A new paradigm in composition
There is a most important difference between the Diagonal Method and the Rule of Thirds. Concerning the Rule of Thirds, people do consciously place subjects like horizons and lampposts on the lines of the Rule of Thirds. I know, because many of my students tell me that they do this. Most of the time these parts are not particularly important, concerning content. On the other hand, photographers (unconsciously) place details on the lines of the Diagonal Method which have an important meaning in the narrative of the photograph, or are important to the photographer in a psychological or emotional way (and are immediately seen by the viewer). This is the least understood aspect of the Diagonal Method, but at the same time the most important one.
It is, like someone from Vietnam told me, a "new paradigm in composition". Using the Diagonal Method, one can detect for instance, things in which the artist was interested in or, see in a quick glance the most important details of a photograph or painting. This means that compositional arrangements are linked with content. This is new. The Rule of Thirds and the Golden Section are theories, and the theory is that the composition will get "better" if you place subjects on certain lines or cross points.
But the theories do not say that the details will become more important concerning content, when they are placed on the given positions.
Clearly, the narrow definition of the word "composition" is meant in these cases. In addition, I found in my research that the Rule of Thirds and the Golden Section "do not work", meaning that one can place subjects on certain lines, but this does not necessarily lead to a better composition. More often it will lead to a worse composition, because the overall intuitive framing of the picture is violated by a rational decision. The theories of the Rule of Thirds and the Golden Section are contradictory to rule No. 1 in composition: "The overall intuitive framing of a picture is always more important then the placement of details".
With the Diagonal Method, the overall intuitive framing and the placement of details are done at the same time, because both are done unconsciously. So rational manipulation cannot destroy the total composition. Rational manipulation is sometimes necessary but the combination of intuition/feeling and thinking is always paramount in getting good compositions. Therefore it is important that the placement of details is done unconsciously, as is the case with the Diagonal Method.
Does the DM gives a better composition?
That depends on which definition one uses of the word "composition". In the narrow sense composition can be stated as "the arrangement of elements within a square or rectangle". My opinion is that works of art could get somewhat better as a result of the use of the DM, viewed in this narrow sense. In my Master Classes "Composition in the Arts and Photography" I use a broader definition of composition: "the total design of a work of art". In this sense the composition can get a lot better, because viewers will see immediately which details are important, concerning the meaning of the photograph or painting.
Searching for theories versus doing experiments
Brian Thomas tested 98 famous paintings in his work “Geometry in Pictorial Composition” and found a lot of geometric forms in these works but he did not reach a conclusion concerning a particular method which was used more often than others.
My opinion about this kind of research is that it is unlikely that one would find anything conclusive. If I would not have done visual experiments, I also would have found nothing interesting. I did not start with a theory, but with looking and experimenting. Also it was not my goal or intention to look for geometrical forms in art or to find a new compositional method.
For me the important thing was that the DM actually worked, whereas the Rule of Thirds and the Golden Section are non-proven theories.
My view on composition
After years of careful study I found that "composition", as in "the total design of a picture", is not arbitrary or subjective, but objective.
It is scientifically proven that within 360 milliseconds a person can see meaning in a random compilation of visual stimuli.
It is also demonstrated that people found certain factors, such as contrast, symmetry, balance, grouping, isolation and metaphor, more interesting than not, by measuring their brain activity while looking at these factors, by V.S. Ramachandra. I tested this, by trying to select three photographs per second from a large number of random photographs, with "composition" in mind. And I found that this is possible. In one third of a second it is not possible to formulate any (subjective) opinion about a photograph, there is just not enough time to be able to do this. So, my conclusion is that composition is visual. This means that composition is not arbitrary, nor rational, nor subjective.
In cognitive psychology, this is called "Nativistic Perception". In "The Psychology of Art and the Evolution of the Conscious Brain", Robert Solso says: "This first stage of the perception of art is largely independent of conscious control, and we are, in effect, enslaved by photons and physiology. Here, we "see" essentially the same thing. The shapes, colors, patterns, and organization of forms are sensed and processed by your eye and brain in the same way as they are processed by everyone else's. It is simply a matter of nativistic perception...." He continues: "To me, it is somewhere between surprising and and astonishing that so few art scholars have taken heed of this fundamentally important aspect of "seeing".
Is it possible to select three photographs per second, concerning composition? Yes. Since I have more than 40 years experience of selecting and analyzing photographs, and because I am a photographer, I am more "equipped" to do this than other people.
But the public, the average person, is also able to make a distinction between "good" (or "major") art and "bad" art or trash. This is why major art and artists like Rembrandt and van Gogh are recognized by the public. If this would not be the case, than we would be at the mercy of art critics and directors of galleries and musea (no offense).
New discovery in January 2016
I always wondered how it is possible for artists to place details on the bisection lines so precisely. After almost 10 years of research, it finally dawned on me. They did not follow or choose the bisection lines at all! They were just placing a detail which is important to them, on an equal distance to both the lines of the frame of a certain corner. When this detail is exactly on the same distance from both frame lines, it is in the most balancing or harmonious way, and at the same time in the most obvious and conspicuous place. This also explains the (unconscious) accurate placing of details.
Does this new discovery alter is some way the existing Diagonal Method in a theoretical or practical way? No, not at all, on the contrary: everything falls into place. It becomes completely logic and understandable. This is what artists would do: using their feeling and intuition, in stead of using a mathematical way, as using the bisection line, with is illogical for artists.
Actually, my first discovery, in May 2006, was that the points in my initial experiment were at the same distance from the two sides of the frame of a corner. Back then I was looking for a mathematial explanation, and I thought that the bisection line was the answer. So now I have reached full circle, but with the full understanding of 10 years of research.