Cosmically we find that matter organizes around centers, which are often marked by a dominant mass.... In the vastness of astronomical space the rotating galaxies and the smaller solar or planetary systems are free to create such centric patterns, and in the microscopic realm so are the atoms with their electrons circling around a nucleus.... (vii)

Therefore,

....just as almost every organic and inorganic subject is shaped around a center, centricity is an indispensable structural property of any composition in the visual arts. The interaction between the two spatial systems [the cosmic and the parochial] generates formally the complexity of shape, color, and movement that our visual sense cherishes.... (x)

Such observations allow Arnheim then to take meanings from the ordering of particular paintings; speaking of Giotto’s “Deposition,” he says that

.... the agitation of the mourners had to be counteracted by stabilizing factors, to impart the surpassing dignity and significance of the scene. The sweeping gesture of the bending disciple is fastened by the position of his head to the balancing center of the composition. This stabilization compensates for the momentariness of the gesture and gives it the permanence of a monument—a monument to grief. If the figure were placed away from the center, this effect would not obtain. (85)

Arnheim extends this notion of the natural central movement of things outwards geometrically to speak of the top and bottom and left and right sides of paintings: for example, in comparing Cézanne’s “The Card Players” to a Baroque painting called “The Chastisement of Amor,“ Arnheim says that “the horizontal extension of the Cézanne stresses the sideways exchange between equals; the dominance of the vertical in the frame of the Baroque painting strengthens the theme of violent subjugation” (96).

Similarly, Molly Bang, in Picture This: Perception and Composition, a book in which she widens for adults her work with helping elementary school children learn about pictorial composition, ties how we compose images to our bodily experiences of the physical world:

The upper half of a picture is a place of freedom, happiness, and triumph; objects placed in the top half often feel more “spiritual.”

When we are high up, we are in a stronger tactical position we can see our enemies and throw things down on them. Down low, we can’t see very far; things might fall on us and crush us....

The bottom half of a picture feels more threatened, heavier, sadder, or more constrained; objects placed in the bottom half also feel more “grounded”....

There is an odd corollary here, which at first seems contradictory: an object placed higher up on the page has “greater pictorial weight.” This simply means that our attention is drawn to the same object more, or it feels more important, if it is high up than if it is lower down. We must feel that most things truly “belong on the ground,” and we are perturbed when this is not the case. All other things being equal, if we want to put more emphasis on an object, we tend to place it in the upper half of the page. It tends to feel freer, less attached to the earth, and lighter, but it also has “greater pictorial weight.” (77-78)

In Reading Images: The Grammar of Visual Design, Kress and van Leeuwen draw out such observations in order to apply them to words and images together on a page:

....when pictures or layouts make significant use of the horizontal axis, positioning some of their elements left, and other, different ones right of the centre .... the elements placed on the left are presented as Given, the elements placed on the right as New. For something to be Given means that it is presented as something the viewer already knows, as a familiar and agreed-upon point of departure for the message. For something to be New means that it is presented as something which is not yet known, or perhaps not yet agreed upon by the viewer, hence as something to which the viewer must pay special attention. (187)

Think of our flow charts and timelines, almost all of which start on the left. Kress and van Leeuwen also speak of the meanings that hold for the top and bottom of pages:

If, in a visual composition, some of the constituent elements are placed in the upper part, and other different elements in the lower part of the picture space or the page, then what has been placed on the top is presented as the ideal, what has been placed at the bottom as the real. For something to be ideal means that it is presented as the idealized or generalized essence of the information, hence also as its, ostensibly, most salient part. The Real is then opposed to this in that it presents more specific information (e.g. details), more ‘down-to-earth’ information (e.g. photographs as documentary evidence, or maps or charts), or more practical information (e.g. practical consequences, directions for actions). (193-194)