When an innately sensitive observer views a picture ignoring saliency, balance remains to direct the eye. With perfect pictorial balance there is no controlling agent. One becomes attentive to the whole picture, and the eye is able to move smoothly through it instead of being attracted to one form after another. This is what Roger de Piles describes as seeing the whole picture at one time “le tout ensemble” 14. It was found empirically that artist particularly painters had to be used as observers. Painters have been shown to view pictures differently than untrained individuals10, 21,22, 23,24. Antes showed that fixation patterns distinguish painters from non-painters, and Koide et al using a prediction model of a saliency map showed that artists are less guided by local saliency than non-artists so that the effects of balance would be more manifest25. Painters look carefully at pictures for long periods of time so that previous salient aspects are no longer so. In addition, perhaps, artists have an innate disposition to do this.
As noted, polarization destroys the aesthetic effect much more than the effect on eye movement. It would seem that polarized light somehow inhibits the aesthetic feelings associated with the eye movements. To those who equate an aesthetic effect with preference, the aesthetic aspect of this type of balance has not been proven. However, the judgment of preference is a high level cognitive response based on culture and fashion. Geometric forms, strongly contrasting forms or many different equally prominent forms that cannot be combined conceptually force the eye to focus on each particular form. With respect to the latter case, for example, if there is a picture with a distinct mouth in one corner, eyes in another, a chin in a third and so forth, they are seen as distinct salient objects. However, if combined to form a face, they are not likely to be viewed that way. Geometric forms also command the attention and might be interpreted as pictures within the picture. On this level color is never a salient feature. Previously I made a distinct difference between a perfectly balanced picture and all others in order to understand the studies. However, this is not completely applicable to the lived experience where as a picture appears increasingly balanced without these other distracting factors, it will appear increasingly harmonious and unified to those who are sensitive. The state of imbalance will include the geometric or visual state of imbalance as well as these other factors. It is the ability of being able to move smoothly through a painting that determines the degree to which it will seem harmonious and unified.
Normal viewing seems effortless because we are accustomed to the work performed by the eye muscles. However, balance continually exerts a force that differs in each quadrant such that no matter what is being seen, the eye cannot become accustomed to it. No one complains of visual fatigue when intently watching a moving image on an LED screen where balance plays no role, but they do when looking carefully even briefly at pictures. This fatigue seems to limit any study to perhaps 16 pairs or less at a time. The key element is viewing carefully; casually leafing through a picture book is different.
A flat surface with no marks, i.e. one coated with an opaque layer of paint but gradually modified so that the upper half is slightly darker, also cannot be seen as coherent. There has to be some surface quality for this part of the visual system to recognize an object. It has been shown that forms in nature have a fractal quality, that fractal images have an aesthetic quality and that the visual system has evolved to respond to natural conditions24,26,26. Therefore, it can be inferred that the part of the visual system that calculates balance is also most sensitive to fractal forms. The visual system is designed to work best in this fractal environment and not the world of manmade objects that are linear and uniform causing the eye to jump from one form to another (see comments on Cézanne in addendum A). The author has observed that binocular vision is necessary to observe the percept.
Since balance is a low level percept resulting from object luminance, it must have evolved for some other reason. It is doubtful that such a calculation is an accident without evolutionary significance such as has been suggested for the perception of polarized light18. As previously described balance could be an early evolutionary method to follow a moving object. Visual balance employs imaginary or virtual lines, and the ability to do this in other situations has been demonstrated in vertebrates as primitive as the shark that can see the illusion of kanizsa Figs. 27,28. Using balance the visual system would identify the object by this vector and the virtual rectangle which represent all the points of light that make up the object. Although this is constantly changing, once done the visual system has “locked on” to it and can therefore distinguish it from all the other points of light. A complex object of whatever size is reduced to moving vectors and an illusory rectangle. Even if it stops moving, the vector and rectangular halo would remain visible where it might otherwise blend in with the ground. The rectangle guarantees that at any moment either the prey or predator is located within its boundaries. This model explains how balance has evolved to have an effect on eye movements. It also permits the determination of balance in non-rectangular pictures or those seen at an angle.
The solution to the calculation of balance in non-rectangular pictures which previously could only be done empirically is demonstrated with Fig. 3. The lower half is identical to the balanced Fig. 4. Both have a luminance of 124.8. The upper half of Fig. 4 has a luminance of 115.5. Were this image to be balanced then the upper half of Fig. 3 would have to have a luminance of 115.5. However, if the light energy or luminance flux is spread out over the total area that includes the black rectangles then the luminance of the total upper half including the black areas will be less. This is calculated as follows: the luminance of 115.5 multiplied by the number of luminous pixels of just the upper half of the picture is equal to the luminance L of the upper half including the black rectangles multiplied by the pixel area of the upper half.
(189,360 − 54,000) x 115.5 = 189,360 x L, so that L = 82.6. Changing the upper right and left quadrants of Fig. 3 so that their pixels have an average luminance of 82.6 (including the black rectangles) creates a balanced picture.
One can object to the results of this paper as reducing the art of painting to painting by numbers if one were to view pictorial balance as the primary aesthetic objective of painting. Of course, were one to do so, the painting would have to be exhibited under precise conditions and might not look so good otherwise. There has long existed the idea that great art appeals to the intellect and trivializes that which appeals to the senses. At some point that which appeals to the senses is at such a level that it achieves an intellectual importance of its own as in “I had never imagined that something like that could exist or be done; it introduces a whole new level of thinking.” With art one simply cannot separate one from the other.
Perhaps the most marked characteristic of this aesthetic effect (a really coherent picture)is that the attention is riveted in a powerful involuntary way. This is not contemplation. It is, as Delacroix describes it so eloquently cited below, different from the peak effects of other art forms which can be riveting in their own way - no tearing, shivering or trembling so that how or where a low level response is interpreted on a higher level must be sought elsewhere29, 30, 31. An approach to understanding this might be through understanding the effect of polarized light.