Meme Index - Glossary - Faspeel Game - Last "Helper Memes" Essay - Next Essay
Introduction
The idea of a memetic state is useful for engineering design purposes, or for visualizing simple systems, but it may be problematic for large organic systems about which little is known to begin with. We can see them memes and the agents, but we can't see the "states," as such.
We may be able to define or describe a state in an alternate way, for example, "this is the state we're in, because we just saw a specific sequence of memes deployed." We might call these sequences, or cascades, and they may work for us in a similar way to detecting high-energy, short-lived particles in a cloud chamber attached to an atom-smasher (1), that is, if we see a sequence of memes in succession (2) that may tell us what state we are in (3), and thus what is likely to happen next. We may also be able to play the sequence in reverse and get an idea of which coherent state (4) we came from.
So cascades of memes may be interchangeable with our preëxisting ideas of memetic states. So with enough
observation of functioning memeplexes, we may actually be able to
construct state diagrams, deployment descriptors, and
state matrices from that direct data.
This may bring me closer to my idea of implementing chess as two "societies" in conflict, governed by memetic systems. I originally devised the game Faspeel as the simplest possible boiling down of the game of chess, i.e., four squares and two pieces, but I may have taken a wrong turn there. As I discussed in my previous essay on "Helper Memes" (5), it may be difficult or impossible to model the behavior of any memeplex without taking helper memes into account, that is, every global decision that a system makes to change its state is taken with the contribution, sometimes passive, of all its members.
My idea is for a simple chess-like, checkers-like game, all the pieces with the same move profile, which could produce trees of possible moves, and with basic sets of memes that the pieces would use to communicate with one another to decide the next move.
Simple Chess Game
Let's try calling it "Chimple" (simplified chess). I'm thinking a 4 x 4 board, with a row of white pieces at one end and black at the other.
fig. 1. Starting Board for Chimple
The pieces are able to, say, move forward and sideways by one, and attack diagonally. If they reach the other side of the board, they turn into diamonds, which are able to move and attack backwards.
fig. 2. Mid-game, two pieces replaced by diamonds
The endgame is when one side can no longer move (all pieces pinned) or has their last piece taken. Stalemate is when neither side can move.
That should about do it.
Memetic Inventory in the Game
The idea here is that all of the pieces together, on one side for starters, but perhaps all pieces on the board, make up a memetic community. Pieces are agents, and they have memes they may deploy, such as want-to-move! or move! or capture! The other pieces deploy alliance and immunomemes to either support or curtail.
Chess programs tend to do things like look ahead and try to find the optimal moves for the whole group. In memetic societies, decisions are taken differently. Pieces, agents, tell each other what to do, and the other pieces either accept or object to these memes in order to reach a decision.
We need to have a way for an agent to volunteer to move, to suggest that someone else move, to support these suggestions, to oppose them, to just let it slide, to offer alternatives, and perhaps other things. Notation is something to be settled, but basically immunomemetic notation.
agent.move!
agent1.pitch!agent2.move!
null!
oppose!
counter! (counter the oppose!)
accept! (support the oppose! or counter!)
support!
The idea is that memes have memetic debt, and if they don't succeed, then the deploying agent incurs residual memetic debt, and this affects their status, giving the other agents the idea that they don't have to support that agent, or that the action taken is ill-advised.
Once a move is decided, we could split out which of the possible moves for a given agent, or we could make it all in one.
agent.left! agent.right! agent.ahead! agent.back! agent.capture-left! agent.capture-right!
So what about meme cascades that end in an object! memes, in other words where any pitch for a move is shut down? Do we do a re-do? Or do we just extend the cascade? Let's call the pieces along the first row a, b, c, and d. So a starting move of the game could be:
1. a.ahead!b.null!c.null!d.support!
2. b.pitch!a.ahead!c.null!d.null!
3. a.ahead![b, c, d].null!
4. b.pitch!c.ahead!d.oppose!a.ahead!
5. b.pitch!c.ahead!d.oppose!c.pitch!a.ahead!b.null!
#1 is pretty simple, b and c take low-risk routes, while d sticks his neck out a bit more, which could translate into higher status...somehow. d is investing and gets payback. #3 is even more simple--everybody makes little or no investment, so effectively no increase in status--all garnered by a. In #4 b's pitch is overruled by d, and a comes in to propose herself to move ahead.
This raises the question (7) of when does it all end. One obvious possible "state" is the state of where everybody has deployed a meme. If this ends in a move being asserted, then the move happens and it's the other side's turn. If no move is asserted, then it seems logical that the sequence continue, i.e., that all agents are allowed to throw down again with a new spate of deployments. Everybody has to do something, if only deploy the null! meme. Or do we just make deploying further memes optional? Who says we will ever converge to a move? I guess one rule is that you may only deploy a meme if somebody has first deployed a move suggestion.
This is looking fairly arbitrary. Until an action has been taken, there is a chance to deploy a meme about it. So shall we say that when a new move suggestion is made, everybody else has the chance to either support! it, oppose! it, or do nothing (null!). How about pitching a counter-suggestion, i.e., another move? Again, non-convergence is an issue, and pitching a whole new move is not really an immunomeme (or an alliance meme). We start to see some states emerging.
[Start, Halt].agent.move! => Reply.agent.[oppose! => Halt, [support!, null!] => Move => Start]
Note that oppose! can either be let to slide by with a null! or sent back with a counter! or another agent can get on the bandwagon (for more status...?) with accept!
This implies that every possible move has an infinite set of possible cascades of memes to arrive at it. Each meme has a memetic debt (even null!)--do we set that to some arbitrary value, or allow it to vary throughout the game, or what?
On Status
The big thing is not so much whether a given move is a "success," though this may be a factor, but whether a given wrangling session ends up favoring the initiating agent. For instance, an agent may say "I want to move" or "I think so-and-so should move" and then the other agents either deploy the null! meme, acquiescence, or support the move openly, and then perhaps which exact move is to be made, again support or oppose this.
The way this might work is that each time an agent succeeds in getting their program followed, the other agents recognize that this agent is high-status, in other words, their future proposals are likely to be supported again and again. At the outset of the game, no agents know what the other agents' power and status are, but learn this as the game proceeds.
This may all have to do with residual memetic debt, that is, that each agent makes a certain investment in each attempt at a deployment, and that is either paid back (with interest) or is lost if the meme fails.
Agents should perhaps somehow keep track of which other agents tried to deploy which memes and whether they succeeded so as to predict future behavior.
This may be set up at the outset of the game.
Meme Cascades in the Game
The idea here is that any and all positions of the board are the result of a cascade of memetic deployments by both sides (5). But we can ask how things start up.
Each board state in the game has a number, which is effectively a 16-digit base-3 number (8), which even accounting for sparseness, is a large number, but still, each has a distinct number.
Let's Dive In
For the sake of simplicity, let's say we have two "rounds": Decide and Move. A player is picked to move, the decision, and then that player picks which move to make (if only one is possible, then no decision needed).
For decision memes, let's go with:
pitch!(player) 2 points. a player suggests that a given player move (if allowed)
oppose! 1 point. oppose the suggested move
support! 1 point. support the suggested move
null! 0 points. let whatever happens happen
For movement memes (if allowed):
left! right! ahead! back! 1 point
capture-left! capture-right! 2 points (13), plus 3 for capturing piece?
This would include all of the same oppose!, null!, and support! memes for all of these potential moves.
The system decides based on a random roll (10) who goes first, then keeps rolling for subsequent players until all have gone (11). If a move proposal is opposed, opponent gets a point, all others (except null) lose one or two points, respectively. Opposition (or support) succeeds if opposition in majority, otherwise opponent loses a point, move succeeds and everybody else gets points. Actually, we don't want to award points until the entire cascade is complete.
If move fails, start over with a new cascade (or sub-cascade).
The effect is that as pieces (players) keep losing in decisions, they become less and less likely to be picked first.
One problem is how players decide which memes to deploy. In a given cascade, which we may have to remember somehow, we end up in a new "state" and upon arriving at that state a given player has either won or lost points. This could look like "a pitched a moves, b nulled, c opposed, I supported, and we all (more importantly I) lost points" or "a pitched b moves, b supported, c opposed, I supported, and I got points," something like that.
If everybody somehow remembers that something went well, and they see it happening again, then they can either try something new, or get on board again. This is starting to look like the definition of a state.
It does not, however, look much like the society learning how to play the game (12).
Cascades, Matrices, and Memory
Okay, so we have a cascade, which is basically a pitch for a move which finally through some potentially lengthy, even unbounded, series of memes, and this is basically a big, long alliance/immunomemetic string of memes. But it is also a trip through a series of memetic matrices, albeit possibly sparse ones (initially). At the end of every cascade, there is a total payout for each participant. Can we treat this as the "final" transition in the final matrix, or do we spread it around, or is it applied to the "first" transition?
A state for a given agent is a series of memetic deployments by the other agents (so far) with their own choices. For example, if one agent has deployed a move, and another has, say, opposed it, then we can support it, or oppose it, or null! it, without knowing what the next and final agent is likely to do. If we support, then the last agent may oppose, and we lose. If the state already exists, then there are potentials for each choice based on whether previous deployments have "won" or "lost". For example,
a.move!(b).b.oppose!c.[-2:support!, 1:oppose!, 3:null!]
So we want to make this some kind of random choice, but how to do it? Supporting a move like this (14)
If a certain deployment has failed in the past, it may yet succeed in the future. Perhaps some kind of average would serve.
I'm thinking that the history of the world of this memeplex is a series of "moves" from pitch! to yes! or no! and finally move!(1-8) (15). For example, p!y!n!y!m!(x)p!y!y!m!(x)p!n!n!n!p!....
A memetic cascade is a series of memes. I'm still working on how to translate this into a memetic matrix. A collection of related cascades, i.e., where only a few memes differ, or it goes along a sequence and then breaks off, is like a tree. A tree can perhaps be mapped onto a collection of matrices, after the fact, to describe the behavior of the memeplex. This would look like a sampling of various parts of the tree that looked the same, i.e., had the same (lengthy) sequences of memes. That is, if the same sequence was followed 20% of the time by one deployment, and 60% something else, and so forth, this might look like a matrix of probabilities. In other words, after any sequence of memes, there is a next deployment, by some agent, with some probability, e.g., this agent took this action in these cases, and this other agent did this, while the others did nothing in any case that came up.
Summary & Conclusions
Still lots of problems. Ultimately there is the problem between arbitrariness and things that derive from a small core of (arbitrary) decisions. I want to come up with an interesting game model that models memetic group behavior in an interesting way.
The behavior of a group is a series of meme deployments, or a cascade. There may be a way to map this behavior into a system of matrices, which may or may not be interesting, or useful.
A state might be able to be usefully represented by a series of deployments within the larger deployment history, i.e., a sub-cascade within a cascade. If a series appears in various places in a history, with different sub-cascades following it, can it be thought of as a state and those sub-cascades as
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(1) Yeah, yeah, yeah, we say "particle accelerator" and we use "detectors" instead of cloud chambers, but the analogy stands.
(2) The longer the sequence of memes, the more precise our idea of the memetic state may become, but it remains to be seen whether this idea will make sense.
(3) The important thing about a state is that it tells us which memes are now available and to which agents.
(4) We may want to introduce the term of "coherent state" (or some such) as some state that we can reliably identify in the functioning of an organic memeplex through observation, i.e., certain cascades of meme lead to a situation where the meme and agent choices happen reliably from that point. Perhaps think of watching a formal dance, a waltz, a square dance, or folk or native dance, where the dancers respond to the music, and to where they and the other dancers are on the floor. When the trumpets come in and the violins switch to a fast pace, the men separate to one side and the women the other, and the pair at the end dance through the tunnel, followed by each pair down the row, for example. Or the dancers separate and clap their hands, or other such. We might over time notice that when the music does one thing, the dancers do some thing. If we didn't know the dance, we could start to observe patterns. The same with street traffic--if we didn't know the rules and what the signs meant, we could begin to observe patterns and effects, like that the red light, or the red stop sign, is important, and starts and stops cycles of activity. Language is of course a very complex example of this, with grammar one way of modeling what is happening.
(5) I've invented a new term, "helper meme," to include the two symmetric types of memes of immunomemes and alliance memes.
(6) Here is where we need to make a distinction and a decision about how much the two sides of the game interact. If one side makes a move, then that move in a sense is part of the memetic sequence of the other side as well, together leading to the current board state. Any board position is the sum of a sequence of deployments starting from the beginning state. In this sense there needs to be some kind of communication between the two sides, i.e., some kind of immuno/ally meme that is exchanged, perhaps even just "it's your turn." In a more advanced version of the game there might be a more advanced level of communication between the two societies, rather like diplomatic exchanges between nations with strained relations.
(7) Please don't say "begs the question" -- that's a totally different thing.
(8) A sixteen-square board with each space either blank or held by one of either blank, black piece, or white piece is 43,046,721. However, some of these pieces may be diamonds, which means it's a base-5 number, but this is also a sparse board, i.e., there are only ever eight non-zero digits anywhere, which might make the bounding value more like 6,561 or 390,625, which is still a lot. At any rate, each board has a distinct number, and links to each other possible board, which might be another exercise (9)
(9) Two problems: how many distinct board configurations are there, and how do they link to each other? The latter might be interesting since each move takes us to a new board configuration, and although each player only gets one move per turn, there might be regions of the board-space which are richer in future possibilities, and this might have macromemetic ramifications. Is there a quantify that might be derived to indicate "possibility density"?
(10) The random rolls based on who goes next shall be decided by "status" which starts out as zero everywhere, so even money, and then each player who gets a meme through gets status for that meme. null! gives zero points, a move! gets two, and object! and support! get one.
(11) This is a sort of arbitrary solution to the "deployment decision" race condition and jinx event problem, which is still under study.
(12) I hold out a hope that some kind of set of biases, such as status, memetic nexuses, and so forth, could result in a memeplex that could learn and get better and better at a game, but we may not yet be there with this model. For one, there may not be much feedback in terms of capturing enemy pieces or other such advantages. I have not (yet) built in any decision processes as to choosing the best moves, for example, and that may be anathematic to macromemetics, anyway.
(13) It might be interesting to make a capture play pay out for not only the capturing player, or say, the player who orders the capture, but also others. For instance, the player that pitches the move may get points, but the player that makes the move may also get points (or more).
(14) We may want to make a string that does not specify what the move is to be, i.e., just have move! as the meme. We may want to have a string that leaves off the agents as well, i.e., just shows the series of actions.
(15) Each piece can (if it becomes a diamond) move either forward, right, left, back, or diagonal right, left, or backwards right or left, or eight different moves.
