The Three-Body Problem Page 23

  ‘What?’ responded the clearly astounded Doctor. ‘A complete solution to the perturbative three-body problem? But this is more than we dared hope for in the best of cases!’

  His amazement and rejoicing were such that I could not remain quiet, although it would certainly have been more seemly to do so.

  ‘Is it so very important, then? What has he proven?’ I asked.

  ‘Oh, yes, it is of capital importance!’ cried the enthusiastic young doctor, stabbing at the famous formula with his finger. ‘He has given a formula for the mysterious series in terms of known analytic functions, and deduced from this that the classical series describing the motion of the bodies converges, that is, has a real value at any given time, rather than a meaningless, infinite value. That means that in this case, what we call the perturbative three-body problem, that is where one of the bodies is very large compared to the other two, like a star and two planets – our own Earth and Jupiter, as it may be – one is able to predict the orbits of the planets, instead of having no idea whether they will not end up by drifting away through space.’

  ‘Good heavens,’ I exclaimed. ‘I thought it was well known that the Earth orbits regularly about the sun. You don’t mean that without the solution given here, we might have to fear its departing at any moment?’

  ‘Well, no, the nature of the series does tell us that the Earth will certainly continue its orbit for many years yet – but not so very many! We have no guarantee that in a million years it will still be doing the same!’

  ‘Oh,’ I said with a tinge of disappointment. It is perhaps natural for citizens of a country as stable and peaceful as Sweden to feel threatened by the prospect of turmoil a million years from now, but I myself was concerned with far more immediate circumstances. I still wished nothing but to know the name of the author of the fated manuscript. Yet I feared to insist upon seeing it, for I was afraid to hear a reiteration of the professor’s previous refusal. My mind was seared by the image of Arthur, waiting in the dock, silent and withdrawn, scarcely interested in the battle over his destiny waged around him by lawyers, judge and jury – the outcome of which could – would, probably, send him to his death – and the professor was thinking about planets! I tried to speak, to tell him what was in my mind, but tears collected in my eyes, and spilt over. Perceiving them, Professor Mittag-Leffler immediately became distressed. He took several rapid steps about the room, thinking intensely.

  ‘I know what worries you, Miss Duncan,’ he said. ‘And yet – I cannot do what you wish. But wait! Do not give way to despair. There may be a solution.’

  ‘Please tell me what it is,’ I begged him, trying in vain to control my voice which wavered desperately, while Emily and Robert approached me and wrapped their arms around me tightly, looking at the professor with their large eyes full of severity and distrust, like little wild cubs in a lair, suspecting the creature creeping about outside of being a threatening predator.

  ‘I see only one thing to do,’ he said in measured tones. ‘We cannot open the envelopes because the King has forbidden it. The only one who can go against these orders is the King himself. We must petition him with our request.’

  ‘Shall we see the King?’ asked Emily with breathless respect. For myself, I felt as though my very heart was pressed in from all directions with fear. I imagined that the King would certainly refuse a request so puny, as compared with his royal concerns. Even more, I feared that we would have to endure a great delay, while our petition was made with all the proper ceremony.

  ‘The matter is desperately urgent,’ I told the professor. ‘The trial has been going on for two weeks already, and the judgement may be pronounced at any moment, any moment at all. It may even have happened today, for aught I know. There is no time to lose.’

  ‘My relations with the King are close,’ he said. ‘I will send a messenger to the Palace now, with a message to be delivered as soon as he rises tomorrow. I will express the urgency of the situation, and we will go to the Palace immediately tomorrow morning, so as to be already present, should he send for us. If all goes as you wish it, and as I wish it also, I do not hesitate to say, I myself will provide you with conveyance to the station, and with the tickets you need to travel home again. This seems but a minor service which I can render to justice, in the name of mathematics. Let me now have you shown to bedrooms for the night. I beg you will repose yourself as much as possible; I will have you called at six o’clock, that we may be ready for every eventuality.’

  I saw that he understood my feelings, and that there was no need for me to attempt to express them; I saw, also, that he was doing everything that he possibly could to aid me, and that going against the express wishes of the King, in however trivial a matter, appeared absolutely impossible to him – even now, even when it concerned a question of life or death! I pressed my teeth together, not to allow my anguished impatience to burst out (oh, the idea that the very envelope I so desired to open lay within the very house, and we could have seen inside it in a moment! How I longed, but did not dare, to suggest steaming it secretly open over the kettle and then sealing it up again … ) and thanked him with as much calmness as I could muster. He led us ceremoniously and kindly to the hall, and summoned the buxom lady who had bade us enter earlier on, and spoke to her in Swedish; she showed us to the beautifully furnished adjacent guest rooms where we are now. Taking charge of the children, she swept them away, pausing only to say ‘bad, bad’ to me with a motherly smile, from which I concluded, not that the children were misbehaving, but that they were to be washed. She took charge of my valise, also, and I undressed and fell into bed. But thoughts whirled too strongly in my brain, and I finally admitted to myself, Dora dear, that I should not find sleep before I had committed everything to paper, for it has become such a habit with me, during these long, dreadful weeks, that I can no longer do without it, and it somehow relieves my anguish and momentarily restores hope to me. Now that I have given you a complete account of the events of this crucial day, I shall return to bed, and try to sleep, and not to think too much about the fact that perhaps, tomorrow morning, I shall find myself pleading for Arthur, no longer with charwomen, children, policemen, lawyers and mathematicians, but with a king!

  Please pray for me, as always

  Vanessa

  Malmö, Saturday, June 2nd, 1888

  Oh, my dear Dora,

  What a day this has been! I have learnt much, and reality has superseded my foolish imaginings about royalty.

  As Professor Mittag-Leffler had promised, we were called at six o’clock. I was brought tea in bed, and then shown to a large bathroom wherein a steaming bath had been placed, together with large towels and every luxury. I made a detailed toilette, for I detected more than mere politeness in such gracious treatment; I understood that it also contained a component of careful planning in view of our royal reception, in which I admit I could still hardly believe.

  When I took up my grey dress, I saw that it had been steamed and pressed during the night. Once I had put it on, however, I still hesitated to descend, for my hair was wet and I could not do it up. But the kind housekeeper soon reappeared, and towelled my hair kindly, and fluffed it with her fingers, and brushed it with a brush, and bade me with gestures come down to breakfast, and that she would take care of my hair later. It was already beginning to dry and wave thickly over my shoulders, and I felt a little ashamed, as though I were descending in negligee, but I must needs go, so I went.

  I was delighted to see Emily and Robert already installed at the well-laden table before me, happily eating toast with jam, large aprons wrapped around them, laughing together, although their eyes were still small and their cheeks rosy with sleep. The Professor was conversing with them most cheerfully, and he bade me join the meal, and in his kindness and understanding, which I shall never forget, immediately addressed my deepest concerns.

  ‘It is now seven o’clock,’ he told me, looking at a beautiful silver watch he extracted from his pocket, ‘
the King will receive the message in one hour. By then, we shall already be in the Palace, and his response will be conveyed to us immediately.’

  He paused to pass me the various crystal pots and covered dishes and to see that I took a sufficient quantity of each, and then continued.

  ‘I have made the acquaintance of these two delightful children, and am now much more familiar with the full circumstances of your journey and your double quest. I am filled with admiration, and wish to support you in every possible way, for I perceive that you are moved to very daring acts by the simple perception of injustice.’

  I remembered something.

  ‘We are twin souls, then, sir, for I have heard that you insisted on naming, here in Stockholm, the only woman university professor in the whole of Europe, when no other country would have countenanced such a thing, not even Germany, where at least women are allowed to study.’

  He smiled. ‘So you have heard of the famous Sonya Kovalevskaya,’ he said. ‘She is one of the greatest mathematicians alive today, and what may have seemed like a disgrace to others appears a great honour and good fortune to me. I wish you could meet her. I do not ask you anything about the details of your quest, for I perceive that you must keep your suspicions secret until you are certain of their truth, and in any case I know almost nothing of the protagonists, dead or alive. But should all pass as you hope and believe that justice would require, I pray that there may be some future day, when your life is full of peace and pleasantness, and you have sufficient strength and time to undertake the long journey hither once again. I would welcome you here with the greatest pleasure, and introduce you to my dear Sonya who would appreciate you very much, I think. Now, we must prepare our departure.’

  We arose, and the maid removed the large aprons which protected the children’s clothing from the various drops of jam and honey which naturally fell about them. I was amazed and delighted to see that not only had they been bathed and scrubbed to perfection, but somehow, their clothes had been washed and – more surprisingly – dried during the night. They must have kept a great fire burning to accomplish it so quickly, for clothing is generally most reluctant to dry in the darkness. Emily’s dress had been ironed and starched, and her soft, dark hair drawn back with a band, and her shoes polished; the gracious princess I was used to seeing at lessons had returned to replace the laughing gypsy of the past week. Robert also had been washed and brushed and pressed and polished, and looked for all the world like a much-beloved little boy of good family; I perceived more strongly than ever his delicate charm and strong resemblance to Edmund.

  I was led upstairs, where the personal maid of the professor’s wife – who was still asleep – took charge of my hair and wound it with easy precision into an elegant chignon. She perched my hat on top of it, pinned it carefully, and guided me downstairs to where the professor and the children were waiting in the hall, already wrapped up in their outdoor things. The professor’s handsome carriage was at the door, and we mounted and set off through the wide, lovely streets to the capital, the professor bearing a leather case containing the full set of manuscripts and sealed envelopes submitted to the King’s Competition.

  The distance to the centre of Stockholm was not far, and before eight o’clock had struck, we drew up before the Royal Palace. The palace is an extremely regular building, absolutely square and similar on all sides, four stories high, with a grand courtyard in the centre, and four symmetric wings extending from the corners, two from the front and two from the back, enclosing grand esplanades between them. The facades are sculpted in niches in which stand statues. The Swedes call their king’s palace Kungliga Slottet, which sounds quite strange to our British ears, except for the echo it contains of something ‘kingly’.

  We drew up at the front esplanade and descended, whereupon we were immediately surrounded by uniformed guards, who questioned us closely and kept us waiting while they sent for information, before finally ushering us within the precincts of the Palace itself. There, we were shown up and down long and noble halls, to a large antechamber where quite a large number of people were already waiting.

  ‘This is the antechamber to the King’s offices,’ the professor told us. ‘He works here, and receives visits and petitions. We must now wait for an answer to our message, which should have already been delivered. The King has no time to waste, so the message was a brief one; I represented the extreme urgency of the situation and begged him to spare us only a very few minutes. My relationship with the King is a close and trusting one, and I hope that he will be able to send us at least a brief message in answer at any moment.’

  Indeed, we had not waited for longer than half an hour (during which time I was on tenterhooks, not only for fear of a negative answer, but lest Emily or Robert behave in some way incompatible with our royal surroundings) before a uniformed guard entered the room and called for Professor Mittag-Leffler. They spoke for a moment, and the professor turned to us.

  ‘The King will make a short space of a few minutes in his schedule, to receive us, at ten o’clock, upon the departure of the Danish Ambassador,’ he said. ‘I would have preferred to prepare the King by speaking to him myself, but as we have so short a time, we shall enter all together. I shall speak to him first, and you, Miss Duncan, will answer any questions he may put to you. Please remember to conclude each sentence with the words “Your Majesty”.’

  ‘Of course!’ I assured him, rather taken aback at the idea that my lack of experience in dealing with kings might somehow jeopardise the outcome of my quest. I tried to imagine myself speaking to the King, and it was not easy – I felt I must look like nothing so much as Alice respectfully addressing the Cheshire cat! The wait was long; I dearly wished that I had something to read. These many long moments of enforced inactivity, when all inside me is burning to act, have truly proved the most tormenting aspect of my entire journey. However, the time passed; the many waiters and petitioners in the room talked in low voices, so that Emily and Robert felt it was not forbidden to do as much themselves, and I began to catch occasional snatches of the tale of Sleeping Beauty, recounted with great attention to detail. Finally, ten o’clock struck; I wondered greatly what form our summons would take. The large double doors at one end of the antechamber – not that from which we had entered – opened, and one of the uniformed guards appeared in the opening, and called out in stentorian tones:

  ‘The King will receive Professor Mittag-Leffler and his suite!’

  We arose, much to the annoyance of all those in the room who had arrived long before us, and would probably have to wait much longer, and were ushered through the small room beyond, whose main purpose appeared to be to house the guard and separate the King from the noise of the antechamber, into his very Office, where I had my first glimpse of the Royal Personage.

  The King is near on sixty years old. His bearing is noble and haughty, his hair white and scant, his beard grizzled and firm, and his moustache so very long that its two ends extend down into the beard and then outwards in two well-waxed points as long as fingers. He was seated behind a large desk. We remained standing. Although I could not understand a word that passed between them, it was clear that the King was inviting the professor to state his business as rapidly as possible, for he spoke only very briefly. The Professor began by showing him the pile of papers and sealed envelopes which he had collected. The King nodded briefly and said something, and the piles were handed over to him. The Professor then spoke some more, and I heard the urgency in his tones, and knew that he was coming to the heart of the matter. The King said a few words to the professor, and rang a small bell. My heart nearly stopped, as I saw the door opened from the outside by the guard, for I thought we were being summarily dismissed. But the professor shook the hand of the King – one short, sharp shake, as though no time could be lost even for such a brief ceremony, and then saying to me ‘The King will see you alone,’ he allowed himself to be ushered out by the guard. The door closed firmly, and the king addresse
d himself to me in English.

  ‘Professor Mittag-Leffler has told me that you are Miss Duncan, that you come from Cambridge, that you have interested yourself in the murder of three mathematicians there, that you believe the person now on trial, himself a mathematician, is innocent and yet runs a great risk of condemnation, that you believe you know the true course of events, and that one of these envelopes here contains an important proof of your theory.’

  I saw how such a man could be a King. If the country was run as efficiently as this, then it was well run indeed.

  ‘Miss Duncan, I am willing to open and look at the name contained in the envelope whose number you indicate to me, for I know nothing of the contents of the associated manuscript. But I am reluctant to communicate the name which I will see there to you, for I would not somehow suggest the name of the murderer to you by this procedure. However, if it is true that you believe yourself to be informed of his identity, then you need only write down the name on this piece of paper, and the number of the envelope you wish me to open, and I will let you know whether you are right or wrong.’

  I was in a quandary. I was not absolutely sure of the author of the critical memoir – it could be one of two people. I thought of Mr Akers and his medicine. I closed my eyes briefly, sent up a prayer, wrote a name upon the paper, and then the number seven.

  He took the paper, read it, slipped out the envelope numbered seven, slit it open with a silver paper-knife, extracted the paper within, and looked at it. Each of his gestures was as sharp and precise as his speech. He looked directly into my eyes with a nod, and spoke.

  ‘Yes, Miss Duncan. You are correct. I congratulate you on your insight and wish you success in your endeavour.’