The Prisoner's Dilemma (16 page)

‘But, more importantly than that,' Hume's voice now rose in emphasis, ‘we have our histories, we have our backgrounds, we have our
reputations
. We become known for how we've behaved in the past. People already know what to expect from us. They know already whether we've shown ourselves to be co-operators or defectors. And whether we're likely to be so again.

‘You see, the Dilemma resides in the prisoner having only two options in his choices. To co-operate or to defect. But this is where the game departs from reality – because in truth a person cannot
make a good decision until he knows the choice of the other player. Rather like your little boys and their cake, Dunbeath.

‘So, having given the Dilemma a certain amount of further thought, I believe that the key to making this game an insight into our real lives must be to repeat it. But,
openly
. To keep meeting the same person and to have the potential to reward or punish him for his actions. In other words, to deal with him. There can be no dealing in a one-time game where the risk of error is death. But in reality, in daily life, the stakes are seldom so high, nor is the decision so final. So, instead of having a metaphorical book barrier the
opposite
is actually true in life – we actively show people what we're like. If you keep playing the Dilemma in an open way then the game changes and you realise that it pays to co-operate and rational to trust – because you can expect a reasonable opponent to co-operate in return.'

Sophie had been listening carefully to Hume and she now pulled up a chair to sit by the two men.

‘Of course,' she said excitedly, ‘you must be right, Mr Hume. The interests of the prisoners in the game were completely opposed. But in fact, even then, they would have known each other, and on that basis they might have made a different choice.'

‘No, you're not thinking deeply enough, Miss Kant' interrupted Dunbeath sharply, ‘because however much you think you may know your opponent, if there's the possibility of the other person defecting, then you're better off defecting too. That way you'll always get one point rather than potentially getting none. And of course you stop the other man from ever getting five. But if your opponent co-operates you are still better off defecting because you'll get five points instead of three. Whatever the other person does, you are better off defecting.'

Sophie thought for a moment while she considered this.

‘Yes, but perhaps we should not use the word ‘opponent'. It immediately implies conflict and defection. You see, if each person argued in the way you just have, you'll never achieve
anything but one point each – when you could have had three each if you'd only co-operated.'

As she said this David Hume began laughing, his normal easy humour completely restored.

‘Well,' he said quickly, ‘if you imagine two people playing a hundred times and think forward to the outcomes, the range of possibilities must be from one player getting 500 points for always defecting while the other would end up with none for constantly choosing to co-operate. But the other person is bound to defect once he sees that there's no point in co-operating. Neither extreme is feasible. Both people co-operating, on the other hand, would lead to 600 points for the pair and a very easy relationship that would be.

‘But one can see very quickly how tempting it would be if the other person was always co-operating to slip in the occasional defection just when the other player is lulled into thinking that there would never be any change. Five additional points while the other gets none. Yes, very tempting indeed. Imagine, for example, one of our thieves hiding from the captain of the guard. He's been given sanctuary in a monastery where the monks treat him with trust and kindness. How long would it take for him to rob them? To grab five points for defecting while the poor monks would get none for their troubles?'

Dunbeath smiled.

‘Exactly,' he said.

‘But what seems to be clear to me,' Hume continued, ignoring Dunbeath's pointed comment, ‘is that when we find people we like and want to deal with, the game changes. It stops being a dilemma. What begins as irrational behaviour in trusting the other person – to think of the outcome for both people rather than just for themselves – becomes a rational decision in the long run, as long as there is a long run, as both players ought to co-operate.

‘In any case, perfect rationality must be a fiction. To expect it is, if I may say so, to despise your fellow man so much that you
withdraw from his company.'

‘I presume you are referring to me?' said Dunbeath. But he didn't seem displeased by Hume's remark.

‘But it's interesting, is it not,' continued Hume without being drawn to answer Dunbeath, ‘that in the animal world the most robust of the species also seem to be the ones that are the most co-operative. And, shouldn't man, with what my friend Adam Smith calls his ‘specialisations', be even
more
open to the benefits of co-operation.

‘So, is selfishness an animal instinct, and trust – for surely that is what co-operation must be – a civilised one? Are the most successful animal species the ones that are continually attacking each other or those that show the greatest mutual support? I think you'd agree that most observations would point to the latter. Indeed, their world is so often a lesson to us. Everywhere one looks one sees co-operation even to the point of sacrifice. Does not a bird call out to its flock when it sees a cat – even though it gives its own position away? And look at so many of them when they are together. Particularly the more dangerous species. See in what a ritualised way they behave – twisting and retreating, sudden rushes and snapping. But mainly glowers and feints and noise. How interesting, though, that they very rarely do each other real harm.

‘So what might this mean? Well, I think the start point has to be that if we're alive at all then we have to be examples of some kind of successful strategy. The only certainty in life is that our ancestors didn't die celibate. Perhaps the behaviour they employed to enhance our survival was thriving at the expense of the behaviour that failed for other people? This sole fact alone points to us being the living proof of some kind of winning approach. We humans may think that we are subtly individual but really we are just machines bent on survival. What is it that's making us behave instinctively in the way that we do?'

Hume leant back in his chair and picked up his wine again.
Dunbeath was so pleased with Hume's observations that he was now smiling.

‘I am in your debt, Mr Hume,' he said, ‘you nursed me back to life and now you are making me think. I believe I profoundly disagree with your conclusions but I very much look forward to continuing our game.'

Hume set his glass down.

‘Well, I'm delighted to hear that, my lord. I shall greatly enjoy doing so. By the way,' he continued, ‘what was it that you witnessed that made you think of the game in the first place?'

‘What's that, what do you mean, Hume? Dunbeath said with an abruptly renewed sharpness, ‘I've no idea what you can be referring to.'

Hume persisted with his question.

‘When you wrote to me in Edinburgh you said that you had recently witnessed an event that had made you invent the Prisoner's Dilemma. I wondered what it was.'

Dunbeath's stickiness immediately started to return.

‘What? Did I say as much? Well, there was nothing. I can't imagine why I would have said that.' There was a tense silence and Hume exchanged a quick glance with Sophie. Then she rose quietly from the table and started to pick up the used dishes to take back to the kitchen.

* * * 

Early the following morning Zweig returned to the shoreline to finish shaping the branch with his knife. He'd shaved it to be quite straight, stepping down the width of the cylinder towards the end and then bringing out the final section in a bulge. Now he cut slits in the upper part and began to force small stones into them, making certain that they would be held in place as the sodden wood shrank. Eventually he held the finished piece up to the light and then bounced it in the palm of his hand to check its
weight.

It will pass, he thought to himself – as long as it isn't looked at too closely.

He took the oilskin cloth from his pocket that had covered the Domenico Salva. He carefully wrapped it around the wooden cylinder and then ran his hand over the cloth. Bundled up in this way it looked and felt like the lost telescope. He quickly tied it with the original string and then set off to walk back to Dunbeaton.

It was two weeks later and Dunbeath and Sophie were alongside one another at the great table in the tower study. Dunbeath glanced up from their papers and picked up a book of ecliptic tables, now thankfully found under the huge mass of written calculations that Sophie had carefully classified, organised and arranged. He could scarcely believe the changes she'd wrought. For the first time in years he was no longer drowning in paper and he still found it strange to be able to find things instead of having to wade through the quagmire he'd allowed to build up. His hand moved to stroke his chin, pleased too that he'd finally found the time to be clean shaven and the will to attend to his appearance.

A warm breeze came through the open window, gently ruffling Sophie's curls and pulling at the piles of written work, so neatly laid out on the table's surface. Dunbeath moved his head closer to Sophie's as they pored over a mass of celestial charts and interplanetary readings.

She now tapped with her finger at a table covering the measurement of parallax angles.

‘I have thought about our problem overnight,' she said, ‘and I think this is where the error has been stemming from. You see, these lunar distances are changing over time at a rate of half a degree, or thirty arc minutes every hour …' she continued to take Dunbeath through her detailed reasoning and a few minutes later approached her conclusion, ‘…thus I think this could be inducing an error of as much as one quarter degree in longitude or about fifteen nautical miles at the equator. The core issue is one of timekeeping and I'm sure that by always using the periods of the Jovian moons rather than working with a clock we can be sure to resolve this.'

Dunbeath sat back. Sophie continued to study her workings but out of the corner of her eye she was conscious that Dunbeath
was looking longingly at her from the side.

‘I knew I had gone astray somewhere, Sophie,' he said at last. ‘I knew the perfection of the heavens couldn't be at fault. It had to be my error and thanks to you it's now exposed – and furthermore you have a solution. I can scarcely credit this, indeed, I can scarcely credit everything that has happened recently. At last all my years of work and research have come together. That it has is much due to your help. And, of course, to your observation of the Transit.'

Sophie began to bridle gently at his thanks but Dunbeath wouldn't be deflected.

‘I'd worked for twelve years without missing a single reading,' he went on, now looking closely at her, ‘and yet you saved me when I could not continue. And then you've exposed these great errors of mine. Now, at last, the answer is here. You must know how much I am in your debt, Sophie, and I believe these findings are now in a position to be presented at the next meeting of the Board of Longitude. It should be held soon – there's usually one sometime in the spring. They've often been in May in the past and, in fact, I'm surprised I haven't been told of a date yet. I'm convinced these findings will put me so far ahead in the race to satisfy the criteria for the measurement of longitude that the Board will be hard pressed not to award me the Prize immediately.'

He looked again at Sophie and his tone changed. He began to speak to her in a voice of quiet intensity.

‘Sophie, I couldn't have achieved this without you. You may have saved my life when you nursed me through my illness but you saved my life's work too. Will you agree to come to London with me when I go to the Board? I want them all to know of your contribution.'

Then he took a deep breath as if preparing himself to say something vital.

‘Sweet Sophie, I want you to be with me then – and I want you
to be with me when we return. Nothing must come between us. You've brought this old castle back to life. More than that, you've breathed a new life into me – you have changed me. I want you to stay here. Will you consider this?'

Sophie reeled in panic. What was this? Was it a prelude to an offer of marriage? Or did Dunbeath just see her as a collaborator in his research? She had thought she understood him for the impatient, distant man he was …and yet here he was calling her ‘sweet Sophie'. That was singing love songs from the hills for a man like him. She may only recently have washed up in Scotland but she knew enough about these aristocrats to know that they saw marriage more as an opportunity to add wealth and power than anything to do with the heart. And Hume had told her that gain was all that motivated the Urquhain. She hadn't anything to offer. So what could he mean? She thought further and then firmly decided not to press him – she might not wish to hear the answer. She just had to buy time. There were still thirty nine days before her father's debt fell away – and she had to have Dunbeath's protection until then. Whatever it was that he meant, she had to play for time.

Sophie gazed at Dunbeath, looking deeply into his eyes. Then she blinked and looked away.

‘Well, my lord, I'm flattered by what you say. Indeed I am greatly affected. I owe you so much too. You forget that. You, too, have saved me.'

As she spoke she listened to her heart. There was undoubtedly a great affection there for the man, in spite of his anger and restless arrogance. But perhaps what had begun as a fascination in her had not yet turned to love? Perhaps it would? And did it matter anyway? If he should mean to press for marriage then the security and status that he could give her were far more than she could ever have hoped for. In any event, marriage or not, if she stayed with Dunbeath she would be able to do so much – she would greatly prize working with him to continue their research
together – and there was little doubt that his great wealth could help her poor father as well.

In an instant she had weighed up her position: her heart might not be full but that could change in time, particularly if his was truly full for her. And her head told her not to show any sign of rejection. She had few options anyway, and anything that protected her from Zweig and the debt had to be agreed to.

‘Yes, I would be very happy to go to London with you,' she said warmly, carefully ignoring any deeper message he may have meant. ‘Thank you. I greatly look forward to hearing of the date.'

She looked down as she tried to steer the conversation away from any further discussion about their future. Her eyes were now on the table and she stretched out a hand to pick up the Domenico Salva from where it lay on a sheet of planetary movements.

‘This really is the most beautiful piece of work,' she said, looking at the chasing of the gold case. She ran her finger over the jewelled exterior and then lifted the telescope to her eye and focused it on a boulder set in the beach at the far end of Dunbeaton Bay. ‘And what superb lenses it has. I've never seen another like it.'

She set it down again and continued to speak quietly and with no small trepidation. She knew the time had come – she had to find out what Dunbeath knew of Zweig.

‘But, why do you think that ship's captain had it? Did he steal it from you? Do you remember he said - ‘how do you think I came by it?' - when he jumped out at us on the dunes? What do you think he meant by that?'

‘I don't know,' replied Dunbeath, suddenly his old sharp self again, ‘I'd never seen him before.'

‘Yes,' Sophie carried on, a slight trace of incomprehension entering her tone, ‘but what do you think he meant?'

‘How could I know what he meant?' Dunbeath was beginning to bridle. ‘I told you, I'd never seen him before. I had no idea who
he was.'

* * * 

Once Zweig had returned the wooden fake to the original's hiding place he'd turned his thoughts towards how he could steer James away from his growing obsession with having the telescope returned to him. The boy had been becoming more querulous by the day and he was now insisting on seeing it again. The previous afternoon, he had even spoken of exposing Zweig to the English army if he didn't get his way. At least with the fake to draw on, the captain felt, he had something that he could wave in front of him if the need arose. In spite of this, he knew that James could only be held off for so long and Zweig now decided that he had to bring forward the second part of his strategy.

The boy was a factor to be considered, that was true, but he was just an irritation compared to the larger plan to win Sophie round. Zweig knew her mind, though, and he was quite sure that the debt schedule was the leverage he needed for his next steps. Sophie had already shown him how aware she was of the dates – and she would know only too well that time was running out for them to return to Königsberg and so trigger the repayment. He could be certain that she would see this as the ticking clock. A further two weeks had passed since he'd seen her on the dunes and he could be sure she would be aware that there were now just thirty nine days left. Many fewer and she would think that Zweig wouldn't be able to make the journey to be back within the hundred days that Kant had set. He couldn't leave things any longer – now was the time to bring matters to a head.

He took a deep breath. He knew there would be much pain in the next part of his strategy and he set his shoulders as he steeled himself for the ordeal ahead. After a few moments he shook himself slightly and began the short walk to the castle. It wasn't long before he came to the top of a large dune and he stopped
there to look down at the granite slab that made up the side of the great Urquhain stronghold.

About a hundred yards from the vast fortress the constant working of the tides had so eroded the front of the dunes that a small raised peninsular of grass and sand stretched out onto the beach. The end of this was in full view of every window on the castle's north face and it was here, he had decided, that would be his battleground.

Having satisfied himself again on his choice, Zweig walked towards the hummock. By now there was such evident purpose in his stride and such great determination in his features that it was plain that his mind was quite set.

He reached the end of the spit and turned towards the castle, checking the sight lines from the windows. Apparently satisfied that nothing would obstruct a view of his position he sat down and carefully folded his legs under him in the way he'd seen practiced by the monks of the east.

Then he closed his eyes.

Above him the sky darkened as rain clouds blew in from the sea. Now, facing towards the largest windows, his eyes still shut, his body stiffened as if he was summoning up his inner strength.

Then he opened them again and his face was composed in a trance of concentration. He stared fixedly at the castle and he tensed again as if distilling every particle of energy to serve his colossal will. Then he leant forward from the waist with such an intense show of force that some strange power seemed almost to shimmer off his huge frame.

This will take much time, he thought to himself. He had to be patient, he had to stay alert.

* * * 

Hume and Dunbeath had moved their game playing from the salon to the dining room. For much of the last two weeks
Dunbeath had been taking part only intermittently, his mind more occupied by the navigation problems that Sophie had recently resolved. Hume had not concerned himself too greatly with this delay and had instead attacked the great Urquhain library, devouring whole sections of the Greek thinkers that he'd found on its shelves.

But, with the solving of the celestial problems, the Dilemma was drawing the two men together again and they now sat opposite each other at one end of the long table, the record of their recent turns spread out between them. Flames from half a dozen enormous logs in the great fireplace threw their shadows about the room and the ornate plasterwork and fierce staring caryatids seemed almost alive in the glow. Above the pair's hunched backs, a vast barrel shaped ceiling of raised strapwork and long, pendulous roof bosses loomed over them, a masterpiece that dated from the time of King James.

Sophie sat next to Dunbeath, glancing occasionally at a large sheet of paper on which she'd been keeping the score.

Hume sighed and sat back in his chair.

‘We do not seem to be progressing at all, Dunbeath. Yet again you have chosen to defect. Whilst I know your logic in doing this I can only repeat that I can see no encouragement to deal with someone who never shows any sign of reciprocating my evident wish to co-operate.'

‘But Hume,' replied Dunbeath crisply, although in a far less provocative tone than he'd used during their earlier games, ‘even though you know how I shall always play I still don't understand why you can't see that I am beating you. And that must surely be the mathematical lesson of the game.'

‘No,' said Hume firmly. ‘Sophie and I were discussing this yesterday and we've both concluded that it is exactly this belief that exposes the Dilemma's fundamental principle. And it is this. We believe it is a mistake to talk of ‘beating me' or to see the game as one of winners and losers.

‘If this is so, then nothing is ever
added
, nothing is ever built. Sophie has called this a ‘nil sum game' because if one man's gain is exactly matched by the other man's loss then there is no gain, nothing is created, the sum total is, indeed, nil. But even the small boys with their cake showed that co-operation – although it was based on greed and the fear of losing –
can
add something. In their case the gain may simply have been an outcome of unusual tranquillity but if one thinks of it as peace between warring factions then that is indeed a giant step forward.

‘The trouble with these nil sum games is that if one man is winning only at the expense of the other person losing then there will never be a lasting relationship. How can you ever trust someone who you know is always trying to beat you? Indeed, did we not come near to losing our friendship over your own strategy? And was it not your insistence that you were beating me and that this was all that mattered that led me to give up on you? On the other hand any merchant will tell you that while he would wish to profit from you, he wishes you to profit also. In that way you can both be satisfied. And the likelihood is that the two of you will then continue to trade.'