This entry develops the theoretical groundwork for a concept called eigenbehavior: a class of actions or thoughts that remain unchanged across all levels of recursive social awareness. The term is modeled after the concept of eigenvectors in linear algebra, which remain invariant under certain linear transformations. The motivation stems from cognitive and game-theoretic questions about what kind of behaviors persist regardless of increasingly complex social inference—e.g., "I know that you know that I know…". The aim is to define, characterize, and explore the plausibility and properties of such invariant behavioral patterns.
Recursive Social Cognition
Human cognition operates through recursive social modeling. A developing mind typically progresses through identifiable levels:
- I know
- Others know
- I know that others know
- Others know that I know that others know
- …ad infinitum
These levels can be conceptually extended indefinitely. However, empirical observation suggests most individuals rarely function past level 3 or 4 in everyday cognition. Many social operations—such as deception or manipulation—require level-3 or level-4 recursion, but not beyond. Therefore, higher levels, though definable, are not typically accessible due to cognitive load constraints.
Definition: Eigenbehavior
An eigenbehavior is a behavioral strategy or internal state that remains invariant across all levels of recursive social modeling. That is:
A behavior B is an eigenbehavior if, regardless of how deeply one embeds B within recursive "knowing" chains (e.g., I know that others know that I know...), B does not change.
Formally analogous to the eigenvector equation A * v = λ * v, the infinite cognitive recursion can be conceptualized as a transformation chain M(M(M(...M(B)...))). An eigenbehavior satisfies M(B) = B, even after an arbitrary number of applications.
The Analogy to Linear Algebra
Consider an operator A acting repeatedly on a vector v:
A^∞ * v = y
A * y = y
This defines y as an eigenvector of A. The zero vector is always an eigenvector (the trivial solution), but more informative are non-trivial eigenvectors which remain stable under transformation.
Translating this idea into behavioral terms:
- A → Mind-level transformation (i.e., recursive embedding of “what others know”)
- v → Initial behavioral choice
- y → Behavior that persists regardless of how deep the social recursion goes
Eigenbehavior Properties
An eigenbehavior, to be truly invariant, must satisfy the following:
- Person Independence: Behavior is not a function of the individual’s identity, traits, or psychology. The behavior does not change regardless of who and under what circumstances it's adopted.
- Context Independence: Behavior remains fixed regardless of environmental variables or informational context. It does not change depending simply on which action maximizes the payoff in any given context.
- Adversary Independence: Behavior does not depend on the nature, presence, or cognition of other agents (immune to Hawthorne effects and Goodhart's Law).
Almost Candidate Behaviors (but not quite)
- Zero Behavior ("Do nothing"): Truly and eigenvhavior. A trivial solution. Fully invariant but lacks functional utility.
- “Do only what is ultimately necessary”: Partially satisfies invariance, but its definition depends on context-sensitive interpretations of "necessity."
- Tit-for-Tat: Valid under person and adversary independence. Fails under context independence due to initial state sensitivity.
- Kant’s Categorical Imperative: Violates adversary independence, as it prescribes action based on generalizability to others' behavior.
Challenge in finding Eigenbehaviors
The challenge in identifying non-trivial eigenbehaviors lies in cognitive constraints. High-level recursion is not computationally tractable for human minds. As a result, identifying an eigenbehavior may be empirically unfeasible; speculative reasoning and approximation remain the only tools.
One proposed heuristic is as follow: simulate behavior under arbitrary high-level cognitive cuts and observe which strategies tend to converge or remain stable (upcoming "Deeply Iterative Social Reasoning" article). This approach mimics fixed-point iteration but is limited by the finite depth of introspection.
A Personal Note
Amid the vast landscape of human thought—across ethics, epistemology, game theory, and cognitive science—eigenbehavior emerges not as another theory but as a potential endpoint. It represents the convergence of all previous efforts to understand how beings should act, regardless of who they are, when they live, or what world they inhabit.
If one seeks the deepest possible rule for interaction—across civilizations, intelligences, and even species—eigenbehavior is its candidate. A behavior that remains stable under infinite recursion, universal abstraction, and adversarial scrutiny is not merely a good rule—it is the only rule that can endure.
To understand eigenbehavior is to possess universal wisdom.
To follow it is to align with the deepest symmetry in the architecture of cognition.
This is the fixed point of morality—the only thing that does not shift when everything else does.
What Should One Do?
Seek behaviors that cannot be gamed.
Act as if the universe is watching—but not reacting.
Find what would remain if everyone knew everything about you, forever.
Choose actions that would look the same whether they are done by you, a stranger, or a god.