​For millennia, enigmatic dark spots on the surface of the Sun have captivated observers, with the first recorded sightings dating back to ancient China, circa 800 BC. However it wasn't until the early 17th century that the invention of the telescope allowed for a more systematic and scientific study of these phenomena, allowing early scientists such as Galileo Galilei to embarked on the meticulous documentation of these spots, pioneering a tradition of consistent observation that underpins modern solar research.

Sunspots are dark regions that appear on the sun's photosphere, which is the outermost layer visible to us. They appear darker because they are cooler than their surroundings, with temperatures ranging from 3,800 to 4,300 Kelvin. This is a significant difference compared to the Sun's average surface temperature of around 5,800 Kelvin.

The formation of sunspots has been linked to the Sun's magnetic field, which arrises from the movement of electrically charged plasma inside the Sun known as the solar dynamo. These vast, powerful magnetic fields can become twisted and tangled due to the way in which the Sun spins faster at its equator than at its poles. This difference in rotational speed is also responsible for the distinctive shape of butterfly diagrams, as we'll later see.
​

Sunspots typically occur in pairs called bipolar sunspot groups, with each spot having an opposite magnetic polarity. The magnetic field lines form loops, extending from one spot to the other. The intense strength of these magnetic fields can hinder convection, the process by which hot plasma rises to the Sun's surface, cools, and then sinks back down. This hindrance in plasma flow results in a relative decrease in temperature. The stronger the magnetic field, the greater the temperature reduction, and consequently, the darker the sunspot appears.
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The number and location of sunspots on the Sun's photosphere follow a solar cycle that lasts approximately 11 years. During the solar maximum, the period of highest activity, sunspots are abundant and mainly found in mid-latitudes. As the cycle progresses towards the solar minimum, a calmer phase, sunspots become scarcer and are located closer to the Sun's equator.

Solar cycle 1, which lasted from February 1755 to June 1766, was the first solar cycle to be extensively recorded. Johann Rudolph Wolf, who discovered this cycle, determined its duration to be 11.3 years. Wolf was inspired by Heinrich Schwabe's 1843 discovery of the solar cycle and collected all available sunspot observations, dating back to Galileo's first telescopic observations.

Through his research, Wolf refined Schwabe's estimate of the average cycle length from about 10 years to 11.11 years. However, due to a lack of reliable observations before 1755, Wolf could not confidently identify earlier cycles. As a result, the 1755–1766 cycle is conventionally designated as cycle 1. Wolf's groundbreaking findings, which he published in 1852, laid the groundwork for our current understanding of solar cycles.
​

British astronomer Edward Maunder (1851–1928) developed a strong fascination with astronomy, particularly solar astronomy, from a young age. His interest was ignited by his observation of a large group of sunspots visible to the naked eye in February 1866.

In 1881, Maunder became the head of the solar program at the Greenwich Royal Observatory in London, where he collaborated with his second wife and fellow astronomer Annie Maunder (1868-1947). Edward's new role allowed him to focus on his own research and investigate potential links between sunspots, solar activity, geomagnetic activity, and the Earth's environment. However, he faced persistent skepticism from the scientific community, including prominent figures like Lord Kelvin (1).

Figure 5 displays the first Maunder diagram, published by Edward and Annie in 1904 and gifted by Annie to the renowned astronomer Walter Orr Roberts, the first director of the High Altitude Observatory in Boulder, Colorado. The diagram illustrates the distribution of sunspots recorded between 1876 and 1902 (north above, south below). These elegant plots resemble butterfly wings and quickly gained the nickname "Butterfly Diagrams."

The original Maunder butterflies are also included in Prof. David Hathaway's comprehensive and updated sunspot chart, created during his 30-year tenure at NASA using 140 years of data (Figure 6). Prof. Hathaway is a leading expert on sunspots and former head of Solar Physics at NASA's Marshall Space Flight Center, and more details of his research can be found at Solar Cycle Science.

I reached out to Prof. Hathaway, who kindly endorsed my proposal to adapt his work into a sunspot project at the 2022 Changwon Sculpture Biennale in South Korea. The Butterfly I chose for the installation occurred during Solar Cycle 20, between November 1964 and July 1980, the period in which I was born in July 1976.

The Changwon Biennale is South Korea's largest recurring sculpture show, and during the fall of 2022 it showcased 69 artists under the title, 'Channel: Particle Wave Duality'. Curated by Director Cho Kwan Yong, Chief Curator Lee Tahe Hoon and Curator Hyojin Nam, the show considered the broad sense of how light and matter interact at the intersection of art and science. 

In preparation for the Biennale, the curatorial team sent out plans and photographs of each of the exhibition galleries, including the main atrium of the Seongsan Art Hall with it's enormous glass ceiling. I'd recently worked on a window installation for a project to design a city on Mars based on the structure of the Ribosome molecule, and asked the Biennale team to measure the 216 panes of glass in the ceiling in order to design the sunspot butterfly installation. 

3D artist and illustrator Tony Cheng then used those measurements to create a computer model of the ceiling so we could experiment with different sized butterflies and predict how the installation would look when viewed from different angles and floors within the building below.
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The final installation consisted of 99 sheets of acetate printed with UV resistant ink to depict an enormous Maunder butterfly diagram for solar cycle 20. The sheets were installed overnight to avoid the heat, and we waited in the atrium early the next morning to watch the sunrise and shine through its own data. The 2022 Biennale opened to the public on October 7th and ran until November 20th.

​References:

1) Soon, Willie & Yaskell, Steven. (2003). The Maunder Minimum and the Variable Sun-Earth Connection. 10.1142/5199.   ​https://www.researchgate.net/publication/335950578_The_Maunder_Minimum_and_the_Variable_Sun-Earth_Connection

ChatGPT: ​Figure 1: DALL-E generated artwork and caption: "A complex and structured neural network diagram. This image is technical and diagrammatic, showing detailed layers of neurons and their interconnections."

Figure 5. Data Flow Diagram (DFD) of Smart Autonomous Vehicular System (AVS). (3)
Creative Commons Attribution 4.0 International
​

Figure 8: Heat map of the deep learning model. The white arrows point to crucial areas. (6)
​

You: ​Finally, please make the following artworks based upon the patterns, structures and colours of diagrams actually being used in AI research at the moment as you listed above.

3) Draw an indecisively postmodern, black and white, pencil sketch based on decision trees used in Ai research.

ChatGPT: The artwork is a striking representation of the complexity and ambiguity often found in artificial intelligence (AI), particularly in the concept of decision trees. It showcases a decision tree depicted in an indecisively postmodern style, where the branches of the tree start and stop abruptly, and diverge in various directions, effectively symbolizing the nature of decision-making processes in AI. These branches are filled with a mix of clear and blurred symbols, some straightforwardly representing AI concepts like algorithms and data, while others remain abstract, open to interpretation.
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4) Make an image of a series of porcelain vessels with unusually complex shapes based on graph-based models used in AI research.

ChatGPT: These vessels display an array of intricate, multi-dimensional forms that mimic the sophisticated structures of graph networks used in AI. Each vessel in this collection is distinct, showcasing the diversity and intricacy of graph structures. ​These vessels are not just artistic objects; they symbolize the intricate relationship between art and technology, embodying the elegance of porcelain art and the advanced, abstract beauty of graph-based AI models.
​

5) Make an image of an enormous, ornate, glass chandelier based on UML diagrams used in AI research.

ChatGPT: ​The image features a grandiose, ornate glass chandelier, brilliantly conceptualized around the themes of UML (Unified Modeling Language) diagrams used in AI research. This enormous chandelier is comprised of a multitude of detailed glass components, each meticulously shaped to represent various elements of UML diagrams, such as entities, relationships, and processes. The arrangement of these components is thoughtfully interconnected, visually translating the logic and structure inherent in UML diagrams, thereby symbolizing the intricate workings of AI systems. Each piece of glass is finely crafted, adorned with elaborate etchings of UML symbols and notations, adding a layer of sophistication and intricate detail to the chandelier. The overall design is awe-inspiring, capturing the vastness and complexity of AI research in a visually stunning and intricate piece of glass art, showcasing both artistic beauty and technical symbolism.
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6) ​Make an image of a piece of land art based on AI research using graph-based models.

ChatGPT:  This expansive outdoor installation reflects the complex network of nodes and connections found in graph-based AI models. Natural elements like stones, sand, or vegetation are used to represent different nodes and pathways, creating a large-scale, physical representation of data networks. The land art is designed to harmoniously integrate with the natural landscape, visually conveying the intricate and interconnected nature of AI systems and emphasizing the fusion of technology with nature.
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7) Design a complex sculpture based on heat maps used in AI research.

ChatGPT: ​This sculpture visually interprets the gradient nature of heat maps through flowing forms and layered structures, representing data density and variation. It incorporates elements that reflect the analytical and data-driven aspects of AI, using shapes and textures to mimic the way heat maps display information. The sculpture is dynamic and multidimensional, embodying the sophisticated data visualization techniques in AI. A blend of colors is used to represent heat intensity, creating an artistic and visually striking representation of a heat map in a three-dimensional form.
​

8) ​Design a confusing, inflatable sculpture based on confusion matrices used in AI research.

​ChatGPT: ​The image illustrates a confusing, inflatable sculpture, ingeniously based on confusion matrices from AI research. This sculpture consists of a series of interconnected inflatable segments, each symbolizing different elements of a confusion matrix, such as true positives, false negatives, false positives, and true negatives. The segments are arranged in a perplexing manner, featuring twisted and intertwined shapes that challenge and disorient the viewer’s perception. This design choice effectively mirrors the complexity and sometimes baffling nature of interpreting confusion matrices in AI. The sculpture is vibrant and abstract, with each segment distinctly colored to represent the various outcomes in a confusion matrix. However, these segments are arranged in a way that creates an overall sense of disarray and complexity, reflecting the nuanced and often intricate nature of data analysis in AI.

 ❉ Blog post 22 on diagrams in art and science covers a project I worked on to design a fictional city on Mars. The blue prints for the city are based on a diagram of one of the oldest and most remarkable molecules ever discovered in the history of biology, the Ribosome. These molecular printers are found in all cellular life on earth, and NASA funded ribosome research is raising some of the most profound and exciting questions about the origins and future of life itself.
 

Figure1: Noctus Labyrinthus (Labyrinth of the night), a vast region of labyrinthine canyons on Mars.

The City:

The 2021 CITYA group exhibition in Hong Kong, curated by Janet Fong, invited artists to explore how humans interact with urban environments in the 21st century. My installation, Noctus Labyrinthus, named after a vast canyon system on Mars, offered a perspective on how urban living might extend into space.

One of my favourite city-related diagrams is Harry Beck's 1933 experimental map of the London underground system (figure 2). What I find particularly interesting is the way the image acts a palimpsest of Beck's mind at work using the diagram as a thought tool. Train lines are sketched out, erased, then re-drawn in a process of connection, disconnection, and reconnection. It's intriguing to note that Beck's background as an electrical draftsman likely influenced his unique approach to this project.

Figure 2: Henry C. Beck, Original sketch for the London Underground Railways Map, 1931,
Pencil and coloured inks on squared paper, 19 x 24 cm

Beck prioritized clarity over geographical fidelity, a step the transport officials considered too radical for the British public of the time. According to the Transport for London website however, "A successful trial print-run showed that it was just what the public wanted. The result was an instantly clear and comprehensible chart that became an essential guide to London - and a template for transport maps the world over." 

Figure 3: "Map of London's Underground Railways. (A new design for an old map. We would welcome your comments. Please write to Publicity Manager, 55, Broadway, Westminster, S.W.1.)"
Harry Beck, Published by London Transport, 55, Broadway, Westinster, S.W.1, [January, 1933]., London, 1933

In preparing for the CITYA exhibition, Beck's sketch reminded me a diagram from biology I'd had pinned to my studio wall since I discovered it in a 2015 paper in the Proceedings of the National Academy of Sciences. Somewhat more complex than Beck's map, it depicts a molecular network a trillion times smaller and four Billion times older than the 1933 London underground system. 

Figure 4 is a diagrammatic unravelling of the large subunit of the human ribosome, courtesy of Anton Petrov and Loren Williams (1), who first published the image in their paper titled "History of the ribosome and the origin of translation". Unusually for a scientific paper, the discussion section describes the field of ribosome research as "posing some of the most profound and exciting questions in science…" (2)

Their use of such emotive adjectives in a scientific text reminded me of the time I'd been reprimanded after an undergraduate biochemistry exam for using the words subtle, intricate and profound to describe what I thought were subtle, intricate and profound chemical processes in the human metabolic system. Professor Baker, then head of department, summoned me to his office to suggest that if I wanted to use such terms I should sign up for creative writing classes in the English department, making it clear that scientific texts were no place for subjective expression.

I realised much later this rebuke had been an important moment in my transition from science to art, and that the sciences could indeed be approached subjectively from a whole range of alternative, creative and expressive aspects, including poetry, music, dance and art. 

Figure 3: Secondary structure of the human ribosome large subunit.
Image courtesy of Anton Petrov and Loren Williams.
Centre for the Origins of Life Research (COOL), Georgia Institute of Technology
Creative Commons Attribution-ShareAlike 3.0 Unported License (CC BY-SA).

​The Blue-print:

Ribosomes are found in all cellular life on earth, and the molecule holds such an important place in biology that the 2009 Nobel prize in medicine and physiology was awarded for the discovery of its complete molecular structure (4). A single one of your cells during mitosis (cellular division) can contain as many as 10 million ribosomes, which form an essential part of the molecular machinery that uses the genetic information embodied in DNA to print the tens of thousands of proteins that builds life on earth and regulates it at a chemical level.

Further studies of the ribosome have involved pealing away the layers of its structure like an onion, to understand how they evolved over the aeons. At the very centre was discovered the highly conserved core of the ribosome (shown below in blue), estimated to have arisen some 4 billion years ago (3). By comparison, the age of Earth is estimated at 4.5 billion years old.
​

Figure 4:  The first six phases of the accretion model of ribosomal evolution.
  From: History of the ribosome and the origin of translation, 2015, Petrov et. al.

COOL receives funding from NASA’s department of exobiology, in the belief that knowing more about the origins of life on earth at the chemical level will potentially help astrobiologists understand what chemical signatures to look for on Mars in their search for extraterrestrial life.

The fact that the structure of ribosomes is so similar across all of life on earth supports the idea that life arose from a single cell or  'Universal Common Ancestor', a theory first proposed by Charles Darwin over 150 years ago. Meanwhile the 'Ribosome World Hypothesis' proposes that the first ancient, primordial ribosomes were self-replicating intermediates between a prebiotic world and the first cellular life forms. 
 
By choosing the diagram of the ribosome as a blueprint for our first extraterrestrial colony, I wanted to connect the molecular genesis of life with its potential futures, and design a poetic emblem for the remarkable moment when organic life attempts to spread out into the solar system for the first time. 

Figure 5: Noctis Labyrinthus

The Labyrinth:

In looking for a suitable location for the fictional martian city I first considered Asimov crater, named after the prolific writer and biochemistry professor Isaac Asimov. The smooth terrain of Arcadia Planitia also seemed an appropriate location. The term 'Arcadia' symbolizes an idyllic, pastoral harmony in Greek mythology. Known as the mythical home of Pan, the god of shepherds, hunters, meadows, and forests of the mountain wilds, Arcadia has been a source of inspiration for artists and writers back to the ancient times.

However I finally chose Noctis Labyrinthus, a region often poetically referred to as the 'Labyrinth of the Night'. This dense network of intersecting valleys and canyons forms a geological maze carved into the Martian crust at the western end of Valles Marineris, the largest canyon in our solar system. In the mornings its shadowy recesses are deep and cold enough to briefly fill with mist at sun rise, adding its mysterious allure.
 
The next step was to make a physical model of a small section of Noctus Labyrinthus, and this involved downloading 'high fidelity stereo-photogrammetric data' from NASA’s ‘High Resolution Imaging Science Experiment’ or HiRISE, the most powerful camera ever sent to another planet (figure 6) (5).
 

Figure 6: A high resolution 'Data Swath' created in a single pass of HiRISE over the Noctis Labyrinthus region of Mars.
​

​Figure 7 is the original image used in my project proposal for CITYA. This false-colour elevation map depicts a region in Noctis Labyrinthus. Blue represents the valley floors and red the higher altitudes of the smooth plateaux. The diagram of the ribosome molecule was added and adapted to fit the terrain, creating a city-like network of interconnected domes and buildings viewed from above.

Figure 7:  Topographic Map of Mars with city plan based on the ribosome molecule.
  Image adapted by Michael Whittle (Courtesy of ESA / DLR / FU Berlin, as part of the HiRISE project).

​Computer programmer and 3D modeler Alan Gordie, who works under the name Organic Computer, has adapted NASA HiRISE data to create 3D representations of geographic features on Mars. I've included a link below to learn more about his modelling process and his other fascinating projects.
​

Alan kindly gave permission to use one of his HiRISE models of a section of the labyrinth, and the data was then adapted for compatibility with CNC milling by Homan Ho at my favourite Hong Kong fabricators 'FabLab Tokwawan'. This finally allowed us to create a large-scale model of a portion of Noctus Labyrinthus in high-density architectural foam, with enough detail to capture all the subtle qualities of the martian landscape.

Homan ran a cutting simulation to check for potential bugs in the data, then started the process at a low resolution to remove the bulk of the foam and create a roughly stepped series of terraces. Switched to a finer modelling blade allowed us to mill the surface with millimetre precision. The tiny craters, rippling landslides, and intricate cliffs gradually became visible, and a small section of actual Martian landscape, 140 million miles away, slowly emerged in downtown Kowloon in Hong Kong. 
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Homan Ho's video footage of the CNC milling process at FabLab Tokwawan in Hong Kong

Homan also sourced iron oxide pigments, or powdered haematite, so we could colour the surface of the model using materials similar to those found in the rusty martian dust. The model was then shipped to and installed in the gallery along with all of the reference materials, drawings, and notes that had gone in to generating the project.

The gallery became a studio for the duration of the exhibition, and the model buildings were printed using high resolution 3D UV-resin printers and gradually added to the model. Their forms were based on designs created by SEArch+ / Space Exploration Architecture, winners of 6 NASA Centennial Challenge Competitions. This team of engineers and architects specialkise in developing human supporting architecture for living and exploring space.

The goal of NASA's 2019 habitat challenge was to create 3D-printed sustainable housing for deep space exploration, including the agency’s planned journey to Mars (6). Find our more about SEArch+'s ambitious projects here:  http://www.spacexarch.com/​
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MARS X-HOUSE is the first place winner in 100% Virtual Design within NASA’s Phase 3 3D-Printed Habitat Challenge.

Once the interior installation was complete, sections of the ribosome diagram were enlarged and attached as semi-transparent, coloured vinyl to the gallery windows, creating a contrast in scale with the city plans and modeled landscape inside.

Noctus Labyrinthus, CITYA 2021 installation view, Centre for Visual Arts, Hong Kong Baptist University

Credit: ESA/DLR/FU Berlin & NASA/JPL-Caltech/MSSS, CC BY-SA 3.0 IGO

This video presents a simulated flight over the eastern part of Noctis Labyrinthus on Mars, as captured by the High Resolution Stereo Camera (HRSC) aboard Mars Express. In order to create it, and image mosaic was built using data collected from eight orbits (0442, 1085, 1944, 1977, 1988, 10497, 14632 and 16684) of ESA’s Mars Express and its HRSC.

The perspective view highlights a unique landscape featuring "graben" - sunken sections of the planet's crust that have subsided relative to their surroundings. These distinctive features were shaped by intense volcanic activity in the nearby Tharsis region. The powerful volcanism caused large areas of Martian crust to arch upwards, stretching and stressing the surface.

​As a result, the crust thinned out, developed faults, and eventually subsided. This geological process created the fascinating terrain visible in the video, characterized by dramatic valleys and depressions that offer a glimpse into Mars' dynamic geological history.

Below are images from project development and links to learn more:

• Explore updates to Becks design and geographical accurate designs at Mark Node's website here.
• ​The Ribosome Gallery created by the Loren Williams research group can be accessed here.
• More of Organic Computers models of Mars and the process of their creation can be found here on the Sketchfab blog "Science highlight".
• You can also learn more about Homan Ho's work at Fab Lab TokwaWan in Hong Kong here.

​

REFERENCES:

1) Petrov, A S., Bernier, C. R., Gulen, B., Waterbury, C. C., Hershkovitz, E., Hsiao, C., Harvey, S. C., Hud, N. V., Fox, G. E., Wartell, R. M., and Williams, L. D. (2014) Secondary Structures of rRNAs from All Three Domains of Life, PLoS One 9, e88222. 2.
 
2) Petrov, A S., Bernier, C. R., Hershkovitz, E., Xue, Y., Waterbury, C. C., Grover, M. A., C., H. S., Hud, N. V., Wartell, R. M., and Williams, L. D. (2013) Secondary Structure and Domain Architecture of the 23S rRNA, Nucleic Acids Res. 417522-7535.

3) Petrov, Anton S. et al. (2015) History of the ribosome and the origin of translation. PNAS, 112:50. Pages: 15396 - 15401. Online: www.pnas.org/cgi/doi/10.1073/pnas.1509761112  
https://www.pnas.org/content/111/28/10251

4) Ramakrishnan V. 2002Ribosome structure and the mechanism of translation.
Cell 108:557-2; PMID:11909526; http://dx.doi.org/10.1016/S0092-8674(02)00619-0
2009 Nobel Prize in Medicine, Online: https://www.nobelprize.org/prizes/chemistry/2009/illustrated-information/
 
5) NASA HiRISE DTMS: https://www.uahirise.org/dtm/  

6) NASA Centennial Challenge. Online:  https://www.nasa.gov/directorates/spacetech/centennial_challenges/overview.html
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​

References:
​
1) Schlemmer, Oskar, pg 28. The letters and Diaries of Oskar Schlemmer (1958), ed. Tut Schlemmer, trans. K. Winston, (Evanston, IL. Northwestern University Press, 1990)

2) Conzen, Ina, Oskar Schlemmer: Visions of a New World, Staatsgalerie Stuttgart (Hirmer Verlag, 2016)

3) Marcia F. Feuerstein (2019) Oskar Schlemmer's Vordruck: an absent woman within a Bauhaus canon of the body, Theatre and Performance Design, 5:1-2, 125-140, DOI: 10.1080/23322551.2019.1605767

4) https://www.researchgate.net/publication/221571982_Man_in_espacemov_Motion_Analysis_in_3D_Space

5) https://www.gsd.harvard.edu/2019/05/in-space-movement-and-the-technological-body-bauhaus-performance-finds-new-context-in-contemporary-technology/

6) https://www.artforum.com/print/197707/oskar-schlemmer-s-performance-art-35972

7) ​https://www.nytimes.com/1986/05/25/arts/art-view-schlemmer-s-noncommittal-muse-came-to-life-on-stage.html?smid=url-share

1) Glimpse into the left side of a human skull, about 1651
© Royal Collection Trust / Her Majesty Queen Elizabeth II (CC BY-NC-SA 4.0) 

6) The Vitruvian Man, c. 1490
Pen and ink with wash over metalpoint on paper, 34.6 cm × 25.5 cm

9) Giacomo Andrea Da Ferrara, c. 1490
Biblioteca Ariostea, Ferrara (Cart. Sec. XVI, Fol. Figurato, Classe II, N. 176, Fol 78V)

❉ Blog number 19 on diagrams in art and culture covers a recently completed installation for the Yi Tai Sculpture and Installation projects curated by Andre Chan for Hong Kong's 2021 Art Central. 
​​

​Current estimates date the origins of anatomically and genetically modern humans in Africa to  between 150,000 and 200,000 years ago, and the first major dispersal of these populations to Asia and Europe is believed to have occurred around 65,000 years before present (B.P.) (4). (Figure 3)
 
DNA haplogroup maps help trace patriarchal and matriarchal human lineages back across time, in order to understand how populations have spread across the globe. Haplogroup maps rely upon measuring distinctive mutations within genetic elements of the genome that vary little over time.

In males such material is found within the non-recombining portions of DNA in the Y-chromosome. For females similar material is found within Mitochondria, energy providing microscopic structures within human cells that contain their own plasmid-like DNA structures.
 
Mitochondrial DNA (MtDNA) comprises only a small segment of the total human genome but has proven highly effective in studying early human populations. MtDNA has the advantage of unusually rapid mutation rates, descends almost entirely through the female lineage (via the female ovum / egg), and shows few, if any, of the effects from environmental selective forces.
​

Figure 6: Artist’s recreation of grid-cell firing patters used to create the custom carpet.

​❉   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

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​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.
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​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
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Figure 5, Missing the Target (Detail)

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​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.

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Figure 6, Richard, Glass, 1989, pencil on paper, 110 x 100 cm

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​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.

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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.
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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.

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​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.

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​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.
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Figure 10: Richard Talbot, All depth, no substance, 2013, Installation view

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​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.
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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.

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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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❉   Blog number 17 on diagrams in art and culture covers some of the ideas, images and research projects I discovered during a spring-time residency on the island of Jeju in South Korea. The two new drawings I developed following my stay there were on show in a group exhibition at the Chusa Memorial Museum from Oct 15th - Nov 17th, 2019.

figure 1: NASA image of Jeju Island 
( United States Geological Survey Landsat data, Robert Simmon, ​Google Earth, 2000 )

In the spring of 2019, I travelled to Jeju island, an eye-shaped volcanic landmass staring upwards off the southern coast of the Korean peninsula. I'd been invited by the Korean artist Mikyung Oh and her husband, the sculptor Do il, to take part in a group residency in connection with the Chusa Memorial Museum, during which time the selected artists were asked to respond to the works of the legendary Korean scholar and calligrapher after whom the museum is named (fig. 2). 

Mikyung and Do il's main studios are in Yongin city just south of Seoul, but they travel regularly with their daughter Yule to Mikyung's hometown on Jeju to maintain the family tangerine orchard. The residency program is run from Mikyung's family home there, alongside a barn converted by Do il in to studio space.

​Once all the artists had arrived at the orchard we were welcomed by a Kayagum concert held beneath the heavy bows of one of Jeju's ancient Hackberry trees. Afterwards, we set about exploring the island and learning more about it's most famous historical resident Chusa Kim Jeong-hui, exiled scholar and man with two hundred names.

figure 3: Chusa Kim Jeong-hui’s masterpiece Sehando (A Winter scene),
​1844, National Treasure #180 ( public domain ) 
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Chusa's journey to Jeju must have been very different to our own. The subtropical island is now Koreas most famous holiday resort, complete with sprawling luxury hotels and Chinese casinos.  An incredible 76,460 flights travelled between Seoul and Jeju airport in 2018 alone, making it the single most crowded flight path on earth. (In comparison, just over 14,000 flew between London Heathrow and New York’s JFK).
​
As you arrive by air the most distinctive feature of the island is Mount Halla or Hallasan, an enormous shield volcano and the highest peak in South Korea. The remainder of the island is relatively flat, which highlights the 300 plus other volcanic cones that protrude abruptly amongst the fields. ​These surface features connect underground as a colossal volcanic network of structures, a so-called ‘magma plumbing system’ that extends up to 60 km deep (figs. 5,6).

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figure 5: Geology of Jeju Island
( Yoon Sun et.al., Korea Rural Community and Agriculture Corporation, 2006, scale 1:150,000. )
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Until only fairly recently very little was known about this subterranean system, but an ingenious new technique has allowed researchers to explore the hidden structures that lie beneath the island's surface. 
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The geology and vegetation of Jeju are in fact so unusual, that large tracts of the island are now protected by law under Unesco World Heritage status. One of the island's major geological features was unwittingly discovered by a farmer installing electricity cables, who watched as one of his posts vanished in to the ground before him. The pole had broken through the roof of a cavernous Lava-tube full of rare rock formations, and large sections of these tunnels are now open to the public, with others being continually discovered thanks to less invasive techniques such as ground penetrating radar.
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figure7: Section of a lava tube system in the North East of Jeju island

During his time on Jeju, Chusa wrote letters and poems to friends and students, taught classes at a local school and wandered the island to pick tea leaves and sketch the local orchids. ​One of the ‘four noble gentlemen’ of traditional Chinese painting, orchids are renowned for their ability to grow and blossoms in barren environments, and scholar-artists used them as a visual metaphor for resilience, nobility and humility, and as a symbol of friendship and loyalty.

Chusa's brush of choice was made of rat’s whiskers, a material which he found combined strength with sensitivity, and also allowed him to abruptly change the direction of his stroke whilst painting. With each new painting he would often coin a new 'Ho' or pen-name when signing the piece, to suggest a particular persona in association with the image.  

Thanks to their ability to migrate and develop to suit different conditions, orchids have evolved in to an extraordinarily diverse family of plants. Their highly specialised roots have allowed them to colonize not only the inhospitable lava rocks and quick draining soils of Jeju, but almost every habitat on Earth, except Antarctica. 

Around 10% of all flowering plants species are now known to be orchids, with somewhere between 20,000 and 30,000 species and over 70,000 hybrids and cultivars. Scientists are currently in the process of mapping out the extensive evolutionary lineage of orchids and in 2017, a study published in Nature Magazine announced that an international consortium of researchers had sequenced the genome of Apostasia shenzhenica, a primitive 'Grass Orchid' whose appearance is only barely recognisable as an orchid. 

By comparing it's genome with known sequences in other species, they were able to estimate the time at which it diverged or 'split off' from other orchids. Their study also gives us a better idea of when the 'Most Recent Common Ancestor' (MRCA) of all orchids existed, now believed to be around 200 million years ago at the dawn of the age of the dinosaurs (figure 9). 

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​figure 9: Phylogenetic tree diagram of MADS-box genes involved in orchid morphological evolution.
Image courtesy of Jie-Yu Wang and Rolf Lohaus (CC BY 4.0)

Critical appreciation of traditional Korean painting often involves an awareness of the negative space or unpainted regions of an art work, and several of Chusa's orchid paintings use the white of the paper at the base of the leaves and stalks to suggest the terrain in which the flower grew (see below).

In developing the two new drawings for the residency on Jeju, I was interested in the notion of absence within an image - what an artist chooses to show and chooses not to, but also in terms of what can be said to lie hidden behind the surface appearance of the things which surround us.

Written within the fabric of nature is evidence of innumerable events that occurred in deep geological and evolutionary time in order for the volcanoes and orchids to exist, and it's only by means of years of collaborative investigation and ingenious new techniques, that we have come to be able to detect and decipher them.

As geologists diagram the molten roots beneath the rock on which Chusa wandered, and geneticists piece together the genetic roots which underlie each of Chusa's orchids, we have come to realise that these structures stretch backwards through space and time in ways that Chusa could never have imagined. 
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Below are high resolution images of each finished drawing, which can be viewed in detail using the control icons to the right of each image.  Beneath these are a collection of Chusa's own orchid paintings, which now comprise a digitized collection available online here as part of Google's Arts and Culture Project.

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​Tear glands, tear ducts, tear drops
(Lacrimal gland and ducts with Lithospheric anomalies)
Michael Whittle, 2019, Ink pencil and watercolour on paper, 111.2 x 78.9 cm

References:
Jung-Hun Song et.al., 2018, Imaging of Lithospheric Structure Beneath Jeju Volcanic Island by Teleseismic Traveltime Tomography, Journal of Geophysical Research: Solid Earth, 10.1029.
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​Online: https://doi.org/10.1029/2018JB015979
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The roots of the Orchid
(Divergent phylogenetic tree with common ancestor and desiccation) 
Michel Whittle, 2019, Ink pencil and watercolour on paper, 111.2 x 78.9 cm

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References: 
​Guo-Qiang Zhang et.al., 2017, The Apostasia genome and the evolution of orchids. Nature 549: 379-383
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Online: https://rdcu.be/bUj7h

Chusa's Orchids:

Figure 1: Pupil, Michael Whittle
2013, Ink on paper, 82 x 82 cm
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Figure 3: ​Johann Zahn - Emission Theory, “Oculus Artificialis Teledioptricus Sive Telescopium”, 1685.

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​Visual data from the tiny foveal region is given maximum priority over that collected from the rest of the retina, with approximately half of the nerve fibers in the optic nerves carrying information from the fovea alone, while the remaining half carrying information from the rest of the retina. 

It's an interesting realisation that this tiny high resolution part of your vision is about the same size as your thumb nail held at arms length in front of your eye. Rather than the eye acting as a camera that takes in a complete image, the act of looking is in fact a process of diagramming the world using that tiny region of high resolution information provided by the fovea.

One of the pioneering researchers of how the human visual system relies on such diagrammatic eye movements was the Russian psychologist Alfred Yarbus (1914-1986). Yarbus conducted several influential experiments using suction caps attached to the eyes to track eye movements while participants viewed various images and scenes. His most famous study, published in the book "Eye Movements and Vision" (1967), demonstrated that the way people move their eyes while looking at a picture depends on the task they are given or the information they are seeking. 

Figure 13 shows the results of one such experiment, and the rapid series of twitching eye movements, known as saccades, that scan the world around us as we process our surroundings. Nicholas Wade from the University of Dundee (UK) & Galina Rozhkova from the Institute for Information Transmission Problems at the Russian Academy of Sciences (Moscow) have compiled an excellent website detailing the work of Yarbus, and how his discoveries laid the foundations for the study of human vision and cognition: https://yarbus.eu/faces/.

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❉   Blog post 15 on diagrams in the arts and sciences is a reading list for Diagrammatology, the academic study of diagrams. A short introduction is given for each publication along with notable quotes and links for purchase / download. 
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INTERACTIVE
​CONTROLS
HERE ↓ 

Tree of knowledge, Chrétien Frederic Guillaume Roth, Fold-out frontispiece of the first volume of the indices to the 'Encyclopedie, ou Dictionnaire Raisonne des Sciences, des Arts et des Metiers', (Encyclopedia or Dictionary of the Sciences, Arts and Professions), edited by Denis Diderot (1713-1784) and Jean d'Alembert (1717-1783). 

​The diagram sets out a genealogical relationship between various arts and sciences, with the left, middle, and right branches influenced by the threefold classification in the philosopher Francis Bacon's 1605 book "Advancement of Learning".

This blog post is a recommended reading list on diagrammatology, and was posted to coincide with a lecture tour of UK universities and art colleges in the spring of 2018. The lecture focuses on the philosophy and semiotics of diagrams in the arts and sciences, and the following books were selected to give an idea of the depth and breadth of diagram research in relation to this subject. The recommended books range from general readers to specialised academic texts, and these are followed by a series of 'classic texts' that remain in print today because of their continuing importance.

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REMARKS:

Bender and Marrinan's book outlines the ways in which diagrams have come to play such a central and formative role in European visual thinking and knowledge production. John Bender is Professor in Interdisciplinary Studies at Stanford University and Michael Marrinan is Professor of Art History, also at Stanford. If you were to draw a Venn diagram of their combined professional interests and specialisations, then this collaborative book has emerged from a complex intersection near the centre of their overlapping sets. 

The Culture of Diagram is wide in historical scope and forward thinking in an important and influential way, so much so, that the title is commonly used to refer to the recent resurgence of interest in diagrams, diagram making and diagrammatic thought in the humanities.

From Roland Barthes 'The plates of the encyclopedia' to the cubist paintings of Braque and Picasso, and from the poetry to Mallarme to the work of the Quantum physicist Neils Bohr - The Culture of Diagram constructs a pan-historical web of texts, pictures, formulas and figures, whilst foregrounding the diagram as tools for blurring boundaries and highlighting the production of knowledge as process. 

More quotes:

'For Braque and Picasso, the shift to diagram entailed thinking past the surfaces that separate things in the world, piercing their outer skins, and searching for ways to trigger memories of comprehension that might be tactile, auditory, or olfactory rather than visual' p.205

'Users of diagrams, unlike viewers, are functional components inseparable from the system in which they are imbricated... Users of diagrams practice correlation to make working objects. Modernist self-reflection is not the goal.' p.72 

CONTENTS:

Illustrations / Acknowledgements
1. Scenario
2. Diagram
3. Descriptions
4. Visualisations
5. Numbers
6. Crossings
Notes / Bibliography / Index

REMARKS:
​
The interactive diagram of the tree of knowledge at the start of this blog embodies the metaphysics of the English Philosopher-Scientist Francis Bacon. It's structure is arboreal or 'treelike' in how it conceives and depicts the structure of knowledge as a hierarchy of order and linearity. The continental philosophy of Gilles Deleuze can also be described as diagrammatic, but in the sense that it resembles the structure of a rhizome, a web-like underground plant stem whose growth appears to be aimless and disordered.

The focus of Zdebik's book is on Deleuze's visual aesthetic theory and the visual devices in Deleuze's writing. Deleuze conceptualized his theory as a form of painting, and as such, promoted the need to shift from figuration into abstraction. Like Deleuze, Zdebik's prose is rich with complex analogies and metaphors - hence the image of 'a squid that carries a contorted mammal inside of it on a virtual level'  quoted above.

This is a demanding text whose chapters require several careful readings and access to primary source texts (ie. Deleuze's original writing), as well as an acquaintance with the school of continental philosophy (often referred to as the deconstructionists or poststructuralists). 

From an artist's perspective this is a rich, complex text full of important insights that suggest a new relationship between philosophy, art and diagrams, and for this reason is well worth the effort. Deleuze was proposing a way to think about philosophy through art using the diagrammatic art work of Paul Klee and Francis Bacon (the artist) as exemplars. Zdebik highlights the abstract depths to which Deleuze took the concept of diagram in his attempt to sketch out a rhizomatic relationship between philosophy and art.

CONTENTS:
​​
Preface \ Introduction: What is a Diagram? 
1. Constraint and System as Vegetation: Diagram and Visual Organization
2. Black Line White Surface
3. Gilles Deleuze's Diagram (Complicated by a Comparison to Immanuel Kant's Schema)
4. The Extraordinary Contraction
5. Skin, Aesthetics, Incarnation: Deleuze's Diagram of Francis Bacon-An Epilogue
​Notes \ Bibliography \ Index

REMARKS:

​James Elkins is a trailblazing scholar of visual imagery with an output as varied as it is prodigious. Chapter 13 of his book The domain of images is devoted to diagrams, which Elkins opts to refer to as 'Schemata' in reference to the philosopher Immanuel Kant's use of the term to describe the visual and imaginative aspects of diagrammatic structures. 

​A close reading of the text is a disjointed and fragmented experience due to the way Elkins has chosen to structure the layout of the book. His exacting use of footnotes and intricate system of references requires time, effort and note making on behalf of the reader. It feels as if Elkins is playing with the limitations of the physical book as an analogue version of a hypertext, a format which would have allowed him to include an even more diverse proliferation of images and ideas. 

Elkins writing is always dense, lucid and engaging, and his use of technical terms is precise and never feels unnecessary. The glossary at the end of the book is a very welcome addition for a subject already oversaturated with specialist jargon and multiple definitions, and it's a shame more authors don't do this.

An Investigation on the Borderlines of ​
​Phenomenology, Ontology, and Semiotics
​

REMARKS: 

The Danish philosopher Frederik Stjernfelt's Diagrammatology is an ambitious, heavyweight, academic tome that positions the diagram as central to epistemology - the philosophical study of knowledge and knowledge production. Because of the ubiquitous nature of diagrams, the various roles that they play in knowledge production has been investigated from a variety of standpoints in a variety of fields. Stjernfelt's book proposes a unifying framework that underlies the complexities of the topic - the development of a semiotics based on iconical realism.   

In the first part of the book Stjernfelt reexamines the mature work of the American philosopher-scientist (and founder of semiotics) Charles Sanders Peirce, in particular Peirce's doctrine of 'diagrammatical reasoning', which mainly includes diagrammatic construction, observation and manipulation. Stjernfelt proposes an interpretation of Peircean semiotics and Husserlian phenomenology that builds on similarities between the two, then in the second part of the book presents three possible domains of application: biosemiotics (DNA as code), picture theory (an art historical picture plane analysis) and literary theory.

Diagrammatology has received praise for its sheer ambition and for the fluency and meticulous clarity in which it is written, but the price paid for having introduced so many complex topics is that many of the ideas can't be explored to enough depth. Any one of the subjects chosen by Sternfelt could have given rise to a similarly sized book in its own right, such as the diagrammatic analysis of the art historical works in Chapter 13. However Diagrammatology opens up many exciting new avenues for further research, and is likely to be remembered as the book whose title has become synonymous with an entire field of diagram research.

REMARKS:
​
Over a period of about five years the Austrian artist Nikolaus Gansterer corresponded with a number of other artists, theoreticians and scientists and then worked to compile, edit and illustrate 'Drawing a Hypothesis - figures of thought'. The texts range from insightful essays on the nature of diagrams and diagram making to creative writing and fictional narratives, sometimes in reaction to several of the 160 schematic drawings provided by Gansterer. It's a beautiful designed and thoughtfully put together book and, incredibly, it's available in its entirety as a pdf on Gansterer's own homepage here:     FIGURES OF THOUGHT pdf.

It's definitely worth finding a printed copy however, to fully appreciate the effort that artist Simona Koch has put in to the design of the book, which was quite rightly included as one of the ten most beautiful books of Austria 2011, and awarded bronze medal at the annual book design competition 'Best Books from all over the World in 2012'.  

An insightful review of the book can be found here written by Gert Hasenhütl: 
Drawing a Hypothesis?

REMARKS:
​
Writing on Drawing is a collection of diverse essays that consider the multifaceted nature of drawing to highlight its importance as a cognitive process. In his introduction to the book Steve Garner, editor of these invited essays, describes the domain of drawing practice and research as characterised by diversity. Garner suggests that if drawing is to emerge as a distinct domain in its own right then practitioners from fields as diverse as computer science, history, psychology, education and fine art need a way to chart and better understand how drawing connects their disparate fields, all the better to facilitate interdisciplinary communication. 

Another contributing practitioner, and world expert on the diagrammatic systems of perspective, is Richard Talbot, whose essay 'drawing connections' gives a fascinating insight into how his artistic research and practice inform one another, to the benefit of both.  

More can be found about the work and research of Richard Talbot here: Richard Talbot.org ​

REMARKS:

Aimed at a general audience, this selection of 100 historic diagrams is broad in scope and remarkably open in terms of its definition of diagram. This leads to a very interesting collection, and examples include: diagrammatic illustrations of Dante's inferno, elegant patent diagrams for the first automobile, a diagram of Thomas Edison's light bulb, Nazi propaganda maps, sewing patterns and IKEA flat-pack furniture instructions. Descriptions and explanations are kept to a minimum but provide good starting points.

The books title however is a little misleading, as many of the diagrams are merely interesting diagrammatic records of technological progress, rather than instruments of change and progress as diagrams in their own right. Florence Nightingale's ingenious rose charts for example, or the early exploded diagrams of artist engineer Mario Taccola were both arguably more influential as innovative diagrams than say the schematics for Edison's lightbulb or Apple's ipod. 

Christianson's book does however capture the excitement of creative innovation that's associated with diagrams, and their potential to allow for the cross fertilisation of ideas between specialisms, surely something which is more relevant now than at any other time in history.

More quotes:
​
'The great diagrams depicted in the book form the basis for many fields — art, astronomy, cartography, chemistry, mathematics, engineering, history, communications, particle physics, and space travel among others. More often than not, however, their creators — mostly known, but many lost to time — were polymaths who are creating new technologies or breakthroughs by drawing from a potent combination of disciplines. By applying trigonometric methods to the heavens, or by harnessing the movement of the sun and the planets to keep time, they were forging powerful new tools; their diagrams were imbued with synergy.'

REMARKS:

This somewhat specialist academic publication falls into two distinct parts, as shown in the contents list below. Part I provides a concise overview of the historical rise and fall of the diagram in Geometry following the advent of ideal lines and points and the invention of non-Euclidean geometries. Part II describes how this distrust of deduction techniques based on spatial intuition in geometry (ie. geometric diagrams) was in fact mirrored by a parallel distrust of diagrams in logical calculi. 

This is a clear and meticulously written introduction accessible to non-specialists in Geometry and Mathematical Logic. Whilst Greave's conclusions at the end of his book hesitate to make predictions about the future role of the diagram in either Geometry or Logic, they do leave one wondering whether we may yet see a reemergence of diagramming in these fields in a similar way the diagrammatic renaissance in Quantum Physics (- See this earlier blog post on Diagrams in Physics: Meta-engines of creativity - Diagrams in physics).  

​The CSLI (Centre for the Study of Language and Information) is based at Stanford University and Mark Greaves is the Director of the Joint Logistics Technology Office at DARPA.  
​

REMARKS:

The diagram plays a number of crucial roles in Architecture, most obviously as a fixed set of instructional plans that dictate how buildings are to be built, ie. blueprints. However diagrams also facilitate the more dynamic, fluid and creative process of building design generation, and even the modelling processes involved in predicting and analysing how individuals or crowds move through and interact within rooms, building and city streets.

Because diagrams play such fundamentally important roles in architecture, a dense theoretical framework has arisen around their function, especially during the 1980's, and editor Mark Garcia has commissioned, collected and introduced 26 essays from leading international academics, architects, theorists and professional experts. These ideas are illustrated with a full-colour critical collection of over 250 of the most significant and original diagrams from around the world, many of which are previously unpublished.

As the quote from the ever insightful Sanford Kwinter illustrates above, discussion of the diagram in these essays ranges far beyond the confines of architecture to include its conception in philosophy, design and art.
​

CONTENTS:
Introduction: Histories and Theories of the Diagrams of Architecture (Mark Garcia).
Part I: Histories and Theories of the Diagrams of Architecture.
Diagrams of Diagrams: Architectural Abstraction and Modern Representation (Anthony Vidler).
Scientific Management and the Birth of the Functional Diagram (Hyungmin Pai).
Urban Diagrams and Urban Modelling (David Grahame Shane).
Dummy Text, or the Diagrammatic Basis of Contemporary Architecture (Robert E. Somol).
Diagram: an Original Scene of Writing (Peter Eisenman).
Poetics of the Ideogram (Leon van Schaik).
Diagrams in Multisensory and Phenomenological Architecture (Joy Monice Malnar and Frank Vodvarka).
The Hammer and the Song (Sanford Kwinter).
Part II: Multidisciplinary Dimensions of the Diagrams of Architecture.
Diagramming the Interior (Mark Taylor).
Diagrams in Landscape Architecture (Jacky Bowring and Simon Swaffield).
Inhabiting the Forest of Symbols: From Diagramming the City to the City as Diagram (Brian McGrath).
Diagrams and their Future in Urban Design (Peter A. Hall).
Diagrams in Structural Engineering: Applied Diagram – Engineering Precision (Hanif Kara).
Spatial Notation and the Magical Operations of Collage in the Post-Digital Age (Neil Spiller).
Part III: Architects of the Diagrams of Architecture.
The Diagrams of Bernard Tschumi (Bernard Tschumi, Bernard Tschumi Architects, interviewed by Mark Garcia).
The Diagram and the Becoming Unmotivated of the Sign (Peter Eisenman, Eisenman Architects).
Expressive Abstractions: The Diagrams of Will Alsop (Will Alsop interviewed by Mark Garcia).
Diagrams (Ben van Benkel and Caroline Bos, UNStudio).
Diagramming the Contemporary: OMA’s Little Helper in the Quest for the New (Wouter Deen and Udo Garrtizmann, OMA).
Between Ideas and Matters: Icons, Indexes, Diagrams, Drawings and Graphs (Alejandro Zaera-Polo, Foreign Office Architects).
Metacity/Datatown (Winy Maas, MVRDV).
Atlas of Novel Tectonics (Jesse Reiser and Nanako Umemoto, Reiser + Umemoto).
Parametric Diagrams (Patrik Schumacher, Zaha Hadid Architects).
NOX Diagrams (Lars Spuybroek, NOX).
Part IV: Epilogues.
Architectural Evolution: The Pulsations of Time (Charles Jencks).
Epilogue (A Beginning of Other Diagrams of Architecture and the Futures of the Diagrams of Architecture) (Mark Garcia).
Select Bibliography / Index

On Growth and form, D'arcy Wentworth Thompson 1945 edition
(first published in 1917)

​An Introduction to the Town Planning Movement 
and to the Study of Civics 
first published in 1915

Alejandro Guijarro, STANFORD III, 2012, C-type print, 117 x 240 cm
​

Alejandro Guijarro, BERKELEY VIII, 2011, C-type print, 117 x 174 cm
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Alejandro Guijarro, SLAC V, 2012, C-type print, 117 x 180 cm
​

Notes:

1) C.F. Gauss quoted in Gauss zum Gedächtniss (1856) by Wolfgang Sartorius von Waltershausen
2) Andrew Hodges, Online at: http://www.twistordiagrams.org.uk/papers/
​3) Arkani-Hamed, quoted in 'A Jewel at the Heart of Quantum Mechanics' by Natalie Wolchova, online
at: https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/
​4) Jacob Bourjaily, quoted in 'A Jewel at the Heart of Quantum Mechanics' by Natalie Wolchova, online
at: https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/
​

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.

​​

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
​

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.

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

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

Image 1: Michael Whittle, Clouds, glands, tributaries, 2007, Ink on Paper, 133 x 125.5 cm
​

Image 6: Clouds, glands, tributaries (detail 4)
​Inner upper eyelids complete with meibomian (tarsal) glands and ducts

​

Figure 3: Yves Netzhammer, Untitled, Seilzeichnung, 2011, 
​Rope, metal, wood, glass and colour, variable dimensions
​

Figure 6: Yves Netzhammer, The Arrangement of Two Opposites While
​Their Maximum Contact Is Under Generation
2005, Kunsthalle Bremen, Germany
​

❉ This is the ninth 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: Portrait of Marcel Duchamp for Life Magazine taken in 1952 by Gordon Parks,
in front of Network of Stoppages (1914),
Oil and pencil on canvas, 148.9 x 198.12 cm

The young modernist poet, dramatist and writer Jacques Nayral (a pseudonym for Joseph Houot) wrote the forward to the catalogue for the 1912 exhibition of Cubist art "Exposicion d'art cubista" at the Dalmau Gallery in Barcelona. Nayral described how “[t]he Mathematical spirit seems to dominate Marcel Duchamp. Some of his pictures are pure diagrams, as if he were striving for proofs and synthesis.” (1)

We have already seen in a previous post how Duchamp's training as a young artist was founded upon the diagram, having studied during a period in France when students were made to practice mechanical drawing as opposed to the traditional historical modes of figurative and landscape.

Trained in ‘the language of industry’, (2) Duchamp remained fascinated with the detached, objective qualities of technical diagrammatic drawings, proclaiming his desire to create “paintings of precision” with a “beauty of indifference.” (3)

He also spoke in interview of how he wished to "go back to a completely dry drawing, a dry conception of art. I was beginning to appreciate the value of exactness, of precision and the importance of chance… And the mechanical drawing was for me the best form of that dry conception of art… a mechanical drawing has no taste in it. (4)
​

The steps Duchamp took to refine his work towards being beautifully indifferent images of precision are visible in the two paintings above, made within a year of each other. Chocolate grinder number 1 (1913) is painted in traditional perspective and the illusion of three dimensionality also relies upon its strong shadows and graded colouration. On the other hand in Chocolate grinder number 2, the object is depicted in what could be described as a conceptual landscape: a neutral and shadow free environment of flat colour and a strict one point perspective.

Despite his fascination with the diagram Duchamp continued to seek out new ways to subvert this mechanical, ‘anti-expressive’ system of geometrical depiction on a number of levels, such as his attempts to incorporate chance and chaos in to his artistic process.

In "Three standard stoppages", the artist claims to have dropped metre long pieces of string from a height of one metre and traced the outline they made upon landing. These shapes were then cut out of strips of wood and presented in a box as a set of alternative, two dimensional standard metre lengths.
​

Figure 4: Marcel Duchamp, 3 stoppages étalon (3 Standard Stoppages), 
1913–4, replica 1964,  Wood, glass and paint on canas, 400 x 1300 x 900 mm
​
​

Asked what he considered to be his most important work, Duchamp replied that "As far as date is concerned I'd say the Three Stoppages of 1913. That was when I really tapped the mainspring of my future. In itself it was not an important work of art, but for me it opened the way - the way to escape from those traditional methods of expression long associated with art … For me the Three Stoppages was a first gesture liberating me from the past.' (5)

It is important to take into account what was happening within the world of science at the time these works were being made, and Duchamp's active interest in the popular science books of the time.

In "Science and Hypothesis" (1902) for example, the mathematician, theoretical physicist, engineer, and philosopher of science Henri Poincaré posed the question of whether or not it would be 'unreasonable to inquire whether the metric system is true or false?'. At almost the same time, two other noteworthy figures  Hermann Minkowskiand Albert Einstein were already setting about redefining our most basic understanding of the very geometric fabric of reality for the first time in well over 2000 years. (6)

Also of special interest to Duchamp at that time was the work of the French humorist Alfred Jarry (1873-1907), creator of Pataphysics, or the 'science of imaginary solutions'. Jarry developed this imaginary subject to "examine the laws governing exceptions, and … explain the universe parallel to this one", and it is easy to see how Duchamp was drawn to such a novel, humorous and profoundly revealing idea with its suggestions of alternative realities with their own physical laws. (7)

The wooden templates of Duchamp's "diminished metres" were later used to design the pattern of lines in his painting "Network of Stoppages" (Reseaux des stoppages), shown below.
​

Figure 5: Marcel Duchamp, Network of stoppages (Reseaux des stoppages),
​1914, oil and pencil on canvas, 198 x 149 cm
​

The networks are depicted on top of what appears to be a replication of Duchamp's earlier painting "Young Man and Girl in Spring", oil on canvas, 1911, albeit rotated through ninety degrees.  This is a subtle contrast of cold chance diagrammatically visualised against the image of a symbolic fertility rite or creation myth.

The large glass subverts the dry, mechanical visual language of objectivity by applying it to subjects that it wasn't designed to address, namely the psycho-sociology of human courtship and sexuality, or what would previously have been called romanticism.

​[Due to the complexity and art-historical importance of The Large Glass and its accompanying notes, it will be covered in a future post dedicated to that work alone.]

An often overlooked work that questions our notions of ideal forms in geometry with a poetic pathos is Unhappy Readymade, a so called 'assisted readymade' created by Duchamp around 1919 (See figures below).

Foreshadowing the production processes of Sol LeWitt, Unhappy Readymade consisted of a simple set of instructions sent by post as a wedding gift to his sister Suzanne Duchamp and the artist Jean Crotti, so that, in the words of LeWitt, “the Idea becomes a machine that makes the art.” (8)

In an interview with Pierre Cabanne, Duchamp described his instructions for Crotti to buy a

"…geometry book which he had to hang by strings on the balcony of his apartment in the rue Condamine; the wind had to go through the book, choose its own problems, turn and tear out the pages. Suzanne did a small painting of it, ‘Marcel’s Unhappy Readymade.’ That’s all that’s left, since the wind tore it up. It amused me to bring the idea of happy and unhappy into readymades, and then the rain, the wind, the pages flying, it was an amusing idea… " (9)

​

Duchamp’s unhappy readymade sets out to highlight the contrast between ideal geometric forms which exist only as concepts, their manifestation as token textbook diagrams of ink on paper and the results of weathering on the text book.

The Duchamp scholar Linda Dalrymple Henderson points out that this was in fact one of the artist's last specific comments on geometry, and that the book used was a copy of Euclid’s elements so that, ironically, the plane geometry of Euclid was in contrast to damage caused by the wind and rain producing distortions in the diagrams as “non-Euclidean deformations of the Euclidean geometries in the text.” (10)

In a letter to his sister, Duchamp wrote: “I liked the photo very much of the Ready Made sitting there on the balcony. When it all falls apart you can replace it.” (11)

Duchamp also suggests that this is a lesson to be repeated, a reminder of the fundamental difference between an essentialised, idealised, conceptual landscape of perfect forms, and the chaotic nature of decay and change, which composes our everyday experience of the real world. Some years later Duchamp told one interviewer that “he had liked disparaging ‘the seriousness of a book full of principles,’ and suggested to another that, in its exposure to the weather, ‘the treatise seriously got the facts of life’”. (12)
​

Below is a scanned reproduction of the British, Victorian mathematician Oliver Byrne's 1847 edition of Euclid's Elements. Created almost a century before the Dutch artist Piet Mondrian made geometrical red, yellow, and blue lines so famous, Byrne titled his edition "The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners".

Downloadable copies are available in various formats courtesy of an Internet Archive at the University of Toronto Libraries here: Downloadable formats

​Or as a pdf here: Downloadable pdf.


​Click on the pages of the book below to turn them:
​

Oliver Byrne (1810–1890) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering. His most well known book was this version of ‘Euclid’s Elements’, published by Pickering in 1847, which used coloured graphic explanations of each geometric principle.

​The book has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements. Information design writer Edward Tufte refers to the book in his work on graphic design and McLean in his Victorian book design of 1963. In 2010 Taschen republished the work in a wonderful facsimile edition.     ( Wikipedia link )

​

References:

1) Nayral, J. (1912) preface to Galeries J. Dalmau, Barcelona. Exposció de Arta cubista. (April – May 1912) Reprinted in Guillaume Apollinaire: Les Painters Cubistes. Breunig, L.C., Chevaliare J. Cl. Paris: Hermann (1965) p. 181
​2) Nesbit, M. (1991) The Language of Industry. In: The Definitely Unfinished Marcel Duchamp. De Duve, T. (Ed.) Massachusetts: Cambridge: The MIT Press, 1991. pg.356.
​3) Duchamp, M. Salt Seller: The writings of Marcel Duchamp (Marchand du sel). Eds. Sanouillet, M. Peterson, E. New York: Oxford University Press, 1973. p. 30.
​4) Duchamp, M. As quoted in Sweeney, A conversation with Marcel Duchamp, NBC Television interview, January 1956.  Sweeney, J.J. (1946) Eleven Europeans in America: Marcel Duchamp. Museum of Modern Art Bulletin 13, p. 19-21. In: Dalrymple Henderson, L. (1998) Duchamp in context: Science and technology in the large glass and related works. New Jersey: Princeton University Press.
​5) Duchamp, quoted in: Katherine Kuh, The Artist's Voice: Talks with Seventeen Artists, New York 1962, p.81.
​6) Henri Poincaré quoted in: Herbert Molderings, 'Objects of Modern Scepticism', in Thierry de Duve (ed.), The Definitively Unfinished Marcel Duchamp, Cambridge, Massachusetts 1991, pp.243-65, reproduced p.247 Arturo Schwarz, The Complete Works of Marcel Duchamp, revised and expanded edition, New York 1997, pp.594-6, reproduced pp.594, 595, 596
​7) Alfred Jarry quoted in: Dawn Ades, Neil Cox and David Hopkins, Marcel Duchamp, London 1999, pp.78-9, reproduced p.78
​8) LeWitt, S. (1967) Paragraphs on Conceptual Art. Art Forum. June, 1967
9) Cabanne, P. (1971) Dialogues with Marcel Duchamp. Originally published: London: Thames and Hudson. p. 61.
​10) Dalrymple Henderson, L. (2013) The Fourth Dimension and non-Euclidean geometry in Modern Art. 2nd Revised Edition. Massachusetts Institute of Technology. p. 283.  
11) Duchamp, M. (1920) Letter to Suzanne Duchamp. In: Affectueusement, Marcel: Ten Letters from Marcel Duchamp to Suzanne Duchamp and Jean Crotti. (1982) Francis Naumann, M. Archives of American Art Journal, Vol. 22, No. 4. pp. 2-19.
12) Tompkins, C. (1998) Duchamp: A Biography. New York: Henry Holt and Co. Inc. p.212-214

Figure 3: Sol LeWitt, Location of a circle, from the series:
The location of six geometric figures (circle, square, triangle, rectangle, parallelogram and trapezoid).
1974, Set of six etchings, Edition of 25 10 AP.
​

Figure 4: Sol LeWitt, The location of six geometric figures
(circle, square, triangle, rectangle, parallelogram and trapezoid). 
1974, Set of six etchings, Edition of 25 10 AP.

Figure 6: Leonardo da Vinci, Profile of a Man, plant, geometric figures etc. 
(also known as the ‘Theme Sheet’) (detail)
​c. 1448, pen and ink, Windsor Castle, The Royal Collection.
​

References:
1)  LeWitt, S. (1967) Paragraphs on Conceptual Art. Art Forum. June, 1967
2) Ibid
​3) LeWitt, S. (1969) Sentences on Conceptual Art. In: Art and Language, No. 11. (May 1969) p. 11
​4) Celant, G. (2009) (First published:1988) The Sol LeWitt Orchestra. In: Sol LeWitt: 100 views. Eds. Markonish, D. and Cross, S. MASS MoCa in association with Harvard University Press, p. 27.
​5) de Waal, C. (2013 ) Peirce: A guide for the perplexed, London: Bloomsbury Academic. p.88.
​6) Baume, N. (2001) Sol LeWitt: Open cubes. Exhibition Catalogue. Hartford: Atheneum Museum of Art.
7) Lewitt, S. quoted in: LeWitt and Miller Keller, A. Excerpts from a Correspondence, 1981 – 1983. In: Suzanne Singer, ed., Sol LeWitt wall drawings, 1968 – 1984. Amsterdam: Stedelijk Museum, Eindhoven: Van Abbemuseum, Hartford: Wadford Atheneum, 1984. p. 18-25.
​

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