模倣子 Alliances and Nexuses in Chess Model

 Memetic Index - Glossary - Chess Model Article 


We're looking at the good old familiar chess board as a collection of individuals who together decide to make moves. In a human population we see things like memetic nexuses (1) and alliances (2). They learn as a group. The way in which human beings (agents) behave memetically is a psychological question. The way in which our chess pieces behave will be according to some formal model, ultimately arbitrary. The objective will be to try to find some models that seem to work satisfactorily. The next step will be to observe the statistical behavior of actual groups of people and tweak our formal models to more closely track what happens in real life.

In macromemetic theory we have concepts such as residual memetic debt, alliances, immunomemes, and memetic nexuses. We want to have these concepts modeled explicitly in our chess memeplex. In this way we can extract the influence of these structures in our chess model, and then hope to extract them from real life data. If we can identify the agents involved in alliances and nexuses, the memetic debt associated with identifiable meme transactions, and how immunomemes are employed, we can start to quantify these things. The ultimate goal is to have observable phenomena (the deployment of memes, by whom, how, with what frequency) which we can quantify, and laws that that translate those measured quantities into numerical predictions, and furthermore, numerical predictions as to how a system may be controlled by engineered interventions into the system in question.

Notation for Memetic Nexuses 

The idea here is that one piece, say, the queen, expresses a "preference" for a given move, and that this would make it easier or harder for other pieces to "vote" for the same moves. I've hypothesized previously that memetic nexuses are directly related to "power." Alliance behavior also seems to be related to power.  They may be two prongs, or maybe even fundamentally the same thing. I explored notation for chess moves in my previous article on chess notation. 

fig. 1. Three Moves to get King out of Check

White has to decide how to get their king out of check. A bad way would be to advance the queen, or the move "WhiteTurn.qd2!" Moving the bishop with "WhiteTurn.bd2!" is at least a little better, with the possibility of an even trade. Finally white can advance the bishop's pawn "WhiteTurn.c3!", which can also lead to a good trade, as well as forcing the bishop to move.

WhiteTurn.[ qd2!, bd2!, c3! ][a1-ap].[ support!, oppose! ] => RelieveCheck

fig. 2. Expression for all possible Moves and piece (agent) "voting"

Let's say the queen "dislikes" sacrificing herself to get out of check. Let's further say that the bishop "likes" the idea of the pawn moving forward. We could try denoting the using immunomemetic notation. 

WhiteTurn.qd2!qd1.dislike! => NoQueenSacrifice
WhiteTurn.c3!bc1.like! => BishopLikesPawn

fig. 3. Queen and Bishop express preferences for two moves

We can think of these as "virtual states" or "hidden states" in that the system does not really "stop" on them and we don't really need to name them explicitly. They are handled by immunomemetic notation. How this can act as a memetic nexus is as follows. Those pieces that are "listening" to the queen (4) can assume that other pieces are listening to the queen as well, and so if they throw their weight behind her "disliking" the "queen sacrifice" move, there will be a lot of support for the move, and that the move will succeed. In other words, they gamble a certain amount of memetic debt, or open a memetic loop, being fairly comfortable that they will get that memetic investment back (3).

(a1)  WhiteTurn.[ qd2!, c3!, bd2! ] [a1 -ap] .[ support!, oppose! ] => MoveChoice
(a2)  WhiteTurn.[ a1 -ap ].[ like!, dislike! ].[a1 -ap].[ support!, oppose! ] => MoveChoice

(b) WhiteTurn.qd2!qd1.dislike![ q, r[a, h]1, n7 ].oppose! => MoveChoice
(c) WhiteTurn.c3!bd2.like![ b[c, f]1 ].support! => MoveChoice

(d1) WhiteTurn.c3![ [a-c, e-h]2, d3 ].oppose! => MoveChoice
(d2) WhiteTurn.c3![ [a-c, e-h]2, d3 ].dislike!
[ [a-c, e-h]2, d3 ].oppose! => MoveChoice

fig. 4. Contrast Nexus-Influenced Versus "Random" Deployment Decisions

First off, the "MoveChoice" state is a compelled state that the system goes into when all of the "like!/dislike!" and "support!/oppose!" deployments have been made, and some selection method determines which move is actually made (8).  Let's look at figs. 4a1. and 4a2. The difference is that some agent "recommends" a course of action (memetic deployment) prior to other agents having the opportunity to deploy their memes. We see this in the state transition diagram.

fig. 5. State Diagram showing nexus-supported and unsupported transitions

The idea is that we have two parallel memetic pathways, one involving a "like!" or "dislike!" before and the other not. In the figs. 4a., 4b., and 4d2, we can almost see "move!nexus.dislike![ nexus subscription cohort ].oppose!". In other words, we may have found our embedded notation for memetic nexuses, that is, the agents (cohort) who are subscribed to the nexus are indicated in the deployment descriptor, if the individual agent "decides to deploy" the given meme being supported by the nexus.

One thing to note, too, in fig. 4d2., is that all of the pawns are complaining about the pawn being thrown into harm's way. They all protest. In the case of the bishop or the queen, one player is making a case for or against, only one voice being raised, and the others deciding, guessing, whether there's enough charisma to get the measure through or not. In the pawns' case, an onlooker knows how many people are likely to vote for it, since they all complained, deployed a "dislike!". In other words, in fig. 4d2 it's "the mob" and in figs. 4b and 4c, it's the charismatic leader, the demagogue if you will. I will write up one or two ways to actually model this programmatically in the appendix. 

One takeaway is that the meme "agent.support!" is much more "uncertain" than "nexus.like!agent.support!". In the former the agent is taking a wild guess as to whether anybody else will support it, and risking losing the bet and accruing residual memetic debt (the worst outcome for a memetic agent). On the other hand, if the nexus has deployed a polarizing message, then there is a chance that others will rally to the cause, especially if the cohort is large and loyal. Finally, we may be able to enbed the cohort membership in the deployment descriptor in the form of the "list" following the meme deployment following the "like!" or "dislike!". It remains to be seen how well this will work. It's important to remember that these are two different memes, so the perceptions of risks and rewards and even if a given agent considers one or the other to even be in his memetic inventory, are all potentially different.

Implications for Alliances 

With the immunomemetic-style notation, we see how it applies to alliances and now to nexuses. The syntax is very much the same, if not identical. We may not need a separate treatment for alliances in this essay. More may be revealed later, but for now let's look at what we have. For instance, the queen "suggesting" a given move, she is acting as an ally to all of her members (and those who may not be members but who join in on an ad hoc basis (6)).

Conclusion & Summary 

First, it's possible to model a nexus behavior using immunomemetic-style deployment descriptors. Further, it may be possible to embed the nexus subscribing cohort in the deployment descriptor, perhaps in a useful way.

The notation has led us to an interesting relationship between nexuses and alliances, and so may give use a clear idea of how to define, represent, and masure power. As memetic engineers, out goal is exact and relevant measurement, and the application of laws of a quantitative science in order to create (or consoliate) power where it does not exist, or to dismantle it where it does and is being misued, and all without bloodshed, unlike with practically all major power transitions in history.

Further Research 

One area is the loss/gain of status of agents, nexuses, and agents who follow them. This is both whether a meme is chosen for deployment (residual memetic debt). Also there is how well the game is going. How might it work to give all agents a kick (+1 points) if they bet on a successful deployment (or anti-recommendation), and each agent also have a kick up or down if they supported it based on another piece's recommendation. The power of a memetic nexus (or mentor) ultimately stems from how many others continue to follow their deployments.

How useful is our representation of memetic nexus cohorts in immunomementic deployment descriptors? Will it prove unwieldy? Is it easy to read and understand?

Can we look at historical checkmates and back-propagate them in order to train and analyse.

Competition of two societies (opposite colors on the board). For example, central control by queen (or other) versus more democracy, or uncooperative pawns, and so forth.

How can the system "learn" without having to add a lot of notation and behind-the-scenes stuff? Can a memetic nexus lose currency, or the perceived value of their recommendations?

Also, once we have a microcosm going, how can we begin to use it to model real life situations? How to identify these first test groups?



模倣子 State Progression in Chess

Memetic Glossary



Concrete Models of Nexus-Based Deployments 

All possible moves are the memes, but there are only a few moves per turn, and some might be absurd (whether we can judge that at this point is unclear). The first order of business is working out which move gets run. It's arbitrary, and a number of methods could be suggested.

One. The point value of each piece is applied against the "oppose!" or "support!" memes, add them up as I suggest in the previous essay.  Another would simply be to count the number of deployments, one piece, one vote.

The next thing, once the memes are selected, is to list the winners and the losers and decide how to reward or punish them. This is a memetic loop, residual memetic debt kind of concept. Each piece makes an investment, a bet, and if they win or lose (based on the previous considerations), what happens? This could be thought of as the "selection function" in genetic algorithm design.

With a memetic nexus, it's a mix of things. If you have a setback, it might not always be easy to say for certain that it was your faith in your memetic nexus' memes that was the culprit. Plus, there tends to be a lot of collateral emotional investment (which is probably directly related to residual memetic debt, by th way), but that' shouldn't be an issue in our early stages here.

At the end of the day, it comes down to the difference between the likelihood of deploying "agent.meme!" and "nexus.bias!agent.meme!". If the agent sees no great difference in the risk reward of these two memes, then his faith in the nexus has either not developed yet or has collapsed under the weight of a series of failures (7).

How do we model this?

One simple way is that if a given piece consistently gets her suggestions passed is attractive.

More on this later!



(1) Memetic nexus refers to a central agent connected to a collection of other agents via a "short jump" wherein the cental agent pumps out memes to all of them simultaneously. I have not yet put together a good notational description for this, but I think the same immunomemetic notation may serve well.

(2) An alliance is a configuration where a benefactor (or mentor) deploys memes which enable a beneficiary (or protegee) to deploy memes they would not otherwise be able to do (score a goal, secure a job interview, etc.). I use the same notation for alliance interactions as for immunomemetic exchanges. This makes a certain sense since immunomemetic memes and alliance memes alike serve to modify the effect of one meme to produce a different state from the one "intended." For example, "State1.protegee.run-downfield!mentor.pass-ball! => PassComplete" or "State2.mentor.block!protegee.score! => MadeGoal" or "State3.agent.try!enemy.block! => Blocked!"

(3) Memetic debt is "incurred" by deploying a meme, which opens a memetic loop. The loop is closed when the expected resonance to the deployed meme actually happens, for example, the group decision one supported is taken, the audience laughs at one's joke, and so on. An open question is whether there is additional memetic reward associated with the resonance success. This is almost certainly true, and needs to be accounted for, and this is going to be critical to quantitative memetic engineering down the track. For now we make arbitrary decisions in our model. There is also the idea of an agent losing status, so the weight of their liking/disliking and even the success of a group deployment diminishes (or grows).

(4) One aspect of a memetic nexus which is not contained by this simple notation is the idea of agents "subscribing" to the nexus. All we see is that the queen "likes" something, and this potentially influences the choices of the other agents. This isn't like an ally, where a new state is created (potentally a hidden one) that enables the protegee or benefactor to get to a new state that would be impossible otherwise. This nexus notation (which is the same notation) just expresses that a meme was deployed by the center of the nexus, but does not tell us which agents are going to respond. This would be some behind-the-scenes matrix or such, possibly with weights, possibly with each agent having some kind of internal state, possibly resembling a memeplex itself. Anyway, what we want is that if the queen (or the bishop) deploys a "like!/dislike!" meme, it signals that the following memes in the deployment descriptor might be a better-than-average choice. Another factor is feedback as to the record of successes garnered by subscribing to a given nexus. If it continues to go well, it might become more and more attractive somehow, which is what we would expect from our model.

(5) This final move selection method may be highly contrived for now. I may write up some ideas in the appendix.

(6) I have never stipulated that a memetic nexus cohort has to be a definite list, or that it cannot be fluid. The key feature is that agents who consume the nexus' memes and then use them with other members of the nexus are effectively members. If the queen recommends a move, she is doing the same thing, that is, making a given meme appealing for a large number of agents. So we see through this new notation for nexuses that alliances and nexuses are potentially very similar, if not identical, and so their both having a relationship to the memetic definition of power may be vendicated.

(7) What about an agent's overall assesment of how the game is going, and linking that to the performance of nexuses. Some kind of more sophisticated approach would be needed, but what? It may be pretty arbitrary. We're looking for group behavior coming from following of simple memetic rules and a clear notation to discuss then. It may well be that pieces could have their own, different criteria for how well it's going. Crazy example: the pawns, in addtion to tracking successful deployment decisions, could also worry about how many pawns have been killed off over time. For instance, if they're followed the queen's advice for a series of moves, the moves have been accepted (closing memeic loops), but half the pawns have been captured over that time, and they don't like that, so they start to ignore the queen.

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