Game Theory and Peace

Since beginning to attend the Herndon Friends Meeting, I have been considering how to live peacefully. While game theory may seem an oversimplification of complex concepts, I think it can provide a context to comprehend some very simple lessons about living peacefully.

One of these game theoretic considerations, called the Hawk/Dove Game, is due to a behavioral ecologist named John Maynard-Smith. Consider a population of birds with two strategies with regard to conflict over resources: There are doves, who will always share the resource with another but will always back down and take nothing if challenged. And there are hawks, who will always fight over the resource, gaining all the resource on winning the challenge, but will suffer an injury on losing.

Essentially the conflict over resources will result in a pay-off matrix looking something like this:

The way to read this matrix is that two players can choose two different strategies. When both players choose the Hawk strategy, each wins the resources R half the time and the other half the time it gets injured with payoff –I. If a Dove meets a Dove they both share the resource every time. On the off-diagonal entries, we show the average payoff to Player 1 in the first position, and the average payoff to Player 2 in the second position.

The question posed by Maynard-Smith is, given the parameters of the above payoff matrix, what would be the stable proportion of hawks and doves? Let H denote the proportion of hawks in the population and D = 1-H, the proportion of doves. And, without belaboring the point, the proportion is H = R / I. Observe that as long as I > R > 0, the proportion of hawks and doves will be well-defined, that is 1 > H >0.

A couple of interesting inferences are immediate. First that as long as R > 0, i.e. there is a perceived reward for fighting, there will be hawks in the population. It just seems immediate to me that sharing resources more equitably makes R smaller, and there would be less to be gained by (and therefore less need for) fighting. Second, note that as long as I > R, i.e. the cost of losing exceeds the reward of winning a fight, there will be doves in the population as well. But if it is perceived that there is more to win by fighting than there is to lose, doves will be extinguished from the population. The lesson for me in this is that if the true cost of fighting is fully accounted for, there would be more peace. George Fox declared that he "lived in the virtue of that life and power that took away the occasion of all wars". Perhaps that virtue is the spiritual insight that the parameter I >> R and that R ≈ 0, that the costs of fighting far outweigh the paltry benefits.

I feel like for myself if I think through the payoffs when I am tempted to fight, I can come to a greater realization of peace. But how do you deal with people who don't see these payoffs and are still living in the delusion that there is something to be gained by fighting? In that case the game changes to one called Prisoner's Dilemma and the dominant strategy is to always fight, since no matter what the opponent does, there is more to be gained by fighting than by cooperating. But even in this case there are some further insights from game theory.

One approach is to think about what happens when the game is played iteratively? A political scientist Robert Axelrod hosted a contest between computer algorithms playing the iterated Prisoner's Dilemma. He found that successful algorithms tended to be:

1. Polite, not the first to be aggressive.
2. Forbearing, slow to retaliate.
3. Forgiving, quicker to cooperate again after a run of retaliation.
4. Generous, not striving to score more than the opponent.

To me this suggests that such ostensibly altruistic behaviors are actually self-interested. Perhaps the right term is enlightened self-interest.

Finally, the rules of game theory are that the players do not communicate or negotiate, and that players only act rationally. Of course this is not true in real life, and this kind of analysis underscores the importance of transcending mere rationality and striving for deep connections, trust and communication.

Hymns

The hymns that were sung at my Grandma's funeral were so beautiful and moving to me. I don't know why entirely, but I know that part of it is because they make me think of her, and the way she used to hum them as she busied about the kitchen. I guess they make me homesick for an irrecoverable simpler time in my life--my lost innocence perhaps. I also think of all the other people I've known who I sang those hymns with who are also gone now. And of course there is a beauty in the simplicity of their melody and harmony, and the sincerity of the untrained voices that sang them. It is amateurism in its purest form--singing just for the love of it. I still frequently play them on the piano, out of the 1959 edition of "Old and New." They're still among my favorite music.

There is an old joke about Unitarian Universalists (a religious community of mine) about why we're such bad singers--we're always reading ahead to see if we agree with the words! Well I confess it is not the words so much that speak to me in these hymns. Some do: "Live for others everyday", "Break thy bread with hand unsparing", "There's a wideness in God's mercy", "A corn of wheat to multiply must fall into the ground and die", etc. But these hymns speak in ways far beyond words. I think it might have been my high school choir director who advised us, concerning the religious language in a piece of music we performed, that she wasn't asking us to sign it, just to sing it! There's a deep truth to that, as I found in this essay by D.H. Lawrence that resonates with me.

Hymns in a Man's Life
by
David Herbert Lawrence
1928

Nothing is more difficult than to determine what a child takes in, and does not take in, of its environment and teaching. This fact is brought home to me by the hymns which I learned as a child, and never forgot. They mean to me almost more than the finest poetry, and they have for me a more permanent value, somehow or other.

It is almost shameful to confess that the poems which have meant the most to me, like Wordsworth's Ode to Immortality and Keats's Odes, and pieces of Macbeth or As You Like It or Midsummer Night's Dream, and Goethe's lyrics, such as Uber allen Gipfeln ist Ruh, and Verlaine's Aynte poussela porte qui clancelle -- all these lovely poems which after all give the ultimate shape to one's life; all these lovely poems woven deep into a man's consciousness, are still not woven so deep in me as the rather banal Nonconformist hymns that penetrated through and through my childhood.

Each gentle dove
And sighing bough
That makes the eve
So fair to me
Has something far
Diviner now
To draw me back
To Galilee.
O Galilee, sweet Galilee,
Where Jesus loved so much to be,
O Galilee, sweet Galilee,
Come sing thy song again to me!

To me the word Galilee has a wonderful sound. The Lake of Galilee! I don't want to know where it is. I never want to go to Palestine. Galilee is one of those lovely, glamorous worlds, not places, that exist in the golden haze of a child's half-formed imagination. And in my man's imagination it is just the same. It has been left untouched. With regard to the hymns that had such a profound influence on my childish consciousness, there has been no crystallising out, no dwindling into actuality, no hardening into commonplace. They are the same to my Man's experience as they were to me nearly forty years ago. When all comes to all, the most precious element of life is wonder.

Even the real scientist works in the sense of wonder. The pity is, when he comes out of the laboratory he puts aside his wonder along with his apparatus, and tries to make it perfectly didactic. Science in its true condition of wonder is as religious as any religion. But didactic science is as dead and boring as dogmatic religion. Both are wonderless and productive of boredom, endless boredom.

Now we come back to the hymns. They live and glisten in the depths of the man's consciousness in undimmed wonder, because they have not been subjected to any criticism or analysis. By the time I was sixteen I had criticised and got over the Christian dogma.

It was quite easy for me; my immediate forbears had already done it for me. Salvation, heaven, Virgin birth, miracles, even the Christian dogma of right and wrong - one soon got them adjusted. I never could really worry about them. Heaven is one of the instinctive dreams. Right and wrong is something you can't dogmatise about; it's not so easy. As for my soul, I simply don't and never did understand how I could "save" it. One can save one's pennies. But how can one save one's soul? One can only live one's soul. The business is to live really alive. And this needs wonder.

I have some differences with Mr. Lawrence, though. First I'd love to go to the Lake of Galilee and see those places mentioned in the Bible where Jesus lived and taught. I hope some day I will. (I also would love to go to Crocknacrieve, Ireland to stand on that ground where the first Conventions were held.) Also, my arrival at a critical approach to Christian dogma was about 10 years later than his, and not so easily adjusted to. But his description of his pre-critical naivety and his post-critical naivety that the hymns he loved connected is a bullseye for how I feel.

I also got kind of a thrill because I knew those prayers we sang before meals. Here is my favorite one of all. I was tempted to just start it myself at the picnic after the funeral, and I kind of wish I had:

To Thee who doth the ravens feed
And lilies clothe with beauteous dress.
For rich supply of all our needs
We raise our song of thankfulness.

I am so grateful for Grandma and the many gifts she gave me. Those hymns are among the most dear.

A Broken Relic

The picture to right is a work of art I participated in at Unitarian Universalists of Sterling. (Click this link for background information.) I say "participated", because it was a collaborative, experiential artwork.

This project took a a lot of effort and I tried diligently to make this work. I synchronized my watch every few weeks with www.time.gov, perturbed many a speaker by putting up the mark on sunny Sundays at precisely the same time of day. Nevertheless I did not control all the variables. My guess is that the mirror moved though I don't know exactly why. I intended to put some hot glue on the hinge when it was installed, but it didn't get done. But though the analemma didn't close the way I intended, it is not because of some earth-moving cause. It would have been nice to for this project to go exactly as planned. What a tight, clean demonstration that would have been. But perhaps it is better that it did not. Maybe there's a deeper lesson here than I imagined.

I admit that I feel a certain disappointment, frustration, even shame in the fact that this project did not work out as well as I'd have liked. I have never failed so publicly before. I am accustomed to revealing my work after I have had a chance to edit and revise it. But this project put the creative process itself on public display.

I think there is a theological lesson in this. As it is human nature to do, anything that is sufficiently complicated or unpredictable tends to be attributed to a will or consciousness. We still do it all the time--with our pets, our cars, other people, even ourselves! When the object is the universe itself, we refer to this persona as God. This is not the only way to conceive of God, but it is a common one.

Before Newton's incredibly simple mechanistic description, the motion of the planets had been viewed as capricious and unpredictable. So this newly discovered rational order radically changed the nature of God's involvement with the universe in the minds of Enlightenment philosophers. God was perceived as a purely rational being that conceived of a perfect universe, created it ex nihilo, and set it in motion. This God is the ultimate planner and controller. This viewpoint was also heavily influenced by Renee Descartes, who's famous dictum is "I think therefore I am." Newton's discoveries allowed Enlightenment thinkers to be tempted to buy fully into Descartes' point of view. The ideal human being and by projection God was conceived as a rational agent in control of its fate. But we are not what we like to imagine we are, just ask Darwin or Freud. While Darwin's view of human origins had a reassuring mechanistic aspect to it, there was a disturbing element of chance involved. The adaptations that nature selects for arise from random mutations--the vast bulk of which are detrimental--and not from a cognitive process of rational intention. And Freud showed us that the rational persona we project to the world is really a fabrication, and that the bulk of our personalities are rooted in irrational processes we are not even fully conscious of.

Ultimately creativity is mostly an irrational process arising precisely from the making of mistakes, sorting through those mistakes, and finding something of beauty. That beauty is then refined and presented as if it had occurred all by itself. Consider the process of evolution. All species arise in response to conditions that are geologically momentary. The vast majority of all species that have ever existed are extinct, and it is the fate of all. As I described in the previous post, the process of scientific discovery is itself unscientific. Darwin and Freud left us a description of nature that implies a God that takes risks and mostly makes mistakes, and is only dimly aware of what it is even doing. A very different picture than the Enlightenment God.

Mistakes are a part of life, and admitting mistakes as soon as they come to awareness is a good practice. For one thing, it mitigates the consequences of the mistake itself and doesn't compound it with the further mistake of deception or disregard. But also it allows one to live in the truth. I guess I never could have failed this spectacularly unless I had attempted to do something bold. And there is a lot to be said for bold action. Of course it can be reckless and one should always "look before leaping". But one can also remain always looking and never leaping. That is itself a big mistake.

Finally, I feel like I have to fix this. I know the dates for all the marks, and I can calculate where the marks "should" be for those dates after the mirror slipped. I can re-aim the mirror, and fix it in place better this time. I think I will use a different color of metal for these "artificial" marks--maybe brass. Some people--I know they're trying to be nice--have said that they love the analemma the way it is. Well, first it isn't an analemma the way it is. And second, it is a marred work of art. It is a bit offensive for someone to say that they prefer you artwork after it's been marred. It says they didn't really appreciate its original concept very much. But I gueess as a gesture of goodwill, I will leave the "errant" marks up. When/if I get it done, I'll post another picture.

On the Road with Jesus, Romulus, and Buddha

There are two stories in the Gospel of Luke about post-resurrection appearances of Jesus. One is to two disciples as they travel along the road to Emmaus, and the other is to the apostle Paul on the road to Damascus. In the Life of Romulus, written at about the same time as Luke's Gospel, by the Greek writer Plutarch, we have another post-death appearance story, with intriguing similarities.

Evidently there were multiple stories that were told in the first century about heroes who appear to their friends after death while traveling on the road. The heroes' bodies disappear mysteriously after their deaths, and it seems to be their purpose in appearing later on the road to explain why--that they were sent from heaven for a divine purpose as an example to humanity and to establish a holy community. That purpose being fulfilled, they have been called back to their heavenly abode.

The different way that the heroes appear after death is interesting to me. Jesus appears as a stranger, not immediately known to his friends in Luke's gospel account. It is through the hospitality and generosity of breaking bread that he becomes recognizable. But Plutarch describes Romulus as immediately recognizable as a mighty warrior.

Here are the relevant texts:

Excerpt from Gospel of Luke

Now that same day two of them were going to a village called Emmaus, about seven miles from Jerusalem. They were talking with each other about everything that had happened. As they talked and discussed these things with each other, Jesus himself came up and walked along with them; but they were kept from recognizing him.

He asked them, "What are you discussing together as you walk along?"

They stood still, their faces downcast. One of them, named Cleopas, asked him, "Are you only a visitor to Jerusalem and do not know the things that have happened there in these days?"

"What things?" he asked.

"About Jesus of Nazareth," they replied. "He was a prophet, powerful in word and deed before God and all the people. The chief priests and our rulers handed him over to be sentenced to death, and they crucified him; but we had hoped that he was the one who was going to redeem Israel. And what is more, it is the third day since all this took place. In addition, some of our women amazed us. They went to the tomb early this morning but didn't find his body. They came and told us that they had seen a vision of angels, who said he was alive. Then some of our companions went to the tomb and found it just as the women had said, but him they did not see."

He said to them, "How foolish you are, and how slow of heart to believe all that the prophets have spoken! Did not the Christ have to suffer these things and then enter his glory?" And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself.

As they approached the village to which they were going, Jesus acted as if he were going farther. But they urged him strongly, "Stay with us, for it is nearly evening; the day is almost over." So he went in to stay with them.

When he was at the table with them, he took bread, gave thanks, broke it and began to give it to them. Then their eyes were opened and they recognized him, and he disappeared from their sight. They asked each other, "Were not our hearts burning within us while he talked with us on the road and opened the Scriptures to us?"

They got up and returned at once to Jerusalem. There they found the Eleven and those with them, assembled together and saying, "It is true! The Lord has risen and has appeared to Simon." Then the two told what had happened on the way, and how Jesus was recognized by them when he broke the bread.

Excerpt from Life of Romulus

Julius Proculus ... presented himself in the forum; and, taking a most sacred oath, protested before them all, that, as he was traveling on the road, he had seen Romulus coming to meet him, looking taller and comelier than ever, dressed in shining and flaming armor; and he, being affrighted at the apparition, said, "Why, O king, or for what purpose have you abandoned us to unjust and wicked surmises, and the whole city to bereavement and endless sorrow?" and that he made answer, "It pleased the gods, O Proculus, that we, who came from them, should remain so long a time amongst men as we did; and, having built a city to be the greatest in the world for empire and glory, should again return to heaven. But farewell; and tell the Romans, that, by the exercise of temperance and fortitude, they shall attain the height of human power; we will be to you the propitious god Quirinus." This seemed credible to the Romans, upon the honesty and oath of the relater, and indeed, too, there mingled with it a certain divine passion, some preternatural influence similar to possession by a divinity; nobody contradicted it, but, laying aside all jealousies and detractions, they prayed to Quirinus and saluted him as a god.

These stories put me in mind of the advice of the iconoclastic ninth-century Buddhist monk Zenji who wrote, "

If you meet the Buddha on the road, kill the Buddha. If you meet the patriarchs or the arhats on your way, kill them too...

Who cares if you saw Jesus or Romulus on the road? What authority does that give you or them?

Borg & Borges

The name of this blog is Orbis Tertius, which means Third World in Latin. The name was used by Jorge Luis Borges in his short story, Tlön, Uqbar, Orbis Tertius. (It also can refer to the planet Earth, which is the third world of our solar system.) Borges was way ahead of his time, and one could argue that the Internet is in some ways a Tlön. But why I love the story is because of how it portrays the power of ideas and of reality-as-perception.

Ideas matter, according to Marcus Borg, who says, "Ideas matter much more than we commonly think they do - especially our world-views and values, namely our ideas about what is real and how we are to live. We receive such ideas from our culture as we grow up, and unless we examine them, we will not be free persons, but will to a large extent live out the agenda of our socialization."

It is really hard for me to say it better than that. Basically we imagine our own reality. Our existential reality is really a huge conspiracy. Say what? What if a brick falls on your head? Did you just imagine that? No. But all of your attempts to make meaning of it come from you.

Science is one way to assimilate our sense experiences into a coherent reality. Clearly it has been extremely successful, witness the technology necessary to put this blog before our eyes. But it definitely has its limitations. There is a tight circle of tautology in saying that the only truth is a verifiable hypothesis. Who has verified that?

Moreover, the process of scientific discovery is itself unscientific. The creativity necessary to imagine new hypotheses, and the experiments necessary to corroborate them comes from a mental process far removed from the scientific method. It is only after the results of the experiments are analyzed and while the reports are being written that the scientific method is employed. There, the results are sanitized of all the non-scientific part of the process.

It's the same in mathematics. The way you think of a proof is almost never the way you write it down. There are some musicians I've heard of, Mozart I think, that wrote their compositions down all at once without making drafts first. And maybe there are "stream of consciousness" writers who don't make drafts. But most people are not like that. And I suspect that even these "savants" have something like a draft being compiled in their heads.

Hello World

I am going to try Blogger to begin a blog. I really have no purpose for this other than to express myself from time to time.