A Harmony of Spheres

Over the years Dominic Hopkinson has created artworks as both an individual and as part of a group of artists, scientists, and makers through the Leeds-based collective, The Superposition. He has also worked as a technician for the artist Peter Randall-Page, with whom his own work as a sculptor shares many similar concerns.

In April 2015 BasementArtsProject presented the work of Hopkinson in an exhibition entitled A Harmony of Spheres. The exhibition was put together in the space of four weeks which, when considering the lengthier processes that generally accompany the planning of exhibitions, was no time at all. Hopkinson is based in Pudsey, West Yorkshire a convenient twenty-minute car journey from BasementArtsProject in Beeston, South Leeds. Another factor in the short turnaround for this exhibition though was the idea of isolating one strand of Hopkinson’s practice and curating a very focused and analytical exhibition, guiding people through what could seem like the cold, hard realms of science and mathematics, but in the manner of an intimate BasementArtsProject exhibition. After making a visit to Hopkinson’s studio in early April and discussing the concepts behind his work, a number of email exchanges led us to A Harmony Of Spheres an exhibition that would effectively explain Hopkinson’s engagement with closest packing theory and the importance of the golden section in art, architecture and most significantly in nature. 

For A Harmony Of Spheres the main window was uncovered allowing the front exhibition space to be flooded with natural light, whilst the exhibition space at the rear remained in darkness with individual works spot lit. In the rear space, all of the works were plaster and delicate in nature, the spotlights highlighting the contours and voids of pieces that were in some places as thin as paper. In the front exhibition space the works were predominantly stone with a small selection in plaster and bronze; here the objects had more weight and solidity referring to a particular thread in Hopkinson’s practice. Whilst the theme of closest packing theory was picked up in pieces such as When Haeckel Drew the Radiolarians (main image), 29+50+30+82(cusnznpb), 2011, and Kissing Isaac Newton an avenue of inquiry opened up that crosses the boundary between the worlds of two and three dimensions. Here computational models are used as a way to explore an action that is possible in the world of the virtual but not the real.

The consensus among all of the exhibitors at BasementArtsProject seems to be that the character of the gallery space, despite its many issues, creates a very singular atmosphere. One of the most distinctive features of the space is the well-worn, distressed and exposed surfaces which exude an atmospheric resonance. The work entitled Kissing Isaac Newton (2011) had for a number of years been gathering a patina in Hopkinson’s garden, giving it a certain quality that none of the other works on display at BasementArtsProject had. Whilst this particular sculpture in Ancaster stone still retained the accuracy and attention to detail of his other work, the effect of environmental factors had altered the colour and texture of the piece. Thus I noticed that in the warm glow of evening sunlight it seemed to merge with the wall behind it, the shadows and colours blending the contours of the work with the crumbling painted plaster and stone backdrop. Yet from certain angles the piece also appeared to be emerging – rough-hewn from the very fabric of BasementArtsProject. This rather organic basement setting seemed to bring out an intriguing aspect of Hopkinson’s work.

Bruce Davies: When we first started advertising your exhibition Debs of BasementArtsProject, tweeted a comment about ‘posh gallery work in our basement’ that made you laugh. I think this is quite significant in terms of how you view the process of exhibiting. Would you like to say something about this?

Dominic Hopkinson: Yes, I remember that! First of all my work has a particular aesthetic associated with its finish, not exactly stylised, but definitely tight, complete. Also the nature of my chosen materials, particularly the plaster pieces, have a pristine quality due to the colour of the material and so exude a sense of austerity. Secondly, I knew that BasementArtsProject’s normal process was not to show a complete or pre-made body of work, but to have the artist engage in a dialogue with the exhibition space over a period of time. The space is unusual in many ways, it is a basement in a private residence, it is not fitted out as a white space gallery, there are obvious traces of previous artists work on the walls, and so provides many points of engagement for artists to react to.

I knew all this and so was aware of what I felt was a gamble for both the curator and myself, to break the style of exhibition and show the BasementArtsProject audience something very different in feel, style and approach. This felt risky for me too because until then I had only shown my work in ‘white spaces’ and had built up an installation process that revolved around high quality finishes, and a pristine almost laboratoryesque delivery of the work. This would have to change if I were to do justice to BasementArtsProject as a philosophy and a venue. Finally it was also a lovely thing for Debs to have said, and gave me confidence in what I was doing.

Have you ever gone down the route of explicating one particular avenue of work before?

This approach was new to me, and was actually something that evolved out of bringing the work into the space for the first time. Previously I have tended to show my work as a single body, made up of various strands of research into different mathematical and scientific ideas that then function as a whole. The crossovers in research and concepts are then available to the audience and each body helps to put the others into a wider context thematically. However for this exhibition I felt that I needed to be much stricter in the selection of included works, partly due to the amount of available space and other physical constraints, but mainly because I wanted a pared down show with fewer works jockeying for position. This led to a discussion about removing a major strand of my more recent work from this show, but which also led to the idea of a more BasementArtsProject style residency/intervention to take place in 2016 based upon the work not included this time around.

Can you discuss the title A Harmony Of Spheres and the reasoning behind the selection of works which led to it?

The second sculpture I ever made, and my first stone carving, which I did on my foundation course, was of a sphere, I’ve not stopped working with them since, really! The sphere is a fascinating mathematical and sculptural object; it is the most efficient mechanism for enclosing space; it has the greatest volume to smallest surface area ratio of any object. It is made up of an infinite number of flat planes in the same way that two-dimensionally a circle is made up of an infinite number of straight edges.

The sphere is the foundation block of the Platonic solids, and has acquired a special place in philosophy, metaphysics and culture more broadly. I see the sphere as analogous to atoms, cells, molecules, planets etc. and am interested in how nature maximises its efficiency by utilising this form at every level of scale. I use the term ‘analogous’ wisely though, since there are no perfect spheres found in nature, each expression of this form is subtly deformed at every scale. My work attempts to mirror this perfect/imperfect paradox, using plaster cast forms that are a measured, equal quantity (so each are identical in size and volume) and allowing the process of making the work to deform these individual forms while retaining their essential simplicity.

Because the final selection of work was almost exclusively based around ideas of spheres, closest packing theory and the Platonic solids it seemed appropriate to find a title for the exhibition that bound these ideas into a coherent concept. The title A Harmony of Spheres is a distortion of ‘The Harmony of the Spheres’, a trans-disciplinary idea that unites cosmology, astronomy, mathematics, and music theory, and has been a major vehicle of the Pythagorean current in the intellectual history of the West. The astronomy of the Pythagoreans marked an important advance in ancient scientific thought, for they were the first to consider the earth as a globe revolving with the other planets around a central fire. They explained the harmonious arrangement of things as that of bodies in a single, all-inclusive sphere of reality, moving according to a numerical scheme. Because the Pythagoreans thought that the heavenly bodies are separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound – the ‘harmony of the spheres’.

You talk about the deformation of forms in the process of making. Could you explain how your theories are reflected in your working methods and casting? I’m thinking in particular of On Growth And FormSmall Geodesic and Half A Cloudy Sun.

My aim in these works is to attempt to represent organic form and process at varying levels of scale. By this I mean looking at the physical properties of atoms, cells, molecules etc, how they form in nature, what are the physical constraints acting upon these forms, and how do the physics and mathematics dictate and define their formation, orientation and location in three-dimensional space. When cells divide and grow they have to obviously fit into a space, and in order to achieve this with the maximum efficiency, the cells have to follow the rules of closest packing theory. This is a piece of mathematics that acts as a blueprint for how the cells fill space, from which a highly ordered level of structure is derived. This structure is intrinsically linked to the concept of the golden section, or phi, an irrational number that is associated with art and architecture as well as the natural phenomenon of phyllotaxis, how plants grow with a spiralling motion that is a response to how the cells in the plant’s growth buds pack together.

Closest packing theory works best with perfect spheres, but cells are not perfect, they are also soft and malleable and can deform to fill space slightly differently to spheres. I utilise the process of casting the plaster pieces in order to mimic this malleable-ness and deformation from a potential perfect sphere. By filling balloons with liquid plaster of a measured quantity I am able to set rules in place that act as analogies to the constraints found in nature. The balloons are theoretically the same volume, the same size, yet when they set hard they are all subtly different shapes. Each piece is allowed to set, taking on the external form of the mould it’s cast into and the curvature of the balloon caused by pressure, then the next one is placed next to the first, allowed to set and so on. This process means each successive piece is impacted by the constraint of the mould and its relationship to the previous pieces in much the same way as in the natural process. I set rules and boundaries for each work; the shape and size of the mould, the volume of plaster in each piece, then I try to take a back seat, as the artist, to allow the work to develop on it’s own within these parameters. I try not to interfere with the packing process as far as I can, trusting that the maths will generate an interesting outcome for me.

The specific pieces in question, however, show the reverse or negative of this process. I have cast the negative space that is normally a void, absent, in the other pieces, and made it solid. It is a way of showing that the unnoticed space around sculpture is as important for understanding form as the form itself. The piece On Growth and Form is titled after a book of the same name written by D’Arcy Thompson in 1917. This is an analysis of the way things grow and the shapes they take, how the laws of physics and mathematics have nearly as big an impact on animal and plant morphology as Darwin’s more famous theory of evolution by natural selection. Thompson’s book has become something of a classic text within the sculpture community ever since it was written, since it looks at form and its generation from a materials and process driven perspective that is immediately recognisable to the sculptor.

Scale is an interesting subject in relation to how you cast the plaster pieces. You have said in the past that you are always interested in peoples’ reactions to what they think the shapes refer to, whether or not they perceive them to be on a massive scale or microscopic. I think of one example you give, where a child related one sculpture to the texture of the surface of their tongue. You have talked to me about the subject of the ‘Infra slim’. Would you be able to say something about that, perhaps and how that theory relates to the use of the balloons when casting in plaster?

Although I make the work with a specific sense of scale in mind, I am aware that different people interpret the work at various scales, from the sub atomic micro level to the object, organism macro level. I am not prescriptive about this process of interpretation, and I actually enjoy and collect the responses of the audience which vary from atoms, dough balls, the surface of your tongue to breast implants! In fact it is an important element of my work that it has this ability to provoke different scales, and some of the best and funniest interpretations have come from children. I believe that this is because the mathematics that drives the growth process in nature, and that I try to represent in my work, is so fundamental that we can do nothing but recognise this at an instinctive level, without the need to understand or even be aware of the mathematics. Humans are nothing if not pattern recognition animals.

The ‘infra-slim’ is a concept that I came across years ago when reading about Marcel Duchamp, in a book, I cannot recall its title, and it is an idea which I have never come across again since. In this, he discussed the idea of the infinitesimally small gap that must exist between the surface of an object being cast and the interior wall of the mould. This was what he called the ‘infra-slim’. It is a concept that interests me, and I am aware of the idea when using balloons to cast my plaster objects. Indeed this exists at multiple levels in my process; each piece has an ‘infra-slim’ between the plaster and the balloon, each piece also has one between each external surface of the balloons as they are packed next to each other, and each piece has an ‘infra-slim’ between the external surface of the balloon and the interior of the box/mould. The ‘infra-slim’ exists at an extreme level in my process since the latex of the balloon has the ability to stretch to create such a thin membrane, and thus allows the pieces to get so close to each other as to create further ‘infra-slims’.

I think that Duchamp felt that, theoretically, there had to be a tiny gap between object and mould in order for the piece to be released from the mould. If the ‘infra-slim’ didn’t exist then it would be impossible to remove the object from the mould, as the friction would be so strong that they wouldn’t separate.

I like the idea that if the ‘infra-slim’ did not exist every time we sat on a chair or touched a surface, at a sub-atomic level, we would become fused to it!

Well, strictly speaking the phenomenon of the ‘infra-slim’ only really applies at a more macro level, at the sub atomic level the relative distance between each atom is so great that in effect matter is actually about 99% space. The only thing that stops us falling through the chair when we sit on it is the force acting between the atoms that bind them together!

Your plaster sculptures looking at Platonic solids and packing theory seem to depict something of the delicate nature of reality, cleverly designed structures threatened by the very fact that they exist at all. Yet the topological sculptures based on computer simulation, of which more in a moment, seem to work in complete opposition to this. These objects are brought into existence in a manner that locates them very much in the real world. Although there are plaster models, the majority of these works are created by direct carving of stone – Portland and Ancaster limestone and Carrara marble. Instantly these works are bound by gravity, their presence is impossible to ignore for their scale and apparent weight. Is this a conscious decision to emphasise the physical status of something that was once only virtual?

That is a really interesting interpretation and idea and one I wish I could claim for myself, but being honest, I’d have to say that this is not a conscious decision on my part. The decision about which piece of work is made in which material is both an intellectual one and a practical one which depends on a number of factors. All of the plasterwork is made using the casting process that I have refined over many years, a process that is integral to the concept of cell division/replication and the other ideas already discussed. If these works were made by a different process, say carving, then they would, for me, lose so much of what makes them interesting, and lose important theoretical elements such as their size/uniformity/malleability/colour, not forgetting the ‘infra slim’ .

I love the idea of making solid a virtual object by carving, but I think that for any abstract piece of sculpture this is what happens, you take an idea that is as ephemeral or virtual as anything can be, and you produce a physical manifestation of that idea in a material, using process and tools. Yet for my process the decision of which works are stone is more a practical choice, stone has particular qualities that lend it to the creation of accurate forms.

I would say that I have prejudices against certain materials though! Clay for example, holds no interest for me, in its base, unworked form it is just a lumpen mass that has little in the way of character, yet stone has a solidity, a presence that is already sculptural, it exists as an object in its own right. Stone also pushes back at you as you work it, it is hard, unforgiving and irreversible, if you make a mistake it’s very difficult to add back material!

On a philosophical note, stone also demands respect. Some stones are beautiful in their own right, and one feels the requirement to do the material justice in the way it is used to make a piece of work. Will the sculpture actually be an improvement on the original block? Also I’m aware that the material exudes a sense of its great age; when one carves a piece off the block it is the first time anyone has seen that surface, ever, and the first time that particular material has been exposed to the air for at least 140 million years! This seems to demand a certain level respect for the stone that I don’t feel for other materials.

Moving from the back exhibition space into the front there is a slightly different theme . Although closest packing theory carries through in pieces such as When Haeckel Drew The Radiolarians (main image), 29+50+30+82(cusnznpb) and Kissing Isaac Newton the other works follow a slightly different, although not unrelated, course of inquiry.

These works are much more about the geometry of packing perfect spheres, and less about how this process works in organic systems. Each one is a study of how spheres pack in different ways, and how, when left to their own devices within the constraints of the maths, forms and shapes are generated, such as the Platonic solids.

Many of your titles at first glance seem wilfully obscure, but scratching beneath the surface you start to understand that, in actual fact, they are quite literal. Can you discuss the significance of the titles of your works?

The titles of my work are very important to me, as they enable me to embed information about the mathematical and scientific theories without having to rely on paragraphs of accompanying text for each work. Most of my titles contain key words that when put into a search engine provide a great deal of context and explanation. When Haeckel Drew The Radiolarians is a good example. I don’t expect the audience to know who Haeckel was or what Radiolarians are but by searching for these words online you can find out, and get access to further incredible images that hopefully provide a broader context to my work. Some titles though are simply plays on words or make little jokes about the wider context of the ideas behind the piece.

Would you be able to explain how the other works in this room convey the idea of how a sphere can be turned inside out?

These pieces are based upon a branch of mathematics called topology, which is a way of manipulating surfaces, or membranes, according to a set of rules. These rules are that the form cannot be cut, creased, folded or loose or acquire more holes than it started with, but you are allowed to pass one surface through another! This is all very theoretical but is widely used in contemporary maths, indeed there is a well known T-shirt produced that has a pictogram equation ‘donut = coffee mug’ printed on it because according to the rules of topology the two forms are one and the same! It’s a bit of a geek joke I guess!

I found online an example of how topology can be used to turn a sphere inside out and was fascinated at the incredible variety of forms that the transition goes through. A freeze frame of this process was the basis for these pieces, although I ‘allowed’ myself to break the topological rules in order to produce a form I was pleased with, hence the sharp, ‘folded’ edges.

The final piece that I would like to talk about is Doing Evolution After Lara Favaretto. Can you discuss the genesis of this piece and its unfinished status?

This piece is a variation on the topology of turning a sphere inside out, which I see as a process of evolution in the sense of the transformation of the form, yet obviously includes an interpretation to Darwinian evolution. The title derives from the specific origin of the stone, in this case Carrara marble. Early in 2015 the Italian artist, Lara Favaretto, presented a performance piece on the steps of the Henry Moore Institute in Leeds, here a series of large blocks of Carrara marble were worked on by volunteers with no carving experience. The sound of the process of hammer on chisel, chisel on stone, was recorded and this became the artwork presented in the gallery. The concept was for the marble to be completely reduced to rubble, negating both its form and the idea of ‘classical’ sculpture, but due to the time constraint of the process, at the end of the performance the blocks of marble were still virtually intact. I was able, along with two of my students to salvage the marble, from which the piece in question was created.

Personally, I have been made aware that many consider the process of stone carving in contemporary art more redundant than the old chestnut regarding the ‘death of painting’, but I like the juxtaposition of the old, classical materials and processes being utilised to render contemporary scientific and mathematical concepts. I am more than aware of the paradox involved and wilfully engage it. The title therefore acknowledges Favaretto’s original work, yet for me also contradicts or defies her own personal thesis about the place of stone carving in contemporary practice. I have yet to decide whether all the work I make using ‘her’ marble will be titled with reference to Favaretto, or not.

The reason this work was listed as ‘unfinished’ reflects an important part of my process. I wanted to include this piece in the exhibition at BasementArtsProject due to your links with the Henry Moore Institute, since you have worked there for the last 12 years, and because it was also my most recent piece of work. Yet I was conscious that I had possibly rushed its completion to this effect, so decided to show it with the unfinished caveat attached, thus providing myself with the opportunity to revisit the piece after the show. However, I often spend time assessing my work after completion, both at a conscious and unconscious level, trying to analyse its success, or whether it suggests further ideas and work. This process often sees me re-evaluate pieces, sometimes many months after completion, with a view to creating further work. In the case of this specific piece I have to admit that I am still in two minds as to whether it is finished in its current form or not. Time will tell, but it is part of my process.

Main image: Dominic Hopkinson, When Haeckel Drew the Radiolarians, 2010, Ancaster and Portland limestone (photo: Adam Glatherine)

The Harmony of Spheres, BasementArtsProject, Beeston, Leeds
18, 19, 25 & 26 April 2015.

Aurora Corio