1. "Westhoff's Diagonal Method: Unraveling Photography"  -
      by  Fleur Jongepier

I first came in contact with the Diagonal Method in September 2006, when I took up a photography course offered by Edwin Westhoff. When we got into discussing The Rule of Thirds and composition in general, Edwin introduced us to his recent discovery: the Diagonal Method (hereafter DM).

            First things first: I do not believe, and nor does Edwin, that there are set rules in composition. This has particular consequences for the DM, for it raises all kinds of questions. Like: if there are no such rules, what is the DM good for? How can a theory of composition be discovered when there aren’t even set rules for it in the first place? For now, I will not go into the discussion of whether there are rules in composition or not. Because either way, the DM remains a powerful theory, as will hopefully follow from this article, so for now it suffices to leave that discussion aside.

My first thoughts concerning the DM were rather sceptical. I shall specify these worries or "objections" of mine, because I can imagine others having the same worries as I had. Afterwards, I will show there’s an appropriate answer to all of them.

            First of all, I was worried its proposed success might just prove to be leaning on "wishful thinking". The central question being: to which degree is it likely for one to want the photograph to pass the test? For instance, photograph X passes the test because a diagonal crosses exactly between both eyebrows. Wouldn’t we have let the photograph pass the test if the diagonal crossed the eye (or both)?

            A second difficulty I stumbled upon, was the amount of credibility that is necessary for the DM to be credible. Over 30%, 50% or even a 100% of the tested photographs? When is the DM credible? I found, in testing the photographs, some surprising examples of how the DM cut right through the central elements. Yet, there were also numerous photographs where I wasn’t quite sure to let the picture "pass" or "fail" the DM-test. Obviously, the problem of credibility is thus closely related to "wishful thinking". In fact, both problems circle around the acknowledgement of what counts as an important or vital element in a photograph. Is this acknowledgement suggestive, and should it perhaps be universal?

            I shall be very clear on the last question: central elements in photographs that are on the diagonal bisectrix are not there for some underlying universal reason or (mathematical) rule. I will not hesitate to say that they are on the diagonal bisectrix for suggestive and subjective reasons. This is an important point to make, because it implies that diagonals on either eyes or eyebrows are both legitimate, because we are not to justify this legitimacy. This might sound rather odd, but in fact it’s rather simple. When holding a sheet with the proposed diagonals over a particular photograph, and you find that, for instance, the left eye is crossed by such a diagonal, it means that the photographer, on purpose or unconsciously, had his or her focus on precisely this eye (or whichever element in question).

            Of course, it is hereby not meant that every element in a picture passes the DM-test. It does not necessarily follow from a diagonal crossing a cheek for example, that precisely this part of the cheek is essential (or, better said, that the photographer found this part essential).The reason for this reduction of legitimacy of central elements lies in the exact precision of the DM, which is precise on one millimetre. A cheek, to continue on the same example, covers a relatively large area and cannot be qualified as "an element". The statement of such precision is a heavy one. The Rule of Thirds works approximately, but in most cases this approximacy is insufficient and hardly ever consistent. The DM is restricted to particular elements of interest in a photograph that are not to be "close to" a diagonal but rather precisely on the diagonal. This 1 mm-accuracy is important because this increases the method’s credibility. Whereas the Rule of Thirds applies to large areas, the DM applies to small elements only which makes the cases in which the diagonal is indeed on the element more significant. Also, the problem of wishful thinking is diminished since all elements that are not on the diagonal with a distance of 1mm will not past the test, whether we want them to or not.

            A third problem I’d like to mention is the question of dominance: what is more important, the crop of a photograph or the diagonal on the elements? What I’m aiming at here is that different crops or compositional layouts in one photograph change location of the bisectrix. Theoretically we could crop every picture in such a way that the bisectrix is in fact always on an element or another. This however, is obviously not the intention. When taking a photograph, the photographer takes a certain angle and afterwards he is able to adjust the proportions and make a different crop. Cropping the photograph until a diagonal cuts through an important element can lead to awkward results. Of course the overall layout is more important than the presence of diagonals cutting certain elements. In some cases however, it could be the case that a slight crop on one side in order to place the element on the diagonal could’ve improved the photograph. 

            Due to the problems named before, I tested 100 famous photographs to see whether the 1mm accuracy is correct (when photographs are approximately 16 cm. on the longest side). I picked 100 photographs out of hundreds, because a fair amount of photographs is unsuitable since there are for instance no central elements (e.g. landscape photography) or the layout of the photograph made it impossible for diagonals to be meaningful. For the remaining 100 there were 68 photographs where a diagonal cut through an important element. In several cases there was more than one working diagonal. I believe it is unnecessary that all photographs that are suitable for the DM should pass the test. This is because, once again, the DM is no rule for composition.

            Then, you might ask, what is it’s function? Well, DM’s value lies mainly in the fact that we can, for a part, get to know the photographer’s focus or centre of attention. Furthermore, we can improve photographs. In some cases we can crop the photograph (when speaking of millimetres and 1-2 centimetres maximum) in such a way that the diagonal cuts right through the element. Sacrilege for the photographer? Maybe, but photographers don’t always get it right the first time. They do the cropping afterwards, too.

The DM works on intuition, and this is why it’s so effective. Even amateur photographers have the habit of making a picture with correct "use" of diagonals. For some still unknown reason, photographers themselves (and artists, but this is another story) seem to have an integrated structure of these diagonals. It might be the case that, when intuitively choosing a composition, they make use of this structure.

As being very analytical myself, I saw no future for DM since it rests on terms such as "subjective", "suggestive" and "intuition". When testing many pictures and works of art, however, I couldn’t convince myself of this being coincidence or wishful thinking anymore. My best advice for the ones that have become curious or critical on DM is to test photographs themselves, as I have done. Do keep in mind that not al photographs qualify to be tested at all. It still is photography, which is a form of art that is defined by dozens of factors that make a photograph a good photograph. The DM is ‘just’ another, but a strong one, that allows us to unravel the secrets behind the photograph just a little more.

Fleur Jongepier

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2. The problem with using "rules of composition" -
     by Edwin Westhoff

As you can see in the article by Fleur Jongepier, I do not "believe in set rules of composition". Actually, I do not use the word "rules" in my classes, except when I have to explain something in relation to a certain known rule, such as the Rule of Thirds. The reason is rather simple. As a photographer, sooner or later you will encounter a situation in which you have to break a rule of composition, because the purpose of the photograph demands this. This could be the case with all the rules. There are simply too many exceptions in actual photography. So forget rules. In stead we could use the term "points of attention". Many times there are certain factors that are needing attention. Let's take the horizon as an example. Normally you will have to check whether the horizon is exactly straight, level. But it is no rule. It is perfectly legitimate to place it under an angle, when the purpose of the photograph demands this. You see this sometimes in a movie, and in movies these kinds of things are most of the time planned very much in advance. 
Other factors often also need attention: the location of a rather small object in the frame, the direction in which a person looks in relation to the placement in the frame, what to do with vertical lines, how to compose clouds, etc. You can follow a certain rule, or go against it when necessary.
The important thing is that the results (of either following or breaking them) have a meaning.
We "read" photographs and we use general, unconscious ways of reading them. So, using the example with the horizon, when a person sees a photograph with a level horizon, he reads this in a certain manner, and when the horizon is under an angle, the person reads it in another manner, it has another meaning. But both meanings are legitimate or good, depending on what the photographer wants to communicate. In criticizing photographs this matter gets specially important.
One cannot simply dismiss a photograph because a certain rule is not applied. If you do not understand a photograph, you have to know the meaning of it. In classes, you can simply ask the photographer what the purpose of a photograph is. Most of the time all the elements and the way the photograph is made, fall into place. If not, certain things have to be altered in relation to the purpose of the photographer, but not to our own believes (in rules of composition).

3. The Golden Ratio -
    by Edwin Westhoff

In order to be able to understand the meaning and use of the Golden Ratio (in history) it is necessary to distinguish the different area's where the Golden Ratio is used:
1. Mathematics (e.g. the ratio 1:1,6180339)
2. Geometry (e.g. the Golden Triangle)
3. Architecture (e.g. the pyramid of Cheops)
4. Nature (e.g. the human body)
5. Esthetics (e.g. the Golden Ratio in photographs and paintings)
In this article (and on this website) were are mainly concerned with esthetics (in photographs).
Historical background of the Golden Ratio.
Albert van der Schoot writes  in his book (Agora, Baarn, 1999) "De ontstelling van Pythagoras" (which could be translated as "The Disproposition of Pythagoras"), that the "Golden Section" as an expression and idea was used for the first time in 1864 in English literature and the expression "Divine Proportion" was used for the first time by a Italian monk called Luca Pacioli (1445-1517), in 1509.

Pacioli wrote about mathematics, not about geometry, let alone esthetics. Pythagoras (c580-c500 B.C.) had an exoteric and an esoteric school were he taught mathematics and the symbolic and esoteric meaning of numbers and ratios. Not about geometry. Plato (c427-c347 B.C.) and Leonardo da Vinci (1452-1519) both wrote about the "Divine Proportion", but nothing in their work points to the ratio of 1:1,618, according to van der Schoot. What Plato and da Vinci meant was probably the general proportion in the cosmos, and not a very precise mathematical ratio. (See also: The Vitruvian Man and the Golden Section)

Since the expression "Golden Section" was used, first in 1864 in England and also in 1835 by Martin Ohm (1792-1872) in Germany, this term was more and more used in general and was also used in connection with paintings and drawings. To this day artists, critics, reporters and even scientists write about the Golden Section as if this is a proven ratio of beauty in art works. Van der Schoot discovered that the Golden Section as an ideal of beauty in two dimensional art, is actually..... a myth.

A different matter is the use of the ratio of 1:1,618 in architecture. It could well be that this was used in the construction of the Great Pyramid. I did not research this, so I do not know.

Anyway, if this was used, it was not called the "Golden Section", because this term originated in the 19th century. Also because of this, Pythagoras could not have known about he Golden Ratio or Golden Section, since the term did not exist in those days. Of course I don't mean by this that the proportion of 1:1,618 did not exist then, but that the meaning which was given very much later (concerning the ideal of beauty in two dimensional art), was simply nonexistent. It was just a matter of mathematics during the time of Pythagoras. In architecture the same mathematical aspects could have been made three dimensional. But esthetics  is something entirely different.

When we look at certain objects which allegedly contain the Golden Ratio, such as a particular shell, a bull, or a painting, the Golden Ratio is almost in every case not really present when we take a precise measurement. Of course it is possible that a few painters deliberately constructed their paintings according to the Golden Ratio. But in that case the composition is an artificial one.
As stated earlier in section 1, it is widely known that the Rule of Thirds is based on the Golden Section (rather the Golden Rectangle). This statement becomes rather interesting when one knows that the Golden Ratio as an ideal for beauty in two-dimensional art appeared to be a myth.
When you base a theory on a myth, you cannot expect that the new theory becomes more realistic than the original myth. Especially when you know that the core of the myth, the ratio of 1:1,6180339, is completely removed from the new theory. By removing this ratio, the Rule of Thirds becomes an empty shell.

4. Bottom-Up and Top-Down perception and the Diagonal Method -

    by Edwin Westhoff

Robert Solso found two aspects of viewing art:
1. Nativistic or bottom-up perception
2. Directed or top-down perception
The first one is called "bottom-up" perception by cognitive scientists, because it begins with the basic physical stimuli. Light comes back from whatever subject and goes "up" through our lens and hits the retina and forms an image while being processed by the brain. "This kind of perception is based on the fact that people have certain inborn ways of seeing in which visual stimuli, inclusing art, are initially organized and perceived" (Solso: The Psychology of Art and the Evolution of the Conscious Brain, 2). This is about the same as the conventional explanation by scientists of how we see: light comes through our eyes, falls on the retina and we "see". We could say that this kind of perception in itself is rather "objective", although it is virtually impossible not to connect meanings to it.

There is another theory, which is named by Plato and Rupert Sheldrake: we (also) project the image of what we see onto the object. Let's say we are looking at an oak-tree. We see the oak because it reflects light into our eyes but we recognize it as an oak because we project an image of it back onto the tree. This is possible because we saw other oak-trees in the past, or photographs or drawings of oak-trees.This explains the fact why we find it almost impossible to recognize something that we never saw before, because we have no image of this in our "image-bank". (If you saw "What the Bleep Do We Know" part I, you will remember the story about the indians who did not see the ships of Columbus, because they had no image of ships in their "image-bank").
Top-down perception is "subjective" because everything that we experienced since our birth, which is different from person to person, is projected on the subject we are looking at. This explains also the fact that different persons almost never agree on what they find beautiful. And when you ask them why they find a certain painting or photograph beautiful, they often cannot give a precise reason for it. This is not surprising because an image can evoke so many (often deeply hidden) unconscious experiences that it is almost impossible to rationalize them all or to make them conscious. (This is "the problem with beauty", the last article of this section.)

My theory is that the working of the Diagonal Method is a combination of bottom-up perception and top-down perception. Both the artist and the person who looks at a work of art are (of course) concerned with bottom-up perception. The Diagonal Method (of following the bisection lines of 90 degree angles) is part of the recognizing-ability of bottom-up perception.
The artist however is at the same time projecting his interests and likings on the scene and (unconsciously) chooses certain details as most favourable. These details are unconsciously placed on the Diagonals (or bisection lines), because of the way bottom-up perception works. His whole character, his believes and his temporary interests are at work in this activity, without his conscious knowledge. And this is the activity of the top-down perception.

When we think of the Rule of Thirds in this perspective, we can see the following differences:

first: the four lines of the Rule of Thirds are almost certainly not a part of bottom-up perception in the way that people unconsciously would follow these lines (of the Rule of Thirds), and second: people (who use the Rule of Thirds) think that they have to place details on the lines or cross points of the Rule of Thirds, not because they find these important or emotional, but because they think that the composition will get better as a result of it. So this is a conscious act based on a (invalid) theory.
Of course the DM is not the only way to attract attention. Human figures, strong lines, contrast and white spots (among other things) will certainly attract attention. But in these cases the attention is drawn because of these factors, and not because of the Rule of Thirds.

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Bibliography (concerning all articles and texts by Edwin Westhoff)

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Burian, P. & Caputo, R.: National Geographic Fotogids, National Geographic Society, Washington, 1999.
Campen, Cretien van: Gestalt van Goethe tot Gibson (Gestalt from Goethe to Gibson), Universiteit Utrecht, 1994.
Eco, Umberto: Storia della Bellezza (The history of beauty), Libri S.p.A., Bompani, 2004.
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Freeman, Michael: The Photographer's Eye, the Ilex Press Limited, 2007.
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Hartel, Markus: Urban Expression, Digital Photographer, Issue 74 (Sept. 2008), London / Nijmegen, 2008.
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Mante, Harald: Der Punkt und störende Punkte, Photographie: maart 1997.
Mante, Harald: Freie Linien, Linie und Begleitlinie, Linienkontrast, Linienteilung, Photographie, maart 1998.
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Schnelle-Schneider, Marlene: Wie Bilder wirken (How images work), Photographie, maart 1997.
Schnelle-Schneider, Marlene: Optische Anordnungen - Figur und Grund, Photographie, maart 1998.
Schoot, Albert v.d.: De ontstelling van Pythagoras (the "disproposition" of Pythagoras), Agora, Baarn, 1999.
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Westhoff, Edwin: De Diagonaal Methode, Focus (magazine), Feb. 2007, Haarlem.
Weston, Chris: What's the Right Way to Compose my Picture? Practical Photography, April, 2006.
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Yarbus, Alfred: Eye Movements and Vision, Plenum Press, New York, 1967.
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NOTE
The original title is sometimes translated into English. This does not mean that this book is obtainable in English. It is just a service so that readers can see what the book is about.