Agent

An agent is any entity that can observe, interpret, and respond to meaning—including observing and changing itself.

Agents are participants in an ongoing conversation about reality. None is a passive “receiver of information”—they actively shape what things mean through their attention and interpretation of the meaning of things. Most importantly, agents can reflect on their own thinking processes, creating loops of self-awareness that allow them to adapt and evolve.

In Recurgence, agents emerge naturally from the field of meaning itself. They are both shaped by the patterns around them, and they actively participate in shaping those patterns for others.

Mathematical Context

Formally, agents arise as bounded, self-referential submanifolds $\mathcal{A} \subset \mathcal{M}$ of the semantic manifold, characterized by four essential properties:

\[\mathcal{I}_{\psi}[C](p,t) = C(p,t) + \int_{\mathcal{M}} K_{\psi}(p,q,t) \cdot (C(q,t) - \hat{C}_{\psi}(q,t)) \, dq\]

where:

$\mathcal{I}_{\psi}$: interpretation operator parameterized by agent state $\psi$
$C(p,t)$: coherence field at point $p$ and time $t$
$K_{\psi}(p,q,t)$: interpretation kernel encoding agent’s attention mechanism
$\hat{C}_{\psi}(q,t)$: expected coherence under the agent’s belief structure

Agents also exhibit selective attention through:

\[S_a(p,t) = \frac{e^{\gamma_a \cdot V_a(p,t)}}{\int_{\mathcal{M}} e^{\gamma_a \cdot V_a(q,t)} \, dq}\]

where:

$S_a(p,t)$: attention distribution of agent $a$
$\gamma_a$: attention sharpness parameter
$V_a(p,t)$: value function encoding agent preferences

See more: Mathematics / Agents and Interpretation

Properties

Certain key properties distinguish agents within the semantic field:

Recursive Closure Systems’ capacity to observe their own observation, creating self-awareness that stabilizes into persistent identity patterns.
Semantic Participation Agents are observers of the field that actively shape it through their attention, interpretation, and communication with other agents.
Adaptive Coherence The ability to maintain structural integrity while evolving in response to field dynamics and interactions with other agents.

Examples in Practice

This concept manifests in various forms throughout reality:

Human observers Reading and interpreting this document right now—you’re actively participating in the process of making meaning.
AI systems Digital architectures—ones that can model and modify their own processes—creating feedback loops of self-improvement and adaptation.
Institutions Organizations that develop self-reflective governance structures, allowing them to evolve their own rules and purposes.
Ecosystems That regulate their own dynamics through feedback loops, maintaining stability while adapting to change.

Mathematical Context

Properties

Examples in Practice

Further Reading