Introduction
I've already laid out some notation for how to represent a chess board as a memetic society with 32 citizens and a very large number of clearly defined states and clear ways for describing and denotating them (4).
I'd like to explore the idea of how the board progresses from state to state, that is, how does each subcohort (the white and the black) decide which move to make next? I've proposed looking at it from the standpoint of a deployment decision competition among the various players on a given side who are actually able to move. If we go back to the laws of macromemetics, in particular the second, we can imagine memetic exchanges, like pieces could "holler" and "whisper" to each other (1,2), helping them to arrive at a next move.
What about memetic nexuses, alliances, immunomemes, and maybe even the three-narrative model?
Group Selection of Deployments
Let's look at a notation that tries to depict each piece (agent) being able to "support!", "oppose!", or "demur!" (17) any move that could be made at the given board state. We ultimately want to include ideas such as:
a. the "strength" of a given piece (9) adding weight to its support or opposition to a move
b. a piece's "prestige" going up or down based on whether a move "succeeds"
c. the long-term consequences of support (or opposed) moves impacting a piece's "prestige" (16)
We want to include the concepts of memetic debt, alliances, and memetic nexuses. These would probably include something like messages (memes) passed between pieces, to induce them to support one idea or another, with the promise of (memetic) reward. We then treat all the memes for the non-moving pieces like immunomemes, which may either "support!", "oppose!", or "demur!". In a general expression where there are agents (a) 1 through p, and memes (moves) 1 through n. The asterisk (*) denotes restriction to pieces and moves which are available at the given board state.
WhiteTurn.[ [ a1-ap ]*.[ m1!-mn! ]* ].[ [ a1-ap ].[ oppose!, demur!, support! ]
fig. 1. Expression for Deployment and Public Reaction
Here things start to look more like an immunomemetic expression, which also looks like an alliance behavior. We can start with all of the possible opening moves, without the immunomemes at first, to see what they look like. Again, here's the notation for all the spaces and moves on the board, and I've noted the names of the twelve possible opening moves.
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| fig. 2a. Annotated Chess Board and all Opening Moves |
Note that I'm using all lowercase for the chess algebraic notation, since I want to show them as agents, not states (7). In other words, not "Nb1" or "Nc3" but "nb1" and "nc3".
fig. 2b. All Opening Moves, Each Piece as Its Own Agent
Now we can try adding the immunomemes that determine whether each move actually happens (11). Each piece (agent) gets to deploy one meme in response to one move, or even no meme at all (12). Note that all agents
These approval memes are effectively asynchronous, that is, they can all be happening all at once, while the actual move is synchronous, only able to happen once all the dust has settled (13). We need some kind of way of selecting which move happens, for the sake of this model.
A Gigantic Quantity of States
The number of configurations for a chess board is enormous. It may be on the order of a google, or a billion trillion googles (10120).
In state transition matrix (agents by available memes), we see the opening move (18) like this, with two possible moves for each pawn and two for each knight. To save space, we'll denote the pawn moves as +1 and +2, instead of a3, a4, b3, b4, etc. We could devise a similar notation for the knights, e.g., north-right, north-left, with east, west, and south being impossible on the first move.
| memes! / agents |
+1 | +2 | na3 | nc3 | nf3 | nh3 |
| a2 | S1 | S2 | ||||
| b2 | S3 | S4 | ||||
| c2 | S5 | S6 | ||||
| d2 | S7 | S8 | ||||
| e2 | S9 | S10 | ||||
| f2 | S11 | S12 | ||||
| g2 | S13 | S14 | ||||
| h2 | S15 | S16 | ||||
| nb1 | S17 | S18 | ||||
| ng1 | S19 | S20 |
fig. 2a. Transition Matrix for Opening Chess Moves
Each transition leads to a new state, which in turn has transitions (moves) to other states. Clearly, we'd require a google of these state transition matrices needed to describe all possible options for all possible games. However, there is a commonality between transition matrices and deployment descriptors, so we could describe the following game by the following string of deployments (memes).
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| fig. 2b. A simple game opening |
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| fig. 2d. Next Move: Bishop Checks King |
The notation we've developed so far may be enough to support a useful model. The following is just an example.
Pieces all have point values: pawn = 1, knight / bishop = 3, rook = 5, queen = 9, king = ∞. Just for instance, we can use these values to weight the support or non-support of a given piece for a given action. In a deployment situation, for example:
WhiteTurn.nc3![ q, [a-c]2, bc ].oppose![ ra, [g-h]2 ].support! => WhiteTurn
queen:9 + (pawn x 3):3 + bishop:3 = 15 "opposed"
rook:5 + (pawn x 2):2 = 7 "support"
WhiteTurn.b2.b3![ b2, bc3 ].support! => BlackTurn
pawn:1 + bishop:3 = 4
fig. A1a. Knight move defeated, pawn move supported
A move may be thus defeated, but are we still left with the possibility of ties? There are eight pawns, four knights and bishops for 12 points, 10 points worth of rooks, and a queen worth 9. It's unclear how or if the king should vote (one point? tiebreaker?). We could say, for the sake of argument, that however many moves are approved, the highest-scoring one wins (counting support less opposition) and the king breaks ties. If nobody pushes for a move, or they all get shot down, then the king picks one.
Clearly. this is a very contrived example, something suitable for a programmatic implementation, for example. In this simple example there is no learning, and there is no possibility for alliances (how might we add this?). A piece (agent) who takes part of a successful memetic deployment, that is, votes to support it or oppose it, needs to get or lose points, which makes his power, his memetic currency greater or lesser in future votes. This is also unimplemented in our simple example.
One possibly fruitful direction is the concept of "ostentation as (ostensible) memetic currency," or some kind of display, like finery and ostentation (among birds and humans) as a signal of memetic power (follow me and you'll do well).
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Appendix
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Until now I have maintained that a MIAO is more of a concrete object, to which memetic deployment opportunities attach, but this doesn't translate into useable notation. It occurs to me that a MIAO, implemented as a meme, acts in a kind of alliance-forming way. For example, the US Flag is an icon, and apple pie is iconic, but less so if by itself. The Statue of Liberty is a symbol both of emigration and of American patriotism which even xenophobes freely and non-ironically embrace. The 4th of July is America's National Day. So we have memes like "july4th!", "pie!(apple)" (as opposed to "pie!(pumpkin)" or "pie!(cherry)"), "statue-of-liberty!", "us-flag". Here we see how the icon, or the MIAO, of the 4th of July ("july4th!") strengthens the other memes or changes their meaning. July 4th makes apple pie prevalent over other pies, and the Statue of Liberty is about patriotism more than emigration.
fig. A2. MIAO-like influence of US icons on other memes
So what does this have to do with chess as a memeplex?
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Bibliography
模倣子 Notation and Dynamics of Alliance Theory
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Footnotes
(1) To continue with this whimsical example, a knight who's able to jump to a position affording a better control of the center might "call out" to the other pieces something like "I'm keen to move" which could cause a transfer to a different state where the other pieces are less inclined to move themselves.
(2) This is perhaps similar to my "See-and-Say Steering Wheel" proposal. I'll probably write a whole piece about this elsewhere. The point is that traffic road rage is theoretically exacerbated by the lack of memetic inventory available for drivers to communicate (exchange memes) with one another. The simple expedient of adding a few more horn sounds (3)
(3) The See-and-Say horn sounds should be iconic, and with an even distribution of "positive" and "negative" ones. For instance, cat meowing, dog barking, farting, cow mooing, rooster crowing, and so forth. Some of these sounds might be considered "aggressive," or "mocking," while others are friendlier. Actually, this is all theoretical. Research needs to be done as to how many horn sounds would be optimal, or even minimal, and which ones "work best," and what that might mean. The hope is that some of these kinds of questions might be illuminated by the chess model, how pieces might "talk to" each other in order to arrive at a move decision.
(4) I'm interested in some kind of "many worlds" model of the progression of the board. It might be useful for developing some kind of genetic (memetic) algorithm for refining the behavior of the system, which might include immunomemetic systems (5).
(5) What role do immunomemes play in the chess system? How about alliances? These are really important questions since I've been developing these things lately, so they should fit into any meaningful model of anything. Another thing to consider is memetic nexuses. All of these things should figure strongly in a miniature model of society and help it to function.
(6) Each piece makes its own "recommendation" for what the next move should be.
(7) agents and memes are denoted by hyphenated lowercase, memes with an exclamation mark after. States are CamelCaps, with underbars if needed.
(8) Using lowercase for chess pieces is unambiguous except for the bishops, so it should work.
(9) I think I need a term for this, perhaps "memetic karma" or "memetic currency." Agents see other agents as favoring one or another deployment, and depending upon their "status" those deployments are seen as more or less favorable. Are these two quantities related, the same thing, totally separate? At this point we're starting to put together an artificial model. "Status" may be something between each agent, or perhaps an agent has "global status." The minions of a kingmaker may perceive said kingmaker more highly than random people. The agent who fails in deployment face-offs may also lose self-confidence in addition to the (social) confidence.
(10) "Evil triumphs when brave men do nothing." This happens when there is no other meme to be deployed with hope of success. Even if there seems to be no valuable effect, deploying something as a collective and not in step with a bad movement can perhaps be valuable.
(11) We assume that each player "voting" only gets one vote, that is, in favor, opposition, or tacit acceptance, of only one possible move. This is just a simplifying choice, however. One can easily imagine agents supporting multiple possible outcomes in one form or another.
(12) Again, deploying no meme at all may be a physiological impossibility. That is, if somebody deploys a meme that you recognize, then by definition you must react, even if it's to take no outwardly discernable action, or even recognize it at a "conscious" level. For example, you always recognize words and sentences in your native language--they just jump right into your head, fully formed, without a lot of "conscious" pre-processing. In our modeling, it's probably useful to simplify and posit that it's possible for an agent to not react at all to a given move, or to any moves.
(13) One can imagine memes being passed back and forth, publicly or between individuals, to control the way they deploy their memes. Something like "canvas!" or "prompt!" or "pitch!" or "query!" (like a subscriber to a nexus asking which meme to deploy). We may be able to integrate this later.
(14) Immunomemetic notation refers to stacking memes up. This effectively "hides" a state (15). This works for alliances, "agent.attempt!ally.help!agent.succeeds!" or "ally.set-up!agent.success!". Immunomenes work to block other memes. Meme deployments, by definition, cause state transitions, and immunomemes prevent such changes, or redirect the system to "safe" states. For instance, while with "State1.agent.attempt! => State2", agent gets what she wants, but with "State1.agent.attempt!enemy.block! => State1" has an enemy sending the system back to State1. But again, by definition, there is a state that "attempt!" sends the system to, and then "block!" sends it back, but we don't bother to name this "virtual state."
(15) There are three kinds of "hidden state," but the idea is the same. The system does not stop in the hidden state (or "virtual state" or "compelled state") and one is obliged to immedaitely deploy a meme to get to another state, and the choices of states and memes are limited. One truism is "agents hate compelled states." And example of a compelled state where the agent is hurled into one of two states depending on environmental circumstances (what the kids are up to when the parent barges in, which they don't a priori know). The concept of a "compelled state" first appears in my first Dining Philosopher's essay. If a state does not compel an agent to another state (in an undesirable way), or there are interesting transactions that take place but are hidden in a "black box", then a "virtual state" is a neutral term. This sort of thing happens when an immunomeme is deployed to block the effects of a deployed meme, and the system goes back to where it was or to a different state. We don't really care about, to give a name to, the state that exists between the deployment of a meme and it's defeat at the hand of an immunomeme. This looks like "State1.agent1.meme!agent2.immunomeme! => State1" There's a state between the deployment of the two memes, obvious, but there are no deployment choices there, and except for maybe an "awkward pause," nothing interesting happens in that state, so we might call it a "virtual state."
(16) A piece becoming more prestigious based on whether the moves it supports actually getting made and the positive or negative impact said moves have on the game. The latter is a complex question. Any number of algorithms, such as back-propagation from when a valuable piece is captured, or when an enemy (or friendly) king is checked. This will probably be "behind the scenes" to the notation we'll build in this essay. The simplest case is random, possibly using piece "points" as "status" values, and no change in status over time.
(17) The "demur!" meme doesn't really do much, that is, agents deploying it or not makes no difference. However, a piece can deploy it against themselves, that is, they don't "oppose!" or support" their own move. For instance, the queen's knight opener, "WhiteTurn.nb1.na3!" (or just "na3!") lacks an immunomemetic term, so we don't know if we can evaluate whether any other agents support or oppose, even the knight itself. If we put "na3!nb1.demur!" we know that it's an immunomemetic expression. If we hold that a move cannot be made until the support or opposition can be evaluated, then this notational convention helps.
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