Introduction to Social Dynamics
Social dynamics is the study of how individuals interact, form relationships, and navigate social contexts. This framework uses mathematical concepts from set theory and n-dimensional space's to model these complex human interactions.
Social dynamics can be understood as the intersection of contextual action spaces between individuals, where positive-valued actions form the foundation of relationships.
Figure 1: Visualization of how relationships form as the intersection of individual action spaces within a contextual boundary.
Action Spaces and Set Theory
In set theory terms, we can define:
- C = The contextual space (universal set of possible actions in a situation)
- A = Person A's action space (subset of C that A can/will perform)
- B = Person B's action space (subset of C that B can/will perform)
- R = Relationship space (intersection of valuable actions: A ∩ B)
- VA(x) = Value function for Person A on action x
- VB(x) = Value function for Person B on action x
A relationship R can form when:
R = {x | x ∈ A ∩ B, VA(x) > 0, VB(x) > 0}
Figure 2: Set theory representation of social dynamics, where R represents the relationship formed from the intersection of action spaces.
The 8 Rules of Social Dynamics
1 Contextual Boundary of Actions
All relationships are defined in a social dynamic. That means that there is an imaginary space of all possible actions bounded by the context of the current situation.
Figure 3: Actions are bounded by the contextual space of a situation.
2 Relationship Formation Through Positive Value
You form a relationship by bounding that contextual space by the group of actions that give you overall positive outcomes when put together. Both parties can expand the space by adding actions that have positive value to them from the context in the definition of relationship.
Figure 4: Relationships form in areas where actions have positive value for both parties.
3 Composition of Social Dynamics
Social dynamic is made by all dynamics containing it.
Dynamic is contextually separate action space of the same group/individuals.
Figure 5: The overall social dynamic is composed of separate contextual dynamics.
4 Penalty and Avoidance Principle
Each party can penalize any action putting strain on the dynamic. When the overall dynamic becomes negative, those individuals avoid it.
Figure 6: As actions incur penalties and the relationship value becomes negative, avoidance occurs.
5 Cost of New Action Definition
Definition of a new action is costly as its expected value is unknown.
Figure 7: New actions have unknown values and thus carry higher cognitive and social costs.
6 Gravitation Toward Known Positive Value
People tend to their known and previously defined positive value spaces.
Figure 8: Social actors gravitate toward known positive-value action spaces and away from negative ones.
7 Opening Possibilities Through Subtle Signals
You can open the possibility of an action that will let the other person define it if they want. This is usually done subconsciously through body language and constraining action space to the desired action.
Figure 9: Subtle signals open potential action spaces that the other person can define or reject.
8 Contextual and Personal Boundaries
You can't force a relationship if person is not in the context or if they denie it.
Figure 10: Relationships cannot be forced when either the context or individual boundaries prevent them.
Mathematical Representation of Social Dynamics
Value Functions and Decision Making
We can express an individual's decision to engage in a relationship as a utility maximization problem:
Ui(R) = Σ ( Vi(a) - Ci(a) ) * pi(a)
Where:
- Ui(R) = Value of relationship R for person i
- Vi(a) = Value of action a for person i
- Ci(a) = Cost of definition = uncercanty
- pi(a) = Probability (expressivness or acceptance of your expression) of action
A person will engage in a relationship when Ui(R) > 0, and will leave when Ui(R) < 0.
Figure 11: Mathematical representation of value functions in a relationship space.
Real-World Examples of Social Dynamics
Example 1: Workplace Relationships
In a workplace context, the set of possible actions is bounded by professional norms, company policies, and job roles. The formation of positive working relationships occurs when:
Scenario Analysis
Context C: Professional office environment
Person A: Manager who values efficiency, clear communication, and punctuality
Person B: Employee who values autonomy, recognition, and work-life balance
Relationship R: Forms where their values overlap - when the manager provides recognition and reasonable autonomy (positive value to B) while the employee delivers efficient work and clear communication (positive value to A).
Breakdown Potential: If the manager enforces rigid control (negative value to B) or if the employee consistently misses deadlines (negative value to A), penalties accumulate until the relationship becomes strained.
Example 2: Dating and Romantic Relationships
Dating contexts show clear examples of all 8 rules in action, particularly the opening of new action possibilities (Rule 7) and the impossibility of forcing relationships (Rule 8).
Scenario Analysis
Context C: Dating and romantic interactions
Opening Possibilities: Subtle signals like extended eye contact, casual physical proximity, or open-ended questions about weekend plans create space for the other person to define further actions.
Value Creation: Both parties gradually expand the relationship by introducing actions with mutual positive value - shared activities, emotional support, physical affection.
Boundary Respect: If one person doesn't experience positive value from the interaction, attempts to force a relationship will fail, demonstrating Rule 8.
Example 3: Friend Groups and Social Circles
Friend groups demonstrate Rule 3 (composition of social dynamics) and Rule 6 (gravitation toward known positive value).
Scenario Analysis
Context C: Social gatherings and group activities
Multiple Dynamics: A social circle contains multiple pair-wise relationships, each with its own dynamic, creating a complex system where some subgroups have stronger positive value than others.
Value Patterns: People tend to spend more time with those subgroups where they experience higher positive value, demonstrating Rule 6.
New Member Integration: When new people join a group, there's a higher cost (Rule 5) as everyone must define new actions with uncertain value. This explains why established groups sometimes resist expansion.