Thank you for being patient with me Paul. It took me over a week to get through the book with my schedule (even though it is not that long at all.) First, before getting to the book, I should point out that your comment here: “However, these ideas, armatures, are pervasive in many texts.” is an appeal to ad populum. No amount of belief or popularity can make something a fact.
In addition, I too have listed to Myron Barnstone’s lectures. Unfortunately, his claims too are often unsubstantiated. I know Mr. Barnstone claimed that much of his own design work utilized secret and sacred geometries, but in the interest of being as straightforward with you as possible, if he did–I see no noticeable aesthetic advantage at his disposal.
Now—as to the book. Here’s my thoughts on it:
Well, I have finally made it through “The Painter’s Secret Geometry: A Study of Composition in Art” by Charles Bouleau. If you aren’t familiar with the book, it is the much-lauded go-to text for sacred or secret geometry (related to pictorial composition) fans. Several colleagues have put this book as evidence for the historical application of secret or sacred geometry in the arts, so in the interest of being open-minded, I thought I’d give it a fair go.
Although the book contains some fairly dense, flowery language, it introduces some straightforward ideas regarding visual relationships and proportions early on. The author thoughtfully explores the relationships between artwork and environment (i.e., architecture), the impact of a frame on the artwork, our egocentric sense of scale, and how the distorting of proportion can have a significant effect on our perception of subjects.
Bouleau is very clear in the introduction that the book is not a treatise on painting, nor is it a book on the history of composition. This latter claim is a tad confusing as what follows is one claim after another involving the use of geometric devices throughout much of art history. The author goes on to state that the book is “a study of the internal construction of works of art, a search for the formulae that have guided, over the centuries, the distribution of various plastic elements.”
So how does Bouleau accomplish this study? Does he pour over the many writings left behind by his chosen masters regarding their process? No. Rather what comprised his “study” was the spending of five years “questioning hundreds of artists through thousands of canvases.” (In other words, he observed paintings and measured stuff.)
So can this be a productive method of inquiry? Obviously, we can be forced to turn to less reliable lines of inquiry when more ideal lines are unavailable. However, we would need to be very careful about the pitfalls inherent to “less-desirable” routes. In Roger Fishler’s paper, "HOW TO FIND THE “GOLDEN NUMBER WITHOUT REALLY TRYING,” he addresses the problem with inferring design strategies from measurements alone. He writes, “Most of the papers involving claims concerning the “golden number” deal with distinct items such as paintings, basing their assertions on measurements of these individual objects. As an example, we may cite the article by Hedian. (H. Hedian. “The Golden Section and the Artist.” The Fibonacci Quarterly 14 (1976):406-18). However measurements, no matter how accurate, cannot be used to reconstruct the original system of proportions used to design an object, for many systems may give rise to approximately the same set of numbers; (see R. Fischler. “Theories mathematiques de la Grande Pyramide.” Crux Mathematicorum 4 (1978):122-29. and R. Fischler. “What Did Herodotus Really Say? or How To Build (a Theory of) the Great Pyramid.)” Environment and Planning 6 (1979):89-93.] for an example of this. The only valid way of determining the system of proportions used by an artist is by means of documentation. A detailed investigation of three cases for which it had been claimed in the literature that the artist in question had used the “golden number” showed that these assertions were without any foundation whatsoever.”
For more information on the specific cases referenced:
R. Fischler. “The Early Relationship of Le Corbusier to the 'Golden Number.!”
Environment and Planning B. 6 (1979):95-103.
R. Fischler. “An Investigation of Claims Concerning Seurat and the ‘Golden Number.’” To appear in Gazette des Beaux Arts.
R. Fischler & E. Fischler. “Juan Gris, son milieu et le nombre d? or.” Canadian Art Review 7 (1980):33-36.
R. Fischler. “On Applications of the Golden Ratio in the Visual Arts.” Leonardo 14 (1981):31-32.
Bouleau doesn’t seem bothered by the fatal flaw in his approach as he confidently moves forward with a salvo of arbitrary geometric overlays built upon seemingly arbitrary measurements and unbridled pareidolia. I will at least admit that I was impressed with how creatively he attempted to establish a valid foundation for the application of musical proportions to pictorial competition. This was done by simply juxtaposing seemingly arbitrary musical notes against a fresco. (Note: There is absolutely no reason to think that a reassignment of proportions that are demonstrably useful in one domain will carry any advantage in another.) Nevertheless, Bouleau goes right on ahead, utilizing relationships found with music throughout the book. Not only that, he often employs incredibly ill-defined concepts in relation to these topics —unity, harmony, and consonance (terms that he admits in his conclusion are “generally vague and ambiguous.”)
Now I can continue to pick apart paragraph after paragraph but really, what would be the point? The fact is Charles Bouleau’s book is not a serious investigation of anything. Instead, it is a fantastical tale (almost a form of historical fiction) that meanders through a dense forest of apophenia. A serious investigation of this topic would include documentation from the artists and corresponding sketches, designs, or cartoons that would have borne out Bouleau’s claims (not a collection of hand-selected armatures that Bouleau built after the fact.) In lieu of good documentation, we find an emaciated parade of uncompelling exhibits, including a snippet from a letter from Durer about perspective, David Sutter sharing a quote attributed to the Greek philosopher Plutarch which mentions rules, lines, measures, and numbers, and a few landscape sketches from Claude Lorrain with obvious enlargement/transfer grid lines that Bouleau believes are something much more. (To Bouleau’s credit, he at least mentions that the “experts” see Lorrain’s grid lines as enlargement/transfer devices.)
In an almost laughable conclusion, Bouleau states that today’s artists are seemingly not utilizing these secret geometries today—not because there exists no good evidence to accept that they may provide any aesthetic advantage whatsoever—but because of the “difficulties met with in applying it” or that today’s artists are engaged in “an art of negation and revolt.”
To conclude, I am sad to report that this book does not (and should not) compel any reader to accept Bouleau’s claims. This book does not describe a scientific or serious academic endeavor. Rather, I would describe this as a colorful collection of apophenia’s greatest hits.
Looking forward to hearing your thoughts on this Paul. 
. Thanks for this, such a simple thought in hindsight and yet suddenly allows me to discard a large chunk of non understandable dogma… I hope I used the right words there 
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