Some Perspective on Overlay Nonsense

Nothing seems to persuade proponents of sacred geometry, golden spirals and dynamic symmetry that the countless armature overlays put forward as functional “evidence” are ultimately nonsensical. Here’s a few examples:


If I shot an arrow into a densely wooded forest, you might not be surprised to learn that I’ve struck a tree.

Now if I go and paint a star-shaped target around the arrow in the tree, and you knew that I did—what could you possibly conclude about the impact of the target’s shape on my archery performance?

Now let’s say a champion archer comes along and shoots an arrow into that same forest striking a another tree. Just as before, I add a star-shaped target around the arrow. Can I then reasonably conclude, because the same star-target can be drawn around the both arrows, that the nature (shape, size, etc.) of the target is providing some functional advantage relative to what we define as archery? Should the fact that one of the arrows was shot by a champion archer impact my conclusion?

Now what if I add in that the mathematical and historical significance of the star shape—or that “stars” are ubiquitous in the universe—should that inform your conclusions about the inherent functional advantage of the shape in this context? Does that help you to reasonably conclude anything about the relationship between the target’s shape and functionality/advantage relative to either archer’s performance?

This idea is analogous to the many armature-overlay “demonstrations” that continue to be made for sacred geometry, dynamic symmetry, golden spirals, etc. in regard to pictorial composition. Please know that the countless armature overlays sent into me demonstrate absolutely nothing. You’re just continuing to draw targets around arrows thinking it’s one day going to be considered compelling evidence. Helpful hint: it’s not.


This would explain why I spent countless hours over the years reading and attempting to apply these theories but could never make them fit into my understand… because I always have to understand something before I can use it :joy:. 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 :grimacing:.

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I’m surprised to see rejection of the idea, it makes me curious. I certainly understand your point as I have worked with these as well, and even taught them to students wondering if they do apply. However, these ideas, armatures, are pervasive in many texts. With all due respect, have you seen or read Bouleau’s book, The Painter’s Secret Geometry? After reading some of it and looking at it many times, realizing he came to his diagrams after the fact, the secret does seem coincidental. But, then there is Myron Barnstone’s lectures referencing Bouleau, which are highly dependent on the armatures and he seems to have grip on how these measures show up in drawing and painting not just in renaissance but up through Van Gogh, Manet and even to Ellsworth Kelly. And, Barnstone’s teaching of drawing and design is deeply integrated with the armatures, the golden section or dynamic symmetry.
I am not intending to argue with you or change minds here, the realist art being taught by Waichulis is deeply fascinating and intellectually challenging without the dynamics. So more power to you as I see you as a powerful guide.
If I may add, I think the armatures are a tool one may employ it if needed, or use part of it like “the rule of thirds” which is derived from these star like diagrams. Some painters today use it to organize their compositions, like Edward Povey, who posts his compositions with armature overlays to his Instagram page. But then I work with a very well known landscape painter who does not use them in anyway, he has training from major atelier’s and teachers. I’m pretty sure he knows them but doesn’t use them.
In any event, it has been interesting to see your take on armatures, you obviously don’t need them or feel like it’s something that will improve what you have developed. I do find your methods fantastically successful in developing drawing skills in my students as they follow a logical sequence of basic building blocks. In that idea alone, there is some relatable content to the armature in that points, horizontals, verticals, diagonals help us locate, relate and divide proportions in a rectangle. I appreciate the opportunity to participate in a conversation here.
Thank you!


This is great Paul. I’ll get to this later today after some painting time. Hope you are well!

I was looking forward to your reply :slightly_smiling_face: :slightly_smiling_face:
You must have gotten absorbed into painting.

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Yes and No! Yes, I am painting—but to make sure I could address your comment as thoroughly as possible I purchased Bouleau’s book and spent the last week or so examining it carefully. Hence, the delay. However, never fear—I put aside some notes on the text that I would like to share as soon as I can get a tiny bit of time to do so!!! (I’m on it!!!) :smiley:

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Fantastic! Looking forward to your thoughts.

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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. :slight_smile:

Thanks for the reply. Just to be clear my intent is to have a conversation more casual than an academic point of view.
As for as populism I could care less. I mentioned these sources as examples that put forth the idea you said was nonsense in a post of a strong opinion and metaphor. As you now have researched very well articles debunking the myth and critiquing Boileau it seems to me it’s one of those issues with art one can, take it or leave it.
(I agree with you about Barnstone’s painting and drawing.)
I know a former Barnstone student who lives and work near me, a sculptor who uses the golden proportions in his work of realist bronzes. However he has recently chosen to work more intuitively interestingly enough.

I guess the point you made, with citations, is that historically these armatures and “golden”divisions were not in use as much as some writers, critics, historians say they were based on the opinions of the writers, critics and historians you found. I agree the ideal proof would be direct documents which align with anecdotal records of usage. And then to see that documented over and over. Also I think we’ll documented visible proof in many drawings the use of grids and armatures for enlargement may add to this confusion.

So you bring up another point of interesting discussion by saying - (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.)
My question for you is this: could the reason be to note a similarity of usefulness between proportions in two domains is to recognize something about human nature and human preferences to aesthetic production? A humanistic view which may be the motivations for the myth.
I wonder if the motivations for seeing proportions of nature in the works of human beings is part of a more humanistic, philosophical line of thinkers. Is it New Age thinking? Some kind of Romanticism? Not that Myron was one of those but in your research to determine these ideas as nonsense do you come across anything that would lead to that?
To reduce my question even further. Then why is this idea around?

I think ideas like sacred geometry persist because they are more attractive to some people than the logically sound, evidence-based alternatives. It’s a part of human nature. We prefer romantic, superficially simple concepts to the messy, complex reality of our world.

Thanks Orlando, can you cite the evidence-based alternatives? I want to be clear I understand your distinction. I appreciate the input.

Hey Paul! Yes-I probably come across far more pedantic than most. It’s one of the consequences of being an uber-art-nerd. Lol!

As to take it or leave it—I think that sacred geometry, the golden ratio, dynamic symmetry, etc., can be useful in some contexts. They can be shown to offer new spatial considerations for practitioners (although arguably undifferentiated from colloquially random) as well as perhaps to achieve a sense of communion with artists of the past. My arguments “against” are focused on the falsifiable claims put forward. In that context, as an educator, avoiding the issue world seem to make me complicit in the propagation of problematic, unsubstantiated claims. It’s like finding a chapter titled “stork theory: take it or leave it” in a textbook on embryology. If I were teaching that class, I’d immediate get a different textbook.

Your summary of my point is very close:

I guess the point you made, with citations, is that historically these armatures and “golden”divisions were not in use as much as some writers, critics, historians say they were based on the opinions of the writers, critics and historians you found.I’m not saying that they didn’t use it. I’m stating that, at this time, there is not compelling evidence to conclude they did. If I were arguing that they in fact did not, the burden of proof would be on me to substantiate that claim. As such, proponents still have all of their work ahead of them to provide evidence that might compel a reasonable individual to accept their claims.

And yes, there is indeed confusion and conflation found with Bouleau’s book in regards to classifying or assigning function/intent to observed lines. I would say that it’s an analog of equivocation. As an artist, you are likely intimately aware of all of the uses for a simple line. To imply that most lines are evidence of sacred geometry is intellectually dishonest (or a willfully ignorant conclusion at best.)

To your question: “Could the reason be to note a similarity of usefulness between proportions in two domains is to recognize something about human nature and human preferences to aesthetic production?”

This is a brilliant question Paul and my answer would be: absolutely! As humans, we are forced to navigate the understanding of something new in terms of what we already know. There’s no way around that. In fact, there are many famous stories and anecdotes of brilliant minds in this arena doing just that. One story that comes to mind is the tale of Sir Issac Newton trying to organize color in a manner similar to a musical octave. This is the way we work. It’s only when we see that the association or relationship is problematic that we should, as rational investigators, adapt or abandon the framework and replace it with something that is more useful or “closer” to what is indeed the case.

In all of my research, a continually resurfacing truth is that we are prediction machines in search of fluent (easily processed) input to more effectively and efficiently facilitate successful behavior. This means that pattern is visual cheesecake to us. So much so, that we tend to see that cognitive cheesecake everywhere.

I don’t know—maybe the formula for beauty is hiding in plain sight at your local bakery. :joy:

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If we’re talking specifically about Sacred Geometry, it relies on accepting the premise of intelligent design. I won’t attempt to produce evidence that disproves the existence of anyone’s god(s). However, I don’t think the burden of proof rests with me.

I haven’t read through Anthony’s A Primer on Pictorial Composition yet, but I see that it has citations to many peer reviewed scientific journals. That could be a good place to start if you’re looking for literature related to how human perceptual preferences might have evolved.

Other examples of concepts that people find attractive would be the proposed healing properties of crystals, magnets, and homeopathy. My understanding is that all experiments have either disproved such properties, or have used flawed methodology which biased the results. For example, this page discusses studies using magnets.

It has been a very nice morning to read your response,
Anthony, and Orlando. Thank you both!
Anthony, I’m glad you steeled your viewpoint for me, and others for that matter.
I did a very quick and easy search myself and found a similar discussion from 2013 on James Gurney’s blog. And the points being made here are very similar. To summarize -

  • List item

the use of Fibonacci sequence, or golden mean, or harmonic intervals, or dynamic symmetry can be useful, informative to practicing art.

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Claims to its use historically are easily questioned and the burden of proof is on those who assert its use.

There is a human response to patterns, alignments and spatial relationships to which we assign beauty.

To keep the list short, finally, there are many ways to achieve compositional arrangements.

I’d like to include this blog post from a response to James Gurney’s blog


Speaking as one who did her graduate work in neuroscience, I think that whether the Parthenon or other major works or art and architecture perfectly correspond to the Golden Mean is not quite the issue. It might be more useful to say that our visual system has evolved to extract information from a scene by moving our gaze in particular ways. There are certain proportions, certain combinations of lines, that conduct, stop, and start the gaze in patterns that evoke pleasure. (The reasons we perceive these patterns as pleasurable are a discussion for another occasion.) This pleasure is what we call “beauty.” The Golden Mean simply moves our eyes and stimulates our perceptual system in pleasure-evoking ways. The proportions don’t have to be precise and the correspondence with the Golden Mean doesn’t have to be exact, because eye movements aren’t precise. Nor does the architect/artist have to consciously understand the mathematics or the biopsychology underlying this principle; he just knows that he is making something beautiful, and the reason it is beautiful is unimportant. But as the human perceptual system has probably not evolved significantly in the past 2500 years, the beauty created in the Parthenon is valid today as it was when it was built.


James Gurney blogspot. 2013

It’s all cheesecake! Thanks for the great discussion!

Likewise, thanks Paul and Anthony!

Speaking of James Gurney, I can highly recommend his book, Imaginative Realism. The Composition chapter includes topics on using eye tracking and heat-maps to objectively measure how viewers’ eyes move across an image.

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That really does’t make a great deal of sense. Our brains are plastic to our experiences (which vary immensely between individuals and groups of individuals in different places), our perception of beauty is too. Forget about over 2500 years, there are things I thought were beautiful just years ago that I don’t think are anymore. There are some things that I would have never considered beautiful as a child but now do etc.

I think Andrea was making a broad generalisation based on evolutionary psychology. That would allow for variations in aesthetic response between individuals, as well as variations in a given individual’s responses over time.

Hello Maneesh, that line is not my opinion or observation. I accept your take on it. The quote is from a much longer response to the same topic, the use of the Golden Mean in design, on James Gurney’s blog from 2013.

To the points Paul shared:

the use of Fibonacci sequence, or golden mean, or harmonic intervals, or dynamic symmetry can be useful, informative to practicing art.

I do think that many things can be deemed useful relative to one’s goals. As I said earlier, any of these “devices” can be used to make one feel that they are in some sort of communion with celebrated artists from the past. However, the real issue in this case is that the function (“use”) is never clearly defined in a manner that differentiates it from random. This is one of the means by which these devices continually skirt the perils of careful investigation.

There is a human response to patterns, alignments and spatial relationships to which we assign beauty.”

Gurney is partially on track here. Many sources (including myself) will almost always refer to humans are pattern seekers or pattern recognition machines. I would argue however, that humans are more appropriately described as pattern generating machines. Discernible regularities do exist in the environment in a wide variety of domains—however, it is only when we apply meaning to a discernible, perceptible regularity do we give rise to pattern. We find good evidence for this with the existence of visual completion, subjective contours, and pareidolia.

Gurney’s simplification that we assign beauty to specific patterns, alignments and spatial relationships can be misleading. Such assignments are quite context dependent. This means that it is not the spatial relationship alone per se—but rather it is what is presented to be related to a potential observer. This may sound like a pedantic distinction, but it is important to make clear that a “measurement” is not doing the heavy-lifting where assignments of beauty are concerned.

For lack of better terminology—Andrea’s comments just make her seem completely off her nut. First, no—the Parthenon does not “perfectly correspond” to the Golden Mean. See: Markowsky, George. “Misconceptions about the Golden Ratio.” The College Mathematics Journal 23.1(1992): 2-19. Web. 17 April 2010.

Second, the statements that “There are certain proportions, certain combinations of lines, that conduct, stop, and start the gaze in patterns that evoke pleasure.” and “The Golden Mean simply moves our eyes and stimulates our perceptual system in pleasure-evoking ways.” are demonstrably false. Yes, our eyes engage in saccadic movements and fixations in an attempt to garner information from the visual field. Should this type of movement cease, the visual system would begin to shut down. And yes, within that effort, certain stimuli will impact movement and fixations. However, there is NO good evidence to demonstrate that our eyes are “moved in pleasurable ways” by the golden ratio. If this were the case, you would think that this phenomenon would have at least been mentioned in Yarbus’ work. See Yarbus, A. (1967). Eye movements and vision (B. Haigh & L. A. Riggs, Trans.). New York: Plenum Press.

In applying the golden spirals to Yarbus’ eye tracking records find no such correlation. However, we do see what we would expect if the eyes move to fixate on what is believed to be useful visual information.

In regard to “the human perceptual system has probably not evolved significantly in the past 2500 years, the beauty created in the Parthenon is valid today as it was when it was built.” It is true that humans may not have changed all that much over the past 2500 years relative to the common timeframes discussed in evolutionary biology. However, perception is not the only system involved in assignments of beauty. This is like saying that, in regard to a coffee machine, the filter is responsible for the coffee. It does play a significant role, but it is not the whole story.

To this point, beauty and aesthetics can be very complex subjects. In the realm of pragmatic, predictive strategies for the navigation of aesthetic issues—it is important to understand that certain resolutions are far more useful than others. For example, like Maneesh pointed out in regard to changing preferences over time, it is not terribly useful (generally speaking) to try and predict which flavor of ice cream (vanilla, chocolate, or strawberry) would be favored. However, as humans, we can confidently assume that a predilection for sugar and fat will be in play. This latter statement is an example of the level of resolution that I find most productive in discussions of aesthetics.

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