Follow the Golden Ratio from Africa to the Bauhaus for a Cross-Cultural Aesthetic for Images

Audrey Bennett is a University Diversity and Social Transformation Professor at the University of Michigan and a Graduate Program Director and Professor of Art and Design in the Penny W. Stamps School of Art and Design. She is also a former Andrew W. Mellon Distinguished Scholar of the University of Pretoria, South Africa, and a former College Art Association Professional Development Fellow. Her publications include: “Towards an Autochthonic Black Aesthetic for Graphic Design Pedagogy”; “How Design Education Can Use Generative Play to Innovate for Social Change”; Engendering Interaction with Images; “The Rise of Research in Graphic Design”; “Interactive Aesthetics”; and “Good Design is Good Social Change.” Audrey Bennett is the co-editor of the Icograda Design Education Manifesto 2011 and a member of the Editorial Boards of the journals Image and Text (South Africa) and New Design Ideas (Azerbaijan). She sits on the Board of Directors of the College Art Association.

Bennett recently presented “Radical Design Pedagogy: Towards an Autochthonic Black Aesthetic for Graphic Design Pedagogy” at BIPOC Design History in an educational series called “Black Design in America: African Americans and the African Diaspora in Graphic Design.”

This essay was originally published in Volume 6, Issue 1 of Critical Interventions in 2012. PDF version available here.

Follow the Golden Ratio from Africa to the Bauhaus for a Cross-Cultural Aesthetic for Images

The golden ratio, a mathematical relation that often arises in fractals and other scaling geometries, is known for its ability to affect visual beauty (Livio 2002, 179). As a result, communication designers have used it throughout history to compute a plethora of visual compositions. For instance, many designers use the golden rectangle, a popular compositional grid derived from the golden ratio, to organize verbal and visual information into eye-catching images. However, within the discipline’s literature our European predecessors, primarily ancient Greece, receive most of the recognition for being the sole contributors of the golden ratio to interdisciplinary discourse. Very few references in the discipline’s literature acknowledge Africa as the one of the primary contributors of knowledge about the golden ratio. In this paper, I challenge the assumption that golden ratio structures originated solely in ancient Europe. Scaling designs reflecting growth patterns are actually more common in Africa, and thus it is no surprise that geometric relationships for growing forms have an independent origin there. There is even some evidence that this African tradition of dynamic geometry may have made its way to Europe via sources such as Fibonacci and others.

Herein I respond to Robert Bringhurst’s The Elements of Typographic Style, Kimberly Elam’s Geometry of Design, and Tim Samara’s Making and Breaking the Grid: A Graphic Design Layout Workshop by noting that the African contributions are conspicuously absent in their accounts. My aim is to weave into the discourse other perspectives from anthropology, architecture, and mathematics that suggest that Africa’s golden ratio exemplars predate the instances that create the current origin story.

Specifically, I introduce perspectives that suggest that the structures derived from the golden ratio that organize typographic compositions and even structure living spaces also has presence in traditional African architecture, and that this presence extends further back than sites and artifacts in Greece. Two important examples derive from the analysis in Eglash (1999). The first is the chief’s palace in Logone-Birni, Cameroon. This historical architectural site has a golden ratio scaling pattern embedded in its spatial design. The second is a similar scaling pattern in the Temple of Karnak from ancient Egypt.

These additions of African design in the story of the golden ratio need not be limited to merely correcting an incomplete history. We can use it to broaden perspectives on how the golden ratio can be used; to encourage its incorporation in the design of images that resonate cross-culturally. From existing cultural artifacts and spatial designs that reflect the golden ratio and other patterns, they can extract cultural grids—a phrase I introduce to explain the phenomenon of grids found in cultural artifacts and man-made and natural spaces that can apply to communication design practice, particularly to the printed or digital page—to yield cross-cultural resonance during the interpretation of images in the communication process.

The problem with cultural aesthetics and a cross-cultural solution

We are symbol-using animals (Burke, 1966). As such we make symbols to share information with each other. These symbols communicate meaning that includes our cultural values and identities like social class, professional affiliation, educational achievement, religion, gender, among other things. An amalgamation of symbols forms a cultural aesthetic that is recognizable and interpretable because it reflects shared cultural values between the communicator and his/her target user. That is, a symbol or set of symbols communicates meaning only to those who understand the cultural cues embedded in the visual form.

Since the time that humans originated—which some geneticists argue occurred some 150,000 years ago in Africa (“We are all African now”)—we have self organized into different cultural groups based on religion, ethnicity, age, gender, geography, linguistics, political affiliation, nationality, impairment, among other categories. And each cultural group has its own set of values and ways of expressing them aesthetically.

However it was probably not until relatively late in human existence that unique verbal expressions emerged in interdisciplinary discourse to represent the general phenomena of culture and aesthetics; what Luhmann would call a second-order observation. Used in early Greece to mean multisensory sensation, the word aesthetics acquired its contemporary meaning of “sense of beauty” in 1750 due to German philosopher Alexander Gottlieb Baumgarten in his publication Aesthetica. By 1871 another culmination of second-order observations gave us the contemporary sense of “culture”: anthropologist Edward B. Tylor defined it as “that complex whole which includes knowledge, belief, art, law, morals, custom, and any other capabilities and habits acquired by man as a member of society.” If we put those words together, we get the phrase cultural aesthetics which this paper defines as a sense of beauty determined by cultural values, or sensory treatments that reflect culture and epitomize sensory beauty.

Cultural aesthetics reflect the values of a specific cultural group or individual within that group. A basic example of this is the repeated use of a symbolic motif; for example the cross appears in Christian images ranging from architectural forms to textiles. These geometric forms would be much less frequent in Jewish designs, where

the Star of David would be far more likely. One can also experience and observe cultural aesthetics aurally in the ways that nations around the world speak different languages, or even through the tastes of food. Collective values can often be symbolized in the patterns and symbols of national flags. No two countries have the same pattern and/or symbol, though they may share similar colors and political ideals.

Cultural aesthetics carry important meaning in our everyday lives—on an individual basis and collectively in our communities. For instance, they can define our identity in relation to the cultural groups to which we belong. They also communicate meaning on an individual basis; and that meaning may be determined by the collective values of a larger cultural group to which they belong. Thus, cultural aesthetics can provide us with a sense of belonging to a community of people that share the same Values.

Cultural aesthetics also bring meaning to our individual lives through their presence in our spatial interactions. For instance, African art historian Suzanne Preston Blier notes that dwellings of Kings and Queens [in general] are “impressive palaces marked by [visual] beauty and labor-intensive construction” (Blier, 1998). But an African palace created by clay and straw may seem completely alien to European ideas of labor intensive construction. Thus it is the cultural group—Africans in this case—that determines the way that ‘beauty and labor intensive construction’ are manifested aesthetically—which typically includes design complexity as depicted in the examples analyzed later in the article. Thus, royal dwellings from different cultures around the world may have substantive differences in their designs since their aesthetics are derived from the culturally specific values of the group.

African-American cultural critic bell hooks writes in “The Aesthetics of Blackness: Strange and Oppositional”:

In contrast to her sister, hooks finds significant meaning in the childhood space of her family’s house. Through its cultural aesthetics–that is, the way that Baba situated the objects in relation to each other and other components of that physical space (e.g. the window and doorway, decorations, etc…)—hooks extracts life-long meaning. Baba created a variety of experiences for members of the family, the primary users of the space, through the way she inhabited their home. And although hooks and her sister are members of the same cultural group—Baba’s family—they have different responses to the cultural aesthetics of their home because they have other cultural differences like age.

Like Baba we all use aesthetics to communicate to others within our respective cultural groups or communities in the way that we dress, speak, practice religion, among other ways by which we live out our lives. When we socialize and interact with people from different cultural groups, we learn about their values and observe the aesthetics they use to communicate their culture. In some cases, their culture fuses with ours—like when we adopt words from other languages into our own native tongue. Sometimes when we try to communicate aesthetically about people from different cultures from our own, particularly when we imitate their cultural aesthetics, the consequences can range from cultural stereotyping to violence. Examples of the latter occur frequently between religious cultural groups where cultural boundaries are more definitive. In religion, the perceived misuse of another religions’ cultural aesthetic have lead to acts of violence like those committed as a result of caricatures of an Islamic religious symbol of the Prophet Muhammad appearing in publications in the West (“Arson and Death Threats as Muhammad Caricature Controversy Escalates”). Whereas, the former impact, stereotyping, occur frequently between ethnic cultural groups where the boundaries are more blurred and less definitive. 

Consider universities—an institution comprised of individuals from different cultures in terms of ethnicity, age, geography, gender, impairment, etc. These universities adopt mascots or nicknames to represent collectively their sports teams. Some universities in the United States, like Dartmouth College, have used a symbol of a Native American as a mascot to represent team spirit. In the case of Dartmouth, its student life webpage describes how the college acquired a Native American mascot around 1920 from Boston journalists. However, after decades of protest by various organizations to the use of Native Americans as university mascots, many universities have retired their Native American mascots for more culturally appropriate mascots. It wasn’t until five decades later that Dartmouth College’s Board of Trustees called an end to its use of its Native American mascot for Big Green; today the college even denies ever having an official Native American mascot. 

Further evidence of cultural stereotyping that can occur from the misuse of cultural aesthetics can be seen in many infamous and perennial representations of African-Americans in mainstream media. Coon, mammy, sambo are a few of many negative representations of African-American culture created by non-African-Americans around the time of slavery that have saturated media throughout history and made an imprint on the public’s memory—generation after generation. A recent Art Directors Club Call for Entries (2006) continues this tradition in an image of an African-American man with a red afro in a Ronald McDonald costume standing under the title “Pimp My Brand”—a cross-cultural blunder that design critic Steve Heller calls “a 14-karat tactlessness” (2005).

Co-existing with the aforementioned cross-cultural blunders are more apropos representations of African-American culture created by African-Americans themselves.

Their contributions to either critiquing or re-inventing representations of African-American culture can be found broadly in the traditional arts, film, literature, and even communication design. For instance, in his film Bamboozled, African-American filmmaker Spike Lee intentionally re-presents numerous stereotypes of African Americans as a cultural critique of mainstream society’s historical representations of his culture. Cultural critics like Spike Lee, film producer Tyler Perry, and artist Robert Colescott among others seek to determine and understand the nature of aesthetics for their own culture through re-presentation of the stereotypes.

There is a dire need for more culturally-appropriate representations of African-American culture; and, in response to this lacuna, the late African-American communication designer Sylvia Harris (1998) encouraged African-American students entering the profession of communication design to translate cultural resources such as the ARFICOBRA art collective, or even musical rhythms from African-influenced music such as jazz, into culturally-specific designs. She also suggested that they seek creative inspiration from the work of Caucasian artists and designers whose work shows the influence of African-American culture (126). Since art influences communication design, it is no surprise to find discourse in communication design that encourages students to look at the work of African-American artists like Aaron Douglas—one of the leaders of the New Negro art movement of the 1920s—for artistic techniques and strategies to translate into visual language (127).

Though these suggestions are viable in providing creative inspiration to novice African-American designers, the question my previous work (Bennett 2003) sought to answer was: Is there an autochthonous aesthetic for African-American culture, defined by African-American communication designers? In response to this question, I posit that mathematics could be an unexpected pathway by which African-Americans could develop cultural aesthetics for communication design. Specifically, I argue for the use of African fractals (Eglash 1999) as a resource for the visual semantics of the communication designer’s canvas—a printed or digital composition that diverse users access for information and/or an aesthetic or cultural experience. With the emergence of Eglash’s observation of fractal geometry in African settlement architecture, art, hairstyles, and other indigenous cultural artifacts, and the rise of ethnomathematics and cultural design as schools of thought, an untapped opportunity has surfaced, offering a new path from African art and design history to a culturally-specific aesthetic for present African-American communication designers. Some of my own efforts in this area have been through a collaboration with Ron Eglash to develop Culturally Situated Design Tools (CSDTs), a suite of web applets that allow underrepresented ethnic youth to simulate African artifacts (like African art) and practices (like Cornrow braiding) by using indigenous mathematical concepts and algorithms. However, these tools are not restricted to only African designs; in Figure 1 we see an artistic pattern created by one of the children in our workshop, based on a Native American design practice. It is particularly interesting since the original Native American practice is not fractal, but this student added a fractal character to their design: perhaps an influence from their previous exposure to the African fractals software.

However, the use of these mathematical principles to convey cultural aesthetics has not been explored collectively by African-American designers despite the growing accessibility to diverse cultures in communication processes. The leveling of the world (Friedman 2005) through technological development has had a profound impact on the communication of images in society. Since the publication of Friedman’s book, internet usage in Africa, the Middle East, and Latin America has increased dramatically in all three regions. We are now living in a post-globalization age with increased and open access to most cultures around the world through the World Wide Web and other communication technologies that can virtually extend across geographic boundaries. The continuous emergence of technologies in our post-globalization age, engineered with Web 2.0 coding, continues to create unprecedented opportunities for global interaction in the consumption of images. As a result of the world flattening, cross-cultural communication is now the norm; and, there is a dire need for aesthetics that communicate across cultures. When communicating visually via media networks, cross-cultural resonance is paramount for attaining communicative effectiveness (Bennett 2011). The integration of fractal patterns, for instance, in the construction of design grids and the positioning and treatment of elements within a composition can be the thread that weaves a cultural aesthetic that communicates African-American heritage and culture and those of other ethnic groups as well.

Thus a new appreciation for the African geometric heritage need not be parochial; it can contribute to the development of aesthetics that communicate across different cultures. I posit that the cultural aesthetic of space can lead to a cross-cultural visual aesthetic through the use of cultural grids—that are, more specifically, an organizational network of horizontal, vertical, diagonal, and curvilinear lines and shapes found in cultural artifacts and spaces that can apply to communication design practice—particularly to the printed or digital page—to yield cross-cultural resonance during the design and interpretation of images in the communication process. In fact, if we return to hook’s description of Baba’s house from the essay An Aesthetic of Blackness, she defines aesthetic as a “way of inhabiting space (65).” By space here she means domestic space and the way that Baba inhabited her house with objects. Thus, the previous definitions of cultural aesthetics could be combined and broadened to say that cultural aesthetics are the interaction of sensory treatments including spatial organization based on cultural values that creates a sense of beauty. In this paper I purport that the golden rectangle is a cultural grid that has the potential to yield cross-cultural aesthetics that provide aesthetic appeal to users.

Designing Cross-Cultural Aesthetics with the Golden Ratio

The golden rectangle depicted in Figure 2 is a visual manifestation of the golden ratio (1:phi). That is, its sides reflect a golden ratio. The ratio of ‘a’ to ‘b’ is the same as the ratio of ‘a plus b’ to ‘a’. Delineating a square on one side of the golden rectangle creates another golden rectangle. If we repeat the delineation of a square in each new golden rectangle that forms, in the same direction (clockwise or counter-clockwise), we obtain a golden spiral.

Within the discipline of communication design practice, the golden rectangle is a tool that professional designers use to render aesthetically-pleasing images and experiences. Livio supports this assertion when he states that “numerous authors have claimed that the golden rectangle is the most aesthetically-pleasing of all rectangles” (178). Indeed, generation after generation of communication designers use the golden rectangle to organize information visually and guide users to meaning. They regard the golden rectangle as a mathematical grid that yields visually appealing aesthetics—particularly in regard to typographic harmony in book design grids. The golden rectangle could be considered a “multicultural grid,” in that it is a grid that corresponds to an organizational structure shared by many different cultural groups, and when applied to the layout of information has the potential to yield an outcome that resonates cross-culturally with many different cultural groups. Yet, when considering its cultural origin, the golden rectangle is usually associated with only one culture—the ancient Greeks with a line of more general European descent that runs through Leonardo da Vinci right up to the Bauhaus.

Because of the usefulness of golden rectangle grids to organize and structure information on printed and digital pages throughout history, the question of where the golden rectangle originates has relevance to its use for yielding cross-cultural aesthetics. However, communication designers probably did not invent the myth of a Greek origin for the golden rectangle; they may be merely repeating the claims made elsewhere. For instance, according to communication designer Kimberly Elam (2001, 6), the golden section rectangle originates in early Greek civilization. Even when designers consider grids more broadly, Africa is usually left out, as in this quotation from communication designer Tim Samara (2002):

The exclusion of Africa from historical accounts of the origin of the golden rectangle is worthy of scrutiny. Contrary to most accounts, there is no mention of the golden rectangle in any Greek written sources, and the example most prominently used, the Parthenon, also fails:

However, if the Greeks did not contribute the golden rectangle, who did? Typographer Robert Bringhurst provides a hint in his account:

As Eglash notes, there is no evidence that ancient Greek mathematicians knew of the Fibonacci series (89). However Badaway (1965) found a use of the Fibonacci series (1, 1, 2, 3, 5, 8, 13…) in the layout of temples in Ancient Egypt.

Greek mathematician Euclid did describe ratios between lines or figures such that they created the phi relation, but writes about it like this:
“The line AB is cut in extreme and mean ratio at C since AB : AC = AC : CB”

There is no mention of such ratios being “golden” or special in some way that is relevant to design. The most famous representative of Greek architecture, Vitruvius, worked exclusively with proportions that can be expressed in whole numbers, rather than irrational proportions that the golden ratio would require. This was in keeping with the ancient Greek distaste for irrational numbers and the infinite series, which clashed with Platonic notions of mathematics as static perfection existing in an eternal, unchanging ‘realm of the Forms.’ African designs, on the other hand, deliberately make use of such iterative sequences, since they fit well with the African cultural emphasis on fecundity, fertility and cyclic aspects of life. One can hear this dynamicism in African polyrhythmic music, and see it in iterative architectural designs such as Karnak and Logone-Birni.

Since archaeological evidence shows that Egyptian civilization was founded when groups traveled down the Nilotic valley, it is no surprise that these traditions of recursive form were continued in Egypt. In the original sub-Saharan architectures the structures are not largely determined by quantitative formula; the Egyptian version thus provides a more formal version of the sub-Saharan recursive tradition. It is not unreasonable to speculate that Fibonacci brought the sequence from North Africa where it was used in the weights of a scale balance as well as architecturally.

As shown in Figure 4, we can postulate then that the golden ratio originated in Sub-Saharan Africa, migrated north possibly to Egypt, and then traveled to Italy and onward around the rest of the world.

Another example of iterative sequences in African architecture can be seen in the palace of the Chief in Logone-Birni, Cameroon (Figure 5). This structure epitomizes culturally defined visual beauty and intensive-labor construction through its complex spatial design. The palace is relevant to the discussion on the evolving need for crosscultural aesthetics because of the mathematical concept embedded in its architectural design. It uses a fractal grid characterized by the repetition of similar shapes at ever diminishing scales (Eglash 1999).

As Eglash notes, the path that one takes to navigate the palace’s space approximates a “golden spiral”. In other words, the iterative construction of the palace—from tiny rectangles to larger and larger rectangles—naturally lends itself to the golden rectangle construction for the overall form, even though the match along any one wall is far from Perfect.

Logone-Birni and Karnak are evidence that early Africans used mathematically related organizing principles, such as the recursively generated ratios related to the golden rectangle in their architecture and settlement design. These examples predate the use of such designs in Europe; and quite possibly contributed to their European utilization through travelers such as Fibonacci. Other routes by which this knowledge may have entered Europe could include Rosicrucians, alchemists and other mystics interested in ancient Egypt, as well as the group of mathematicians and artists sent to Egypt under Napoleon in 1799. My previous work (Bennett 2003) notes that these recursive traditions of Africa offer a new basis for thinking about Black cultural influences in communication design. Here I’ve extended that argument, noting how the golden rectangle and its related iterative constructions add additional insight into what can constitute a cross-cultural aesthetic in communication design.

Conscious use of math principles in the communication design process

The question that remains is: how might communication designers graphically translate mathematical principles like the golden ratio and grids derived from its formula into a visual aesthetic that communicates cross-culturally? A good place to start might be with the terms shared between the disciplines of communication design and mathematics and used to describe the fractals that the golden ratio creates—like translation, rotation, repetition, and scale. The way that mathematicians define translation is similar to the way that communication designers define it in relation to the positioning of elements within a compositional space. Communication designers subconsciously use translation to create a variety of visual effects that include making elements look related. Scaling is particularly important in its use for contrast in size in communication design; and, contrast is a key to creating visual hierarchy. That is, change in size brings attention to particular elements in a given composition while smaller elements recede to the background and are barely visible. Communication designers frequently use repetition to unify a composition and make it less predictable during interpretation in order to attract the attention of users and make them linger for more information.

The Temple of Karnak in Egypt provides a unique golden ratio grid (that is, successive members of the Fibonacci sequence converge to phi). Figure 6 shows how this architecture could be used to develop modular, scaling units for a visual layout. The palace of the Chief in Logone-Birni, Cameroon provides two more useful architectural structures that can translate seamlessly into compositional grids. The first grid is from the aerial photo in Figure 3 that shows the compartmentalization of a physical space, that is, how rooms are situated in relation to each other. When translated into the compositional grid in Figure 7, the designer can use it to compose a layout of verbal and visual elements that convey African-American cultural heritage and Western values.

A second architectural grid associated with the palace of the Chief in Logone-Birni is of the path through its space. The grid in Figure 8 generalizes the golden spiral path through the palace’s space.

This grid is commonly known as a golden rectangle within the design community. On a practical level, it has been used prolifically as a tool to render aesthetically pleasing graphics and experiences. Thus we can reinterpret the golden ratio’s role in design as having a new dimension in its cultural connotations; one that includes African culture among other cultures; an interaction between Africa and the West. The application of golden ratio to the architecture of information is thus limitless for communication designers: it can move between the universal and the local; between a sense of beauty tied to histories and places, and a sense of beauty that transcends those boundaries. Further research and practice along these lines could be valuable not only in better understanding visual culture trans-nationally, but also in helping designers of all nations better utilize these geometric illuminations from ‘the dark continent.’

Conclusion

The two historical African sites discussed in this paper are significant because of the well-known mathematical concept embedded in both of their spatial designs—a phenomenon that has relevance to the history of communication design and African-American design identity. The following excerpt from a prominent national organization’s website supports the need for the inclusion of African contributions to Western communication design history and theory:

The low percentage of members from under-represented ethnic groups—particularly African-Americans—in the AIGA community may be due to those designers or prospective designers not being able to see themselves reflected in the rhetoric of the discipline—in its symbolic visual codes passed down from one generation to another through the discourse. Designers from these under-represented ethnic groups may feel a need to belong or a greater sense of belonging to professional design communities like AIGA, the professional organization for design, if they are able to see their culture reflected in the discipline’s discourse on what constitutes good design. However, if the golden ratio concept was present in historical Africa or actually originates from there, then Africans and their African-American descendants play a role in the development of good design standards in the West. No longer should African-American designers feel left out of the discipline. All along they have been included—from the Bauhaus to the present. Thus, the use of the golden ratio as a tool for generating cultural aesthetics should have additional significance to the ongoing engenderment of agency in African American designers and a sense of shared ownership of the communication design discipline—a factor that could be used to attract more African-American designers in order to at least diversify the discipline.

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“We are all African Now,” last modified Summer 2009