On Monday February 26, we’ll be presenting the results of last term’s Three Pillars of the Digital project as a Monday Evening Lecture (5:30pm in E002, KX). The last talk we gave in this programme, two years ago, outlined the goals and outlook of the Fine Art Maths Centre as a whole. Here’s Andrew with Part 2 (you can read part 1 here).
We approach mathematics as a creative practice, one that has been transformed in the last 100, 150 years. Increasingly, mathematicians would subscribe to the line that their subject is the ‘science of pattern and structure’.
As such, its possible connection to art and design should come to the fore.
We reiterate – school mathematics is largely comprised of eighteenth century techniques of calculation. It is not modern. FAMC counts itself amongst a number of pedagogical initiatives complaining about post-16 mathematics education and the dominance of calculus.
We live with the inherited consequences of an education system that forces poor choices on youngsters at 15 and ones still dominated by the desires of universities that teach science, medicine, engineering: they don’t want to teach calculus, so algebra and calculus suffocates the school curriculum.
There is lots of other maths. All of it is legitimate: much of what we teach is cloistered in the maths undergraduate curriculum for no good reason: it is appealing and amenable to students for whom numbers, algebra and calculation is a turn off.
This situation is exacerbated by poor academic organisation across the English university sector – marked by increasingly unproductive and entrenched divisions of intellectual labour.
Art – relative newcomer to the university structure – suffers here more than the established academic disciplines, because in truth art is not a discipline. It is not formed and defined by well-defined objects of study, techniques of presentation or methods of research.
Art lives on the absence of such boundaries and delimitations. All life, intellectual and otherwise, is open to art practice. Mathematics is no exception. This means that, like philosophy, art is non-disciplinary. Everything is open to art practice – every other discipline can become its material.
The prevalence of the digital and the complexity of contemporary life – where mathematics serves as the handmaiden to transformed technology and modern political economy of communication, information and complex asset structures – means that artists are increasingly drawn to mathematics and associated domains of knowledge such as computing.
This is a promise, a challenge and a demand.
Artworks are intellective and expressive: they relate to the world, raise and address questions, and can, in addition, appropriate philosophy and mathematics, inter alia, as material for their productions. Art can turn all to its own ends, but also is required to if it is to maintain the promise inherent in art – that it can express truth in previously unrealised or more powerful manner.
Viewed in this way, we can return to an older debate within German Idealism and its legacy from the nineteenth century onwards. The Jena Romantics, for example, characterised Art as the medium within which all knowledge, including Philosophy and mathematics, can be gathered and extended.
For the nineteenth century Romantics, the modern novel best captured this possibility: its form allowed for the results of modern disciplines to become material in a larger-scale construction. It led to the notion of the Gesamtkunstwerk – the composition that brings all manner of arts together with new and expansive expessive power.
What new forms are offered by computational power and the mathematics underpinning and organising it? By expressive power I mean to include all subjective capacities – sensibility, intellection etc. – the concept, in turn, underscores the debates around the superiority of particular arts.
This fundamental character of artworks is the truth underlying the magpie instincts and healthy autodidacticism of artists.
But this demand is threatened by a dilettantism or casual consumerism – these materials cannot be held together by the subjective attitude or enthusiasm of the individual artist.
What expressive power can be marshalled? Can the results of those technical disciplines be organised adequately?
In a slightly different context, the German philosopher, Theodor Adorno wrote:
Modern works … must show themselves to be the equal of high industrialism, not simply make it a topic. … The substantive element of artistic modernism draws its power from the fact that the most advanced procedures of material production and organization are not limited to the sphere in which they originate. [Adorno Aesthetic Theory p. 33-34].
These comments about high industrialism – think the film or computer game industry for a ‘visual’ comparison – apply also to the creative practices of mathematics. Can such a technical procedures be made amenable to the sphere of art? Arts and humanities has been shedding technical components of the curriculum over the last 30 years, missing the manner in which these technicalities embody alternative ways of thinking.
Maths as technical discipline does not give itself up to idlers in the garden of knowledge – its elements cannot be absorbed by osmosis or consumed in a single gulp.
As mathematicians say, you cannot ‘grok’ mathematics – it is something with which one wrestles continually and gradually one develops skills and insights.
But that resistance to appropriation is perhaps what is missing from the arts and humanities, which still seem beholden to a nineties idea of Theory, capital T, that offers little more than a jargon or a standpoint on the world, postmodernism still – in that it is consumerism at the level of ideas.
Much contemporary theory evangelises for maths and science, in the sense you might find in accelerationism or speculative realism. But this evangelism is not what is needed.
The evangelist brings the good news – but is not the source of the good news. The evangelist treats mathematics and science as a authoritative revelation rather than something that can become integral material for artistic production. Evangelism offers the semblance of participation – it worships maths and science inappropriately.
“Theory” replicates what Manny Farber in 1962 called the temptations of ‘gilt culture’, the ‘white elephant art’ that wants to make the big claims, wants too hard to be meaningful. Farber instead extols a
termite- tapeworm-fungus-moss art [that] goes always forward eating its own boundaries, and, likely as not, leaves nothing in its path other than the signs of eager, industrious, unkempt activity … eating away the immediate boundaries of art, and turning these boundaries into conditions of the next achievement.
[Farber, ‘White Elephant Art and Termite Art‘ (1962)]
Here then is the challenge and demand for undergraduate pedagogy.
In the abstract we can return to a vision from 100 years ago – Walter Gropius’s take on the Bauhaus:
The Bauhaus felt it had a double moral responsibility: to make its pupils fully conscious of the age they were living in; and to train them to turn their native intelligence, and the knowledge they received, to practical account in the design of forms which would be the direct expression of that consciousness.
Walter Gropius (1923)
Fully conscious of the age they were living in. Its workings, procedures and techniques. What mathematical topics are amenable without prerequisites to an authentic relation to art practice?
Our remit: Works get made that otherwise wouldn’t. Our primary aim is to create mathematics provision that sits naturally within the students’ disciplines. Our approach exposes students to new ideas, but also provides technical grounding when appropriate. Hopefully, artworks are then produced which would otherwise not get past initial ideas.
Success would be judged on that criterion – to open possibilities for skill development otherwise closed down for lack of technical support.
We have pioneered an innovative ‘no prerequisites’, ‘practice oriented’ approach to meeting the authentic mathematical needs of undergraduate and postgraduate art students.
Our workshops have concentrated on different aspects of geometry and programming. In tutorials recurring topics have included: group theory and symmetry; combinatorics; data analysis and visualization; 3D modeling and graphics engines; programming; perspective (especially in the context of sculptural and installation work).
Our students have also asked about: differential geometry; topology; linear algebra; financial mathematics; traditional calculating devices such as abacuses; game theory; Latin squares; tilings (including spherical tilings); polyhedra; optical illusions; hyperbolic geometry; symbolic logic; graph theory and the mathematics of rivers.
A 30 or 45min tutorial cannot exhaust any one of those questions. In many cases, we can only give guidance on where to start so that the magpie instincts can be directed initially in the most productive ways. Sigma fund us to cover any topic that might be covered on the first-year undergraduate mathematics curriculum, but we endeavour not to be bound by that disciplinary setting.
As we develop our project we plan to develop workshops in abstract algebra, group theory, graph theory and linear algebra.
Another caveat: Nor do we assume that our task is a one-way transmission of mathematical knowledge to artists, or the policing of legitimate application. Perspective and its mathematical underpinnings forms a central part of our provision – in this field, renaissance Italian artists pushed geometry forward by investigating new methods for organising the depiction of three dimensional space in the two-dimensional picture plane. Centuries later, mathematicians developed those insights into Projective geometry.
Instead of being a minor province in the empire of Euclid, perspective geometry was logically a much vaster empire. – Cayley
Tellingly, today, Perspective is disappearing from art education and what remains in diplomas and foundations appears ill-conceived and divorced from any intellectual content. We have had to go to comic book illustrators to pick up some of the fundamentals of three-point and curvilinear perspective or alternatives such as isometric and axonometric projections.
The ways of thinking encapsulated in alternative perspective systems are important for thinking about space – they are not simply outmoded representational techniques (or a kind of foreshortening).
Here, though it may seem we have championing a return to skills-based education, we are actually championing learning a broader range of thinking techniques. A broadening of vision. This is what we emphasise in our first FAMC publication on Euclidean Geometry – drawing-led, practice-led mathematics which brings ways of thinking to the fore, along with practical applications.
New (and old in the case of geometry) ways of thinking are needed – we are living through a phase where whole media may collapse as sites of autonomous meaning production. Not by any natural process, but because those involved did not meet the challenges and were content to do the comfortable thing, the familiar but moribund. Though the commercial afterlives may be sufficient for some.
It is self-evident that nothing concerning art is self-evident anymore, not its inner life, not its relation to the world, not even its right to exist. … It is uncertain whether art is still possible; whether with its complete emancipation, it did not sever its own preconditions.” Aesthetic Theory p. 1
The separation of mathematics from art subjects is ingrained, but is a historical accident – a result of the histories of educational institutions and policies rather than anything that follows from the disciplines themselves.
Both art and mathematics are involved with creating concepts and new ways of seeing. What we hope to achieve by highlighting visual and spatial mathematics is that potential connections are closer than commonly imagined.
There is no shortcut to this mediation and what we offer at FAMC is only a first step towards achieving the potentials that may lie therein.
Mathematics is not about being good at mental arithmetic as it was until 200 years ago – it is about learning to see and present things in new ways through the creation of abstract concepts.
Grothendieck described mathematical creation as follows:
a vision that decants little by little over months and years, bringing to light the ‘obvious’ thing that no one had seen, taking form in an ‘obvious’ assertion of which no one had dreamed
When I read that, it seems as if art’s terrain had been stripped from it. The challenge for art is to demonstrate that this is not the case. And it may be that this new age of computer-led visual or spatial mathematics again, as in the renaissance, opens the possibilities for new artist-led discoveries.
The modern world is very different even from that of twenty years ago. There are plenty of quick takes on the contemporary world being peddled, but a practice that is adequate to today may need to take new steps into the abstract the better to underpin practice with intellectual firepower.