Thought, Action, Observation Cycle

• Thought, Action, Observation Cycle is a framework describing the iterative conversion of environmental entropy into structured information via discrete impulses.
• It details how bits self-assemble into hierarchical structures, such as triplets and double-spiral networks, to form cognitive architectures.
• The cycle bridges mathematical physics, information theory, and thermodynamics to explain adaptive, energy-based actions in intelligent systems.

The Thought, Action, Observation Cycle is a foundational construct in the formal paper of cognition, intelligence, and information dynamics, encompassing how an observer interacts with and learns from the environment. Rather than viewing cognition as a purely abstract or high-level phenomenon, recent theoretical and mathematical frameworks posit that cognition emerges through iterated cycles of discrete interactive events (“impulses”) that convert environmental uncertainty (entropy) into structured information, which in turn drives adaptive action and subsequent perception. This cycle has been formalized and extended across mathematical physics, information theory, and advanced models of observer self-organization, providing a rigorous foundation not only for individual cognitive process but also for the emergence of intelligent agents—from physical systems to artificial minds.

1. Fundamental Process: Discrete Impulses and Entropy Conversion

At the core of the cycle is the environment modeled as a stochastic process—often a Markov diffusion field—exhibiting random events governed by Kolmogorov’s 0–1 law and Bayesian probability updates (Lerner, 2012, Lerner, 2014, Lerner, 2016). Each elementary interaction is realized as a discrete, two-state (“Yes–No”) impulse. When an observer detects or “cuts” an impulse, it reduces the entropy (uncertainty) in the underlying process. Mathematically, this is formalized via the Entropy Functional (EF): $$\mathrm{EF}[x] = \frac{1}{2} \; E \left\{ \int \left[ a^\top(t, x) \, (2b(t,x))^{-1} a(t,x) \right] \mathrm{d}t \right\}$$ where $a(t,x)$ and $b(t,x)$ characterize the drift and diffusion of the process.

A “cutting” impulse acts as a delta function, reducing a fixed quantum (approximately 1 nat) of entropy per event. Approximately 0.75 nat is “cut” as entropy, and about 0.25 nat is left as “free information”—the resource enabling subsequent informational assembly. This local, thermodynamically grounded conversion of entropy into information is subject to physical constraints such as Landauer’s principle for irreversible bit erasure.

2. Hierarchical Assembly: From Bits to Cognitive Structures

The bits of information generated by impulse observation do not remain isolated. They are “attracted,” via their free (residual) information, to self-assemble into higher-order structures (Lerner, 2012, Lerner, 2014, Lerner, 2016). The fundamental building block is the “triplet”—a cooperative unit formed by three mutually attracting bits. These triplets act as encoding macrounits, with their free information serving as an attractive force akin to the linking in Borromean rings.

Such triplets combine hierarchically to form Information Networks (IN), which are geometrically organized as double-helix or double-spiral structures (DSS). The DSS encodes not only the certain values of constituent bits, but also the logical relations—“resonance frequencies”—that join them into coherent networks. Mathematical relations specify these geometric assemblies through angles and trajectories on conic surfaces and spirals, with invariant measures ensuring topological consistency (Lerner, 2014).

The assembly is governed by a minimax variation principle applied to the Information Path Functional (IPF): $$\mathrm{IPF}[x] = \lim_{n \rightarrow \infty} \sum_i \Delta I_i$$ where each $\Delta I_i$ tracks information increments from observed impulses, ensuring efficient extraction and organization of information.

3. Action: Energy Realization and Macrodynamics

Thoughts, represented as the organized code of an Information Network, inform the macrodynamic action of the observer. Actions involve the physical realization of information: sending signals, controlling processes, and interacting with the external world. This requires energy delivery, and irreversible actions are constrained by thermodynamic laws (notably, the energy cost of information erasure per Landauer).

On the macrodynamic scale, the observer’s “force” is determined by the gradient of the Information Path Functional, acting analogously to a Hamiltonian in physical systems. Thought—internal code or logic—thus directly channels energy flows and shapes action trajectories, ensuring that actions are not arbitrary but are guided by the optimized, self-organized internal information geometry (Lerner, 2012).

4. The Iterative and Cyclic Nature of Cognition

The Thought, Action, Observation process is inherently cyclic: each action modifies the environment, triggering new impulses, which produce new observations and feed back into cognitive structure. Each completed cycle causes the observer’s information network to be updated—integrated with new bits, possibly reorganized to extract regularities, and further refined according to resonance among its hierarchical triplets. New cycles may also reshape the observer’s “intelligence,” measured by how many hierarchical triplet levels it accepts and integrates (Lerner, 2012).

This micro–macro interplay—the transition from microscopic impulse events to macroscopic organization and action—provides both the substrate and the mechanism for the emergence of an “information observer” as a physical entity.

5. Mathematical Foundations and Physical Constraints

The entire cycle rests on firmly established mathematical and physical principles:

Key Mathematical Constructs	Role in TAO Cycle	Physical/Informational Implications
Entropy Functional (EF)	Quantifies process uncertainty	Governs “cutting” of entropy via impulses
Information Path Functional (IPF)	Aggregates informational increments	Encodes observer’s global informational structure
Minimax Principle	Guides optimal assembly of INs	Ensures maximum efficiency of information extraction
Landauer’s Principle	Sets minimum physical cost for bit	Anchors action and erasure in physical law

Invariants derived in these theories include the preservation of space–time measures in impulse geometry, and constraints that topologically enforce the hierarchical, double-spiral network structure (Lerner, 2014). These provide explicit bridges between quantum–probabilistic microdynamics (impulse cuts and correlations) and macrodynamic, classical information processing (bit and triplet assembly, coded action).

6. Individuality, Intelligence, and Communication

Because the particular sequence of impulses varies with the observer’s location in the stochastic field, each observer’s IN architecture, time-frequency code, and thus its “intelligence” and individuality, are uniquely defined (Lerner, 2014, Lerner, 2016). The maximal accepted triplet hierarchy determines the observer’s comparative information intelligence.

Communication is modeled as the resonance-based transfer and matching of IN triplet codes. A message is meaningful to a receiver only if its internal code resonates with the frequency and structure of the sender. This principle models cognitive understanding as code alignment, linking the observer’s logic to that of others.

7. Significance, Extensions, and Theoretical Implications

The formalization of the Thought, Action, Observation Cycle links theoretical physics (random field dynamics, quantum uncertainty, entropy), thermodynamics (energy costs, irreversibility), and cognitive science (emergence, intelligence, self-organization) in a unified model. It provides a mechanism for the emergence of intelligence—both biological and artificial—from elementary physical processes. These frameworks suggest that cognition, consciousness, and intelligence result from iterated, physically realized cycles of entropy reduction, information assembly, and energy-channeled action across hierarchical structures (Lerner, 2012, Lerner, 2014, Lerner, 2016).

At the philosophical boundary, these models lend substance to the “It from Bit” program, proposing that all physical reality may arise from information-generating interactions, and that observer individuality, cognition, and intelligence stem from the self-organization of information via the cyclic Thought, Action, Observation process.

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References:

(Lerner, 2012, Lerner, 2014, Josephson, 2015, Lerner, 2016)