Source: Miles Cole

Like the physics of a black hole, the novel¡¯s plot is simple, yet confounding

Someone must have misled me, for one fine morning, without having done anything wrong, I was teaching a book I could not understand. Or channelling Franz Kafka, so I told myself earlier this year while leading a senior seminar on his novel The Trial. Unlike the protagonist Joseph K., who never seems to wonder how this happened, I am asking myself not just how I found myself in this situation, but what the experience might mean for my vocation as a teacher.

Rather like the physics of a black hole, the novel¡¯s plot is straightforward, yet confounding: Joseph K. wakes up one day to find his apartment commandeered by strange men. Representing a shadowy legal system, they announce, between bites of K.¡¯s breakfast, that he has been charged with an unidentified crime. One year later, still ignorant of his crime, K. is executed in equally dark, yet farcical circumstances.

My own story is, if not as shocking, nearly as simple and slapstick. A historian of modern France, I had agreed to teach a new class with a good friend and colleague from the English department, David Mikics, on the history and literature of nihilism. Our notion was that the word is most often misused or abused, banalised or satirised; our goal was to salvage its meaning and take the measure of its contents. And so, our syllabus proposed one itinerary among others of nihilistic thought, tracing its path as it careered between the pages of fiction and history over the course of the 19th and 20th centuries. After a long look at the Book of Job, which framed several questions we wished to ask, we leaped to Stendhal¡¯s The Red and the Black. With a steady gait, we then read Turgenev¡¯s Fathers and Children (as it was called in our translation), Dostoevsky¡¯s The Brothers Karamazov, bits and pieces of Nietzsche and Schopenhauer, and I. B. Singer¡¯s Satan in Goray.

While these works posed all sorts of interpretative challenges, they also offered many footholds. Not only was it fairly easy to situate them in their various historical contexts, but we could also situate ourselves, though with greater effort, within the text. The narratives, though subtle and complex, follow clear arcs, while their protagonists, no less subtle and complex, invite the reader to explore the ways in which their stories can be grasped, perhaps even applied to our own lives. They offer, in short, what the literary theorist Wayne Booth called friendship: ethical guides to how we might best lead our lives.

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But then, little more than halfway through the semester, we began Kafka. And though we finished the novel two weeks later, Kafka has not finished with us, or at least me. I remain stymied by a book that refuses narrative. Or, which is more or less the same thing, a book that refuses meaning ¨C and seems to accept this state of affairs. Gershom Scholem, the great scholar of Jewish mysticism, described Kafka¡¯s world as one bathed in revelation, but ¡°a revelation seen of course from that perspective in which it is returned to its own nothingness¡±. Of course? I asked myself this question, with equal measures of despair and derision, as I tried to lead my class through the novel. Rather than offering an arc, the story flatlines from its harrowingly ludicrous opening to its ludicrously harrowing end.

This is not to say the novel did not enthral my students ¨C it most definitely did. But what was the nature of this attraction? Was it because its indescribable dreadfulness had been domesticated by countless seminars and syllabuses, commentaries and criticism? I could not help but recall Lionel Trilling¡¯s disenchanted riff on the appeal of the abyss, which announces to students: ¡°Interesting, am I not? And exciting, if you consider how deep I am and what dread beasts lie at my bottom. Have it well in mind that a knowledge of me contributes materially to your being whole, or well-rounded, men.¡± Or, was it that the students, more knowing and sensitive than Trilling allowed, chattered busily to suppress the knowledge that this particular abyss has no bottom?

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To be honest, I babbled more busily than they did. How could I not? No doubt because I am a historian, I am irrevocably yoked to the belief that narratives are essential to our collective and individual identities. As a historian, I spoke about the predicament of Jews living in the ramshackle and Byzantine Austro-Hungarian empire on the eve of the First World War. As a German-speaking Jew in Prague, a city convulsed by Slavic nationalism and virulent anti-Semitism, was it not possible that Kafka grafted his acute sense of isolation and alienation on to Joseph K.? Indeed, was not K.¡¯s situation, as Kafka drafted his story during the summer of 1914, hauntingly similar to that of his contemporaries? Was not Europe about to tip into a cataclysm ¨C sentenced to death ¨C for reasons no one could explain or fathom?

Historical interpretations: I had a million of them, as I did biographical readings. Listen, I told my class, Kafka broke up with his fianc¨¦e Felice Bauer shortly before he began writing The Trial. And in his diary he described his climactic and turbulent meeting with Bauer as his trial. Even autobiographical references were not wanting: at that very moment, I was enmeshed in a hallucinatory situation with the university administration, one that seemed scripted by Kafka and bizarre enough to make me laugh. Although I refrained from discussing this in class, I prided myself that this experience sharpened my ability to teach the novel. When I told students that Kafka, when he read aloud the first chapter to his friends in Prague, frequently shook with fits of laughter, I thought of my own travails.

But, of course, my bureaucratic struggles were not at all like K¡¯s, while my historical allusions failed to make full sense of the novel. A few of my students described the novel as a labyrinth, and they are right. But rather than the Minotaur waiting at the centre, there is something far worse: nothingness. My various glosses, I realised, were confessions that the narrative, like that black hole, swallows orbiting interpretations, along with light itself, leaving nothing behind but its own nothingness.

For the German satirist Kurt Tucholsky, The Trial was unlike any other book. After a few dozen pages, readers know the sort of book they are dealing with. But with Kafka, not so much: ¡°Here you know nothing, you grope in the dark. What is this? Who is that?¡± Indeed. These questions are not answered because they cannot be answered. But as a historian and teacher, I wonder if this is truly our predicament. It is perhaps too much, or too naive, to expect hope from a narrative. Yet shouldn¡¯t our students at the very least expect more than mere despair? Like Tucholsky¡¯s response, so too my response not just as a reader but also as a professor: what is this and how do I profess it?

Robert Zaretsky is professor of history in the Honors College, University of Houston.

I had a doctorate in the subject ¨C what could possibly go wrong?

My guilty secret is that the topic I have found the most difficult to teach is the one I know most about: the origins of the Mau Mau Emergency in colonial Kenya. Picture the scenario, fellow teachers: one of the most complex subjects in African imperial history, second only to the ¡°scramble¡± for Africa; a compelling story full of murders, oathing ceremonies and white people behaving badly that led to one of the most tragic and unnecessary episodes in 20th-century decolonisation. Add to this bright enthusiastic undergraduates, never having ¡°done¡± Africa, so chomping at the bit. Finally, yours truly: author of doctorate on its origins; author of book on said origins; and author of three articles on, yes, you guessed it, those damn origins. What could possibly go wrong? Answer: just about everything.

When you know (or think you know) a lot about a subject, the tendency is to both under- and over-prepare at the same time. By that I mean I actually thought less about the structure of the lecture and seminar than other topics. I felt safe in the knowledge that I had about 60 pages of notes and lecture handouts that were thicker than Tom Cruise¡¯s insoles. As a result, 30 minutes into the lecture, I was on slide number 45 of my PowerPoint presentation¡­

Unsurprisingly, glassy-eyed students started to fade and cross their arms. Ten minutes before the end I was still only halfway through my material. I had gone into too much detail on the history of colonial occupation in Kenya; the crisis of moral authority in Kikuyu civic culture; the political economy of land shortage; breezily summing up the Governor ¡°asleep at the wheel¡±, as an epitome of the dialectics of domination, the contradictions of colonialism and the crisis of patriarchy¡­

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The next year, I tore up my notes and deleted the PowerPoint slides. I started from a blank sheet of paper and closed my eyes, asking ¡°what image first comes to mind for 1952 Kenya?¡± Three Hobnobs later, it was a photo of a young Princess Elizabeth next to a dashing Prince Philip, looking at a trout stream at Sagana fishing lodge, which she had been given as a wedding present by the ¡°people of Kenya¡±. At nearby Treetops, she would be told that her father had died. Eureka! It unlocked the topic as it needed to be told to second-years. I now teach it as a race war, using just three big crisis points. I start with the famous photo. When I come to write this up as a textbook, I will use this picture to explain why, from this moment, such a powerful symbol of white innocence, vulnerability and goodness doomed Mau Mau to be so misunderstood and mishandled.

Joanna Lewis is lecturer in the history of Africa and the British Empire, London School of Economics.

Questions often have two right answers, but students confuse them

Here is a topic that stands out in my mind as being particularly challenging to teach.

If you asked me, as someone who studies animal behaviour, ¡°why do blackbirds sing?¡± I could answer that question in one of two ways: either in terms of ¡°proximate factors¡± or ¡°ultimate factors¡±. First-year students often find it difficult to understand the difference between the two.

Proximate factors are those concerned with mechanisms, while ultimate factors are those concerned with evolution.

So the proximate explanation for why the blackbird sings is this: the increase in day length in spring triggers changes in the bird¡¯s brain; this results in the release of certain hormones that cause the testes to grow and produce testosterone; and this, in turn, stimulates the bird to sing. That is the physiological mechanism of birdsong.

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What is the ultimate explanation? By singing, male blackbirds (only males sing) simultaneously announce their ownership of their territory (telling other males to keep out) and their availability to females (¡°come on in¡±). Blackbirds cannot breed without either a territory or a partner, so singing is adaptive in that it ensures that blackbirds reproduce ¨C obviously an evolutionary advantage.

Almost all biological questions can be considered from these two different perspectives: they are both correct, but students often confuse them. The problem is exacerbated because biology is often taught by academics who consider only one or other of these processes. Physiologists or molecular biologists typically think only of proximate explanations; evolutionary biologists typically think only about ultimate explanations.

You can test students¡¯ understanding by asking them the proximate and ultimate answers to questions such as: Why do mole rats give up the opportunity to breed themselves in order to help their relatives breed? Why do owls lay white eggs? Why are male and female chimpanzees so promiscuous?

Tim Birkhead is professor of behavioural ecology at the University of Sheffield.

I ask the first-years if they would die for anything. Of course they would

Every term I make a point of teaching Plato¡¯s Apology to a crew of first-year students. And every term I come very close to regretting it. Students just don¡¯t get it. They think it¡¯s stupid. Why doesn¡¯t Socrates just shut up, quit ¡°corrupting the youth¡± and save his lousy skin? It is not a bad question, but the whole point of the Apology, of course, is to convince a reader that there are worse fates than death ¨C such as living a wicked life.

It is a lesson that¡¯s a little hard to swallow. So I turn to an argument by analogy and I ask questions, lots of them. I ask my students if they would die for anything ¨C really, anything. Of course they would: their parents, their siblings, their best friends, their little dog named Fuzzy. I then ask them to imagine the decisive moment when they decide whether or not to sacrifice themselves for the things that they value most in life. And what if they faltered, what if they decided to let Fuzzy get run over by a bus instead of risking life and limb to save him? The students agree that the guilt would be horrible; indeed, some even go so far as to say that the guilt would be worse than death. And they are not wrong about this, according to Socrates. To give up on those precious things that make life worth living is in fact a form of moral suicide, worse than any physical torture.

But Socrates doesn¡¯t die for Fuzzy. As a philosopher (a true friend of wisdom) he dies for the chance to pursue Truth. And students still don¡¯t get this. Truth seems so abstract and impersonal. Not the sort of thing that is worth dying for. And death, after all, is so immediately scary. So I ask them what is so wretchedly frightening about death. I really ask them. Most of them, after a lot of arguing, agree that what is most terrifying about death is the prospect of coming to the end and discovering that you haven¡¯t lived a particularly good life. That is scary ¨C so final, so helpless, so tragic. I ask them what makes a life a good one. What makes a life worth living? It seems like a natural question. They have trouble answering (like all of us do), but they agree that the question is an important one. Perhaps the most important. Getting an answer to this question ¨C a defensible, meaningful answer ¨C allows one to give a good account of his or her life. And that is, after all, what we want the most when life delivers us to our unexpected end.

I wait a good 30 seconds. Let it sink in. And then let them know that the Apology comes from the word apologia: an account or defence of one¡¯s life. And it turns out that the dialogue isn¡¯t that ¡°stupid¡± after all.

John Kaag is associate professor of philosophy at the University of Massachusetts Lowell.

Students are reluctant to think about how maths fits into the messy human world

For many school and college students, part of the attraction of mathematics is that there seem to be absolutely correct answers. When they get to university, these students may feel more comfortable doing calculations than thinking about complicated human situations. Yet in working life, of course, we encounter complicated human situations on a daily basis. When I began my first job as a mathematician in industry, it was a shock to find that mathematics could have a subjective element, that a fast, approximate answer might be more useful than an exact but slow one and that the way in which one presented mathematics could influence its reception.

My motivation for teaching a final-year module on Mathematics and Society is to bridge that gap by helping undergraduates appreciate the human context of applied mathematics. Students can find it a challenge: they expect maths questions to be clearly defined and to have a single right answer; they like doing hard maths and they are often reluctant to think about how this maths fits into the messy human world. This isn¡¯t what they expected from a maths degree.

I¡¯ve found that role play exercises are a good way to engage the class in complex moral and mathematical situations. Students are presented with different scenarios, which exaggerate the dilemmas mathematicians might face. For example, there is a health scare. With a general election imminent, the factory implicated is in the prime minister¡¯s constituency. The mathematicians have to present the inconclusive results of their analysis to civil servants, who in turn have to recommend whether to take action or to prolong the uncertainty while further research is carried out. Teams of students prepare presentations. The rest of the class play the part of the press, and question the presenters.

In the final debriefing, the most effective question is ¡°Which 10 seconds of the press conference will appear on tonight¡¯s television news?¡± That¡¯s the point at which the presenters realise that sometimes it is the best soundbite, rather than the whole presentation, that will determine the public view of the issue.

Even if (or because) the scenarios are highly exaggerated, and presenters ham it up, students usually report that they have learned a lot. They tell us that they feel much more aware of the issues mathematicians encounter in their professional lives. Some have described it as the best learning experience of their degree.

The main thing I hope students will have learned from the module is that outside the lecture theatre and the exam room, the maths doesn¡¯t always speak for itself. l

Tony Mann is director of the mathematics centre at the University of Greenwich.

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