Noel Gray on Geometry, Virtual Reality, and the Creative Plane

As one among the swelling number of people grounded by covid-19, I’m using newfound time to do something about my backlog of unfinished projects. With the dire news pouring out of Italy, I moved this interview with Noel Gray to the top of my get-done list. In fact, if things were otherwise, I’d be visiting Noel in early May at his home in Treporti, outside of Venice. What follows is an interview from my last visit there.

Lise:  Our conversations over decades of friendship wander freely—figuratively and literally—traversing our lives in Australia, US, Asia, and Europe. We’ve revved up our rapport the past few days around your kitchen table in here in Treporti, so why don’t we plunge right into the deep end. Let’s talk about your scholarly work on the philosophy of geometry and its links with your experience as a visual artist. Tell us about how your work in stone carving and sculpture led you to the path of philosophical research and a doctorate in fine arts? We’ll have to leave your more recent incarnation as a fiction and essay writer for our next interview.

Noel:  Of all the arts, stone carving is the probably the closest to learning or acquiring an understanding of geometry, because it’s working with solid forms. And even when it’s not, the character of stone and the length of time it takes to work it, mean that you’re acutely aware of the form that you’re trying to create, how effective it’s going to be, and how long it’s going take to make.

A drawback with stone carving is that it’s very hard to fix a mistake. With wood, you can fill it and color it, and nobody knows a mistake was made. But with stone carving, there’s no successful way of gluing something back on without showing where it happened. Plus, you can’t cover mistakes with paint since most stone carving leaves the stone’s natural color.

A lot of carvers use compression tools that obviously speed up the process, but you still have to be extremely careful because stone is not flexible or forgiving. A flaw could be in the middle of the stone and you can’t possibly know until you get there. If you go in the wrong direction with a cut, it’s easy to lose the corner or crack the whole stone.

Stone carving teaches a lot about geometry because, first of all, it’s not transparent. You have to be able to imagine the interfaces that take place on different forms as if it were transparent. You work as if you could see those interfaces. So, it teaches how to visualize form. It’s said that when someone asked Michelangelo, “How do you carve an elephant in stone?” He answered, “It’s easy. Just take away all the bits that don’t look like an elephant.”

Stone carving has two basic methods. An artist like Michelangelo almost finishes while going along.  When Michelangelo carved an arm that eventually would be stretching out, he finished the fingers as he went along. Most other stone carvers go through a set of stages. They rough it out to the basic forms, and then refines from that point on. It’s difficult to determine the exact dimension of these finished forms at the beginning.  You can’t add something if you’ve made the head too small. If it’s a large piece of stone and you’ve make a mistake like that, then it’s an enormous amount of work to reduce everything else. Stone carving teaches not only how to think of relationships of forms, but also of their proportionalities.

Before beginning to carve, you have to inspect the stone to determine if it can support your idea. If you want a statue then you need the right stone, the best being Carrara marble. You can’t do it in sandstone because it would just break off. Sandstone particles are almost as hard as diamonds, but sandstone’s molecular bonding is very weak. Marble is opposite. People often think marble is harder than sandstone. As a material marble isn’t strong at all, but its molecular bonding is very, very strong.

Considerations like those require the development of a sophisticated sense of geometry and affine geometry, the relationship of one shape to another and how in the course of work one shape changes into another. If you think of your fingers changing into your hand, which then changes into your wrist and forearm, which changes into your elbow and bicep and then into your shoulder, then these are all transformations of form. In stone carving, you need a clear idea relationships and proportions before you start.

Lise: Is sketching a way of working through some of these problems before you start carving the stone?

Noel: Sometimes. There’s some truth in the adage that a great stone carver starts as a great drawer. Michelangelo was an accomplished drawer. Drawing can be a start, but you want to try to acquire the three-dimensional concept of what you’re doing. Drawings in the form of a plan can help to know roughly the direction. But drawing doesn’t deal with mass. Artists can make a model in clay or other material with flexibility for error and correction, and  then work from there.

Think of Michelangelo’s David. Its size takes into account the viewer’s perspective. A stone carver starts to acquire considerable knowledge of how to think dimensionally. It’s difficult to teach this skill and to explain what goes on in the brain. Much of it is acquired by visual and physical activity on something. I disagree with those who say that some people can do this innately. Like many things, this skill needs to be acquired one way or the other.

 

Lise:    As an artist working with stone, what was your trajectory of developing that facility?

Noel:   I started my art period, I won’t say career, by doing a lot of drawings, and then watercolors and paintings. When I moved into sculpture, I started with aluminum and steel construction. There are similarities between that and stone carving in terms of dimensional thinking, of reasoning, of trial and error. But the processes are fundamentally different. Carving is a of process of reduction.

Lise:    Trial and error are where experience comes in handy. What led you away from the constructivist approach of putting things together into sculpture and to stone carving?

Noel:   Just before I got into stone carving, I left Australia on my first overseas trip. I spent a lot of time in London at the British Museum and the Victoria and Albert Museum. Seeing so many works from different cultures, I started asking if there could be some sort of universal relational system underlying them. I made close to 30,000 drawings, which are now at the University of Sydney’s Power Institute Library in the Department of Fine Arts.

After spending 20 years carving and making things, I discovered my thinking was flawed by the assumption that it’s possible to access a universal set of relationships. As Kant once said, culture is like a pair of glasses that you can’t take off. After doing all that work and exhibiting in Australia and Latin America, I started wondering how I wanted to proceed.

Lise:    Before you realized this problematic assumption, did you ever feel like your work was bringing you closer to an understanding of an underlying universal system?

Noel:   Through the work of drawing and carving, I developed a three-part system, of primary, secondary, and tertiary forms. This turned out to be a good way to teach people how to draw and carve, because instead of trying to draw the desired finished object, it gave them a constructive process, either mentally or physically. They would start by asking, what is it that makes an Egyptian head an Egyptian head? Now, forgetting whether or not that’s a universal principle, the fact remains that there are certain quick drawings you can make with two or three forms and people will think it’s an Egyptian head—even if it’s not—because of the resemblance in the relationships and masses.

Lise:    Your approach emphasizes that looking precedes drawing. Your approach gives an analytical framework for looking.

Noel:   I broke it into three forms because there are only a few primary ones. That allows you to locate the fundamental relational structure of whatever you’re looking at. The secondary forms are the things that start to shift it from being a general statement about Egyptian heads to something more specific. The tertiary forms are the multiple forms that make it look like one person and not another. When carving or constructing anything, it’s a simple and useful aid to start with the basic masses.

It’s hard to imagine any period in human history that didn’t somehow use geometry. The making of stone axes, of flint arrowheads involves sophisticated geometry. People tend to regard stone age technology as primitive, when. in fact, it’s extremely complex. Although I’m a big supporter of extensive techniques for artists because they comprise a history and knowledge that are worth having, I’ve always been drawn to the philosophical and intellectual elements of art. I ended up thinking more about the nature of geometry than what I was making. It seemed more fascinating and elusive. Geometry’s attraction was less its mathematical and more geometry as a thought process. How was it constructed? Why was it so successful?

Lise:    By learning and teaching stone carving, you arrived at the more conceptual side of geometry. Once you figured out how to create art works informed by an understanding of geometry, you wanted to go more deeply into geometry itself.

Noel:   Exactly. But in a way that was unlike many of my predecessors throughout history, particularly during the Renaissance when geometry exploded in Western art, first as a means of rendering perspective. Most of these artists were skilled geometers in the mathematical sense, not just in the sense of making physical drawings. I wasn’t so much interested in that. First of all, when you use the term geometry and you’re talking about antiquity, it’s a generic term. It included mathematics. They didn’t make that distinction as we do today.

Lise:    Do you mean that geometry was synonymous with mathematics?

Noel:   Yes, basically. Geometry was the power. You had to be a mathematician to work on geometric problems. Whenever you’re reading about ancient mathematics and geometry, it’s the same thing. They’re interlaced and not as divided as they are today. Geometry was called “the royal road to truth.”  As long as you knew geometry, it didn’t matter who or where you were. If you did a, b, and c, you’d end up with x, y, and z, like everyone else.

There was nothing left unsaid and it was an effective and convincing tool for ancient philosophers, starting with Plato and ideal forms. That is, the idea that the intellect is a higher plane of reasoning than the senses, because you can think of things that you can’t possibly see, like infinity. But you can think of them, and as thoughts they’re useful. Universals and ideal forms are useful for constructing meaning and understanding the world and nature. What interested me about geometry was, what is the price? Any power structure, any relationship which dominates, always comes at a price.

Lise:    The price is that something is subordinated to whatever has the more power or dominance.

Noel:   Exactly. In early geometry, irregularity was subordinated. For Plato, ideal forms are perfect by definition. They’re not irregular.

Lise:    What is irregularity?

Noel:   Look at any shape in nature and there are no perfect spheres and cones. They’re all irregular objects. In Euclidean geometry, a tree can be reduced to a triangle. All these forms can be reduced to basic geometric forms, and that’s a compelling argument about universality and the fact that these things are true for all people.  For example, the argument that a tree is a tree is a tree for everybody. They all see the same thing. It may have a different significance to them, but it’s still a triangle on a cylinder. That’s a convincing way to understand the nature of nature. It’s also a phenomenal tool for building. It’s impossible to imagine the history of building without the history of geometry.

It later allowed for a man called Thales to prove you could measure the height of a pyramid without physically doing it. He introduced the powerful concept that mathematics and geometry could be an exercise almost entirely in abstraction. This was convenient, because you could design things without having to build them first. In many cases, there are hidden things that can’t possibly be known in advance, but can be discovered in the process of building.

Lise:    Can you talk more about what you mean by abstraction in this context since it has different meanings for contemporary art. Just to come back to the specificity of that moment and your understanding of it—did abstraction mean that something wasn’t physical?

Noel:   That’s the first step. It didn’t require physical engagement with the object you’re trying to measure. You didn’t have to climb up the top and measure the distance. You could measure the side and base of one of the pyramids and determine the height by and using algebra, some of which wasn’t around at that time.

Thales demonstrated by putting a stick in the sand and measuring the length of the shadow and the height of the stick, he found the ratio between the shadow and the stick. The height of the pyramid then could be calculated by measuring its shadow and applying the ratio because its relation to its shadow is the same as the stick to its shadow.

The fascinating concept of abstraction exists not in the two examples, the pyramid and the stick. It exists in the idea that you can use one concept to discover another. A concept such as  proportionality isn’t something physical that you can grab. Abstraction lies in the concept, e.g., proportionality, and the result of applying it to something to accomplish what would require physical engagement if you didn’t have the concept of proportion.

The second crucial moment of abstraction is a discovery by the neo-Platonist philosopher Proclus who compiled Euclid’s Elements. He considered the fundamental problem with Plato’s system to be the fact that intellection, the higher plane of thought encapsulated in ideal forms, is beyond verification by the senses. He asked, how does the mind get from one plane to the other? How does it go from a pure state of ideal forms to thoughts of the senses, where everything is irregular? To solve the problem Proclus conceptualized the geometric plane. By removing “geometric plane” and inserting “imagination,” one arrives at a description of the hierarchical process of the imagination: information comes down to it from intellection and goes up to it from the senses.

Lise:    According to this line of thinking, is the mind-body split an abstraction?

Noel:   Yes. When you make a split, you have to define each element as separate. How do you get from one to the other? If they share a common interface, they’re not really split.

Lise:    They’re continuous.

Noel:   They’re adjacent, but not uniquely separate. The geometric plane Proclus developed, is clever and beautifully expressed, although somewhat obscure. There is a world of  intellection, the world of ideal forms. The senses only see nature, where everything is always changing. Amidst this being and becoming, what is the tree-ness of trees? What remains when everything changes? The geometric plane of ideal forms never changes. But the price for this is hierarchy, the purity of unchanging ideal forms is given a higher value. Impurity must be ignored, subordinated, or expelled.

This occurs in math classrooms across the world when teachers and students draw a circle. Everyone knows it’s not a perfect circle, but acts as if it were. They overlook the circle’s  irregularity, because it’s not significant. Since around 1970 fractal geometry started concentrating on the irregular. The dream was it would finally be possible to mathematize the emotions. The drive to bring everything under the mantle of measurement and mathematics, particularly since the Renaissance, is a hallmark of progress in the history of science.

Lise:    Is fractal geometry what is also popularly known as chaos theory?

Noel:   They’re connected. Chaos theory or fractal geometry are, in a sense, the theory of irregularity or disorder. It has many names depending on what you’re applying it to. The genius in fractal geometry and its first true expounder was Benoit Mandelbrot. Fractal geometry is basically a geometry of the irregular. Mandelbrot wrote a wonderful essay, “How Long Is the Great Britain Coastline?” He shows that it can be infinite. It all depends what is used to measure it. This in turn relates to Heisenberg’s Uncertainty Principle, which states that whatever is measured is affected by the thing used to measure it.

Lise:    I thought it was affected by the act of being measured.

Noel:   Whatever you measure it with is part of that factor. In other words, there’s a very strong subjective element to it. If the English coastline were measured using the size of an ant, you’d end up with a staggeringly large number. If measurement used the size of molecule, it could go on for infinity.

That’s partly why Nietzsche said that size is based on an aesthetic judgment. We have a length of gold in Paris that’s a meter long. How do you measure that? If you keep questioning, it becomes reductio ad absurdum. You can never get to a pure measurement. This is the irony inherent in the hierarchy of purity that is used in geometry and mathematics. An aesthetic judgment lies at the heart of geometry. We agree that this and not that equals a meter, after which we carry on to make complicated measurements and calculations.

My research into the philosophy of geometry explores this foundational aesthetic preference: the need to expel impurity. Yet, it’s simultaneously needed as a reference point, because meaning functions on a binary system. Power requires that someone doesn’t have it, has less of it. All transfer of energy requires a potential difference between the two things. The question is not how to get out of the binarization of meaning. The question is to understand how the components acquire their position in the hierarchy.

Lise:    Isn’t your work also about what is facilitated by that binary structure?

Noel:   First, it creates a hierarchy and gives purity the privileged position. Plato’s ideal forms and the idealities of mathematics are the unchallenged power.

Lise:    What was Mandelbrot trying to make possible beyond a way to measure the irregular?

Noel:   He argued that fractal geometry is the geometry of nature, a natural geometry. There are some good arguments to support this. Other arguments challenge it.

Lise:    But is the underlying idea that irregularity could be measured?

Noel:   Yes, and that’s the interesting development. To make it a science, ironically, you need to create order and predictability, which pushes you back into the purity argument. This happens all the time because to generate this as a dominant thought or paradigm, you have to bring the enemy with you. For credibility, you have to carry order along with you in a philosophically secret way. It’s necessary to maintain the philosophical structure. You can’t just have one half of it. In order to define your position as superior, to demonstrate its superiority, you have to make something else inferior.

When I began my research on the philosophy of geometry, on how geometry works philosophically, there wasn’t much on the subject except a book by Derrida and a part of another by Husserl. My work isn’t a criticism of geometry. It’s a critique in the classic sense—an explanation of how something functions. Why is geometry successful and what is the ground of its success?  I go into philosophical, literary, and other cultural works to demonstrate that geometry functions in all of these; and it uses them, sometimes openly, sometimes not, to bolster its position as the discipline that knows.

If you had epitomize science in one sentence without making a false claim, it would state that science is the truth enabler. It’s what people go to if they want to know the truth about how the trees grow, the distance between earth and the moon. In that sense, science is similar to religion.  It’s also a theory of everything. Science as a way of knowing can encompass everything. It’s an explanation about being and becoming. In that sense, it’s the foundational rock of humanity.

Lise:    Let’s go back to art and geometry. How would you say that this philosophy of geometry that you’ve researched and come to understand is or could be meaningful to an artist in the 21st century?

Noel:   A lot of contemporary art is associated in one way or another with computers and digitization. A certain system or paradigm of thought that’s not all that different from whatever preceded it underlies all those tools and media. We could ask, what does it mean to say that much of 21st century art is a product of the digital age?

Applications and technologies are involved. What baggage are they carrying with them? Husserl once said—and I’m paraphrasing—whatever world you imagine, no matter how fantastic, is always in the style of the world you inhabit. The interesting question for me is, what is the effect, and I don’t mean a necessarily limiting effect, of the baggage that accompanies it? Many concepts of geometry are not much altered by different technologies of production. For example, virtual reality is an electronic version of Plato’s intellection and better allows for production of ideal forms than of physical artworks.

Lise:    Virtual reality is particularly intriguing in this context. It creates ideal forms at the same time as giving people a perceptual experience of them.

Noel:   That’s true. And that’s where it’s ahead of Plato’s intellection and ideal forms.

Lise:    Virtual reality provides a sensory experience of something that doesn’t exist in three-dimensional physical form. In a way, it puts you in someone else’s imagination. Or in an imaginary construction. You’re experiencing something that’s not physical as if it were physical. But you don’t have the power to create it. It’s being acted upon you.

Noel:   This idea of the virtual has an interesting history in the arts and sciences. In the past, if you replace virtual with ideal and idealities, you get a historical continuum. Newton’s laws were built on the principle of a frictionless universe. But of course, friction exists. If you move into virtual reality, you work on the principle that physicality is not present. There may be a sensation of physicality but there’s nothing to touch. There’s no physical thing.

Lise:    What about the so-called discovery of perspective, of representing visual thinking or visual experience in two dimensions? Isn’t virtual reality similar to that.

Noel:   It’s very similar. Some people overestimate the importance of the Renaissance development of what we call perspective drawing, thinking that it creates a one-to-one correspondence in appearance between the drawing and what it depicts. The associated corollary, and art history books used to disclose it when talking about ancient Egyptian and Chinese art as incapable of rendering what was seen. That’s a massive error because it assumes there’s only one correct method to render the visible world.

This peculiar assumption follows from the assumption that perception is universal: everybody can see, and all see the same thing even if what they think about it is different. This way of thinking requires the separation of perception from meaning. Once you start to look at ancient works and realize that they were brilliant at visualizing dimensionality within their own terms.  We don’t know if they saw that buildings get small as they go in the horizon, and if they did, why they chose not to show it. The evolutionary model of art and to drawing is a deadly model to adopt. It’s often called art history.

Lise:    By an evolutionary model, do mean a history of art that’s driven by the idea of progress.

Noel:   Yes, the idea of improvement, that things are better now than they were then. What if we realize that we’re the ones with the limited perspective because we don’t know theirs. But we should be able to try to make some understanding of the complexity of their thinking process. We may not know what they thought. But we see products of their thought and trying to understand them can at least expand our respect for their abilities.

Virtual reality belongs in the long line of thinking about the truth of perception—of what comes closest to the truth. The curious thing about virtual reality is that in some cases, it’s argued to be superior to reality. For instance, its lack of need for physicality is a good argument for claiming that in some sense virtual reality supersedes reality. It makes possible things that probably never could be physically created or built.

By forgoing the need to add a physical element to virtual reality, you can enter a whole different universe of form and expression. That’s certainly a fascinating difference and can be applauded. It opens up a new horizon, keeping in mind as Husserl said, it’s always going to be connected to the world you inhabit. You’re not floating off into some universe where, once you’re there, you can pull up the ladder.

But what is the gauge of physicality? That’s the interesting idea behind The Matrix, where people inhabited non-physical worlds. They were all living in a virtual reality. If you live inside a virtual world, and you experience it as physical, how do you demonstrate the fact that it’s not? This is the Flatland problem. How can a creature living in three dimensions explain three dimensions to a two-dimensional creature? Many people have described Flatland’s discussion of time as a forerunner of Einstein’s formulation of relativity.

Lise:    Can we circle back to geometry and art-making now, contemporary art-making? I’m thinking about that statement of the Venice Biennale curator saying that artists ask questions and ask questions about contemporary life and society, culture, politics. Pretty much everything. You’ve asked a lot of art-related questions through your extensive study of the philosophy of geometry. How could your investigation inform lines of questioning by contemporary artists, including yourself?

Noel:   I’m interested in what virtual reality can teach about so-called ordinary reality, physicality, matter, and so on? What assumptions are necessary for you to be able to describe it as virtual reality rather than merely another conceptual reality you’ve dreamt up?

Lise:    That’s what I’ve been thinking, too. Plato posited a world of ideal forms, of intellection, that supersedes the sensory world.

Noel:   Some people argue that virtual reality is supersedes reality in some aspects. That statement in itself is raises an interesting philosophical question: why does change need to supersede whatever precedes it?

Lise:    That could be one question about virtual reality. But returning to geometry, what about its relationship to stone carving within virtual reality?

Noel:   How would you be a stone carver in virtual reality? What would you be carving? Given that materiality or physicality as it’s commonly understood is made absent in virtual reality, then it could become a contradiction to be a stone carver. Where there’s no stone, there’s no physical form to manipulate. Yet we know that you can manipulate virtual stone so in that sense that you can create a virtual stone carving.

Lise:    Maybe that’s where I’m going with this question, how does geometry and the questions that are made possible through your study of geometry articulate with the concept of virtuality?

Noel:   So, you’re asking what is the role of geometry in the ways we’ve been talking about in relation to virtual reality in contemporary art-making? Many artists have adopted what might be called a fractal perspective, working with chaos theory and fractal geometry together. They use them as the ground on which to make their constructions or creations.

Lise:    Would you say that working in this way has particular aesthetic characteristics?

Noel:   There’s an aesthetic to it, and it’s a means of making. A strong feature of Mandelbrot’s formulation of fractal geometry is the idea of self-similarity. No matter how much the scale decreases, even to the microscopic level, the form has the same self-similar complexity. This can be a difficult concept to fully grasp because it doesn’t mean identical. It means similar in complexity. It also implies that some are not as complex as others, and some are a little more complex. Either way, it means that as you keep decreasing, you either get to infinite complexity or infinite non-complexity.

In this way fractal geometry becomes a philosophical attitude. Artists aren’t necessarily interested in that. For artists and others, an important consideration is that geometry always has been a worldview. It’s not something you can choose to adopt or not. Everyone has a geometric position even without knowing what geometry is. It goes to the heart of how people construct concepts about their universe and themselves, because it has a strong physicality, a strong shape orientation, a strong descriptive notion. In fact, geometry is a theory of differentiation. It’s a theory that makes a cube not a circle, this shape and not that one.

Lise:    As a theory of differentiation, is it the basis for establishing the difference between self and other? It’s that. It’s not me. Is geometry the point of reference that makes possible our notion of a self-contained self?

Noel:   Oh, definitely. Subjectivity and geometry go together like coffee and water. You can have this individual who’s not that individual just has you can have this group which isn’t that group. Some cultures don’t think in that way about subjectivity. For them, a person is not physically separate. Subjectivity depends upon perimeter. In the case of humans, the perimeter can be one person, it can be a group. It’s all geometry in the sense that it requires differentiation. Sometimes differentiation is described in the form of a shape, which is what you might the history of geometry. Other times, separation and difference are built on another concept. If you don’t have a difference, you don’t have meaning. As Derrida points out, the meaning is in the space between the words, not the words themselves. The space of meaning itself is a geometric concept.

Lise:    In a lot of contemporary art, and partly coming out of conceptual art, the artwork itself exists in the space-time of the interaction of the object (physical or virtual) and the person perceiving it, which brings us back to the space of the imagination.

Noel:   Yes, that’s right. That’s why Proclus’s work ought to be resurrected. Perhaps modernize the language a bit. I’m not saying it’s the only plausible methodology, but it’s a brilliant description of how the so-called intellect and senses mediate each other—what he calls the geometric plane (the imagination), which in turn informs and disinforms.

In this sense, virtual reality is a digital imagination. It exists between the physical artist and the physical world. It’s a space where physicality exists as a concept without the baggage of dimensionality, of mass, of weight. Virtual reality forms a wonderful opportunity to explore how the contemporary imagination functions, how it develops, and what it prioritizes.

Lise:    So virtual reality can be seen as an arena along the lines of the geometric plane for asking questions, exploring ideas and concepts?

Noel:   Yes, exactly. Virtual reality is much more than an artwork or a creation. It’s a creative plane.

• Noel Gray books
• Critique and a Science for the Sake of Art: Fractals and the Visual Arts, Leonardo, Vol. 24, No. 3:317-320