Macromemetic Index - Rules of Faspeel
Introduction
There are states of the game, and later I also want to explore the states in the minds of the players, the "belief systems." I may get into the latter in a separate essay, if not here.
Herein I deal with how there are "orthogonal memeplexes" which may be represented much more economically than if they were all completely entangled. As I'll show, the fact that the board locations are clear and distinct ("Near" vs. "Away") and the move positions are all "heads" or "tails" along with the turn-taking of the game, means little or no ambiguity, no "jinx events" (10) or race conditions.
In other words, the superficial states of the system are "well-marked." When it comes to the "belief system memeplexes," I think we can start to look at dynamic learning (forming of new links and matrices, adjusting of weights, etc.). Again, with the orthogonal memeplexes idea--the belief memeplexes of each player are driven by the same memetic deployments, each making state changes within their own confines, for example, when one player does a flip! it changes the state of the whole objective system on the board, and also the "belief systems" (12) of both players, i.e., their "beliefs" about what will happen next.
The Game Memeplex
The board contains the relative positions of the two players "show" coins, either Away or Near. This state we call R. Either player can deploy away! or near! to change to the other state. When Near, a player may bump! the other player's "show" coin, thus reverting the system to Away and revealing their "secret" coin and if it matches the bumper's "show" coin it's a share! otherwise it's a clash! (2).
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| fig. 1. States of the Board |
There are two players, each with state systems, P and Q. Each player's state consists of their "show" coin (on the board) and their "cover" coin (on the top of their "message," covering their "secret" (1)). The state of player P's "show" is Sh or P.Sh and the state of their cover is Co or P.Co. The "show" may be either "heads" or "tails" which we represent as Sh.Ta or Sh.He respectively. Transitions between these states are accomplished by the meme deployments flip! and shuffle! which symmetrically switch the states back and forth. The "show" and "cover" are also independent, effectively.
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| fig. 2. Coin States for Each Player |
What about the "secret" coin? That works out to be an immunomemetic/alliance deployment that immediately follows a bump! deployment (5). It is not part of the visible state of the system (hence the term "secret").
The Overall System
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| R: State of the Board | |
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| P: State of Player 1 | Q: State of Player 2 |
So we see how any one of the deployments depicted above may happen, according to which player's turn it is. Switching between Away and Near states does not impact the state of either player's "show" or "cover" coin, for instance. These states are all orthogonal to, or independent of, one another.
So we can denote the state of the whole system as RPQ, or for instance, QRP--more on this (7) when I get into the deployment descriptors, next. Note that the state of player one's things is P, and player one as an agent is p.
Deployment Descriptors
Deployment descriptors describe all of the individual actions, or memetic deployments, which may take place in this system. In a shorthand, I can describe all of the things that can happen in this system with the following few lines:
PQR.Away.[p, q].near! <=> PQR.Near.[p, q].away!
A word or two of explanation about this equation. Note that PQ appears on both sides. This indicates that the states of players one and two don't change, they remain the same on both sides of the transitions. Note the [p, q] and how it indicates that either agent may deploy the away! or near! meme when it is their turn.
Moving on to the descriptors for the memetic transactions when each player changes their own states.
R[Q, P][P, Q].Sh.[ Ta, He ].[p, q].flip! <=>
R[Q, P][P, Q].Sh.[ He, Ta ].[p, q].flip!
Here we see how the flip! meme changes the "show" state, Sh, from "heads" (He) to "tails" (Ta) and vice-versa. Note how the board state, R, stays the same across the transaction. One of the two player states [Q, P] remains static, while the other [P, Q].Sh changes.
R[Q,P][P,Q].Co.[[Ta,He],[Ta,He]].[p,q].shuffle! <=>
R[Q,P][P,Q].Co.[[He,Ta],[Ta,He]].[p,q].shuffle!
Here's a bit of a twist. The shuffle! meme can either swap the "cover" (Co) from "heads" to "tails" or it can remain the same (6), hence the [[Ta,He],[Ta,He]] to [[He,Ta],[Ta,He]] which denotes how the "cover" may switch or stay the same. The secret, of course, may or may not change as well, but that's not a visible aspect of system state. That is, the other player knows that you shuffled, but not whether you actually changed the "secret" or not, or, of course, whether it's "heads" or "tails."
And then there's the bumping, which is a little different. It only works in one direction, sending everybody to the Away state.
PQR.Near.[p, q].bump! => PQR.Away (8)
Of course, the bump! meme goes into a "compelled state" (5) which results in the deployment of either a share! or a clash! deployment, depending upon the "secret" of the bumped player, before returning to the Away state. This could be represented as an additional state (8) in the R submemeplex, but just putting the bump! meme is a kind of shorthand. Written out:
PQR.Near.[p, q].bump!clash! => PQR.Away
PQR.Near.[p, q].bump!share! => PQR.Away
This is kind of weird and non-deterministic, since in a given system a compelled state could lead to disparate states depending upon the "random" outcome. This is the nature of immunomemes, of course. When we say or do something we hope it will be well received and will lead to a good following state, but we also fear that there will be a bad reaction that we did not expect, and we shall lose face as a result. In an agent's "belief system" they might do a game-theory-like analysis of probable outcomes, but that is for another investigation. For now we just want to describe all of the possible states of the Faspeel game.
Break-Out of All Deployment Descriptors
PQR.Away.p.near! <=> PQR.Near.p.away!
PQR.Away.q.near! <=> PQR.Near.q.away!
PQR.Near.p.bump! => PQR.Away bump! is a shorthand for the two possible outcomes (8)
PQR.Near.q.bump! => PQR.Away
PQR.Near.p.bump!share! => PQR.Away (8)
PQR.Near.q.bump!share! => PQR.Away
PQR.Near.p.bump!clash! => PQR.Away
PQR.Near.q.bump!clash! => PQR.Away
RQP.Sh.Ta.p.flip! <=> RQP.Sh.He.p.flip! Pp flips tails to heads
RQP.Sh.He.p.flip! <=> RQP.Sh.Ta.p.flip! p flips heads to tails
RPQ.Sh.Ta.q.flip! <=> RPQ.Sh.He.q.flip! Qq flips tails to heads
RPQ.Sh.He.q.flip! <=> RPQ.Sh.Ta.q.flip! Q fliips heads to tails
RQP.Co.Ta.p.shuffle! <=> RQP.Co.He.p.shuffle! P shuffles cover tails to heads
RQP.Co.He.p.shuffle! <=> RQP.Co.Ta.p.shuffle! P shuffle heads to tails
RQP.Co.Ta.p.shuffle! <=> RQP.Co.Ta.p.shuffle! P shuffle tails no change
RQP.Co.He.p.shuffle! <=> RQP.Co.He.p.shuffle! P shuffle heads no change
RPQ.Co.Ta.q.shuffle! <=> RPQ.Co.He.q.shuffle!
RPQ.Co.He.q.shuffle! <=> RPQ.Co.Ta.q.shuffle!
RPQ.Co.Ta.q.shuffle! <=> RPQ.Co.Ta.q.shuffle!
RPQ.Co.He.q.shuffle! <=> RPQ.Co.He.q.shuffle!
The foregoing should encompass all of the possible moves at any point in the game.
Implications for Chess
My initial impetus was to model the game of chess as a two opposing societies comprised of individuals cooperating competitively with each against the other society. There might be some kind of evolution process taking place between the memetic systems of each side. Each piece would have its own ideomemplex (14) and the whole "team" would have a kind of shared endomemeplex (11) which would be effectively what was competing against the other side.
My problem was that I was mixing up the rules and strategies of chess and the actual play with the attitudes and decisions of the individual pieces (agents). I think what I've come up with here will prove useful. The state of the game is the separate, external memeplex, and each player has their own ideomemplex. In Faspeel there is no "deployment decision" problem as between the chess pieces, since there is only one "player" effectively.
Next steps might be to make the "cover" and the "flip" and the "Away/Near" all separate "agents" who try to decide which of them has the better chance of advancing the game, as opposed to that decision being monolithic.
It looks like the "game theory" (Nash equilibria) aspects lie primarily in the endomemeplexes, rather than an analysis of the board state (exomemeplex). This is the AI implication of this approach. A brute force, or optimized brute force approach to chess (or any such game) consists in looking at the board and deciding the best move based upon projected possible countermoves. The approach I suggest looks mainly at the other's likely intensions. In Faspeel, there is only the board situation, and what I think the other player is trying to tell me. There is never enough information to pick the next best move based just on the board itself.
If I can learn that the other player favors advancing their bishops in certain situations, is generally cautious about getting their queen out, is excessively willing to sacrifice pawns, or do trades, and so on, I can focus on what they are likely to do, and maybe where that will land me, and not worry about what they are very unlikely to do. Also, it might allow me to play an "intimidation game" or a "tricky/trappy game" which might otherwise be impossible to attempt.
Such a model, if computerized, could potentially learn the play style of any number of master chess players, based upon the moves of their documented games, perhaps later beating them at their own game, or allow more junior players to "play with the Big Boys" without actually having to schedule a match (13).
Conclusions & Further Investigations
I've put forward the idea of "orthogonal" or "independent" submemeplexes, and also a notational system for these in terms of state transition diagrams and deployment descriptors which appear to be useful. The hope is that these concepts and techniques will go a long way towards reducing the complexity associated with description and analysis of (some) memetic systems.
There may be implications for long-standing real-world modeling problems which I've yet to effectively address (10). Submemeplexes, artificial as they may or may not be, provide a way to represent the system without "everything being connected to everything".
One idea I had, which I will explore in a future essay, is how to model "belief matrices" or "belief endomemeplexes" (11) which govern how each player "thinks" the other player is going to act. The bad news is that these will certainly be messier that what we've seen here, but the good news is that they may be orthogonal to the physical state memeplexes in a similar way to how these are orthogonal to one another. In other words, adding an increasingly complex, or one for which there may be multiple possible implementations, system for modeling things like strategies, beliefs ("they want to cooperate" or "they're trying to trick me" or "they're just playing randomly" etc.) will result in no linking between the submemeplexes. The other playing flipping their coin is a meme that changes the physical states of the system, and it may also change my beliefs about what is happening, but the state changes in both of these memeplexes will be decoupled. At least that is my hope.
Ultimately, I have the goal in mind of modeling chess as a memetic system. It occurs to me that rather than modeling the ideomemetic behavior of each player in Faspeel, it might be more in the right direction to model the "show," the "cover," and the near! away! or bump! meme decision all as separate agents that then use game theory considerations to decide which one goes. Hopefully that will be "cleaner" than what I was thinking of, and be a step in the right direction for the chess project.
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(1) Per the rules, each player has a stack of two coins, one on top of the other,
(2) This rule may vary (3) but when the coins (share!) match each player gets two points and when they conflict (clash!) both players flip coins to work out the result (3).
(3) In a clash! both players flip coins, and if they both come up "tails" the bumped player gets three points. Otherwise, the bumping player gets one point. (4)
(4) Variations on this, which comes to "The Dating Game", are that on double heads the bumping player either gets zero points, or gets two points, and otherwise gets one. The zero points one is the "cautious version", the two-pointer the "aggressive version" and the one-pointer the "even money version." So called because with "even money" there is no advantage to trying to work out the other player's signals and just "going for it."
(5) There is an "implied" or "constrained" state (9) that exists between the bump! deployment and the immediately clash! or share! deployment. This means that the bumper initiates the action, but has no power over what happens next, which is effectively an immunomemetic/alliance deployment by the bumped player.
(6) A player may shuffle their "message" coins without actually changing anything, or by changing the secret and keeping the covering coin the same.
(7) Orthogonal states may be listed in any order, and without period delimiters between. Contrast this with the state of the show coin of, say, player 2, being "heads" which we denote as Q.Sh.He in other words, the "show" coin state, and the value of that state are substates of player two's state, hence, period delimiters. The state of player two "contains" the substates of "cover" and "show" and each of these may have a state of "heads" or "tails" so all possible states are: Q.Sh.He, Q.Sh.Ta, Q.Co.He, and Q.Co.Ta. If the state Q is mentioned without substates on both sides of a deployment descriptor, this means that nothing about that state has changed during the deployment.
(8) The two memetic pathways, in immunomemetic/alliance notation look like: PQR.Near.[p,q].bump!share! => PQR.Away and PQR.Near.[p,q].bump!clash! => PQR.Away. There are several options for representing this on a state transition diagram. One is to have a "compelled state" or "virtual state" (9) into which the bump! meme enters, and two memes, clash! and share! exit. Another is to have two compound memes going from the Near to the Away states.
(9) I have not as of yet officially settled upon a notational convention for a compelled state, that is, like the "cloud" symbol I use for regular states. What I have been using more or less consistently so far is a cloud with no name on it, indicating that once entered the state is immediately exited and nobody has any decision power in the choice of the outgoing memes.
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| fig. 9.1. compelled State form | fig. 9.2 immunomemetic form |
(10) Some things that come up in modeling multi-agent, real-world memetic modeling are jinx events, race conditions, and deployment decision. If two agents "want" to deploy a meme at the same time, or actually deploy memes at the same moment, or the relative time it takes agents to "get ready" to deploy a meme, or to decide to do so, or even stages of deploying memes based on growing or dwindling support of other agents. The artificial turn-taking associated with a game simplifies things, obviously. But orthogonal submemeplexes are a away to think about more complex systems without it all rapidly turning into one giant blob with all states potentially connected to all other states via all possible memes, ultimately with a plethora of "weights" attached to every possible interaction. I may have to deal with that soon enough in the next essay on endomemetic systems to do with Faspeel and "belief matrices" and such.
(11) An endomemeplex (as opposed to an "exomemeplex," i.e., an externally visible memeplex (13), which we usually just call a "memeplex") is a system internal to an agent which that agent uses to decide how to interact with an (the) exomemeplex. The endomemeplex accepts external (and internal) stimuli, deploys internal memes (which we can call "decision processes" (12)) based on internal states (which could be termed "beliefs" (12)), and finally produces memetic deployments into the exomemeplex (which could be termed "decisions" (12) or "actions" (including the "null meme" or "doing nothing").
(12) "Beliefs," "decision processes," and "decisions" in the phraseology of macromemetics may or may not resemble what one conventionally regards as such, naturally.
(13) When we consider the interaction between an individual's endomemeplex (or ideomemeplex in the case of a single individual (14)), one can see the possible therapeutic value of such activities as playing video games. A primary anxiety of the individual in taking decisions is immunomemetic pushback from others, or more to the point, that the system state will be pushed into an unfavorable configuration for said individual by their making a misstep. A video game, for example, provides a "state reset" wherein the individual's mistakes do not have permanent effect. One is able to play out the same series of memetic deployments over and over without that primary fear of long-term consequences. However, the ability to "roam around" for an extended period in an environment where immunomemetic consequences are suspended may have many benefits, even therapeutic ones.
(14) A subtle distinction may be drawn between endomemeplexes and ideomemeplexes. In memetic hacking (15), one tries to get a picture of a cohort's overall propensity to respond to given stimuli, e.g., likelihood to vote for a certain candidate, buy a certain product, engage in racist/sexist behavior, etc. Members of a memetic cohort share large portions of a "shared endomemeplex," e.g., speaking the same language or dialect, religious beliefs, recognized symbols, preferred foods and activities, etc. and also, importantly, fears about being bullied by their fellows about things, even if nobody in reality "believes" them. Every individual has their own internal ideomemeplex that governs their behavior, and this tends to be an "overlapping set" with the cohort/societal norm endomemeplex. You could say that an ideomemeplex is an "implementation" of an endomemeplex, which is in turn an "abstraction" of a group's "values and predilections."
(15) Memetic hacking (a term I invented long ago and which I've stuck with) is the process of probing individuals to try to get an idea of what sort of memetic responses they exhibit, and possibly are likely to exhibit later. An example of "passive" memetic hacking might be wearing a T-shirt with a certain slogan or image around, to see what response it gets. No response anywhere might suggest that there is no resonance in the cohort to the given meme. Active positive or negative response, or just widespread recognition might suggest that the given meme could be used to influence the cohort. "Active" or "aggressive" memetic hacking consists of asking individuals questions or posing hypotheticals, or offering free/discounted items to see if they are accepted, or even more nefariously, perhaps, seeing how individuals respond to things like "confidence schemes" or "fake news." In memetic hacking, we are ostensibly trying to get a picture of the endomemeplex of a cohort, but we are doing it by investigating the ideomemeplexes of a collection of individuals.
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