Escher and Coxeter: a mathematical conversation

On Monday 5 June 2017, Professor Sarah Hart from Birkbeck’s Department of Economics, Mathematics and Statistics gave a prestigious Gresham Lecture at the Museum of London. Andrew Silverman, Learning Development Tutor in the School of Business, Economics and Informatics reports on the lecture.

Gresham College crest in hyperbolic geometry. Credit: Sarah Hart

Gresham College crest in hyperbolic geometry. Credit: Sarah Hart

Gresham College was founded in 1597 and has been providing free lectures within the City of London for over 400 years. Walking down from the dusty roads of the Barbican into the cool and quiet of the Weston Theatre, the audience was transported into a conversation between an artist and a mathematician, Escher and Coxeter. Told with infectious excitement and humour, Professor Hart wove the story of the lives of these two figures and their friendship through the mathematics and the artwork that fed into one another.

Born on 17 June 1898 in Leeuwarden, Holland, the youngest of five brothers and moving with his family to Arnhem when he was five, Maurits Cornelis Escher would eventually go on to study at the School for Architecture and Decorative Arts in Haarlem. His father was a civil engineer and his brothers all became scientists. Escher himself almost became an architect before switching to graphic arts. He later quipped that it was only by a hair’s breadth that he escaped becoming a useful member of society.

Escher began by producing woodcuts and lithographs featuring mainly landscapes. An example of this was the 1931 lithograph Atranti, Coast of Amalfi. But in 1936 his work went in a new direction, becoming more abstract; according to Escher, he had replaced landscapes with mindscapes. The woodcut Metamorphosis I, produced in 1937, exemplifies this change and is clearly a ‘mindscape’ adapted from the 1931 piece.

What could have triggered this change? In 1922, Escher visited the Alhambra palace in Granada, Spain; his second visit was in 1936. The buildings we know today were constructed in the mid-11th century by the Moorish king Mohammed ben Al-Ahmar. One of the key points about Moorish art, and Islamic art more generally, is that it is not permitted to contain images of living things; it is instead rich in symmetry and tessellations of tiles. Escher was able to combine this richness of geometric design with images of ‘living’ things (albeit at times mythical living things), thereby leading to works such as Angel and Devils (1941), produced in ink rather than wood.

Donald Coxeter, or Harold Scott Macdonald Coxeter, was born on 9 February 1907. His name was originally going to be Harold Macdonald Scott Coxeter, until they realised that this would have been HMS Coxeter, more a ship name than a baby name, and so the name was changed. As a schoolboy, Coxeter became so engrossed in geometry, at the expense of other subjects, that one teacher told him he was only allowed to think in four dimensions on Sundays.

In 1936, the year Escher’s art took a new direction, Coxeter took up a post at the University of Toronto. When asked what the point of pure mathematics is, Coxeter responded: “No one asks artists why they do what they do. I’m like any artist; it’s just that the obsession that fills my mind is shapes and patterns.”

In 1954, the International Congress of Mathematicians was held in Amsterdam. To coincide with this, a major exhibition of Escher’s work was held in the Stedelijk Museum in Amsterdam. It was here that Coxeter and Escher first met, when Coxeter bought a couple of Escher’s prints.

Incidentally, another mathematician who visited the exhibition was Roger Penrose, who was a Reader and then Professor of Applied Mathematics at Birkbeck from 1964 to 1973, and later became Professor of Geometry at Gresham College, London. After seeing an impossible staircase in Escher’s Relativity print, he came up with the concept of a ‘Penrose triangle’.

Professor Hart explained the mathematics behind the regular tilings in three geometries: plane (Euclidean), spherical and hyperbolic geometry. She managed to put the concepts across in such a way that even someone with no prior knowledge could walk away with a good basic understanding, and the images presented were an excellent way of getting a more intuitive sense of what was really going on.

Escher learnt a great deal from Coxeter, to the extent that when Escher created a picture based on a new geometrical concept, he would refer to it as ‘Coxetering’. But in turn, Coxeter also learnt from Escher. For example, Escher’s 1959 work, Circle Limit III, led Coxeter to a new understanding of the hyperbolic disc. By looking at the spines of the fish in the image, Coxeter realised that Escher had found equidistant curves and produced them incredibly precisely. In this way their friendship was a true exchange of ideas – a mathematical conversation.

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Arts Week 2017: “Doing and thinking: methods in practice-based research”

Dr Maria Kukhareva, Educational Developer at the University of Bedfordshire reflects on the interaction of creativity and academia following a workshop as part of Birkbeck Arts Week 2017.creativity-academiaAs an interdisciplinarian (both by background and by own curiosity) I seek opportunities to be amazed by the way different disciplines and approaches interact, the conflict and tension borne out of this process, and the turbulent energy and questions it has potential to generate.

I recently participated in the ‘Doing and Thinking’ workshop during Arts Week, which gathered an exciting and diverse crowd of practicing artists, researchers, and artist-researches – both Birkbeck’s own and external enthusiasts, like me.

Here, I broaden the focus of the workshop and turn to the discourse around creativity, rigour and scholarship in higher education – and what it means for the creative practitioners and researchers, as well as the wider academic community.

“Is it alive or is it ref-able?”

What the workshop discussion demonstrated very quickly and relatively clearly, is that there seems to be a vast and deep ocean between the mysterious continent inhabited by the creative practitioners, and the equally mysterious land of “this is how things are done in academia”.

The ocean was represented by a heap of colourful cards with research (and life?) related words on our tables. As we were shuffling through them, we realised we could not agree on the meanings, values and emotions of some seemingly common words, for example:

impact (think: theatre performance versus academic publication)
serendipity and intuition as a driving force (think: visual arts versus systematic research)
discomfort and doubt (think: open creative process versus evaluation outcomes)

In fact, words and language in general continued to be the cause of frustration, namely the incompatibility of creative output (a painting, a book, a film) and the academic language accompaniment (a thesis).

One could almost imagine how creativity and its magic, so necessary for any artist’s existence, breaks into pieces on encountering the academic expectation. As if to become an academic scholar, an artist needs to give up a part of their soul in exchange for the gifts of rigour, systematic inquiry and strictly formatted self-expression and self-representation. As if the fruits of your labour can either be ‘alive’ or ‘ref-able.’

But… is this really the only way to cross the ocean?

“Follow your nose”

Let’s view creative practice – whether you are a professional artist, early researcher or an educator in any given field – as something you NEED. Whether it’s where you experiment, or where your intuition, or some other undefined drive pushes you to create news things. It’s where a part of your soul lives; it’s something that fuels your daily activity. It’s what inspires your signature pedagogy, your authorial voice and what gives it life – as demonstrated effectively by Emma Bennett, Katherine Angel and Catherine Grant.

If this is what your creative practice does, then not only does it not go against the ‘traditional’ academic activity, with its rigour, systematic approach, structure, format and language – rather, creative practice makes the academic activity possible and interesting, from teaching to publishing.

The messy, unstructured creativity with a mind of its own, should be preserved and nurtured, rather than ‘re-trained’ when entering the world of traditional academic boundaries and standards. As Thomas Fisher has pointed out, creativity can be a rigorous process.

In other words – ‘it’ needs to be alive to be ref-able.

I would like to invite the reader to consider the following questions:

  • How and where do your practice and research activity co-exist?How disparate or how close are these two preoccupations? Do they fuel or hinder each other?
  • Which one of these (research or practice activity) offers more scope for creativity?
  • How does your creative and experimental activity drive your signature approach?
  • And lastly, how can we preserve and nurture our creativity, while we are developing our academic identities and careers?

On that note, I am off to read Katherine Angel’s book!

Contact Maria Kukhareva:
University of Bedfordshire profile


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Arts Week 2017: Mr A Moves in Mysterious Ways: Selected Artists from the Adamson Collection

Martin Birch, untitled drawing (Mr A moves in mysterious ways). Credit: Adamson Collection / Wellcome Trust.

Martin Birch, untitled drawing (Mr A moves in mysterious ways). Credit: Adamson Collection / Wellcome Trust.

The Adamson Collection is, in every sense, a remarkable archive, encompassing a vast and varied body of work that spans both five decades of asylum history and myriad approaches to artistic practice.

Mr A Moves in Mysterious Ways: Selected Artists from the Adamson Collection, curated by Dr Heather Tilley and Dr Fiona Johnstone, features painting, drawing and sculpture selected from some 6000 art objects, all produced under the guidance of pioneering art therapist Edward Adamson (1911-1996) by residents at Netherne Hospital in Surrey, a long-stay mental asylum, between 1946 and 1981. As part of a launch event a panel discussion was held in Birkbeck Cinema, where therapists, curators and artists alike shared their insights into Adamson’s life and legacy.

David O’Flynn from the Adamson Collection Trust and Val Huet from the British Association of Art Therapists spoke respectively about the development of Adamson’s work and ethos; the process of securing and displaying the collection – a task fraught with challenges, curatorial and conceptual – and about Adamson’s continued relevance to art therapy today.

Adamson defined himself not as a therapist, but as an artist; despite being instrumental in the foundation of the British Association of Art Therapists, he did not align himself with any one theoretical position. Adamson was an independent thinker who maintained his identity as an outsider as an act of affinity for those whose work he inspired and preserved.

Initially engaged at Netherne as a researcher into the relationship between mental illness and creativity, Adamson’s job was to encourage patients to produce work for clinical analysis. However, after the study ended in 1951, he established a studio where residents at Netherne were allowed to paint freely. He came to believe that making art was therapy enough; that creative expression could provide people with a bridge back to themselves. Working in this way Adamson amassed a staggering amount of material, writing the artist’s name and date of completion on the back of each piece, and so preserving not only the art object but the personal narratives of individuals otherwise anonymised by institutionalisation.

In exhibiting the work he collected, Adamson believed he could reengage the artists with a society that excluded them, and challenge pre-conceived ideas about the capacity of the mentally ill to contribute meaningfully to culture. As Val Huet emphasised in her talk, Adamson’s lasting impact upon contemporary art therapy was in situating “art at the heart” of therapy; extending artistic agency beyond the borders of allotted therapy time. As continued cutbacks to mental health budgets put pressure upon this practice-based approach, a reassessment of Adamson’s pioneering work becomes more topical, timely and, potentially, radical.

Beth Elliott, a trustee of Bethlem Gallery, and their artist-in-residence Matthew, spoke about the development of artistic practice inside the institution, and the unique pressures, restrictions, and surprising affordances of the clinical environment. Matthew’s description of his own process, together with the slides of his vibrant and luminous artwork, was a clear argument for the persistence of practice at the centre of therapy, demonstrating how art within the asylum can be an imaginative escape, a tool for navigation, and a strategy for resistance.

Invigorated by the talks, people headed towards the Peltz Gallery where the work of eight artists is on display, including pieces by Martin Birch from whose arch drawing of Adamson the exhibition takes its title, and Gwyneth Rowlands, whose eerie and arresting painted flints were my personal highlight of the exhibition.

It is worth noting that this is the first time the artists have been named in an exhibition; their work attributed to an individual with a unique aesthetic outlook and approach, not shown as an undifferentiated mass of “asylum art”.  From Mary Bishop’s bold blocks of Constructivist colour to Rolanda Polonsky’s intricate, spooling pencil drawings, the work defends its right to be considered first and foremost as art. This exhibition asks us to consider the meaning of the phrase “outsider artist” and where in that description the emphasis should be placed.

Mr A Moves in Mysterious Ways interweaves a diverse array of narratives – personal and medical. It is an insight into changing psychiatric practice, a celebration of Adamson’s work, and also a testament to eight unique artistic visions and histories.

Fran Lock is a poet and practice-based PhD student in her first year at Birkbeck

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Arts Week 2017: Science as Spectacle

A Magic Lantern Slide Lecture on St. Peter's Basilica, 1897  An illustration from the December 1897 catalogue of T. H. McAllister Company, Manufacturing Opticians, New York

A Magic Lantern Slide Lecture on St. Peter’s Basilica, 1897
An illustration from the December 1897 catalogue of T. H. McAllister Company, Manufacturing Opticians, New York

Ushered into the dark cinema of Birkbeck, the curious spectators witnessed Science as Spectacle. Over an hour and a half on the evening of Tuesday 19th May 2017, Jeremy Brooker, Chairman of the Magic Lantern Society, demonstrated the workings of the magic lantern.

He began by setting the scene with a brief history of the import of the magic lantern on society. He told the story of Faraday’s presentation in January 1846 to the Royal Institute and was not shy when it came to making it clear that, actually, technologically, what Faraday was displaying was nothing particularly impressive given the popular magic lantern shows taking place at the time.

And this was the crux of the presentation: the lantern’s dual purpose for both entertainment and research. The population were now able to see “actual experiments happening in real time before their eyes.” This capability of the magic lantern was displayed in an archive film of thawing ice. Now, through the magnification properties of the magic lantern, one could peer over the shoulder of an experimenter and see what was being done. Jeremy revealed that people of the time were particularly disturbed upon finding out what was living in their drinking water.

But at the same time, the magic lantern was also being used to show things that were not there. The more familiar history of the magic lantern is for its use in phantasmagoria shows, creating ghostly effects that titillated and terrified the audience. Jeremy and partner Caroline displayed the abilities of the magic lantern as entertainment and Birkbeck cinema witnessed popular magic lantern displays of distant lands, changing seasons and, yes, a vanishing ghost and skeleton or two.

What was remarkable about the display was how science and entertainment were so interlinked. The projectionists at the time realised the capabilities of their tool to both entertain and educate and so, for a time, the two went hand-in-hand. After we were shown the layers of matter that make up the human body, we were rewarded with a skeleton jumping a skipping rope. Similarly, whilst we admired the beautiful vistas of icy landscapes under the rippling Aurora Borealis we also learned something about the geography of distant lands. As the precursor to film and demonstration, the magic lantern projectionists knew that both entertainment and education were of equal importance, making the learning engaging and the enjoyment worthwhile, a lesson that is all too often forgotten on both sides today.

This is not to mention the technical ability of the projectionists themselves. Layering slides via three projectors, working the mechanics of the individual slides and managing the transitions required an artistry and practice that was as entertaining and impressive as anything appearing on the screen.

Ultimately, on Tuesday night we were shown not how the machine worked technically but what the magic lantern did for Victorian society. By not dwelling on the technicalities it remains a medium that is exciting, mysterious and indeed a little magical.

Jonathan Parr is studying jointly at Birkbeck and RADA on the Text and Performance MA

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