherical patterns and places comforting (especially when we are at the center) and "complete" (thus satisfying) -- but we may easily mistrust and/or ignore, or even have no conscious awareness at all of this "knowledge" nor any interest in knowing about the spatial systems we live with, not realizing that such knowledge can have any use in art, or how to use it in art. So if we are not already fully aware of how these systems work, and why, it seems like a good idea to learn about these things consciously in order that we can make good use of all this in the art that we produce. And once we have it all in mind, then we need to understand how this knowledge can be useful to us - which I haven't written about here, but will in future posts.

Meantime, if you haven't already, you can read more about the Cartesian grid, and about how gravity influences our perception of the world and even the structures we make to live in, among many other things, in my post called Art, Gravity, Life, and the Cartesian Grid.

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NOTE: All pictures used in this post are in the public domain.

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Round Artworks

Before you start reading this post...

First (bear with me!), I'll provide a very short review of the Cartesian grid and the concentric system -- Not so boring as you may think! (Okay, maybe a little boring, but not complicated.) -- and then some examples of round artwork (tondos) are analyzed, below. You may be surprised at how helpful this might be if you're an artist and aren't already aware of how some subjects are more suitable for a round format than a rectangular format, and that there are different things to consider when you're composing a round picture.

There are two previous posts that you might want to read before you read this one (or you may prefer to go ahead and read this, then go to the others to understand this post a little better if the subject interests you). Here are the earlier posts:

Art, Gravity, Life, and the Cartesian Grid

The Tondo

In reading this present post (on this page) for the first time, you may want to zip through or even skip the first part (about the Cartesian grid and the Concentric system), or just look at the pictures and read the "In a Nutshell" parts. You can always come back to the first part if you're interested in learning more.

Planet Earth as seen from Apollo 17
Courtesy NASA/JPL-Caltech

We live on a round world but because of gravity we make use of a very non-round spatial system, the Cartesian grid, for practical purposes, in order to make things, understand things, etc. (see my earlier post, Art, Gravity, Life, and the Cartesian Grid to understand why).

IN A NUTSHELL: Although the earth is round, "in the parochial view of its small inhabitants, the curvature of the earth straightens into a plane surface, and the converging radii become parallels." (Rudolf Arnheim in the book The Power of the Center) -- The Cartesian grid represents the parallel verticals and horizontals that are so important in our lives here on Earth.

The Cartesian Grid "A co-ordinate system whose axes are straight lines intersecting at right angles"(Ref.)

However, when free of the constraints of gravity (either in real life or in our art), we use the concentric system to understand (and make understood) relationships between things.

IN A NUTSHELL -- "Cosmically we find that matter organizes around centers, which are often marked by a dominant mass.....A concentric system is, by definition, organized around a center....The central point allows for orientation....It creates a hierarchy." (Rudolf Arnheim, in POC) -- The concentric system represents matter or forces of some kind that are concentrated around a center, e.g. the planets circling the sun, or children surrounding their mother, or the fruit of a peach around its pit.

Concentric System (above)

In art we usually make use of both systems, combined.

IN A NUTSHELL: "Together they [the Cartesian grid and the Concentric/centric system] serve our needs perfectly. The centric system supplies the midpoint, the reference point for every distance and the crossing for the grid's central vertical and horizontal. And the grid system supplies the dimensions of up and down and of left and right, indispensable for any description of human experience under the dominion of gravity." (Rudolf Arnheim, in POC)

Combined systems (above)

Depending on what the subject is, what we're "saying" about it, and the shape of the "frame" (or outer edge of the artwork), the artist will focus more on one system, or more on the other.

A tondo (plural: tondi or tondos) is a round painting or sculpture or other circular work of art. The word comes from the Italian "rotondo" (round, or rotund). The tondo's round shape is particularly suitable for pictures that are not about life here on earth - that are, instead, about gods, fantastical space creatures, fairies, etc....things to which gravitational constraints do not apply.

"Not surprisingly we found that the concentric model of composition is enhanced by the tondo format. This does not mean that the Cartesian grid, so strongly advanced by all terrestrial subject matter, is simply suppressed. To be sure, the more fully realized are the compositional requirements of the tondo, the more the grid recedes as a self-sufficient system." (Arnheim, in POC)

Round (or spherical) things in nature and in art are considered "perfect" and "complete" and "stable within themselves" as well as able to be easily moved, intact, from one place to another (and if they're resistant to gravity, or even, at least effectively, not affected by it at all due to being out in space beyond gravitational pull, or in an imaginary realm where gravity doesn't apply, they have no real need for the horizontals and verticals of the Cartesian grid).

Some Examples of Tondos, Analyzed

Madonna and Child, painting by a follower of
Sandro Botticelli (Date c. 1500-1510)
El Paso Museum of Art

The tondo above clearly shows both systems being employed. Note the straight lines of the "throne" behind the Madonna and child. Those show strong evidence of the Cartesian grid system. It looks a bit awkward, as if the throne were painted in its entirety, then cut off using a circular template, but the straight lines of the throne do give a great deal of stability to the design, making the woman and child look very secure.

In this picture, the exact center does not just happen to be the point where the Madonna's womb and the child who came from it meet in the picture; if the artist didn't plan this consciously, he no doubt did so intuitively. This point is the center of the larger "center" which is made up of the child and his mother. The "throne" in the background snugs up around the larger center just mentioned, composed of the mother and child together. This is my own interpretation based on what I understand from the Arnheim books I have studied (as are the other interpretations below, except what is contained in quotes by Arnheim), but I feel quite sure that I am right.

A Desco da Parto Masaccio (1401 – 1428)

The tondo by Masaccio, above, also shows clearly that the Cartesian grid was the basis for the composition (note the strong verticals and horizontals and the perspective lines). It looks as though this "round" scene is just a portion of a rectangular scene, and while the arches are sympathetic with the roundness of the overall shape, and there is nothing "wrong" with using part of a scene that was first designed in a rectangular shape if it looks right, it shows that the artist had adapted his Cartesian-grid-based composition to the tondo shape rather than creating an idea for a picture of this scene that would be perfect for the round shape.

Greek kylix - Youth pouring wine with an oinochoe in Dionysos' kantharos
Triptolème painter

A very awkward composition for a round picture, above. Everything "fits" into the round shape, but only because it was all "squeezed" into place.

Kylix
Achilles tending Patroclus wounded by an arrow
Sosias - c. 500bc

I think that the scene just above is a much more successful composition in the round shape than the one of the "Youth pouring wine." The artist was much more sensitive to the circular edge. The subjects are bending over naturally, rather than tilting as if they're falling over, and there are some very interesting negative shapes around the edge (as well as within the composition). The center of the circle -- the area of most intense focus in a circular composition -- is well-used, too, as there you see exactly what is going on (the tending of the wound) without having to look any further. All the action is centered around this spot.

There is also reference to the Cartesian grid in the above picture, especially in the horizontal "floor" beneath the two men, and in Achilles' close-to-vertical lower back and "skirt." These provide the vertical and horizontal references that make the actions clear, and they also provide stability to the composition. The many diagonals in the picture make the composition appear lively, busy, and tense -- all the more so because they are compared with the "stable" Cartesian references of the floor and of Achilles' back.

Madonna della Seggiola (also known as Madonna della Sedia)
Rafael - 1513-1514

"In the Madonna della Sedia direct references to the angular framework are so thoroughly avoided that the one reminder of verticality, the upright post of the chair, looks almost like a safety device, needed to keep the picture from rolling out of control." (Rudolf Arnheim, in POC)

And note how the vertical post is topped by a ball shape, and also has curves below in different forms. Also note how the chubby baby's round toes relate to the rounded forms on the chair post, which relates to the faces and the baby's elbow, etc. You go from one to the other and go all around the picture, the round shape of the tondo encouraging this. As Arnheim pointed out, the post is the only thing that keeps it all from spinning.

There are so many things that can be written about round compositions that although I have have already written two posts on the subject, including this one, I have barely touched the subject (I may write more). Yet I hope that what I've written, and the illustrations accompanying it, will at least get across the idea that a round composition must be approached very differently than a rectangular one, and that some subjects are better than others in such a format. I also hope that people will be encouraged to try their own round compositions. I'm working on one myself that I started a couple of years ago and put aside. Now that I've learned a lot about composing for this shape, I'm starting over and hope to do it in a more intelligent way.

This animated snowglobe was created by Patti Wavinak of Moon's Designs, who has given permission to use this picture here.

Finally, here is an animated snowglobe. I looked through many, many snowglobe pictures before selecting this one. Most of the pictures didn't show the globes as I remembered them from long ago. The ones I remember had scenes such as this one, and here you don't have to imagine how it looks when you see the "snow falling."

To me this snowglobe picture illustrates something important about round (or spherical) compositions -- They are perfect at depicting another world, a self-contained world that is not where we live -- it is "out there" and not something we can join in (neither can anything in that world join us).

What is more "perfect" and "complete" than a world made up in the imagination -- a world that we sometimes wish we could enter and be part of, but know we can't? It's a world by itself. Something that we can only contemplate.

In order to join that world, we would need to be transformed into something that belongs within it and even then we may not gain entrance...it's hard to imagine entering (or leaving) a spherical "self-contained" object without destroying it in the process. We cannot usually make the leap, except maybe in our dreams.

I will write more about centers in another post. This post focuses mainly on the outer shape of the round artwork, or tondo.

My thanks to Rudolf Arnheim's fascinating books, eleven of which I now have in my own collection. It is because of his books that I have any kind of an understanding of this subject. His book The Power of the Center has been particularly valuable and is the one all quotes in this post are taken from.

Note: Where I have used the initials POC, above, I am referring to Arnheim's book The Power of the Center.

NOTE ADDED OCT. 4TH, 2009: I've written an "introduction" to this post that might be helpful in trying to understand the subject. If you're interested, you can read the introduction in the October monthly newsletter in the Thinking About Art Monthly Newsletter Archives. When you get there, click on the newsletter with the title Thinking About Art Monthly Newsletter - October 1, 2009.

Art, Gravity, Life, and the Cartesian Grid

I realize the title of this post is not very modest, but the post itself is, though I do touch on all of the subjects named. I don't presume to know everything there is to know about all of these subjects, but I want to introduce them and explain what they have to do with each other briefly. I will be writing more about these things, and related subjects, in later posts.

Here are a couple of pictures showing the Cartesian grid, so you'll have the grid in mind while reading what comes after.



The Cartesian Grid

"A co-ordinate system whose axes are straight lines intersecting at right angles"
(Ref: Ministry for the Environment, New Zealand)




3 Dimensional Cartesian Grid
Source: Wikipedia

Definition of a Cartesian grid: "A Cartesian grid is a special case [among grids] where the elements are unit squares or unit cubes, and the vertices are integer points." (Ref: Wikipedia Article on the Cartesian Grid)

Why is the Cartesian grid of any use to us? It doesn't look like much.

Awareness of the Cartesian grid is extremely useful to us, in our lives and in our art, because we live on Earth and so are very much under the influence of gravity (Gravity: The fundamental force of attraction that all objects with mass have for each other); it is gravity that makes those simple verticals and horizontals so necessary in order to understand and interpret our world (as viewed and experienced by inhabitants of our planet).

Gravity is a very strong force that pulls us, and everything we observe and live with, toward the center of the planet. In fact, it's what holds the planet itself together.

The artist who paints (or the sculptor who sculpts, etc.), if what they are depicting has to do with life as lived here on earth, has the effects of gravity in mind, whether he (or she) is consciously aware of it or not, as it is the dominant physical force in our lives. They might not plot their design on a Cartesian grid, yet they see and arrange and understand things as if they were doing so.

But the Cartesian grid looks so simple! (You say.) It's nothing more than vertical and horizontal lines! What do those lines have to do with life, and gravity, and art?

Let's start with the verticals.

The verticals in our lives

We live with gravity all our lives. We feel it as weight. Because we are constantly pulled from down below, we are very aware of what is "up" (pointing away from the center of the earth) and what is "down" (toward the center of the earth). Also, because we are aware (if only unconsciously) that everything on the surface of the earth is being pulled downward (or "has weight") we are inclined to infer that anything that's vertical (standing "up") has energy -- It is alive and alert and/or strong enough to resist the force of gravity.

The horizontals in our lives

Because we instinctively know how gravity works, things that are horizontal seem to us to be unthreatening, peaceful, meek, possibly even dead. They are not resisting gravity.



Photo Source: Wikipedia

When our energy is depleted, we lie down if possible, to sleep or just to rest. It requires no effort on our part to lie in a horizontal position.

The surfaces we walk and ride on are horizontal whenever it's possible to make them that way. Because of gravity, it's more difficult, and uses more energy (and is sometimes dangerous) to walk on or ride on an incline.

The places we live in (or prefer to live in) are usually as flat (i.e., horizontal) as possible because gravity makes it difficult for us to climb, or to descend with care (i.e., so that we will not fall). Even if the terrain is not flat, the floors of the buildings are; and, by the way, if we have flat floors the walls need to be vertical.


Building under construction
Photo Source: Wikipedia

If we lived in a place where gravity had no influence on us, there would be no up, nor would there be a down. There would be no definite verticals, nor horizontals. The verticals and horizontals of the Cartesian grid constitute the basic framework of our lives; everything is seen in relation to this framework.

Diagonals

If something is diagonal, that has meaning for us, too. Diagonals wouldn't have that meaning without the Cartesian grid showing us how they deviate from verticals and horizontals. A diagonal could be something rising, or something descending. (A vertical has already risen; a horizontal appears lifeless and not likely to make any moves.) So, diagonals mean "action" to us; something is happening (yes, diagonals can also imply depth).



Photo Source: Wikipedia
These diagonals do not look stable. It's alarming to see them like this. They're not vertical, nor are they horizontal, but they look like they're in the process of becoming horizontal. These diagonals make us nervous.

Relating vertical and horizontals (and diagonals) in life to those on the Cartesian grid

Standing people, trees, buildings, fenceposts, etc. look to us to be parallel to each other, as the vertical lines in the Cartesian grid are. Horizontals are connected at equal distances from each other to the verticals in the grid to make squares (in two dimensions), or make cubes (in three dimensions), making it simple to locate anything that is overlaid or represented by the grid.

The Cartesian grid helps us make many things that we use. Think of a map, or a pattern for a woodworking project or the grid you might use for transferring a picture from one surface to another. Graph paper is a Cartesian grid.
Furthermore, "The right angles of our living spaces, of chests and sheets, afford a visual order that helps make our lives simpler than they would be, say, in a primordial forest," says Rudolf Arnheim. "And, for the sake of order the Cartesian grid also remains present, actually or implicitly, in our works of art." (Arnheim: The Power of the Center, 1982 edition, paperback, page viii)

So we find the Cartesian grid very useful in measuring, planning, understanding, adapting to, representing and negotiating the spaces around us and in comprehending the meaning of what we see.

Two good links

1) I'm so glad I found this one. It's called The Coordinate Plane. It clearly and simply explains, and shows, how the two-dimensional Cartesian grid is used. Be sure to check what you want to see in the little boxes to the right of the diagram. Click "Grid" first, and you'll see it as it looks in the picture of the Cartesian Grid near the top of this post. Click each of the boxes to see what shows up. Also, you can move that little red dot around with your mouse pointer. When you are completely confused, click "Reset"
(under Quadrant 4) and it goes back to the way it was at the beginning. Be sure to read the definitions and suggestions below the grid. Also, there are other pages listed below that have to do with this subject. Just click on a link to get to what you want to see.

2) Wikipedia article on gravity

Quotations

"In daily perceptual experience, visual orientation in space relates to the Cartesian coordinates of the gravitational field." (Rudolf Arnheim in The Power of the Center, 1983, paperback, p. 197)

"The structure of visual space relies upon the framework provided by the vertical and horizontal. This framework is the visual 'tonic,' the zero base at which tension is at a minimum." (Rudolf Arnheim in New Essays on the Psychology of Art, 1986, paperback, p. 215)

"In the parochial view of its small inhabitants, the curvature of the earth straightens into a plane surface, and the converging radii become parallels." Rudolf Arnheim in The Power of the Center, 1983, paperback, p.vii)

"Parallelism and right-angled relation yield the most convenient framework available for spatial organization, and we cannot be grateful enough for living in a world that, for practical purposes, can be laid out along a grid of vertical and horizontals." Rudolf Arnheim in The Power of the Center, 1983, paperback, p.vii-viii)

"Were it not for gravity one man might hurl another by a puff of his breath into the depths of space, beyond recall for all eternity." -- Roger Joseph Boscovich, Philosophiae Naturalis Theoria, 1758.

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