This Is Tomorrow – Day Five: Maths
After yesterday’s musings on the importance of reflexivity, Maths starts with a perfect demonstration. Head of department Prof. Colin Sparrow – imagine a dry, jovial Alfred Hitchcock – starts us off with a lecture entitled What Is a Maths Department? In it, he details the currents in which they swim: the financial ins and outs, the institutional politics across the university, the impact of higher education policy and tuition fees and so on, and the cross-departmental research efforts.
So what is a maths department? It’s simultaneously a school, a research institute and a hotel and catering service. It’s one of the university’s top departments and a profit-making enterprise. (That profit, Sparrow explains with a gag: Maths is cheap because all you need is a pencil, some paper and a waste paper basket. Sociology’s cheaper. You only need a pencil and paper.)
But it’s also something else. Care in the Community, as Sparrow jokingly puts it. “Looking after this group of people would be more expensive in any other way,” he says. His voices – snail slow and deep – could have been designed for this parched humour and his off-the-cuff gags leave a giddy group of over-tired artists falling about. Sparrow describes part of his role as the troll at the bridge, standing guard at the gates, determinedly not letting the university know what’s going on within and, likewise, not letting those within be affected by whatever’s outside. A maths department, says Sparrow, is “a world largely of our own creation. We entertain ourselves.”
This is, I think, what stays with us all on a rainy Friday; the space, and this goes beyond its physical make-up, that the maths department has opened up. There is something deeply affecting about its spirit. It feels borderline utopian.
Before I go into that, however, I want to zip back to Sociology, to the space I resisted writing about yesterday. In the afternoon, Cath Lambert walks us over to the department’s flexible learning space. It takes about fifteen minutes to get there – a measure, perhaps, of the university’s initial scepticism about the concept. It used to be a student bar, but in the hands of the sociology department it’s become something completely different.
At first glance, it’s rather like a rehearsal room. It doesn’t feel like a room, so much as a space. The walls are white, the roof is high and there are windows all around it. It has the dimensions of a small barn. Beams stretch across the ceiling, below a corrugated roof. Lining the room is a series of lightweight plastic benches, brightly coloured blocks and, in the corner, a clump of saggy yellow beanbags. All of these are returned to position at the end of every session.
That means you step into an empty space. The floor poses a challenge. Any group must therefore negotiate the space and build their own classroom in the moment. The space is one of possibilities. One could line up benches like church pews or scatter beanbags around for individual work. We instinctively use the coloured blocks to form a circle, about the size of a campfire. But even then, there are further options. Some of us perch upright. Some straddle. Some adopt yogic positions. Some sit on the floor and use the block as a backrest.
This space is innately political. Theoretically – though it is, of course, possible to imagine its misuse – it empowers the individual as part of a group and challenges a group of individuals to find its own spatial equilibrium. By not imposing a fixed model, it allows the formation to fit the purpose and the moment. There’s something rather inspiring about that, particularly in terms of performance. How might we allow an audience to shape their own space, to negotiate the terms of this fleeting encounter?
Back to Maths and there are echoes of that freeform model. On almost every wall in the department – in classrooms and offices, in lecture theatres and foyers, in corridors and common rooms – there’s a blackboard. All of them are painted a deep, studious green; a green that’s somewhere between lagoon and swamp; pond green, with just enough algae to maintain the ecosystem but not overrun it. The department has, Sparrow explains, resisted the push for whiteboards, which are ubiquitous elsewhere, and stuck to its chalky guns. All their teaching is done on blackboards. Working with chalk – as awkward as it is – slows the teacher down, allowing those watching to absorb in real time. Several times we’re told that the blackboard enforces the right pace for the human brain.
It’s not just that they use blackboards, however, it’s how they use them. As I say, they’re everywhere, and it’s not unusual to see two people hovering, chalk in hand, in the corridor. At some level, these are their notebooks and, because they’re public, learning and research inevitably becomes collegiate. At around 10.30 that evening, in the middle of a conversation, two of our hosts leave their chairs and chalk up some complex matrix or 3-d graph. Maths just bursts out. Whenever and wherever it strikes, there’s a blackboard waiting.
The blackboard is, in many ways, the mathematicians’ stage. It’s a public space and, as such, rather fascinatingly, chalking something up almost always takes on a performative quality. No one stands by the side and dully clicks through a Powerpoint presentation. Here, there are jokes, about irrational numbers, about knots, about the probability of winning the lottery. There’s flair – a single twist that inverts an equation is presented with a ‘way cool’ flourish – and that flair almost becomes competitive; a sort of Maths B-boying, as Charlotte Vincent puts it. It’s also artistic. They use colour and shapes in demonstrations, admittedly first and foremost for clarity, but everything – the click and clacker of chalk, the formations – is easy on the eye. Perhaps it’s hypnotic, so that information can storm the brain by stealth.
Then there are the spaces within the department. The department’s common room is open and, with it’s purple chairs and green carpet, aesthetically pleasing. There are some surprising furnishings: a fish tank, a globe, an old seminar schedule scroll. And there’s art on the walls: a large abstract canvas – not regimentally abstract, as one might expect, but chaotic swathes of paint – and a portrait of the department’s founder, Prof. Christopher Zeeman, in a swish pink-and-white patterned shirt. His principles still very much govern the department’s operations. The point, however, is that this is not an empty, sterile space. It’s just right – and I can’t pin that down much further. There’s just enough clutter to perform; it takes the edge off any pressure. This is a think-space, but it’s a world away from the rigidity of those precision-engineered beanbags in Manufacturing. You could get lost in thought here all too easily.
That’s the quality that marks out the maths houses. A half-hour walk from the main campus there are six brick modules – probably futuristic once, now reminiscent of German bunkers in northern France – arranged in a circle. This is where visiting lecturers and researchers stay. Build in the late 1960s, brutalism without the sharp edges, they’re listed buildings now. Each has a room at the back, separated from the rest of the house by two doors, with a bed and a desk and a blackboard running uninterrupted all around the room. There are no corners and only two windows, facing onto fields, allowing the mathematician to keep scratching away without doubling back. It’s a cubbyhole, cut off from the rest of the world, designed for hard thinking at all hours of the day.
Back in the department itself, all our seminars take place in communal areas. We’re not alone in that. Other groups are clumped around tables in corridors. Prof. Robert MacKay gives us a presentation on Complexity – the study of immense, tangled systems of individual parts in intricate arrangements, full of clashing feedback loops and interruptions. He hosts it in an atrium, with a higgledy-piggedly scattering of institutional armchairs. As he talks, people pass, look over, slow down, then sit down and listen in, and, over 90 minutes, our numbers almost double. It fuels a fascinating conversation – about whether intuition can, theoretically, be tracked back as a subliminal mental process, about the internet as a combination of both oral and written traditions (“Verba Volant. Scripta Manent.,” a mathematician chips in: spoken words fly away, written words remain), but it’s the simple fact of the spatial dynamic that’s astonishing. If your interest is piqued, pull up a chair.
Mathematicians aren’t a tribe in the same way as other departments. There’s no uniform here, be it suits or slacks. Instead, they make an eclectic conglomeration of fleeces, battered leather jackets, jazzy shirts, waist-high jeans and almost everything in between. There’s a 68-year old professor famous for wearing shorts at all times, bar lectures. Today, apparently, he’s wondering around in a pair of thigh-high denims. Anything goes. There’s no judgement whatsoever here. It would be remiss not to mention that, sometimes, you have to work a little harder in conversation here than in other departments, but I think the mathematicians would be the first to admit that, taken as a whole, social skills might not be their strongest suit. What’s so unusual, however, is that in this space, you don’t begrudge them that in the slightest. There’s a very particular freedom here; a mix of protection and permission. It’s really rather heart-swelling.
In fact, sat around after dinner, there’s a moment that very nearly moves me to tears. Asked what drives him, Saul Schleimer, a topologist (the study of shapes) with a habit of massaging his forehead as one might a tennis star’s cramped thigh, explains that there are just things he’d like to know. He can’t find it all out himself, so he’s enlisting others to join in the search. Sparrow talks of teaching as building a scaffold behind you, so that others can secure the supports while you climb onwards. What we all soon realise is that the top of that scaffold can be a lonely summit. Schleimer reckons that there are about 30 people in the world that he can talk to about his chosen subject without having to start by explaining. There are 30 people, out of all 7 billion us, that he can talk to on a level. It’s a striking moment, but then Chris Goode echoes that thought; he feels the same, only his 30 are chosen – if one can use that word – based on an affinity, be it political, aesthetic or just friendship.
There’s another space, of course, behind all of this that has, thus far, gone unexamined: the university itself. It’s about day three that I – we – begin to feel – really feel – the emphatic absence of the rest of the world. You walk through the streets of Warwick and somehow feel cut off, as if the surrounding fields might just stretch on forever. I’ve hardly glanced at a newspaper or website. I’ve not watched a second of television. Add in the fact that everything you need just appears – we’re fed when we need feeding, caffeinated when we start to lag, our beds are made, our schedules fixed and our journeys taken care of by cabbies – and something starts to shift. Four of us are at Coventry station on Saturday morning – another space altogether – and, conferring, we discover that, despite mental exhaustion, we’re all thinking faster, harder and better than we have in ages. I’d written 1,000 words in 45 minutes that morning. Chris later emails to say that, on getting home, he was told he was speaking double-speed.
This, beneath it all, is what This is Tomorrow is about. The word disruption comes into play halfway through the week. Disruption of routine. Disruption of thought. You’re encountering new ideas, sometimes completely opposed to those that have become habitual, all week. You’re absorbing and assessing at the same time; positioning yourself in relation to them and forging connections between them. At the same time, we’re forging connections within the university, pointing academics towards colleagues they didn’t know existed, cross-pollinating ideas we don’t fully understand. We disrupt as much as we are disrupted.
To end, let’s pop back to maths and, specifically, back to blackboards. It’s 7.30 on a Friday night; the last night of term, in fact. Elsewhere on campus bags are being packed, books are being crammed and tinnies and Lambrinis are being downed. In the Maths common room, a gaggle of post-doctorate students are gathered around a blackboard. Some are stroking their chins. Some are fiddling with chalk. On the blackboard is a three by three gird, a noughts and crosses board, and in each square, there’s another noughts and crosses board. They’re playing.
The game is called four-dimensional noughts and crosses. To win, you only need one line of three in any of the small grids. However, only one small grid is in play at any given time. Which one is determined by which square the previous move is played in. Play bottom right on a small grid and the bottom right board comes into play. The aim, then, is to force your opponent into particular boards at any given times. It looks incredibly complex. It’s actually rather simple as a rule-set, if not in practice. This is noughts and crosses with the requisite forethought of chess.
It is, however, another heart-warming sight, not unlike the coda of hope at the end of a five-act play. The blackboard is, above all else, a space of play. So, in a funny way, is the whole maths department and – zoom further out still – so is the university as a whole.