This week the readings by González, Bier, and Koliji as well as the class discussions revolved around our attempt to understand the corresponding ways in which abstraction, movement, geometry, mathematics, and philosophy work in composing metaphors of space and place.
On Tuesday we developed working definitions of the concepts of abstraction, kinetics, and geometry as intermediary, and today we moved to spatial and architectural expressions that rest heavily on foundations of mathematics and philosophy. We discussed, for instance, how is squaring the circle or the circling of the square a metaphor for carving a sacred space? How do the ‘basic’ works of geometry and mathematics morph in architectural processes and protocols to mediate with the creation of sacred spaces?
Reflect upon these questions, and compose a comment on these or other questions you have thought about in relation to the assigned readings and class discussions of this week. Please, post by SUNDAY at 5pm.
REL 200R Blog Post 2
Arabella Peters
This week I was struck by the concept of geometric patterns discussed by Carol Bier in Geometric Patterns and the Interpretation of Meaning: Two Monuments in Iran. Prior to this reading, I had not considered the significance of patterns in religious architecture. Thus, it presented many ideas for me to muse over. Our class discussion also helped to facilitate this new way of thinking regarding patterns. I was influenced most by two particular quotes. The first one goes as follows, “there is no sense that any one pattern is more significant than any other. As for geometry, there does not seem to be any consistency or progression in the choice of patterns.” This concept of equality within architecture helps to propel a narrative that is conducive to sacredness and religious architecture because it encourages a value that is intrinsic to many religious practices. The shapes and patterns are beautiful in their simplicity and their symmetry. But their beauty also originates from the fact that they are not attempting to be seen. Their purpose is to simply exist and facilitate the holiness of the space, rather than call attention to any particular decision made by the artist.
The patterns fade together to create a general image and experience for the people that chose to occupy the space. This line of thought is further illustrated by the following quote. “Further, each of the patterns is conceived as an infinitely repeating pattern, delimited only by the limits of the space in which it is set. Since each of the patterns is infinite in its conception, rather than self-contained, each could also replace another in any spatial unit. Together, they seem to represent something larger than the forms of their individual expression.” The purpose of the patterns is perfectly articulated in this quote. They are infinite, not self-contained, and replaceable; therefore they are equal. Their purpose is greater than their singular influence. Through this they contribute to a far more potent purpose.
This past week’s readings have really made me think a lot about and wonder what exactly it is in a church, chapel, mosque, etc. that makes them sacred. When you step into any kind of religiously deemed sacred space, things like décor, patterns, or fixtures almost always contribute to the awe and grandeur of the space. My question, however, was what exactly makes one method of ornamentation more impressive than others? How is it that the patterns painted on the wall of the mosque is considered to be sacred, but the pattern on the chairs in Candler Library is not. On the other hand, a Gothic cathedral such as the Notre Dame is decorated so elaborately and differently than the simple, modern aesthetic of the Los Angeles Cathedral, yet both provide to their visitors a sense of grandeur and wonder and both spaces are almost always assumed to be sacred spaces despite their differences. The readings this past week was interesting in that they explained the ability shapes and aniconic art have in creating dynamic expressions. One point made when discussing the effectiveness of abstraction as a tool to be used in the decoration of the mosque was that rather than using figures of people or other live beings, abstract shapes and figures were used forcing the imagination to play a role in the interpretation of the images. When chapels have paintings on the walls of figures, such as Jesus Christ for example, not only is the image telling a very clear and specific story, but it also tells the viewer how exactly they are to see the icon from the story line in which he was involved to even the physical attributes to which he is often now recognized by. Rather than telling the audience entire stories as well as how to interpret and how to imagine certain sacred spaces or images, the use of aniconic and abstract art gives the audience room to use their imagination to come up with their own interpretations and meanings. This opportunity to use one’s own imagination, I believe, leaves many more opportunities for developing and experiencing a sense of elevation and spirituality. The mind and the imagination helps to allow individuals to experience such spirituality and elevation when observing geometric shapes and patterns in the places of sacredness.
When spaces are built with the intent of channeling sacredness and feelings of divinity, geometry plays a key role in the construction and overall creation of that space. Ancient Empires such as the Ottomans, Safavids, and Mughals used geometry as a visual mode of political representation, composing distinctive configurations in architecture that everybody could easily recognize and immediately attribute to their prestigious owners (González, 70). The use of circling squares to create intimate rooms that are meant to inspire awe showcases the effect that geometry can have on sacredness. By creating the Iwans and intricate Muqarnas to embellish such spaces and emphasize the circling of squares, architects have historically been successful in inspiring a sense of awe. This awe, as we discussed in class can inspire people to feel the boundlessness that is often associated with divinity and sacredness. Such architectural practices are extremely important when purposefully creating a sacred space as is mentioned in the Topkapi scrolls that are so frequently mentioned in the readings. I also find it very interesting that nature and vegetation/ plants are so integral in the construction of many sacred spaces. The fact that architects from the Alhambra Palace to buildings in Isfahan utilized nature as a geometric technique to create sacredness is amazing because so many people naturally feel sacred ties to natural spaces as showcased in our readings from previous weeks.
This week’s readings focused on “squaring the circle” and other uses of architecture in creating sacred spaces. To create a circular dome over a square space, squinches must be put in place to support the dome. Square spaces don’t leave the mind with places to wander to- there are a set of four walls to follow. The viewer knows exactly where to stand due to the firm edges. Circling the square creates the opposite effect. A circular room or space has no specific area to stand. There is no given center, and it encourages the viewer to explore. These architectural models create sacred spaces by enclosing an area. A squared circle creates a dome, as seen in the Friday Mosques’ shabistan- or basement area- with intricate arches. These domes are often decorated, requiring complicated calculations to ensure stability. These designs totally capture the viewer, allowing them to be in awe of the space. Islamic art and architecture is aniconic, so they must use details and other symbols to represent holiness. Plant ornamentation is common, it evokes the feelings of those living in the deserts. Palms are used to highlight important pieces of the buildings. The repetitive nature of the patterns in Islamic arts allows the viewer to interpret the space on their own- creating almost a hypnotic sense of understanding. Squaring the circle and circling the square, as well as other details of Islamic art, allow the viewer to feel- rather than telling them how to interpret it.
In general, framing a piece of art-whether with a literal frame or not-contains a piece. It creates a firm edge. By leaving it unframed, there is an implication that it continues past its physical space. Framing can also emphasize the importance of a piece. As seen in the picture we discussed on Tuesday, the star shaped fountain was physically contained by a small wall in an echoing shape. This small area emphasized the fountain, the physical materials and shapes used in the area created a staunch separation from the surrounding garden. While minimal, the fountain and the garden radiated a sense of peace and sacredness, all without using a specific iconic figure. Aniconic art allows the viewer to make their own interpretations, and allows for them to see a holy space as sacred in their own way.
This week’s readings dwell deeper into the creation of sacred space through the lens of geometry in architecture. In the Irano-Islamic perspective, squaring the circle and circling the square through the interplay of geometry and mathematics is representative of a conceptual reality. In Revisiting the Squinch: From Squaring the Circle to Circling the Square, Koliji phrased it as “a higher space of reality.” The square is symbolic of the earth, and the circle represents heaven. In the design of of The Friday Mosque of Isfahan, the interplay between circles and squares is prominent in the horizontal plan, the domes, the vault, and the ceiling plan, essentially throughout the design of the building. Not only the visual appeal of the interlocking geometric patterns makes the space incredibly sacred, but also the meaning behind it manifests the space as a super-reality between the earth and heaven. Similarly, in Bier’s essay Geometric Patterns and the Interpretation of Meaning: Two Monuments in Iran, the geometry and the repetition of patterns create a “an intermediary place,” that consists of corporeality and a special spatiality. Again, the conceptual ideology behind the architectural design is what gives the place sacredness. However, the question now is whether the representation of circles and squares or the visual geometric patterns play a more important role in making a place sacred. Are there other perspectives we can look at “squaring a circle” except mathematics (for example, from a purely visual arts perspective) to understand the creation of a sacred space?
“The ‘Geometries’ of the Alhambra” reading took geometry to a more subjective place for me. In reading the introduction written by Valerie Gonzalez, geometry in Alhambra was made to represent not only mathematical concepts, but also be considered metaphors and representations of kinetic movement. For example, the dome creates an “imaging metaphor” through the use of its rotating stars. Also, the baths in the bathrooms of the Alhambra were representative of kinetic motion. The panels in bathroom have an alternating black and white color scheme that’s laid out in a systematic way. That creates rhythm, animation, and vibration, which are the effects of kinetic movement.
The second reading, “Geometric Patterns and the Interpretation of Meaning: Two Monuments in Iran” by Carol Bier, also focused on the hidden meaning of geometrical patterns. However, this seemed to relate the meaning to the specific religion of Islam. In fact, within the text, the article discusses how the visual geometric patterns were also representations of the ideas within Islam. For example, when discussing the two monuments, Bier described individual pattern types that came together on the Building. He makes a connection between these patterns and the ninety-nine names of God, stating that a single pattern (or name) by itself doesn’t fully represent him, but the collection of the patterns as a whole do.
The third reading “Revisiting the Squinch: From Squaring the Circle to the Circling the Square” seemed to delve more into the practical and mathematical side of the geometry. More specifically, the actual process behind turning a circle into a square architecturally. For example, it explains the method of using a circle’s perimeter to create equilateral polygons and how the vertical transformation of a square into a circle is made possible through the use of arches. While the article does touch on some deeper meanings behind the geometry at the end, the overall focus of the article was centered around practicality and use.
Overall, these three articles project different perspectives of what geometry offers the sacred. While the first two were centered around more meta-physical and higher meanings, the third article seemed to focus on the objective reality behind geometrical structures and architecture. However, I believe all of these perspectives are necessary to understand geometry’s connection to the sacred.
This week I was particularly interested in answering the question of how geometry and its mathematical proportions contribute to the creation of a sacred space. As stated by Carol Bier in “Geometric Patterns and the Interpretation of Meaning: Two Monuments in Iran,” “Patterns that may appear initially to be complex and intricate can be analyzed to identify a unit and its repeat according to an algorithm, often relying upon the principles of symmetry and exemplifying a process that is at once unitary and systemic” (1). Especially in Islamic architecture and sacred space, symmetrical design is crucial to the creation of the space. This article, however, challenged my perceptions of how geometry can be used to form sacred spaces. For example, the article discusses how lines can be used to form patterns with religious meanings. Bier discusses sacred monuments in Iran and says, “the tympanum above the entrance bears a geometric pattern of interlace which form twelve-pointed stars in negative space; in each of these stars, occurring nine times, is the name, Allah (God)” (5). Islamic architecture uses basic geometric structures to form more complex shapes with religious significance. In this example, the star was used to pay homage to Allah, the singular god in islamic religion. I began to understand how the create of sacred space, such as a mosque, is just about the geometrical design as it is about the architectural design.
Bier continues her point by sharing that, “It has also been suggested that geometric pattern and interlace may make allusions to paradise” (7). Beyond the obvious religious connotation and significance of the world “Allah” being used in the geometric design, there are also implicit references that geometric patterns can make. Similarly to how geometric can reflect images of paradise, symmetry in the geometry can reflect the concept of unity and its importance in Islamic traditions. Symmetrical geometry in sacred spaces links “the multiplicity of forms to the doctrine of tawhid,” (7) noting that god, Allah, is one and unified. I also found it interesting how no one pattern holds more significant than another in islamic geometric design. The article makes an interesting comparison to how the geometric design in islamic architecture is similar to the ninety nine names of god. No one is significant on its own, but they all hold significance in the greater picture and in combination with the others. I think this makes a greater argument about the role of symmetry and geometry in the creation of sacred spaces. The thoughtful inclusion of several patterns, shapes, and designs, while seemingly chaotic, is used to construct greater meaning in the sacred space— they each tell their own story, but when combined they tell a greater story about religious values. While geometric patterns may be partially used to create beauty, they are just as much about creating religious significance through both explicit and implicit messages.
This week, I was brought back to my studies of Islam in middle school. My teacher had forced us to memorize and associate pictures of mosques with the names of the building, and I had thought the exercise to be mean and pointless. Why should we have to know what these places looked like?
The readings this week about geometry and Islam sparked a memory of this feeling; as I read Bier and she wrote about Alhambra as a “geometric ornament,” I looked up pictures and suddenly the exercise I had done in middle school made sense (Bier 1). The mosques that are so sacred to Islam are perhaps not only sacred because they are mosques, but because of their beauty. I never had a sense of appreciation to anionic art–it always seemed either simplistic or too abstract or both–but now, looking at images of these mosques, both the simple geometry of the Mosque of Cordoba and the complexities of Alhambra create a feeling of wonder. Although I’m still unclear on the distinctions between circling the square and squaring the circle, I understand that these geometric patterns and architecture are not only triumphs of engineering and mathematics, but of design and of feeling. These buildings manage to invoke emotions in architecture–and perhaps that is what makes them so sacred.
The geometries and mathematics in Islamic and non-Islamic buildings in different parts of the world can create sacred spaces within these buildings because they adhere to exclusive designs and principles not commonly found in nature. Take the Alhambra for example, its use of geometric patterns created using intricate precision with the help of mathematics creates abstract entities that are not typical in nature. Because of this, the mind attempts to make sense of these new and simple yet sophisticated geometries by attributing them to certain things that may be more common and well known in the world outside the Alhambra. For example, Gonzalez states, in “Beauty and Islam,” “the wooden dome virtually emanates the kind of celestial image which we called an ‘imaging metaphor’, created by geometrical patterns of rotating stars.” (pg.76) In other words, the geometrical patterns are attributed to the “celestial” in nature, just because they look like it. What is depicted though, is a lot of geometric shapes that have been put together by the person who designed the structure of this building. In other words, this is not necessarily meant to be “celestial image,” but it gives off that kind of association and therefore, is related to something celestial.
This kind of art is very different from nature in that things that happen naturally are very organic in shape but stepping into the Alhambra takes you into a completely different form of art immensely based on the math of geometry, proportionality and the likes. Because of this, Gonzalez states, “Anyone visiting the Nasrid site at first glance undoubtedly finds himself overwhelmed by the visual impression of extreme geometrical sophistication in the architecture as a whole.” I felt a bit of this sensation when I watched a video on youtube which I will attach to the end of this reflection. It is because of this sensation felt in Islamic buildings that makes them sacred for some. Unlike ordinary everyday entities, the geometry and mathematics of the patterns inscribed in the very core of these buildings transport their observers to a completely different world of inorganic, abstract images and therefore, these buildings are treasured. To others though, these buildings may relate to their ancestors and thus create a prideful and connection to the ancestors who contributed to the creation of this building and thus, a sacred space for them.
Youtube site: https://www.youtube.com/watch?v=Pi0LfRL_L90
This week, we learned about how geometric patterns contribute to the shaping of Islamic sacred spaces by expressing the beauty and grandeur of Allah. One interesting topic we discussed was kinetics in geometry, that somehow a stationary shape can take on motion. Kinetic geometry in Islamic architecture can be seen in the muqarnas whose complex shapes and patterns seem to draw people in and have an almost hypnotic effect on viewers. These intricate three-dimensional designs reflect the complexity of the universe and the never ending uncertainties of life and from just looking at them, devotees can reaffirm their confidence in Allah to guide them. Another example of kinetics in Islamic architecture can be seen in the decorations of the cupola in Comares Hall at the Alhambra. The design of the cupola is made up of repeated intervals of a circle with lines coming off of it, resembling light being emitted by a star. The architecture also takes real light into account as there are arches supporting the cupola while also allowing the sun to shed light on the designs. During the day, the sun casts a light on the stars causing them to sparkle and seem like they are in motion. The repeating star-like pattern of the cupola stems out from one central star and extends continuously. According to Gonzalez, the geometry of the cupola is meant to represent the vastness of the heavens and the central star is a representation of divinity as everything else revolves around it. By incorporating a sacred message in something as simple as geometric shapes, Islamic architecture is able to make an imprint on everyone who’s seen it.
This week’s readings dealt primarily with how geometry and architecture can produce sacred space as well as be conceived of as sacred objects and designs themselves. One of the questions which swirled around in my head as I read this week’s readings, especially the Hooman Koliji reading, was what are the metaphysical properties of geometric shapes? Towards the end of the Koliji reading, he quotes Ardalan and Bakhiar who say, “The square, the most externalized form of creation, represents, as earth, the polar condition of quantity, whereas the circle, as heaven, represents quality;” (302). They describe the sacred properties/reflections these shapes have which are religiously based. In my mind this brings questions of definition as well as curiosity towards how each is characterized and by what qualities. I have heard two dimensional shapes described with lavish adjectives before (i.e. “a strong/bold line” or “lovely angle”), but to draw the connection between shape and sacred is another level of meaning. Of the many questions I have, I will write down a few here, with no hope of giving or receiving an answer. What properties of a two dimensional shape dictate whether it is holy or not? According to the quote above and more in the text, they describe the square’s “polar condition of quantity” versus the circles “quality” as reasoning for why the first is eathly and the second is heavenly, but it seems to me the argument could be made that those are rather arbitrary descriptions of each. Could not a square be thought of as “quality” and a circle as “quantity”? Indeed, these descriptions may reflect more on the cultural conceptions of form and geometry than art and architecture. This begs the question of universality; are these same qualities attributed in the same way across cultures? If I were to encounter an Aztec opus on geometry and architecture, would I find similar reverence for the circle? Do Buddhist monks see the square as terrestrial? To boil the question down to its purest form, how culturally variant are perceptions of geometry? Are there overall similarities or patterns? When thinking of building and compounding shapes, I start to wonder more about the properties of these shapes and how far they extend and to what degree do they change when placed in different contexts. Is a circle still the image of “quality” when placed in relation or overlapping with less “pure” shapes? Perhaps I am wrong to pursue the metaphysics of geometry to doggedly, maybe I am missing the point. Regardless of which shape holds which property or how culturally relevant that idea is to others may be completely irrelevant.
I was surprised to discover that squaring the circle or the circling of the square was related to religion and spirituality. The notion that squaring the circle, the circle being heaven and the act of squaring heaven equating to bringing heaven down to earth, was difficult for me to grasp at first. I questioned why the completeness of heaven was related to the perfectness of a circle and not the perfectness of a square. However, the concept itself does make sense if accepted rather than questioned. I found the description of architecture as a cosmological act beautiful because I find that every act can be connected to one’s spiritual beliefs — even the act of building.
Additionally, the idea of transcendental geometry resonated with me. My partner and I discussed the terms “plant ornament” and “vegetable.” We found that in this specific type of architecture, plants and vegetation were intentionally used as decoration to emphasize the geometrical designs (90). Also, we looked at images of Arabic calligraphy and floral ornaments which demonstrated to us how important the emphasis and incorporation of nature is when creating this sacred space. It’s fascinating how squaring the circle and plant ornamentation reflects the architects perspective of spiritual imagination, yet the same pattern can be found across the world.
This week’s readings and discussions helped me reflect on aniconic design and decoration in comparison with the conventional iconography I am personally used to seeing due to my background in the Christian faith and my time spent in Christian sacred spaces. I had trouble wrapping my mind around the sacredness of aniconic designs before this week. Iconography’s sacredness is easy to pinpoint because these designs directly represent holy figures. However, aniconic designs are quite the opposite, so I wondered where their sacredness could be derived from.
The simplest figures in geometry, such as squares and circles, can represent holy ideas, like earth and heaven respectively. According to Koliji, “From archetypal shapes to exquisitely elaborated geometries, there is a consistent message – an expectation of geometry to express meanings belonging to a higher reality. The triangle, envisioned as a mediating influence between the circle and the square, unifies the structure and decoration. While the former is bound to the realm of reality, the latter seeks to achieve an idealized world. Residing between these two worlds, the triangle holds qualitative attributes and becomes an imaginal being, inviting the viewer to creatively participate in exploring the playful space of ‘depth and surface,’ to contemplate ‘matter and meaning,’ and to be reminded of the ‘temporal and eternal’ nature of human existence.” (p. 302-303).
This triangle is relative to the squinch, or the piece of architecture that relates the square and the circle in order to come together as one. This meshing of the two creates an altogether different idea, such as an ‘in-between’ of heaven and earth. The “temporal and eternal.” Meaning is built right into the design of the architecture.
This week, our class discussed about the definitions of the “basic” concepts such as abstraction, kinetics, and geometry. At first I only viewed them as trivial parts that just make architecture’s environment, but after I learned how those “basic” concepts form an unified harmony and build profound semantics that describe the contexts around, I was struck by the realization that every small parts convey impacts and are worthy of taking closer glimpse. One thought permuted into my head: perhaps, no sacred architectures are just buildings that convey physical shelter, perhaps those sacred architectures serve as multi-faceted shelter in terms of culture, emotions and spirits. In these sacred buildings, meanings surpass meanings. Decoration means more than a mere decoration. Symbol means more than a symbol. Everything tailors something beyond what we normally observe. In Bier’s “Geometric Patterns and the Interpretation of Meaning”, the author provides multiple suggestions about the exact to-be interpretation of Seljuq monuments on the Iranian plateau. One suggests that geometric pattern and interlace of Seljuq provide visual metaphor, making allusion to a paradise, which posit the image of peacocks and pomegranates, while the other emphasizes its protective function as an architecture. There seem to be no exact and correct interpretation provided, which means its function can be interpreted in multiple directions while becoming a location where culture, aesthetics, and spirits harmonize into an uniformity. Likewise, I believe an architecture can be called “scared” whenever, despite its high reliance and dependence of many people, it carries multiple definition and purpose.
From week to another, I am becoming more curious about the impacts and how the cultural and allegorical contexts are shaped in scared architectures and I am very pleased to learn about them,
This week I was particularly struck by how different design styles can point towards sacredness. Coming from a Christian background, I was more familiar with stained glass windows depicting biblical scenes as a focal point in religious space rather than geometrical pattern. In this sense, I am more accustomed to viewing “figures” as ciphers of sacredness rather than the abstract. Due to this, I found this week’s readings very enlightening and novel. On Tuesday, I focused on how abstraction in Islamic architecture leads to a better sense of connection with metaphorical religious thoughts. For instance, an abstract design inside of a dome can influence one to view the pattern as a representation of the heavens. This can force you to enter a realm of metaphorical thinking. As Gonzalez put it, the mathematical abstraction used in Islamic architecture shifts “the perception and the aesthetic appreciation from the sensitive level of corporeal existence to the cognitive level of the mind, the intellect and the spirit.” With no figures present, the aesthetics of these religious spaces allows for a shift towards more inner religious reflection.
This line of metaphorical thinking also permeated into Thursdays reading in the sense that circling the square can be more abstract than squaring the circle. Furthermore, the idea of a squinch connecting the different realms of circles and squares was interesting. I think this ties back in with abstract thinking in terms of how those in the Muslim faith envision the connection between heaven and earth. The squinch is a point of connection and I think in its abstraction it can certainly be seen as a cipher of sacredness.