The Candy Conspiracy. Big progress into immunomemes and immunomemetic notation, and also into alliance theory.
I may have to revisit the three laws of Immunomemetics. I'm thinking that I have a more specific definition for an immunomeme, and which may actually be spanning (covering?). An immunomeme impedes the transition from one state to the next by the deployment of a targeted meme (or individual agent).
Doldrums.schmoe.take-a-shot! => EasyStreet
Effect of immunomeme:
Doldrums.jerkweed.ankle-bite(schmoe.take-a-shot!)! => DownAndOut
Doldrums.jerkweed.ankle-bite(schmoe.take-a-shot!)! => Dolddrums
...I need to try to gather up a bunch of examples. Even from games and other social situations.
Memetic Essay Index
We have an interesting real-life example of how alliance networks can form and how they transform the functional structure (3) of a memetic system (memeplex). We consider a case of two sisters, Amy, the older, and Betty, the younger, where some candy has been placed out of Betty's reach, but where Amy is still able to get at it.
The parents have set the candy is off-limits. Amy is able to get the candy, and Betty is able to complain, which could potentially attract the parents and get Amy into trouble.
We see a behavior where the two sisters cooperate, and we take a look at what form this cooperation takes in the structure of the memetic system when they do so, and how that might shed light on how memetic alliance networks behave generally.
State Transition Diagram
The starting state of the memeplex is GoodGirls where Amy has not yet tried to get the candy. The next state which may be reached is StoleCandy when Amy gets the candy down and starts eating it, or the amy.eat! meme, since Betty is not able to get the candy or eat it herself.
|Figure 1. State Transition Diagram for Candy Conspiracy Memeplex|
Once Amy has gotten into the candy, Betty is free to whine! to attract the parents and get Amy into trouble, which takes the system into ParentsAlerted, which is a terminal state.
A quick note about the whine! meme. It is effectively an immunomeme (5), and is directed against Amy's deployment of amy.eat! As such, we can imagine the following notation:
There is some redundancy here. Obviously Betty deploying the whine! meme is in response to Amy's eat! candy, since they are already in the StoleCandy state, but it does drive home the point that Betty's whining is in direct response to Amy's eating, and indeed the actual meme, e.g., Betty crying out, "Mom! Amy's eating the candy!" actually encapsulates the eat! meme deployed by Amy. This is effectively a notational representation for a parametric immunomeme deployment, and as such may carry a great deal of explanatory power. Do immunomemes always have this kind of self-referential property? We'll look at this some more later.
If Amy managed to get the candy put away again, i.e., deploy the hide! meme, before they wind up in the terminal ParentsAlerted state, they are back in the GoodGirls state and Betty no longer has the whine! meme available for deployment.
Deployment Descriptor Inventory
A key thing we observed in our real-life example was that Amy gave Betty some candy. This does a number of things in the system, as we can see in the diagram. Betty now has the choice between whine! and eat! Betty is still free to whine!, but she would be implicated in the crime, since she is also eating the candy, and the supply of candy would then be cut off.
Let's take a quick look at the memetic inventory of the memeplex.
- GoodGirls.amy.eat! => StoleCandy
- StoleCandy.amy.eat! => StoleCandy
- StoleCandy.amy.hide! => GoodGirls
- StoleCandy.betty.whine(amy.eat!)! => ParentsAlerted
- StoleCandy.amy.bribe(betty)! => Conspiracy
- Conspiracy.betty.whine(amy.eat!)! => ParentsAlerted
- Conspiracy.eat! => Conspiracy
- Conspiracy.amy.hide! => GoodGirls
Table 1. Memetic Inventory Deployment Descriptors
Here I want to consider what I'm calling memetic alliance networks. In our real-life example, Amy gave Betty candy. This gave Betty a larger memetic inventory to choose from, and greater equality, resulting in greater opportunity for memetic resonance (mutual participation in a shared activity, decreased chance for residual memetic debt (1)). Increasing the memetic inventory of an agent generally lessens the risk of alienation by making memetic destitution (2) more remote. It is as yet unclear if these are universal properties of alliance networks.
We know from the first law of macromemetics, however, that deployment of a meme produces a state transition. Since neither of the two existing states, StoleCandy or ParentsAlerted, can be the target of this transition, since both sisters can deploy the eat! meme in the target state, we must have a new state in which both sisters can deploy eat!, i.e., the new state, Conspiracy.
Betty still has unilateral ability to whine! or not. We've considered whine! to be an immunomeme, and so not whining, or
whine! is a suppressed immunomeme or anti-immunomeme. Betty's continually "deploying" this anti-immunomeme is what enables both of them to go on eating. Let's extend our earlier notation for immunomemes:
whine(amy.eat!)!amy.eat! => Conspiracy
whine(amy.eat!)!betty.eat! => Conspiracy
Table 2. Alliance-Based Memes
Or, to combine the two cases:
whine(amy.eat!)!eat! => Conspiracy
This may bring us to the crux of the nature of memetic alliances. An ally is characterized by two things. The first is creating an opportunity for the beneficiary to deploy memes that they could not otherwise. The second is suppression of immunomemes that would impede the beneficiary from successfully deploying memes.
Here we see that Betty is an ally to Amy by suppressing immunomemes where she herself is the would-be deploying agent, i.e., declining to exercise a bullying opportunity available to her. This allows Amy to eat candy, and it also allows Betty to eat the candy. This example may point to the memetic advantages conferred upon an ally by being an ally, but is perhaps incomplete.
Summary and Conclusions
The fact that in this real-life case the younger sister chose the alliance over ratting her sister out to her parents suggests that she is not starved for parental attention, since she had a sure-fire way to get it, but declined to do so. Many children would capitalize on such a chance to enhance their own status and force their parents to become involved.
We're narrowing down how immunomemes work and have developed a promising new notation. Immunomemes operate on the deployment of other memes, with the object of thwarting or redirecting the state transition that goes along with it. The notation immunomeme(meme!)! or more completely:
State1.agent2.immunomeme(agent1.meme) => DivertedState
...solves a lot of the problems I have been wrestling with regarding the categorization of immunomemes.
Finally, this real-life case suggests some ideas which I hope to elaborate further elsewhere about how memetic alliance networks change a memeplex. A couple of obvious observations are that agents that enter into alliances with one another automatically expand the inventory of memes available to all of them, which helps to fend off memetic destitution and its accompanying alienation. This opens up promising avenues for dealing with violence, dysfunction, and apathy generally. Conflicts may be reduced, as we see in this example, by making a choice of memes available to individuals who may have had little or none, or where immunomemes were the only options. Whether a memeplex always becomes more egalitarian in the wake of alliances remains to be seen, and stands as an interesting question to be explored further.
(1) Residual Memetic Debt: related to the concepts of marking and closure, roughly characterized as how well the memetic agent perceives that the memetic interaction has been concluded. A memetic loop is opened when a memetic agent deploys a meme, and said loop is closed when the expected response is received. Opening a memetic loop incurs memetic debt which is paid back upon closing of the loop. If the memetic debt is not (perceived as being) paid back, residual memetic debt is incurred. The ramifications of residual memetic debt are far-reaching, and beyond the scope of this paper.
(2) Memetic Destitution: closely linked to violence, by the way, in fact, may be the ultimate source for expressions of violence in all human societies. Refers to a shortage of memes available for the agent to choose from. Alienation is the result of memetic destitution.
(3) A memetic system (memeplex) consists of a collection of memetic agents, memes, and states, and a description of which memes are able to be deployed by which agents in which states and which states are transitioned to when said memes are deployed. A memeplex may be characterized by a state transition diagram, a set of memetic deployment descriptors, or a set of transition matrices, see (4).
(4) A deployment descriptor, is a complete description of what is involved when a meme is deployed, or "expressed." They look like this:
StartMemeticState.agent.meme! => TargetMemeticState
Memes are in lowercase and followed by an exclamation mark (!). Agents are in lowercase. Memetic States are in CamelCaps. The memetic inventory of a state, or of an agent in a state, or of a whole system, is the list of all deployment descriptors in that system. A deployment descriptor list, a state transition diagram, and a set of state transition matrices are in principle all homeomorphic and convey the same information in different forms.
(5) Immunomeme: a meme whose primary function is to impede curtail the deployment of memes that "change" a memetic system, namely, prevent the transition of the system from one state to the next by thwarting the resonance of a given meme. Immunomemes are responsible for the stability of memeplexes over time, i.e., preventing mutation and the introduction of new memes.
Two New Concepts
- Castles or factories which produce armies, gained by Risk card turn-in
- Always having allied armies, usable by winning poker games
Factories vs. Immediate Armies from Cards
Cards work differently in the New Rules. There is no "perpetual growth" of values of turn-ins, for one. You can either turn in a set of cards at the start of your turn for some number of armies determined by die roll, or at the end of your turn to get a factory on one of your territories. Factories produce two armies on the territory where they are located, forever, but they may be conquered by other players, who then get the armies. For immediate armies from a card turn-in, roll two dice.
Playing Poker for Control
All armies are on the board at all times. If there are only two players, then four of these armies will be allied armies, able to be used by any and all "live" players. Each allied army is assigned at least one poker suit, i.e., hearts, diamonds, clubs, spades, or ♥ ♦ ♣ ♠.
NOTE: The queen shall be the high card in the hearts and diamonds, ♥ ♦ the red suits.
The right to use an allied army is accomplished by winning a hand of poker (or being unchallenged) against the other players. At the end of every successful turn, in addition to a Risk card, a player draws a card from a poker deck.
The way a poker game works is that at the end of your turn, if you have three or more poker cards, you can declare the intent to use one of the allied armies. You must declare which army you wish to use, and if you win the hand, you must win with a card in the suit of that army in your winning hand. If you lose a hand, you may play again only if you have three more cards, which will only happen if you have six at the end of your turn.
Any player with at least three poker cards may elect to join the poker game. If he has more than three cards, he must choose three and set aside any extras.
At the end of your turn, if you have six poker cards, you have to play, and you have the option of doubling down with two hands. You have to ante for each hand, however.
Also known as Eastern United States Hold'em.
To join the hand, a player must have at least three poker cards accumulated, and choose three if holding more than that number, setting the other one or two aside for the duration of the hand. Each player joining the hand of poker must compute the number of armies he would receive for territory, continent bonuses, and factories and place that in his betting pile.
Each player must ante up one army for each hand he is playing (which will almost always be one). The dealer then turns up one card (the "flop"). Betting begins with the player whose turn it is, going around giving all players the chance to check, call, raise, or fold. The dealer lays out the next face-up card (the "river") and betting resumes. A player may go all-in, but this does not result in a side pot. The best 5-card hand made from a player's hand and the two "hole cards" wins the pot. If hands are tied, the pot is split, but if the player whose turn it is wins, and his winning hand contains the suit of the allied army he selected, he gets to use that allied army. Winning players convert all armies in the pot into their own color(s).
Playing an Allied Army
An allied army is played just like your own army. You accumulate Risk cards and poker cards, and may play them as normal to gain armies for the allied army. Only players that win the right to play an allied army may look at that army's cards, or, of course, anything else. Allied armies collect territory and continent bonuses as well as two armies for any factory on its territory. A player using an allied army can initiate a poker hand using the cards of the allied army he controls, though of course any winnings would go to the allied army to be used by the next player getting control.
At the end of a turn, a player is able to transfer as many armies from one territory to another as the largest army he has on any single territory.
For instance, if he has four armies on one territory, and this is the largest army, then he has three troop transfers he can make, regardless of any other armies on other territories. Now, this transfer may be in the form of moving all three armies of the main force to a neighboring territory, or, on the other extreme, moving one individual army on three different places to an adjacent territory. It's also possible to move two armies in one place and one army in another place, so long as the total is less than or equal to three, in this example. Those are what we call "adjacent transfers."
Alternatively, the player may choose to make one single move of a single body of troops, again, numbering equal to or less than the size of the largest army, from one territory to another that may be reached along a contiguous path through territories controlled by the player.
As something of a summary, at the beginning of his turn, a player receives the total count of territories divided by three plus continent bonuses, as normal, unless his troop count was determined by a previous poker game, in which case he deploys however many of those troops left in his "betting pile" after any poker losses or gains. Next, he receives two armies for every factory on any territory he controls. He can play any Risk cards in exchange for armies (by roll of two dice).
At the end of his turn, a player may play cards to buy factories (which start to pay off the following turn).
NOTE: If a player has already counted up his betting pile for a poker game prior to his turn, he does not count up his territory and continent bonuses again upon the start of his turn. He simply places all armies (if any) left in his betting pile. He does, however, get factory armies and may turn in Risk cards for armies, regardless of previous poker participation.
If a player fails to get territory and continent bonuses on his turn, he will get them at the start of his next turn or at the next poker hand he joins, whichever comes first.
QUESTION: Should allied armies that control factories get two armies on that spot even if no player plays them. If so, when should these armies be placed?
Values of Factories and Turn-in Armies
The relative value of a factory versus a set of armies for a card turn-in are both computed based on the average number of turns required to get another set of cards to turn in. In other words, if I turn in for a factory and get two armies per turn, I will get another set of cards to turn in for armies at the soonest after three turns and at the latest by five turns (guaranteed set of three). In that period of time I will get between six and ten armies from a factory. Now, if I roll two dice, I have the chance of 2 to twelve armies. Are the averages of both outcomes eight armies? Maybe. It would work well if so.
I think this works. The probability of getting more or fewer turn-in armies averages seven. So it's seven for all three of 3, 4, and 5 cards, but it also has a greater range...6 to 36.
The value of factory armies is proportional to 6 x chance of getting three-card match, plus 8 x chance of four-card match, plus 10 x chance of 5-card match (100%?).
The chance of getting three cards is three-of-a-kind 1 x 13/41 x 12/40 = 0.095
The chance of one of each 1 x 28/41 x 14/40 = 0.239
So the chance of either happening should be 0.095 + 0.239 = 0.334
And getting three-of-a-kind after 4 draws is the number of permutations on getting two cards of two different types (since three would be a one-of-a-kind) taken from the total number of possible 4-card draws. Probably combinations are okay, since I don't care the order.
one-of-each after 4 should be the same, since you need to draw two cards of two different suits, since any third suit would complete the set, or give three-of-a-kind.
At five cards it's 100% that you'll get one or the other combination.
The results here may be trivial, but I haven't worked it out yet. The crux is that the return on a factory is certain to be 6 at three cards, 8 at four, and 10 at five, and differences in those probabilities of getting a card set could change the average, and then there is also the greater range with turn-in armies by dice.
How to chose four cards, two pairs of two suits, how many different ways to pick them? There are three possible suits, so picking the second card