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Quantitative Memetics

INTERACTIONS

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Mimetic spread is a phenomenon observed in the spread of behaviors and repeated phrases.

Let W be a behavior that is reciprocated between two people. Let set “people” consist of $\{A, B\}$. Add the constraint that each time behavior $W$ is performed by a person, it must be reciprocated by the other person before the sender can perform it again. Let’s define survival constant $\sigma$, which represents the probability of continued interaction. The survivability $S_{n}$ after $n$ turns can be calculated either symmetrically or asymmetrically. In symmetric reciprocation, the survival constant $\sigma$ is applied only after a complete bidirectional exchange (a message and its response), and in asymmetric reciprocation it is applied after every one-way message. This approach can be formalized as:

• Symmetric reciprocation: $S_n = \sigma^{\lfloor \frac{n-1}{2} \rfloor}$
• Asymmetric reciprocation: $S_n = \sigma^{n-1}$

Symmetric communication where $\sigma$ = 0.9:


A —> B | S_1 = 1
A <— B | S_1 = 1
A —> B | S_2 = .9
A <— B | S_2 = .9


Asymmetric communication where $\sigma$ = 0.9:


A —> B | S_1 = 1
A <— B | S_2 = .9
A —> B | S_3 = .81
A <— B | S_4 = .729


For the rest of our purposes here, we will be using assymetrical communication.

A partiality constant, where partiality is how much more likely one person is to reciprocate a behavior than another, increases complexity and more closely models real-life interactions between organisms. Let’s add a partiality constant for each person in set people, represented by function $P$. In real life, partiality differences can be caused for a number of different reasons, including social status differences in groups and success of prior interactions. Here we will always make the highest partiality one, for the sake of simplicity. So for each turn survival probability can be represented as

$$S_n = \sigma^{n-1} \times \prod_{i=1}^{n-1} P(\text{sender}_i)$$

Where $\sigma = 0.9, P(A) = 1, P(B) = .75$:


A —> B | S_1 = 1
A <— B | S_2 = .9 * .75 * 1 = .675
A —> B | S_3 = .9 * 1 * .675 = .6075
A <— B | S_4 = .9 * .75 * .6075 = .4101


this survival-constant probability based interaction is a good model for certain types of interactions, such as passing a totem back and forth between two people. when the interest of the in-joke goes down enough, one party may forget to pass the totem, but the relationship can continue to go undamaged. survival probability interaction is not a best model for something like conversations, where if a dead roll happens early enough, it would severely impact the relationship.

To model something like conversations more closely, we will change the survival probability to the “affinity” value. We will represent affinity for each specific turn as $Y$ and the affinity decay constant as $\psi$. We will continue using the partiality multiplier for each person. Additionally, we will introduce low threshold-cutoffs $\lambda$ for affinity for each person. When affinity for the turn dips below $\lambda(\text{person})$ for either the sender, recipient, or either one, the interaction ends. The affinity formula can be represented as

$$\text{where } x \in \{ \text{sender}, \text{recipient}, \text{min}(\lambda(A), \lambda(B)), \text{max}(\lambda(A), \lambda(B))\}$$

$$Y_n = \begin{cases} \psi^{n-1} \times \prod\limits_{i=1}^{n-1} P(\text{sender}_i) & \text{if } Y_{n-1} \geq \lambda(x) \\ \text{end interaction} & \text{if } Y_{n-1} < \lambda(x) \end{cases}$$

Where lambda is a function of the sender and where $\sigma = .9, P(A) = 1, P(B) = .75, \lambda(A) = .4, \lambda(B)$ = .65$:


A —> B | Y_1 = 1
A <— B | Y_2 = .9 * .75 * 1 = .675
A —> B | Y_3 = .9 * 1 * .675 = .6075


The interaction ends here because $Y_3 < \lambda(B)$

TERMINOLOGY

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• isopart - the part that is the same part. typically used in the context of whoever initiated the dialogue. from Greek “iso” for “same”
• allopart - the other part. typically the non-initiating party in dialogue. from greek “allo” for “other”

A Disambiguation: Let’s have two friends who talk about music frequently. An isopart (one or the other part) can send a song, and each time some talking will follow after about the song just sent. Now, that talking that just happened is part of the previous overarching theme. The terms “dialogue”, “conversation”, and “discussion” could each either refer to the overarching talk about music the theme, or the instance talk about the song that was just sent. This can get confusing really quickly so we will introduce two more terms here to be really clear about what we are talking about.

• themology - From Greek “thema” for “theme” and “logos” for “speech”. Colloquially just “theme”. “Theme” is used plainly in other contexts in English, so the new term is necessary here for disambiguation. ¹
• merology - From Greek “meros” for “part” or “instance” and “logos”. Used to disambiguate for an instance of a discussion/dialogue/conversation about a specific themeology.
  
• thread - Colloquial English for “merology”, coming from a term used on internet for specific discussion on a topic.
• initiate - happens when an isopart starts a merology

NOTATION

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To cleanly describe social memetics here, I will introduce Cabello Notation.

Definitions

Turns will happen in a category a number of times. To denote this, I will use turn quantifier notation. Turn quantifier notation borrows symbols from Regular Expressions (Regex),² but changes the first symbol for “0 or 1” to a percent sign, to free up the question mark for another purpose. But regex notation is not sufficient for our purposes here. Social interactions move in pairs and that is fundamentally important to social memetics. So we introduce some more symbols to turn quantifier notation. The introduced symbols with meanings not in regex [&amp,@] are both corruptions of the letter [A,a]. All the symbols in turn quantifier notation are typable from a keyboard.

EXPERIMENT

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Hypothesis

When two people of relatively equal social standing interact, there will be a perpetual back and forth of these things roughly following the following pattern, and as social standing differentiates, the balance of that pattern will shift [HOW?].

The Pattern:

1. >[ (Iso talks about self) (warranted/unwarranted)
2. >] (Iso talks about Allo) (warranted/unwarranted)
3. <{ (Allo talks about self) (warranted/unwarranted)
4. <} (Allo talks about Iso) (warranted/unwarranted)

Or, simplified, there is a balance in interaction patterns each relationship based on social standing and if the balance gets too far off than the relationship will dry up.

Method

We are testing if the previous patterns follow [THE PATTERNS NEED TO BE MORE CLARIFIED]. The variables are social status between pairs of people, in both one-on-one and group settings.

One-on-one

1. pair people
   1. use ELO ranking to get people of similar social value together
   2. just partner people
2. give them the handout sheet

• need “sign” for them to go together for certain amount of time. solve a simple problem?

Group

0. set a time limit (five days)
   • periodically (once a day) send out an automated message
1. get a group
2. give them a handout, tell them what variables we are tracking
3. questionnaires
   • give everyone who joins the group the elo questionnaire.
   • tell us the three people you are most familiar with
4. we are tracking the number of interactions between people based on elo

EXTENSIONS

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• groups
• connections to neurology
• “warrented/unwarrented”
• differential equasions for how equilibrium shifts according to status

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1. “Topos”, Greek for “topic”, can’t be used here because the “topology” is the name for an established field of mathematics↩︎

2. [https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap09.html#tag_09_04_06]{https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap09.html#tag_09_04_06}↩︎