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❉ Blog number 18 on diagrams in art and culture revisits an interview I made in 2013 with the artist Richard Talbot. Richard is a leading authority on perspective, and Head of Fine Art and Professor of Contemporary Drawing at Newcastle University in the UK. 
Figure 1: Richard Talbot, Random Moves, 1989, pencil and ink on paper, 120 x 120cm
The diagrammatic drawings of Richard Talbot present viewers with a palimpsest of their the own process of creation, or working-out. Each image sits embedded within a network of the construction lines and erasure marks from which it has arisen, and the artist himself suggests that this promotes the idea that the process of drawing itself can be considered the medium of his work, rather than the materials chosen to make the drawings (1).
I first discovered Richard's work in the book 'Writing on Drawing', a compilation of essays edited by Steve Garner, and published by Chicago University Press in 2013. (More information about the publication is available in a previous blog post: Diagrammatology: A reader.) Richard's contribution 'Drawing Connections', comprises chapter 3 of the book, and introduces his studio practice and academic research in to the theory, history and practice of perspective. As a second year PhD student in Kyoto I travelled to the UK at the end of the summer in 2013 as part of a research trip to interview artists and theoreticians working with diagrams. One of the highlights of the trip was the opportunity to talk with Richard in his beautiful studio and office in the distinctive, red-brick, double arches of Newcastle University's Gate Tower. 
The Arches viewed from the Quadrangle, Newcastle University.
MW: You originally had studied Astronomy and Physics ?
RT: I did, but realized early on that I had chosen the wrong subject. I noticed also that you had studied Biomedicine. MW: Yes, so I was immersed in diagrams, especially as I specialised in Biochemistry, which as a subject deals with diagrams on many levels. RT: Yes, when I was at school, all the chemistry diagrams and the glassware we used, I still find very exciting, it still gives me a buzz when I look at those diagrams. Also I suppose that Alchemical drawings which are in a sense diagrammatic, but which also refer to broader cultural aspects and spiritual things. But I think it is that combination of diagrammatic mixed with something else where things become very interesting. MW: Especially for the initiated few who can decode and read the Alchemical imagery and illustrations such as those in Michael Maier’s books. And you were also interested in optics and optical diagrams ?
Figure 2: Ray diagram from 'OPTICKS: A treatise of the Reflections, Refractions, Inflections and Colours of light', Sir Isaac Newton (forth edition, 1730, Available online here)
RT: Again, I always was - by the geometric diagrams of optics: the eye, mirrors, the idea of ‘looking through’, I was interested by that whole system; the picture of the eye, the rays coming in to the eye, or out of the eye. I find all of those things exciting, and I think that it’s because you’re almost standing outside of the system, and you can see what this system is.
MW: That’s something I wanted to ask you about because you had mentioned that you were interested in landscapes, and the idea that maybe the drawings you make are detached, conceptual landscapes. I remember reading 'To the Lighthouse' by Virginia Woolf, and there’s a very short chapter in the middle of the book, which describes time passing in an empty room. But it does so from outside the book, from the detached perspective of an omnipotent narrator, an all seeing eye. I wondered if that was something you were interested in as an artist? RT: Yes, I think so. I suppose maybe it’s this kind of hyper-consciousness, just this thing, observing, and you just become very aware of time and space, and of yourself as a little entity within this. It’s almost as if time disappears. The other thing I remember reading a lot as a student was Nietzsche, and the image of time as a snake eating its tail. He called it ‘eternal recurrence’, where you’re trying to imagine that every moment could be relived exactly the same, so it kind of neutralizes time, because as animals we’re stuck with this as a problem and try to find strategies to overcome that sense of things in the future and things in the past. 
Figure 3: Michael Maier, Ouroboros, Emblem 14, Atlanta Fugens, 1617.
MW: I read that time was something that you would like to take out of your drawings, or perhaps avoid referencing in some way. Also, that you presented the objects in your drawings as Platonic forms, without any signs of wear and tear or reference to scale. RT: Yes, that’s right, I started off by making objects, but always found it really frustrating in terms of size, or what you make it with. But I suppose that a lot of the twentieth century was about that problem, about objects, and their separateness to us all. MW: Such as the use of Plinths to present work ? RT: Yes, for example Plinths. MW: So did you ever regard your sculptural works as models, as a way to perhaps overcome these issues ? RT: I suppose I did think of them as 3 dimensional diagrams, but then I suppose that made me unhappy about the materials they were made from. I always imagined whether perhaps it could be made out of perfect marble perhaps. MW: I started to consider making works from elemental materials, such as aluminium or carbon, just to try to deal with the problem of simplifying or neutralizing that issue of materiality. One of the 3 dimensional works that you made called ‘boat’ was made out of rubber wasn’t it ? Hanging as a collapsed frame on the wall, the skeletal form of a boat. 
Figure 4: Richard Talbot, Boat, rubber, 180 x 30 x 10 cm
RT: Yes, it’s funny that that particular series of works didn’t end up going anywhere; I’m just trying to remember what the actual sequence was. I think sometime in the early eighties, I was put forward for a commission; it was one of those completely random invitations to do something. It was for the Savoy Hotel. It was one of those awkward things of, well, do you design sculpture, or do you use something you’ve already got? So I started playing around with drawings and making cutouts from drawings of things. I ended up with some large sheets of rubber and started cutting it out to see whether it was something I could use. I didn’t intend to end up with something which would hang on the wall, but I did that in the studio by putting it to one side, and it’s quite extraordinary how that works. So it was quite accidental, but was just the recognition of having taken it in to that different area that I didn’t have any control of, so it was quite accidental. It was all cut by hand, so it was a very crisp line cut with a scalpel. MW: About your working process, you wrote very beautifully about that initial process of orientation, the initial white sheet that you approach, and the infinite possibilities you’re faced with - setting up some kind of initial starting conditions. You used the analogy of the Gothic Cathedral with its ground plans, and then the more organic process of construction that follows that. There was also another article in the same book (Writing on Drawing: Essays on Drawing Practice and Research) by Terry Rosenberg about ideational drawing, a process of drawing which I though really suited your work very well. RT: Yes, I mean I must say that I haven’t read fully all of the articles in that book, but have skimmed through them. MW: There were a couple of essays that really stood out for me personally, yours and Terry Rosenberg’s. I enjoyed the way you talked about your use of perspective, not as a tool to create realistic drawings, but as a tool to allow you to use your intuition. RT: Well I think that also goes back to that idea of self-consciousness, sort of knowing that you’re this entity that looks at something from the outside. I used to play around with spatial perspectives, and then I thought that actually one way of neutralizing these issues was just to use it, just to actually use the system. So that to get over that whole issue of viewpoint, for example when you make a piece of sculpture, how do you look at it ? If there’s no best side as it were. So I thought, well if I just take it on full, this issue of perspective, and to absolutely use it as it was set up to use, then it falls by the way side, as an issue. MW: Turning the problem in to part of the solution? RT: I think it’s like sometimes in Mathematics, when a problem can’t be solved directly, they will call on a tool from other part of mathematics, and using that tool they can then move from one place to another. But in the end result, that tool disappears, it doesn’t ultimately play a part in the answer, but it has been a useful tool to get you from one place to another. MW: That reminds me of the role enzymes play in Biochemistry. They’re completely essential to facilitating the process, but don’t take part in a reaction in a way that they are altered themselves in the outcome. RT: Yes, that’s right, yes. So it is a kind of a vehicle, but then it’s using that perspective that makes me then question how it was originally used in the Renaissance, because when you’re actually working with it on the paper, there are so many interesting things actually going on that art historian looking in from the outside wouldn’t grasp. And it is to do with that idea of play, between the diagrammatic and the spatial element. Perspective isn’t all about creating a space, it is about the surface and how these things operate 2 dimensionally as well. 
Figure 5, Richard Talbot, Missing the Target, 1989, pencil on paper, 140 x 80 cm
Figure 5, Missing the Target (Detail)
MW: I was very interested in the way you talked about the depth of space in your drawings, and not using deep space, but keeping things relatively shallow and immediate. RT: Yes, I think that this also relates to my sense of what these Renaissance artists were doing. The picture that is portrayed of perspective is all about getting everything in terms of the horizon. But I don’t actually think that’s it at all. You are really working in a really shallow space. All those Renaissance paintings are also working in a really shallow space, and I think when you’re actually constructing that on the paper, there’s a real, almost physical connection to the space. MW: I don’t normally use colour in my work, it’s actually something I avoid, and have for a long time. Then I came across a book by David Batchelor called Chromophobia. He was writing about colour and how it has been perceived as the additional, the exotic, the lipstick. Or at least that’s how it was regarded by artists and writers who saw it as extraneous. And so I’m interested to ask you how you deal with colour in your work. RT: Well I have to admit as to having always avoided it, as I’ve never understood it. It’s a complete mystery. If I was making a drawing, I can’t see any reason to use colour. But then equally I probably can’t see any reason not to use it. But then I would probably be thinking well, why do I ? But then I know with somebody like Michael Craig Martin, I suppose he’s somebody in the seventies who was producing very austere, paired down work, such as his linear drawings, which were initially all black and white. But then he probably just stopped worrying and started to use incredibly strong colours in his work. And now the colour is really significant to his work. But its interesting that Michael Craig Martin was taught by Joseph Albers. MW: That’s interesting, I didn’t know that. RT: Yes, at Yale. So he would have had a real grounding in colour, and it’s almost as if he, you know – 30 years later or whatever it was – just decided to start using these colours. It is odd how we set rules for ourselves and at the time we kind of need them, but occasionally we just think ‘drop them’, and stop worrying about them. 
Figure 6, Richard, Glass, 1989, pencil on paper, 110 x 100 cm
MW: There were a number of times when looking at your works and reading what you wrote about them that reminded me of mathematics, and the idea of skeletonized forms. The idea of an equation, where the aim is to remove as much information as possible and leave only the knowledge - the process of essentializing something. Also the way that you talk about using intuition, and how intuition can be very immediate, or how it can require you to put the work away for many years. A slow boiler that you come back to much later. Is mathematics something you’re interested in? Or is it restricted to geometry, or patterns of thought? RT: Yes, I’m interested, not in the sense of reading books on mathematics, but when I’m near mathematicians and they talk about what they are doing, I do feel an affinity with what they are doing, and I suppose that with my drawings, they become very complex, but I do have that hankering after something really, really simple. I do have this idea that one day I’ll just be able to draw a line, and that that will be the finish! And in a way I suppose you do occasionally see it in some art works – and think that that is just an extraordinary piece of drawing, but then that in a way embodies everything they’ve ever done – 40 years later they’ve managed to make this extraordinary thing ! MW: Richard Dawkins wrote a while ago about the idea of a conceptual space containing all possible genetic variations, a kind of hyper-space of all possible genetic forms, and I was always fascinated by that idea. I think that also Douglas Hofsteader in Goedel Escher Bach, described the idea that Bach, in composing, had the ability to look over all the millions, well almost infinite combinations of musical notes, and was able to see patterns, islands or constellations of musical forms. And I wondered if that idea was perhaps something you were interested in. A vaguely discernible, fuzzy possibility of the form you’re searching for, and how this idea relates to diagrammatic forms. 
Figure 7: Richard Talbot: Step up, step down, pencil on paper, 120 x 120 cm
RT: Yes, I think that is definitely true, and I suppose that one of the things I am aware of is that in some ways, the drawings all start from the same point. That blank paper, that orientation. MW: The tabula-rasa ? RT: Absolutely, and you know that it could go in a completely infinite number of directions, and yet there is a sense that there is some solution there - that you setting things up. It becomes very obvious sometimes. I wouldn’t compare myself to Bach, but I can see that way of thinking - that there is an infinite number of possibilities, but you alight on a particular form that is true for you in one sense or another. It’s hard to really articulate that process.
MW: How would you describe the relationship between the forms in your drawings and the marks which make up the background from which the image appears ?
RT: I think when I first started using perspective I was still in that mindset of drawing objects as things in space, but then quite quickly I became aware of how potent the workings-out - you know, the plans, the elevations and so on - how potent they were and how they were working with the kind of forms which were being described. It was also in trying to pin things down, I became aware of the balance between leaving things open ended and tying something down and saying ‘this is that form’. It was that form, but not in such a positive or fixed way. I stopped using ink on the drawings. I was using ink to go around the forms I was building, but that stopped. And so I started getting a much more subtle interplay between the workings out, and those workings out would be the plans, and elevations, and a myriad of other kind of connections which were being built, a kind of scaffolding. MW: And you saw inking in as a kind of finishing process ? RT: I did. You know you suddenly think that it has in a way killed off the drawings. Not inking became a way to leave the drawing as an open-ended thing. Perhaps when a work is too ‘closed down’ it can end up being very uninteresting. For example Raphael. I’ve never enjoyed looking at Raphael’s paintings because they seem so overly fixed, whereas, Piero de la Francesca’s paintings seem almost as if they are propositions. 
Figure 8: Piero della Francesca, Flagellation of Christ, c.1468-70,
Oil and tempera on panel, 58.4 x 81.5 cm
Figures 9a,b, Diagrammatic Study of Piero della Francesca:
The Flagellation of Christ (outline and outline proportions) Courtesy of Richard Talbot. MW: Very early on in coming up with the questions that I wanted to ask in my PhD, I pretty much hit the same problem you did in realizing that I had always studied sculpture, but always made drawings. And I thought of the drawings as sculptural drawings and, luckily for me, my teachers at the time thought the same. So I had to decide whether to investigate the relationship between 2D and 3D diagrams - and thus include sculpture, or the way in which artists use diagrammatic image making to a romantic end, a subjective end; the way in which Marcel Duchamp played subject against object and also struggled with the issues of dimensionality. Where do you stand in terms of subject and object ? RT: Yes, well I don’t think I would come down either way, because I don’t think that coming down on either side actually gets you anywhere. I suppose that in my student days, this dilemma about the objective and subjective was helped by there being, at Goldsmiths - which was something which was great about Goldsmiths at that time - was that there was a huge range of practice within the staff. So you did have conversations with people who were systems thinkers, right through to people who were watercolour, or landscape painters. People weren’t trying to ram the stuff down your throat; you were just having these interesting conversations, and then weighing it up about your own situation. Thinking about what you were doing, what you thought you were trying to do, what you were actually doing ! You know, all those worries you have about, you know, ‘is it art ?’ I found myself really being able to make work when I stopped worrying about what side of the fence I was on, and finding a way of working where I felt as if I wasn’t having to choose one way or the other. But both sides of me could be involved in that hankering after perfection. It’s a case of playing these things off against each other. I distinctly remember that when I did my MA at Chelsea, the external assessor we had was Paul Neagu, I think he’s dead now, but he was very well known. He was one of the artists who Richard Demarco brought to this country, alongside such artists as Joseph Beuys. Anyway I remember that the work I’d made at Chelsea had become really quite austere, and extremely minimal, and he said… ‘don’t forget the other side of yourself’, and I realized exactly what it was he meant. That we can easily kind of forget. But then I think that also we need those extremes sometimes, to realize something. We need to go beyond in order to know where the edge was. It’s only when you fall over the edge that your realize there was one ! MW: So there is actually nothing within your body of work that you see as a mathematical proof, some foundation to build upon ? RT: No, I would certainly never say that there is anything that I’m demonstrating that is mathematical, no. I could say that when I was at Goldsmiths, I was taught by people who were involved in systems, and there were several people I knew, for example Malcolm Hughes working at the Slade, who had students working with experimental systems, building computers to generate paintings and so on; and I always felt that there was a problem in that they knew the kind of thing they were aiming for, and that it just seemed as if, well, you could make that painting without that system. It was almost as if they were using that system as almost a ‘get out’. The paintings would always end up looking like lots of other abstract constructive paintings that weren’t made with a system, that were just made purely intuitively. And so I have a distrust of the idea of a system, and I think that that system is always, ultimately being driven by you.
MW: What are you working on at the moment ? RT: Well apart form being heavily tied up in administration, I’ve finished some drawings and I’ve also been playing with film and video, which I can show you if you want. It’s very long drawing, based on a system in a sense, and was a definite play on the standard idea of a single viewer’s perspective. They start with a really basic perspective grid, a ‘unit’, drawn in such a way that I can simply add these units together and extend the space in any direction. Strangely, it adds the possibility of time, in that your eye can travel along the drawing and the space continues always to make sense. The video is another simple grid that is constantly shifting from the 2 dimensional surface in to the 3 dimensional image. Originally I had intended it to be projected on to a screen, but then I had the chance to project it in one of the large spaces downstairs, and the results were quite extraordinary - because it did actually become part of the space, which wasn’t fully intentional, but those were the results. The question of the artist’s intention is also an interesting problem I think within the history of perspective; the well-known analyses of key renaissance paintings demonstrate that the spaces in the paintings are sometimes not quite what they seem to be. There is often some uncertainty, yet it is usually thought that perspective is fixed - that it's an unambiguous and rational thing. 
Figure 10: Richard Talbot, All depth, no substance, 2013, Installation view
MW: Watching the video feels like a trying to solve a puzzle in perspective, there are moments when the lines are like a 2 dimensional pattern of shifting compositions, and then suddenly something in the visual cortex takes over and there’s the impression of instant depth from those very same lines. It reminds me of watching animations of higher dimensional cubes rotating. You think you have understood what is happening and there’s a sudden unexpected shift, you have to grapple with different kinds of depths. RT: Well - I don’t know - It’s to do with my intention, I’m not settling down to produce something which has a specific result. I know they do result in that, but I’m not setting out to do that. I am showing this work – I’ve never tried it before. I hope it works… It’s actually going to be projected on to three screens, the same image, butted up against itself, but slightly out of synch. So the whole thing will be ‘shifting’, so that a more complex thing will be going on. I have no idea what it will look like – it might just look awful, but then I’m trying it – for this show. Grid from Richard Talbot on Vimeo.
Richard Talbot's diagrammatic drawings are further discussed in chapter 3.5 of my PhD thesis, which is available to down load here.
Richard's academic studies in to the origins of linear perspective can be downloaded by clicking on the following link: 
Finally, below are a series of Piero della Francesca's own diagrammatic studies from his book 'De prospectiva pingendi: a treatise on perspective' c 1470 - 1492. The treatise, divided into three books, provides detailed, mathematical instructions, illustrated with numerous diagrams, for creating realistic perspective in illustrations. It was widely known among artists (such as Albrecht Dürer), but also in an academic milieu, where the copies of the Latin translation are thought to have circulated. The book is available to view online at the British Library here.
References:
1) Talbot,R. (2008) Drawings Connections, In: Writing on Drawing: Essays on drawing practice and research (2008) Intellect Books, UK: Bristol, p.55. 2) Hughes, R. 1980, The Shock of the New, London: Penguin Random House Company, p.17.
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❉ Number 13 in a series of blogs on diagrams in relation to the arts. This was the subject of my PhD at Kyoto city University of the Arts, Japan's oldest Art School. Feel free to contact me if you have questions about studying in Japan, the Japanese Monbusho Scholarship (MEXT), what a PhD in Fine Art involves, or diagrammatic art.  Max Ernst, 'Spies', Plate 10, cover illustration for Paul Eluard's book of poetry 'Repetitions', published 1922 " A mathematician, however great, without the help of a good drawing, is not only half a mathematician, but also a man without eyes. " Lodovico Cigoli to Galileo Galilei, 1611 Diagrams hold an important but controversial position in Mathematics, particularly within the field of geometry, where they are primarily regarded as a method of enhancing comprehension of a proof rather than partaking in rigorous mathematical reasoning. A number of simple, cautionary examples of the problematic relationship between Maths and diagrams exist as diagrammatic puzzles, and a famous example is the 'Missing Square Puzzle' shown in figure 1.
The natural limits to the acuity of human vision affects the way that we make estimations about the shapes of triangle A and B, and whether or not their lines are straight. The diagram in Figure 2 reveals that objects A and B are actually 4-sided quadrangles, rather than triangles. Neither of their hypotenuse (the longest side of the triangle ) of are straight lines.  Figure 2: Graph of two false Hypotenuse for triangle A and B, neither of which are truly straight. If we return to look again at figure 1, the small difference in the angle of slope of the blue and red components is indistinguishable, especially when spread across a distance. However in reality, their difference totals one unit of area, and this explains the seemingly miraculous origins of the missing square. Marcel Duchamp was fascinated by the idea of a parallel world of Mathematical perfection that exists alongside the chaos and imperfection of reality and daily experience. This was the subject of the blog post: 'A soggy book of diagrams as a wedding present from Marcel Duchamp', which considered one of Duchamp's less well known projects using a found book of Euclid's Geometry.
The quote I used to introduce this blog is taken from a letter written by the Italian artist Lodovico Cigoli to his lifelong friend the scientist Galileo Galilei. (1) Both men shared a passion for art and science. Galileo's interest in art is the subject of an extensive study by Erwin Panofsky, in his 1954 book 'Galileo as a Critic of the Arts'. Cigoli was interested in mathematics, science, geometry, and wrote an extensive treatise on perspective. For Lodovico Cigoli, a good 17th century diagram provided a visual means of gaining a deeper insight into the mathematics of nature. However, over the course of the following two centuries, the role of the diagram shifted to the extent that it became considered more of a veil that obscured the essence of mathematics, and algebra was proposed as the only way to lift the veil. Writing in the early 18th century, in a statement that anticipates the predominate modern view, the philosopher and mathematician Leibniz asserted that: "...it is not the figures which furnish the proof with geometers, though the style of the exposition may make you think so. The force of the demonstration is independent of the figure drawn, which is drawn only to facilitate the knowledge of our meaning, and to fix the attention; it is the universal propositions, i.e., the definitions, axioms, and theorems already demonstrated, which make the reasoning, and which would sustain it though the figure were not there." (2)  Figure 4: Diagrams submitted to accompany solutions describing the shape of a Catenary curve, by Gottfried Leibniz (Figure 1 left) and Christiaan Huygens (figure 2 right) to Jacob Bernoulli for publication in the Acta Eruditorum, 1691 It's important to bear in mind our visual limitations and the way our brain makes approximations when reading the diagrams of mathematics. This and the fact that real-world diagrams of perfect mathematical objects ultimately rely upon imperfect lines of ink, chalk or pixels. However, the diagram remains an extremely powerful tool and a visual guide in providing an insight into the austere and pristine world mathematical geometry and topology. Leibniz's own notebooks contain an astounding array of diagrammatic sketches that accompany his mathematics, as in figure 4, and the designs and calculations for his 'Universal Calculator', some 200 years before the work of Charles Babbage. For an interesting introduction to the notebooks of Leibniz, see Stephen Wolfram's blog: Dropping In on Gottfried Leibniz. For centuries mathematicians have constructed 3D diagrammatic models to illustrate mathematical concepts to students. A famous collection of these models is housed at the Institut Henri Poincaré in Paris. Between 1934 and 36, the American artist Man Ray made several visits to the Institut to photograph the collection, accompanied by Max Ernst. The Greek art critic and publisher Christian Zervos used the photographs for an article in the Parisian Cashiers d'art, and the images quickly became famous in Surrealist circles. Man Ray described the models that he found languishing in dusty cabinets as 'so unusual, as revolutionary as anything that is being done today in painting or in sculpture', though he admitted that he understood nothing of their mathematical nature. When the Second World War came to Paris in 1940, Man Ray relocated to Hollywood, where he started work on a series of 'suggestively erotic paintings' based on his 1930's photographs. Under the title of the 'Shakespearean Equations', he later referred to the paintings as one of the pinnacles of his creative vision. Below are images of selected paintings from the 'Shakespearean Equations' series, Juxtaposed alongside the original mathematical models they were based upon. Note: An extensive online collection of mathematical models is available here: the Schilling Catalogue of Mathematical models Figure 5: Selection of paintings from Man Ray's 1940's 'Shakespearean Equations' series, shown alongside the models they were based on, from the Institut Henri Poincaré, Paris. An important and influential book on Mathematical diagrams was Eugene Jahnke and Fritz Emde’s 'Funktionentafeln Mit Formeln und Kurven' (Tables of functions with formulae and curves). This landmark publication on complex mathematical surfaces and functions was first published in 1909, and a selection of graphs taken from the 1933 edition of the book are shown below, courtesy of Andrew Witt. As Witt points out in his own blog on this series here: Functional Surfaces I, it's said that the architect Le Corbusier kept a copy in his studio whilst designing the Phillips Pavilion. Max Ernst appropriated from the book for a series of collages and poems in the catalogue accompanying his 1949 exhibition 'Paramyths'.
           Figure 8: A selection of diagrams from the 1933 edition of 'Funktionentafeln Mit Formeln und Kurven', by Eugene Jahnke and Fritz Emde, courtesy of Andrew Witt. AFTERWORD:
Jos Leys, Dodecahedral Tessellation of the Hypersphere: a dissection of the 120-cell in 12 rings of 10 dodecahedrons References:
1) Some 29 letters from Cigoli to Galileo remain, however only 2 letters from the scientist to the painter are left, as the artist's heirs chose to destroy all incriminating evidence of their association, after the papal condemnation of Galileo. (In 1610 Cigoli received from Pope Paul V the assignment to paint the dome of Santa Maggiore Maggiore with the Immaculate Conception, the Apostles and Saints.) 2) Leibniz1704, New Essays: 403 ❉ This is the 12th in a series of blogs that discuss diagrams and the diagrammatic format, especially in relation to fine art. I recently completed my PhD on this subject at Kyoto city University of the Arts, Japan's oldest Art School. Feel free to leave comments or to contact me directly if you'd like any more information on life as an artist in Japan, what a PhD in Fine Art involves, applying for the Japanese Government Monbusho Scholarship program (MEXT), or to talk about diagrams and diagrammatic art in general.  Figure 1: Blank Lines or Topological Bathing, 1980-81, acrylic on canvas, 254 x 691 cm © 2017 Estate of Madeline Gins. Reproduced with permission of the Estate of Madeline Gins Whilst art students in Kyoto, my friends and I were invited by our teacher Usami Keiji to stay with him and his wife Sawako, at their cliff-top studios in Fukui, overlooking the sea of Japan. After a winding drive north through the mountains, we were met with an extravagant lunch of champagne, king crab, and one of Usami's arm-waving, hilarious, impromptu speeches on Foucault. Afterwards, a still-smiling Usami slid a book across the table between the bottles and empty red crab shells, saying only "This is a work of a genius". The book was 'The Mechanism of Meaning', a series of essays and photographs documenting the creation of eighty, large panel paintings made by the Japanese artist Shusaku Arakawa and his wife, the American poet, Madeline Gins, following a decade of collaboration between 1963 to 1973. Usami insisted I borrowed the book, but over the years whenever I tried to return it he would complain that it was too heavy for him to carry, and would ask me, smiling, to look after it well until the next time we met. Sadly, Usami passed away in 2012 and I still have his copy of the book, full of his own notes and comments in the margins about the work of two master diagram makers - Arakawa and Gins. As the legend goes, Arakawa arrived in New York with nothing but a few dollar bills and the telephone number of Marcel Duchamp. More importantly however, he carried with him a letter of recommendation from his mentor, the poet Shuzo Takeguchi, one of Japan's leading art critics and a champion of Surrealism in Japan. As a parting gift Takeguchi had given the young artist a book of his poetry, amongst the pages of which he had hidden a considerable sum of money for the young artist to later discover. Arakawa arrived to heavy snow at JFK airport in December 1961 and, using the little English he knew, made the fated phone call to Duchamp that would gain him not only immediate access to the very heart of New York's artistic community, but would see him become a protégé of Duchamp himself.  Figure 2: Arakawa and Marcel Duchamp at Dwan Gallery, New York, 1966 © 2017 Estate of Madeline Gins. Reproduced with permission of the Estate of Madeline Gins Duchamp arranged for Arakawa to stay in the loft apartment of Yoko Ono as she was away in Japan, and it was there that he met John cage who had arranged to use the loft as a practice space for his group of musicians. It was also through Duchamp that Arakawa was introduced to Andy Warhol, whose attendance at Arakawa's early exhibitions brought a great deal of attention to the young, as yet unknown artist. The year after Arakawa arrival in New York he met Madeline Gins, and a year later they started work together on 'The Mechanism of Meaning', an ambitious collaboration that would take another ten years to complete.* (* Note: The series actually exists in two different versions, one at the Sezon Museum of Modern Art in Japan and the other in the holdings of the recently established 'Reversible destiny foundation' in New York, based in Arakawa and Gins former studio.)
As described in an earlier blog post: " Coffee, diagrams, chocolate, masturbation ", diagrams were at the very heart of Marcel Duchamp's artistic practice and philosophy, having been educated at a time in France when sweeping reforms replaced traditional landscape and portrait studies with a fastidious training in diagrammatic draftsmanship. Duchamp's fascination with the reductive, refined aesthetics of diagrammatic images was clearly something he passed on to Arakawa, who developed his own obsession with diagrams and diagram making. His first solo exhibition in New York at the Dwan Gallery in 1966 was titled simply 'Arakawa: Diagrams', and the Gallerist Virginia Dwan later recalled how she had to dissuade the artist from wanting to sign his paintings 'Diagram', a move she felt was too abstract even for the New York art world. Early works such as 'Diagram with Duchamp’s Glass as a Minor Detail' (Figure 3) are evidence that Arakawa was all to aware of the profound influence his mentor was having upon his practice, and his desire to both pay homage and at the same time break orbit and seek out his own distinctive style. However Duchamp's diagrammatic art 'in service of the mind' would remain a major influence on both Arakawa and Gins as they developed their own master work - 'The Mechanism of Meaning'. Of the 80 panels that make up the series, one acts as an index by dividing the body of works into 16 different groups of paintings like chapters in a text book: 1) Neutralization of Subjectivity 2) Localization and Transference 3) Presentation of Ambiguous zones 4) The Energy of Meaning (Biochemical, Physical, and Psychophysical aspects) 5) Degrees of meaning 6) Expansion and Reduction - Meaning of Scale 7) Splitting of Meaning 8) Reassembling 9) Reversibility 10) Texture of Meaning 11) Mapping of Meaning 12) Feeling of Meaning 13) Logic of Meaning 14) Construction of the Memory of Meaning 15) Review and Self-Criticism 'The Mechanism of Meaning' consists a number of self-contradictory puzzles, instructions and statements presented in a variety of diagrammatic formats. Gins' wide-ranging studies are evident in the works, which reference Oriental philosophy, Japanese and Chinese poetry, English and Physics. Gins also took art classes at the Brooklyn Museum, and it was here that she first met her fellow student Arakawa (who later claimed that he enrolled only in order to extend his American visa). When engaging with 'The Mechanism of Meaning', the panels act in a way like mirrors to the thought processes being used to analyse them, a kind of self referential, recursive process reminiscent of Douglas Hofstadter idea of 'a strange loops'. Many of the texts in the paintings resemble 'Koans' from Zen Buddhism, short puzzles designed to be meditated upon by monks during their training. Viewers of 'The Mechanism of Meaning' are instructed to 'Turn left as you turn right', or to picture a 'Mnemonic device for forgetting' and then 'Imagine a thought which bypasses everything'. Zen Koans are intended to jolt the thinker in to a state of enlightenment through paradox, and the project won Arakawa and Gins a host of intellectual admirers including Italo Calvino, who wrote how "An Arakawa painting seems precisely cut out to contain the mind, or to be contained in it… After studying one of Arakawa’s paintings it is I who begin to feel that my mind is ‘like’ the picture" (1). The French Philosopher Jean-Francois Lyotard described how the work of Arakawa and Gins “makes us think through the eyes.” (2) Such an poignant image is reminiscent of the American Philosopher C.S. Peirce's description of diagrams as 'moving pictures of thought'.  Figure 4: 'About the network of ( perception of ) AMBIGUOUS ZONES OF A LEMON (Sketch No.2)', Ink on paper, from “The Mechanism of Meaning” c. 1963 – 88, Ink on paper (size unknown) Copyright credit: © 2017 Estate of Madeline Gins. Reproduced with permission of the Estate of Madeline Gins and Reversible Destiny Foundation. Figure 4 is a sketch for the panel 'Ambiguous zones of a Lemon', and consists of an entangled network that diagrams the various ways we can consider a lemon. What at first appears to be a humorous take on a lemon's multiple, nuanced qualities, in fact turns out to reveal a great deal about the complex relationship between our objective and subjectively descriptions of reality. To paraphrase the British philosopher Bertrand Russell: an observer, when he feels himself to himself to be observing a stone (or, in Arakawa's case, a lemon), is really, if physics is to be believed, observing the effects of the stone upon himself (3). The distinction between subjective and objective qualities is of fundamental importance to the philosophy of science, where qualities are divided in to primary (those that exist independent of an observer, such as quantity and mass), and secondary (those given by the human senses to an object, such as colour, taste and smell). The categories of Arakawa and Gins play with these distinctions, allowing them to resonate in a way that I term 'Romantic - Objective'. Categories of ambiguous zones:
'The Mechanism of Meaning' series is akin to Duchamp's idea of a 'playful physics', in which objectivity and systems of scientific measure and analysis are taken to their limits, in order to reveal their tenuous philosophical underpinnings. The aim of such an approach isn't simply to undermine the scientific process, for, in the words of Arakawa himself, "If you want to become an artist, you have to become a scientist first." (4) Rather the aim is to creatively test the limits of thought and logic in a way similar to the Philosophy of Ludwig Wittgenstein, the work of whom Arakawa and Gins had read and would discuss at length in their studio. (The style of Wittgenstein's 'Tractatus Logico-Philosophicus' becomes immediately apparent when viewing 'The mechanism of Meaning'.) Gins and Arakawa created a rich new vocabulary to map out the poetic-conceptual terrain their work explored, and their terminology is suggestive of entirely new fields of study. Rather than refer to himself an artist, Arakawa pronounced himself a 'coordinologist', and Gins described herself as a 'biotopologist', and both continued to engage in frequent discussions with philosophers and scientists. 'The Mechanism of Meaning gained world-wide success in the 1970's, and was shown in it's entirety at the Venice Biennale in 1970, and again in Germany in 1972, where it was praised by the renowned German theoretical physicist Werner Heisenberg, winner of the 1932 Nobel prize in physics, who invited Arakawa and Gins as artists in residence at the prestigious Max-Planck-Institute. Heisenberg has the so called 'uncertainty principle' named after him, and it's easy to imagine the appeal that 'The Mechanism of Meaning' had to a mind used to struggling with the indeterminate nature of reality at it's most fundamental level. Below are a series of selected panels from the 'The Mechanism of Meaning' series. I would like to thank the Estate of Madeline Gins and the Reversible Destiny Foundation for permission to use these images, and more information can be found at the Reversible Destiny Foundation homepage, or by following their facebook page here. The foundation recently announced that they will be working together with Gagosian gallery to fully document and represent 'The Mechanism of Meaning' series, in order to bring this important and still highly relevant work Arakawa and Gins to a contemporary audience.
References: 1) Italo Calvino, The arrow in the mind: A review of the Mechanism of Meaning. In: Image, Eye and Art in Calvino: Writing Visibility. 2007, Chpr 20.
2) Lyotard, J.F, In: Reversible Destiny, Arakawa / Gins, Guggenheim Museum Publication, 1997. 3) Bertrand Russell, An inquiry into meaning and truth: The William James lectures for 1940 delivered at Harvard University, London Routledge, 1992, p.72. 4) Arakawa speaking in the film Children Who Won’t Die (2010) Directed by Nobu Yamaoka. 5) Peirce, C.S, quoted in: Brent, J. Charles Sanders Peirce: A life, 1998, Indiana Uni. Press, p.129 ❉ This is the tenth in a series of blogs that discuss diagrams and the diagrammatic format, especially in relation to fine art. I recently completed my PhD on this subject at Kyoto city University of the Arts, Japan's oldest Art School. Feel free to leave comments or to contact me directly if you'd like any more information on life as an artist in Japan, what a PhD in Fine Art involves, applying for the Japanese Government Monbusho Scholarship program (MEXT), or to talk about diagrams and diagrammatic art in general.
Figures 1, 2: Yves Netzhammer, digital drawings, 2010 The working process of Swiss artist Yves Netzhammer begins with what he calls his 'stockpile of conjectures'. This is a growing body of diagrammatic sketches that compose his process of visual thinking, and act as source material for further development into finished drawings, animations, sculptures and installations. Netzhammer's use of computer illustration and 3D modeling programs is a means of distancing the hand of the artist from his artworks, and imbues his work with a concise and highly distinctive aesthetic of economised line, form, colour and movement. In this way, the diagrams, models and video works of Netzhammer embody the characteristics of what Duchamp called "paintings of precision", imagery purified of irregularities and presented in an airless, ideal realm.  Figure 3: Yves Netzhammer, Untitled, Seilzeichnung, 2011, Rope, metal, wood, glass and colour, variable dimensions 'Seilzeichnung' (rope-drawing), was the first art work I saw by Netzhammer in Gwangju, South Korea, in 2011. Part wall-drawing, part sculpture, the focal point of the work is the diagrammatic depiction of a dog biting a human wrist, with the dotted bone of the forearm visible between the dog's teeth. The fingers of hand hold a swab with which an anonymous person appears to be taking a clinical sample from the back of the dog's tongue.
Certain elements of Netzhammer's work are common to other diagrammatic artists such as Mark Mander’s use of cross section, artificial architectural constructs, interconnected forms and lines which divide, connect, and often bind objects and ideas together. You can read more about Mander's work in a previous blog here: Portrait of the artist as a building. Netzhammer first studied architecture and received training in architectural draughting. This is an important point, because of the strong theoretical and practical presence of the diagram within the field since the 1980's. Netzhammer later enrolled at Zurich’s Hochschule für Gestaltung und Kunst, where he attended the figurative arts course. The human form in Netzhammer's work is depicted in a way that highlights its own artificiality. His figures resemble the featureless models used in art school life drawing class, crash test dummies and shop display mannequins. These are presented in spaces constructed in the idealised, neutral style of the computer-aided design programs of architectural modeling. A stark, single light source also helps direct the viewer's attention to the objective, artificiality of this system of visualisation. Below is a series of video extracts that help give a clearer example of how Netzhammer uses the diagrammatic format to create a distinctive, objective visual language which he then applies to emotive, subjective themes in a way that I describe as Romantic Objective. The clips were compiled by the artist himself from an exhibition at Bremen Art Museum in 2006: 'Die Anordungsweise zweier Gegenteil, bei der Erzeugung ihres beruhrungsmaximums' (The arrangement of two opposites while their maximum point of contact is under generation). Figure 6: Yves Netzhammer, The Arrangement of Two Opposites While Their Maximum Contact Is Under Generation 2005, Kunsthalle Bremen, Germany I contacted Netzhammer in 2013 as part of my PhD research into the importance of the diagram in contemporary art. I wanted to ask about the role the diagram plays in his own drawings, installations and video works, and why he opted to work with diagrammatic imagery. He explained that: " It started, in my case, in looking for another way to show a new form of subjectivity. I positioned the computer between me and my thoughts/wishes. I guess, I prefer the diagrammatic “style”, because I’m really trying to find “something” (connected to philosophical questions). Not in the common scientific sense of discovery, but something which appears close to our questions about identity. I hope that an artistic approach to forms of empathy can generate such results, especially, when it comes in a paradoxical format like drawings, which stands in the tradition of explanation. " A full transcript of Netzhammer's answers and other interviews with diagrammatic artists can be found on the research page of this website. Below are a series of video clips of Netzhammer's various projects. More information can be found at the artist's own website: http://netzhammer.com/ and also the online journal: http://www.journalfuerkunstsexundmathematik.ch/ ❉ This is the third in a series of blogs that discuss diagrams and the diagrammatic format, especially in relation to fine art. I recently completed my PhD on this subject at Kyoto city University of the Arts, Japan's oldest Art School. Feel free to leave comments or to contact me directly if you'd like any more information on life as an artist in Japan, what a PhD in Fine Art involves, applying for the Japanese Government Monbusho Scholarship program (MEXT), or to talk about diagrams and diagrammatic art in general.  Figure 1: Mark Manders, view of artist's studio with works in progress The Dutch Artist Mark Manders describes himself as “a human being who unfolds into a horrifying amount of language and materials by means of very precise conceptual constructions”. (1) Manders entered the world of fine art as a writer and text still plays an important role in giving key insights in to his practice. However unlike the artistic self portraits of James Joyce in prose, or Dylan Thomas in poetry, Manders' self portrait is architectural. Since 1986, Manders has been constructing what he calls his 'self-portrait as a building', and uses this conceptual framework to represent the fictional artist 'Mark Manders', a distinct alter-ego that he describes as a “neurotic, sensitive individual who can only exist in an artificial world.” (2) The Diagrammatic format is immediately apparent in Manders' projects as the means by which he marshals the "horrifying amounts of language and materials" that his mind is capable of producing. Diagrams provide method to his madness and imbue his art works with an air of precision, authority and logical rigor, even if we can only guess at their exact function.  Figure 2: Mark Manders, Finished Sentence, 1998-2006, iron, ceramic, teabags, offset print on paper, 336 x 185 x 85 cm Manders' self portraits incorporate the diagrammatic format on three distinct levels: as an aesthetic, as a creative tool and as a means of organising and predicting the ways in which viewers will experience his art works as they pass through his installations. Aesthetically, many of the sculptures are formal constructs presented on table tops and in vitrines, resembling scientific models or experiments left unattended. Stephen Berg described these machines and factory-like constructions as “laboratory constellations for uncertainty and unknowable discoveries, production plants for dissident thoughts, transmitters for contacting the fictional.” (3) The floor plans and delicate pencil drawings show Manders' use of the diagram as a powerful visual and conceptual tool for creation and organisation, whilst the architectural nature of his exhibition installations guide viewers through carefully prearranged objects in a series of constructed environments, which the artist refers to as “memory spaces”. (4)  Figure 3: Mark Manders, Drawing with Shoe Movement / Floor Plans from Self-Portrait as a Building, 2002, Pencil on paper Manders artistic practice is what I refer to as "Romantic-Objective", combining his own highly subjective and existential self-expression with an objective and analytical approach to phenomena mirroring that of science. Writing about his sculpture "Shadow Study (2)", Manders describes the thought processes that underly his choice of objects for the sculpture, and in doing so reveals it to be part exercise in 'material culture' (a kind of ethnography of objects) and part day dream. The visual language however is distinctively diagrammatic, and reminiscent of a highly reduced scientific demonstration or model. " If you think about the evolution of cups, it’s just a beautiful evolution. The first cups were human hands: folded together, they took the water out of the river. The next cups were made from things like hollowed pieces of wood or folded leaves, and so on. The last beautiful moment in the history of the cup was when it got a handle. After that, nothing really interesting happened with cups, just small variations, mainly ornamental. Many generations worked on it, and now you can say that the cup is finished in terms of evolution. A few times a day there is a cup very close to my upper leg bone, and I slowly discovered that if you turn an empty cup upside down there is a shadow falling out of the cup, falling upon my leg. I wanted to keep this shadow, have it and own it, so I turned it into an image. " (5)  Figure 4: Mark Manders, Shadow Study (2) 2010, Metal, porcelain, painted epoxy, and wood / 151 x 65 x 65 cm "Shadow study (2)" subtly references the transparency of bone china, sunlight and shade, and creates a three part visual haiku of upturned cup and the 'pouring of shadow' upon the thigh bone, amplified by the pyramidal structure of the support suggestive of the conical rays of the sun. Mander's heightened awareness of the details of everyday life and the inherent paradox of both their importance and insignificance brings to mind a seemingly timeless quote, often mistakenly attributed to such greats as W.B. Yeats and Bertrand Russell: " The Universe is full of magic things, patiently waiting for our senses to grow sharper. " (6) In the case of Romantically Objective Art, that heightened awareness and sharpness of focus is due in a large part to the use of the diagrammatic format, in all its guises.  Figure 5: Mark Manders, Shadow Study (2) 2010, Metal, porcelain, painted epoxy, and wood / 151 x 65 x 65 cm References: 1) Manders, M. (2010) Parallel Occurrences / Documented Assignments. Aspen Museum of Art, Aspen Art Museum and The Hammer Museum. p.11 2) van Adrichem, J., Bouwhuis J., Dölle M. (2002) Sculpture in Rotterdam, 010 Publishers, p. 60. 3) Berg, S. (2007) Like the night creeping into a shoe. In: In the Absence of Mark Manders. Berg. S. (Ed.) Hatje Cantz. p. 14. 4) Manders, M. (2003) Quoted in: Koplos J. Mark Manders at Greene Naftali - New York, Art in America, April 2003. 5) Manders, M. http://www.markmanders.org/works-a/shadow-study-2/2/ 6) Eden Phillpotts, 1991, A shadow Passes. [OXEP] 2004, Oxford Dictionary of National Biography [Online], Entry: Eden Phillpotts (1862–1960) by Thomas Moult, rev. James Y. Dayananda, Oxford University Press. More information can be found at: http://www.markmanders.org/
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