The Combination Room
Gordon Handley Professor of Mathematics } Trinity College
Sanjeev Ramangita Handley’s student and protégé }
Bernard Rushwell Professor of Philosophy }
Ludolph Wittgemein Rushwell’s student and protégé }
James Canard-Means Professor of Economics } Kings College
Soft April sunlight filtered through the narrow windowpanes of the Combination Room, gilding the tousled hair of a lone man not yet of middle age. His garb was unconventional; grey herringbone tweed trousers, a cricket sweater and a knitted scarf. He had draped a second sweater, of a drab colour, over a wooden framed mirror, opposite to where he sat in a high backed, wicker chair.
He was of slight build and rather short, his legs barely touching the floor. A cigarette protruded at an angle from his compressed lips, as he concentrated on aligning a walnut exactly between the jaws of a nutcracker. When the necessary precision had been achieved, he squeezed the nutcracker hard, using both hands. The nut skittered across the wooden floor, disappearing under the oak table.
“Blast,” he said, snatching the cigarette from his lips, parking it in the ashtray on the table. He contemplated taking a new nut from the bowl, but his sense of duty, not to mention tidiness, forced him to jump up and search for the nut beneath the table.
The errant nut had lodged in a crack between the uneven boards. He was just reaching for it when the heavy door to the room creaked open. Jerking upright, his head struck the underside of the table.
“Drat it all,” he shouted, backing out without the nut.
From a kneeling position, he turned his head to see the round, fleshy features of his student peeping round the door.
“Handley,” the face hissed, through stained teeth and fleshy lips, “I must speak with you at once.”
“What is it Sanjeev? You know the senior rooms are reserved for Fellows only.”
“I know Handley. You are topmost professor and I am still very low, but I have damaged the WC in the staircase, and I don’t know what to do.”
“What do you mean damaged?” Handley asked, rising to his feet.
“It’s the pump-action. I pull the chain, many, many times, but always there are many unhappy returns of the bowel motion.”
“You should report it to the porter. Well, come in, for God’s sake, you’re creating a draft.”
The door opened to reveal a rather uncouth figure in his late twenties, stout and not recently shaven.
“Now you’re here, you’d better sit down. I’ll cover for you if anyone comes.”
“Oh, thank you Handley. But I must explain, the motion was not mine, but some other dirty fellows’. I am still in need of relief, you see.”
“I don’t think I need to know the details, thank you, Sanjeev. As long as you do use the WC and not the garden bed, I will be satisfied. I couldn’t open my window for a week after your last escapade.”
“Most sorry, Handley, but it takes a lot of getting used to this English custom of sitting down to do business.”
“Yes, yes, I’m sure it does, but you must persevere if you are going to fit in with our quaint little ways.”
“I will persevere, Handley, I will be most deciduous.”
“Assiduous, Sanjeev, from the Latin assidere.”
Sanjeev Ramangita sat down on the floor with crossed legs, his large eyes rolled, looking round the room. His gaze lighted on the bowl of nuts, lips moving in the act of silent counting.
“Seventeen nuts, Handley and one on the floor. What do you think it means? Shall I calculate the Goldbach ratio?”
“It means that I accidentally dropped one of the nuts on the floor.”
“Butterfingers. Why do they say that Handley, do the English butter their fingers? ”
“No they don’t; it means dropping a ball in the game of cricket.”
“But what if your ball has already dropped, and what about buttery boards?”
“If you keep asking silly question you will become a butt yourself. Now, if you don’t mind, I would rather like to look at the cricket scores now,” Handley said. He sat down and picked up a crumpled copy of the times from the table.
“I could crack nuts for you.”
“No thank you, I prefer to crack my own nuts.”
Sanjeev fell silent. The ticking of the black clock on the mantelpiece, interspersed with the occasional rustle of Handley’s paper marked the passage of time.
The sound of footsteps and voices echoed in the passage outside the door.
“Shall I hide, Handley?” Sanjeev whispered.
“Well, you might try the wardrobe but I don’t think the smell of naphtha and vegetable curry is an ideal combination. Just stand by the window, and gaze intelligently into the distance.”
“Like Rabindranath Tagore?”
“Yes, something like that.”
While Sanjeev moved to the window, Handley quickly smoothed down his hair and lit another cigarette. He just had time to arrange The Times on the table, with the completed crossword prominently displayed, before striking a pose.
A slim man of medium height entered, talking in fluting tones over his shoulder.
He looked like an animated turtle, snapping out his words with exaggerated clarity. His companion, a decade and a half younger, was very tall and of athletic build. The tall man’s face was gloomy, with dark circles under the eyes. Unusually, he wore no tie. He listened intently as the older man spoke.
“It’s all up to you, now that my Magnum Opus has been published. You must take over the torch and build on what I have achieved. You can see more clearly than I what must come next in the great story of philosophy. It’s a great burden, I know, but I believe you are the only one who can carry the work forward.”
The tall man closed the door behind them and then stopped, transfixed in front of the mirror that Handley had covered with his pullover.
“Isn’t that a bit of a mixed metaphor?” Handley said, “Unless he’s going to burn down the old building first.”
“I thought I might find you here,” Bernard Rushwell said, advancing towards the table where Handley sat. “Perusing the cricket scores, I bet. I wanted to tell you that the prodigal son has returned from Norway, but only on a flying visit. He has some important results to communicate. I was sceptical at first - we had a terrible row - but he has almost won me over.”
Handley wondered why he ought to care about Wittgemein’s return. He knew the Austrian by sight, but had hardly spoken to this new Apostle. He was an Angel himself, but disapproved of some of the newer members of the society, particularly Canard-Means’ Bloomsbury friends.
When Ludolph Wittgemein came over to shake his hand, Handley thought of Mary Shelley’s monster. The Austrian’s grip was surprisingly limp and brief for such a muscular man, but Handley had no desire to hold hands with the chap. He would leave that sort of thing to Canard-Means and company.
With a pang of guilt, he turned to the window, where Sanjeev was casting his broad shadow into the room.
“I would like to introduce my pupil, Sanjeev Ramangita. Bernard, this is Mr Ramangita. Sanjeev, this is the renowned philosopher Professor Bernard Rushwell.”
“I am most honoured to meet you, Sir. I have only just arrived in England, and have yet to conquer the plumbing, but I hope soon to appreciate the greatness of your work.”
“It’s already out of date, I’m afraid,” Rushwell said, “so it may not be worth your while. Ludolph, you should meet Professor Handley’s protégé, Handley expects great things from him when he has learned the ropes. A future Apostle, eh Handley?”
Like the contact between Adam and God on the ceiling of the Sistine Chapel, their hands barely touched; the worlds of philosophy and mathematics repelling each other like oil and water, despite Rushwell’s struggle to make them mix.
“Well, we might as well sit down,” Rushwell said. “Sherry is in order, I think. Ludolphus. Would you do the honours, please. It’s really rather important, you see. Whitehorn and I have laboured in the vineyard all these years and we might have produced a barren crop.”
“Er, no sherry, for Sanjeev, Wittgemein, he’s a Hindu,” Handley said.
“Save it for Canard-Means,” Rushwell interjected, “I asked him to pop in later so we could get his views on Ludolph’s new ideas. Right, sit down Ludolph, we might as well begin.”
Wittgemein moved a wooden chair a little way back from the group, as if delivering a tutorial, and rummaged in a voluminous jacket pocket. He pulled at a battered spiral bound notebook, whose wire had become entangled in the lining. After a brief struggle and the tearing of cloth, he got it out and located the starting point of his notes.
“The world is all that is the case,” he began, in a hoarse voice. “It is the totality of facts, not of things. The world is determined by the facts, and by their being all the facts.”
“Right, this is very compressed,” Rushwell interrupted, “I’d like to say why I think this approach is so important. In the Principia, we tried to forge a link between the most primitive logical ideas to the objects and relations of mathematics. The underlying assumption was that logic was the proper place to start. But, unless we know what we mean by logic we can’t know that it is fundamental to our enquiries.”
“Well, where else could you start?” Handley said, “You could have left well alone. Most mathematicians of sufficient calibre can get on with their business without worrying too much about the philosophical underpinnings.”
“There is the question of rigour. While few could match your standards, Gordon, they still fall a long way short of axiomatic proofs as we have defined them,” Rushwell said.
“Yes, but there is quite a difference between doing real mathematics and merely laying down the law about how it should be done. You may be forgetting that mathematical beauty often determines the direction of an enquiry into fundamental problems rather than a philosophical roadmap. Where we aspire to go there are no maps.”
“Yes, Handley, you are right,” cried Sanjeev, jumping up from his chair, “if you cannot follow the beautiful things in your head, you will never reach the topmost heights.”
“Thank you, Sanjeev. But of course, you do need a very considerable technique to climb the highest mountains, and I suppose that is where you logicians can give us a leg up. Anyway, if you don’t know what you mean by logic by now, you may be in the wrong game, Bernard.”
“But do you know what you mean by mathematics?” Rushwell retorted, adopting his frozen, defensive smile.
“Probably not, but I expect you’re going to tell me,” Handley replied, brushing fallen ash from his trousers.
Rushwell paused for a moment, drew breath and said, “mathematics is the science in which we do not know what we are talking about and do not care whether what we say is true.”
Handley lit a cigarette and paused for reflection. “By the first part, I understand you to mean that we do not know what the objects of mathematics are exactly, since they clearly are not among the things of this world. I’m not too keen on the use of the word science though in this context. For me, a science is not just a systematic enquiry but also one that has empirical connotations. This sort of science has nothing to do with pure mathematics, which is quite unrelated to worldly things. The second part of your reply is more complex. Mathematicians do care a great deal about whether their theorems are true or not, but I suppose you mean true in some absolute, ontological sense. I’m not much of a philosopher, so I can’t instruct you about whether mathematical truth is fatally confined to its own domain or has some mysterious relation to what happens in the real world.”
“Perhaps we should ask Ludolph what he thinks, Rushwell said, looking expectantly at his protégé.”
The Austrian had gone pale and was leaning forward slightly, as if in pain.
“It’s the words, the language, you see, it’s just no good.”
“I’m not sure I understand you, Ludolph, could you explain more clearly?”
“I’m sorry, Bernard, I’m rather tired from the journey. So much is about to happen in the world, all this seems so remote now, even though I know it is the most important thing for people like us. I’m an Austrian remember. If the Balkan war continues much longer, Austria will have to intervene. If She does, She could be at war with Russia, and that will be the end of the world, as we know it. Of course, I would have to return home and fight for my country.”
“Nonsense, it doesn’t mean that at all. I hope Asquith would have the good sense to keep Britain out of it. There is no reason why you should leave England, just to satisfy some chauvinistic instinct.”
“I don’t think you would say that if our country were threatened and you were abroad somewhere,” Handley said. “We all hate war, but we can’t turn our backs on our homeland.”
Rushwell made an impatient gesture with his hand. “If you are able, Mr Wittgemein, we would be interested to hear your latest views on the matter in question.”
Ludolph put his hand to his temple and massaged it a bit before replying. “Very well, what I really would like to say is that you’ve got it all wrong. I know how important you think it is to pin down exactly what logic is, Bernard, but I have come to believe this is a hopeless task. Like Sanjeev said, you see some wonderful truth in your head, but you can’t express it clearly without a great deal of analysis, maybe years of work.“
“Exactly,” Rushwell interjected.
“No, not exactly,” Ludolph said, his eyes lighting up for the first time. “That’s what I’m trying to tell you. Not only is this kind of discussion a waste of time, at least for the purpose of arriving at the truth about the world, it entirely misses the point.”
“And exactly what is the point, Ludolph,” Rushwell asked icily.
“If you keep that frozen smile up much longer, I think I shall go quite mad,” Ludolph said, getting up from his chair to pace up and down parallel to the wall. What is that bally pullover doing over the mirror, anyway?”
“Need to confirm your existence, do you?” Rushwell snapped, his mouth finally hardening into a thin line.
“For Christ’s sake, Bernard, not now. No wonder Othalia has chucked you over. Don’t you realise how cold and cruel you can be sometimes?”
“Perhaps we should continue this another time, when we have all calmed down a bit,” Handley said, stubbing out his cigarette without looking at the antagonists.
”The pullover belongs to Gordon,” Rushwell said, jumping up. “If he accidentally catches sight of himself he will realise the futility of his existence and have to do away with himself. That’s it, isn’t it Gordon. It’s just one of those Trinity things we all have to get used to. We’re all mad in one way or another but we have to learn to get along. Being a cry-baby does nobody any good.”
“But who is this ‘nobody’?” Ludolph asked, turning to smile at Bernard.
“Very funny,” the older philosopher replied. “What now?”
“I do feel rather unwell. I haven’t eaten since dinner last night at High Table.”
“It could be your last, if you don’t pull yourself together. You know damn well how much faith I’ve invested in you. You can’t suddenly walk out now and throw everything away. You could be a Fellow in a few years; we would all support you, wouldn’t we Gordon?”
Ludolph stood up, clutching his belly. “I have a frightful cramp in my stomach.”
“Pie,” observed Handley. “
“Yes,” cried Sanjeev eagerly, “ pi is most important. I have devised many new ways to calculate this wonderful number.”
“No, mutton pie; for dinner; last night at High Table, I’ve been feeling a bit off colour myself,” Handley said.
“That’s why the WC is broken,” Sanjeev said, excitedly. All those dirty fellows have been ridding themselves of impure food and wearing out the pump.”
“I had the mutton pie too, it had no effect on me,” Bernard said, “but then I was weaned on Pembroke pies.”
“A little lamb enclosed within a wheaten shell,” Handley mused. “Sanjeev, would you be so kind as to escort Mr Wittgemein to the staircase, so that he can relieve himself. Meanwhile we will await the appearance of Apostle number 243.”
“243, Handley that is a nice number. It is three to the power of five.”
“I was aware of that,” Handley said, “but it is also the membership number of Professor Canard-Means.”
“But what about the broken WC, Handley?”
“I’m sure a man of Mr Wittgemein’s intellect will find a way round any local difficulties,” Handley replied.
When they had left, Rushwell said, “I hope you will forget what I said in the heat of the moment. I too have been under considerable strain lately.”
“I think we have known each other long enough not to attach too much importance to such little spats,” Handley replied. “You ought to take up something a bit more relaxing than logic.”
“Fortunately for you, you never married. Domestic bliss can end up being an unforeseen torment.”
“And your diversions?”
“Even worse,” Rushwell replied, “the very Devil. Speaking of whom, I think he has arrived.”
A soft-featured man in his thirties with a large moustache entered the room and strolled over to the seated pair.
“Your sherry’s gone cold, James,” Rushwell observed, pointing to the full glass on the table.
“Many thanks,” canard-Means replied. “I just saw your acolyte, accompanied by his Indian bearer, going into the male lavatory. I hope Lindon has not been leading him astray.”
“You’re a little out of touch, Ludolph found the Apostles were not to his taste after all. He’s resigned.”
“Pity, he became so much more animated among his peers.”
“He has important work to do. I think it best if he isn’t distracted by too much empty prattle,” Rushwell replied
“And what is this important work, pray? Some pet scheme of yours in disguise, perhaps.”
“On the contrary, he is working on finding the fundamental object that underlies all propositional forms. Without it, the primacy of logic remains in doubt ”
“And what do you think of these endeavours? I mean, doesn’t this cast doubt upon your theory of types?”
“Exactly. I had to invent that theory to obviate the pernicious antinomies of sets. These infect the basic propositional form, as you know, so a new, primitive notion of the proposition is essential if the whole enterprise is not to collapse like a house of cards.”
“Hark, I think I hear genius approaching now,” Canard-Means said.
Sanjeev entered the room, beaming, followed by Ludolph.
“I trust your expedition has met with more success than Captain Scott’s,” Handley said.
“Oh, yes Handley, much more. Ludolph is truly a great engineer. He pulled the chain many times and listened to the harmonics of the machine. Without even looking, he knew that there was a blockage in the cistern, by the way it sang to him.”
“And what was this blockage?” Rushwell asked.
“I am very ashamed to say it was Carr's Synopsis, Handley. I know you told me to get rid of it, but I still love it very much.”
“What was it doing in the cistern?” Handley asked.
“I need something to read in the WC when your British food causes a blockage. I wrapped it in an oilskin to keep it dry. See, I have it here.”
Sanjeev held up the dripping package, which began to form a pool of water on the floor.
“I think this meeting is adjourned,” Rushwell said, taking Ludolph’s arm and leading him back to the door. “I’ll see you in my rooms, James, should you wish to learn more about the future of philosophy.”