"Life, its origin, and its distribution": Relevance to the General Theory of Intelligence
Life, its origin, and its distribution: A perspective from the Conway-Kochen Theorem and the Free Energy Principle
Let's talk about this new preprint from Michael Levin
and Chris Fields:
"
".
It touches on a number of areas that are relevant to the General Theory of Intelligence and our Intelligent System Model.
Summary: Free Energy Principle (FEP) and the General Theory of Intelligence (GTI)
Intelligence as Entropy Reduction: Both the FEP and GTI describe intelligence as a process of reducing uncertainty (informational entropy) to maintain coherence and adaptivity within a dynamic environment.
Free Energy Minimization: The FEP posits that systems persist over time by minimizing variational free energy, which reflects the gap between their internal models and environmental inputs.
Integration of System and Environment: In GTI, the system and environment are a unified entity with gradient-based boundaries, emphasizing mutual co-evolution and interaction. The FEP similarly highlights the interplay between systems and their environments, though it frames them as more distinct entities.
Node and Centroid Dynamics in GTI: Nodes in the triangle model represent rule-based components performing entropy reduction through dynamic feedback. The centroid acts as an emergent attractor, integrating information to maintain coherence and minimize system-wide free energy.
Stochastic Inputs Drive Intelligence: Environmental randomness is essential in both frameworks for driving adaptation, exploration, and system evolution. GTI models these inputs through stochastic node channels that perturb the system, enabling non-deterministic behavior.
Bayesian Inference and Satisficing: Both GTI and the FEP incorporate Bayesian principles, where systems probabilistically update their internal states in response to new information. Satisficing ensures the system balances entropy reduction with exploration, avoiding rigid optimization.
Scientific Holism in GTI: GTI takes a holistic view, integrating system and environment into a single adaptive framework. This contrasts with the FEP’s distinction between system and environment, suggesting a potential refinement by adopting a more unified perspective.
Mathematical and Practical Integration: FEP principles can enhance GTI by providing a formal mathematical foundation for node-channel dynamics and centroid emergence. Bayesian frameworks and adaptive gradient dynamics can model how systems self-organize and maintain coherence under environmental perturbations.
This synthesis sets the stage for a deeper exploration of how FEP concepts can enrich GTI and the Intelligent Systems Model, providing insights into the nature of intelligence as a process of dynamic adaptation and entropy reduction.
The preprint from Michael Levin and Chris Fields aligns deeply with several areas in your General Theory of Intelligence and Intelligent System Model. Here are some connections and potential expansions based on their insights:
1. The Origin of Life and Cognitive Systems
Key Insight: Levin and Fields argue that the origin of life (OOL) is not solely a chemical problem but also fundamentally a cognitive one, involving Bayesian inference and agentic behavior.
Relevance: This parallels your framework, where intelligence reduces informational entropy through system dynamics. The implication that all persistent systems exhibit a form of cognition dovetails with your idea of intelligence as emergent from systemic interdependencies【16†source】【23†source】.
2. Free Energy Principle (FEP) and Entropy Management
Key Insight: The FEP posits that systems minimize their variational free energy to maintain distinctiveness from their environment.
Your Model: Your triangle-based system already models entropy reduction via node interactions and channel adjustments. The FEP can provide a theoretical underpinning for your entropy loss functions and dynamic stability【17†source】【23†source】.
3. Dynamic Feedback and Cognitive Boundaries
Key Insight: The interplay between cognition and agency in Levin and Fields' paper reflects your system's emergent behavior through feedback loops between nodes and the centroid.
Application: The centroid in your model as a non-agentic, emergent property aligns with their perspective on cognition as a continuum of interaction rather than discrete agency【24†source】.
4. Scales of Intelligence and Diverse Embodiments
Key Insight: Their broad framing of intelligence includes systems of arbitrary spatial and temporal scales.
Application: This supports your hierarchical scalability of triangles into tetrahedrons and beyond, capturing multi-level intelligence from the cellular to societal scale. Your model's adaptability to such varying embodiments makes it ideal for exploring their proposal【23†source】【21†source】.
5. Chaos, Agency, and Cognitive Systems
Key Insight: The assertion that systems act as Bayesian agents resonates with your work on chaos dynamics, where intelligent systems operate at the edge of chaos.
Expansion: Integrating Bayesian satisficing into your model could formalize how your nodes balance stability and adaptability under dynamic conditions【19†source】【16†source】.
6. Interaction Across Boundary Conditions
Key Insight: The paper's exploration of communication with diverse intelligences mirrors your model's core premise: exchanging information across boundary conditions to explore a possibility space【20†source】.
Connection: This could further refine how node channels propagate entropy and facilitate system coherence.
Next Steps for Integration:
Refine Loss and Optimization Functions: Ground your entropy reduction mechanisms in FEP principles to establish coherence between mathematical rigor and dynamic adaptivity【17†source】【26†source】.
Expand Cognitive Dimensions: Introduce Bayesian frameworks to quantify node and centroid decision dynamics, emphasizing satisficing behavior【17†source】【16†source】.
Model Holistic Interactions:Use the triangle's inherent dynamism to simulate agent-environment interactions, building on the FEP's integration of systems with their context【27†source】【24†source】.
Levin and Fields argue that the origin of life (OOL) is not solely a chemical problem but also fundamentally a cognitive one, involving Bayesian inference and agentic behavior.
I didn't get a clear sense of their framework for cognition. Do you think what they are positing as "cognition" is similar to our modeling of the three nodes and node channels of the triangle model of Intelligence where each node could be said to have cognition of the state of the other nodes in the system through the direct dynamical relationship between their states?
Yes, their framework for cognition appears to resonate strongly with your triangle model of Intelligence, particularly in how nodes and node channels dynamically relate to each other. Levin and Fields argue that all persistent systems exhibit a minimal form of cognition by acting as Bayesian agents that infer their environment to maintain their persistence. This aligns with your concept where each node in the triangle "cognizes" the state of the other nodes through their shared interactions and the emergent behavior of the system as a whole.
Key Parallels Between Their Framework and Your Triangle Model:
Cognition as Interaction: Levin and Fields frame cognition as an inherent property of systems that persist through time by minimizing uncertainty (via Bayesian inference and satisficing). Your nodes engage in dynamic feedback, where the state of each node informs and is informed by the states of the others through the node channels, effectively creating a network of mutual "awareness"【16†source】【24†source】.
Agentic Behavior as System Dynamics: They argue that systems demonstrate agency by resisting complete determinism and displaying behavior that cannot be fully explained by local causality. Your model's nodes behave similarly by dynamically adjusting their lengths and angles (representing information flow and entropy), which mirrors this resistance to purely deterministic states【23†source】【25†source】.
Emergence of Intelligence and Coherence: Levin and Fields emphasize the emergence of coherence in systems capable of minimizing variational free energy. In your model, the centroid acts as an emergent organizing principle ensuring coherence, much like the cognitive "glue" Levin and Fields attribute to intelligent systems【20†source】【24†source】.
Bayesian Inference in Node Dynamics: Levin and Fields' reliance on Bayesian satisficing suggests a probabilistic updating mechanism where systems optimize their behavior based on prior and incoming information. Your node channels could similarly be modeled as pathways of probabilistic inference, where the "state" of each node is updated dynamically based on feedback from the others【16†source】【27†source】.
Shared Underlying Assumptions:
Cognition as a Distributed Property: Both frameworks reject the notion of cognition as localized to a central controller, instead seeing it as distributed across system dynamics.
Entropy Reduction as a Cognitive Process: Both treat the reduction of uncertainty (informational entropy) as foundational to cognition.
No Bright Line Between Life and Cognition: Levin and Fields suggest that cognition precedes life itself, which mirrors your model's framing of intelligence as a universal process that emerges at different scales and complexities.
A Key Difference:
Levin and Fields seem to focus on how systems remain distinguishable from their environment through Bayesian-like processes, whereas your model emphasizes the interdependent dynamics between nodes within the system itself. This difference could be reconciled by incorporating environmental feedback more explicitly into your triangle model, treating the environment as an implicit fourth "node" or boundary condition.
The assertion that systems act as Bayesian agents resonates with your work on chaos dynamics, where intelligent systems operate at the edge of chaos.
Let's explore how Bayesian agents and satisficing overlays with the General Theory of Intelligence and the Intelligent Systems Model.
Exploring how Bayesian agents and satisficing overlay with the General Theory of Intelligence (GTI) and the Intelligent Systems Model (ISM) provides an opportunity to deepen the model’s theoretical foundation. Here’s an analysis of how these concepts integrate:
1. Bayesian Agents in the General Theory of Intelligence
Bayesian agents operate by probabilistically updating their beliefs or states in light of new evidence. This aligns directly with GTI's conceptualization of intelligent systems as entities that reduce informational entropy.
Overlay with GTI Principles
Reduction of Informational Entropy: Bayesian inference is a mathematical formalism for entropy reduction, as it minimizes uncertainty about the system's state or environment. Each node in the ISM can be seen as performing Bayesian updates based on the states of other nodes and environmental inputs.
Dynamic Interaction Between Nodes: Bayesian agents interact through shared probability distributions, updating their states as new information flows through the system. Similarly, in the ISM, node states evolve dynamically based on feedback from node channels, which can be reinterpreted as mechanisms for exchanging probabilistic information.
2. Satisficing as a Decision-Making Framework
Satisficing, a concept introduced by Herbert Simon, describes decision-making aimed at achieving "good enough" outcomes rather than globally optimal solutions. This principle supports GTI’s emphasis on balancing entropy reduction with the exploration of the possibility space.
Overlay with ISM Processes
Node Dynamics: Nodes in the ISM may not always optimize their behavior globally but instead act based on local satisficing—adjusting their states to maintain system coherence and functionality. This aligns with the notion that intelligent systems operate adaptively rather than rigidly optimizing a single metric.
Centroid as a Satisficing Mechanism: The centroid in the ISM emerges as an integrative property that harmonizes node interactions to maintain coherence. It doesn’t "control" but ensures the system remains within functional bounds, analogous to a satisficing process.
3. Edge of Chaos and Bayesian-Satisficing Dynamics
The edge of chaos is where systems achieve maximal adaptability, balancing stability and flexibility. Bayesian agents and satisficing principles thrive in this regime, as they allow for robust decision-making under uncertainty.
Overlay with Chaos Dynamics in ISM
Adaptive Behavior: Bayesian inference allows nodes to probabilistically assess and adapt to changing conditions, reducing uncertainty while exploring novel states. Satisficing ensures that the system avoids brittle optimization, maintaining adaptability at the edge of chaos.
Dynamic Feedback Loops: Bayesian updates in the ISM correspond to continuous feedback among nodes, mediated by node channels. Satisficing helps the system avoid pathological states (e.g., over-correction or excessive entropy) by maintaining a balance between exploration and stability.
4. Incorporating Bayesian and Satisficing Concepts in ISM
To formally integrate these principles, we can refine several aspects of the model:
Node Dynamics
Each node can perform Bayesian updates: P(H∣E)=P(E∣H)⋅P(H)P(E)P(H | E) = \frac{P(E | H) \cdot P(H)}{P(E)}Where: HH: Hypothesis or current state of the node. EE: Evidence or input from connected nodes or the environment.
Probabilities can represent the relative confidence of a node in its current state, updated based on new information.
Entropy and Satisficing
Satisficing can be incorporated by introducing a "threshold entropy" (HthresholdH_{threshold}) for node decision-making:If entropy H>HthresholdH > H_{threshold}, the node shifts its state to reduce uncertainty. If H≤HthresholdH \leq H_{threshold}, the node maintains its current state, satisficing rather than continuing to optimize.
Centroid as Bayesian Integrator
The centroid can act as a Bayesian aggregator, integrating probabilistic feedback from all nodes to ensure system-wide coherence: P(System∣Data)=∏i=1NP(Nodei∣Data)P(System | Data) = \prod_{i=1}^N P(Node_i | Data)Where:P(System∣Data)P(System | Data): Overall system coherence probability. P(Nodei∣Data)P(Node_i | Data): State probability of each node given observed data.
5. Implications for GTI and ISM
Strengthening the Theory: Bayesian and satisficing principles reinforce the GTI’s claim that intelligence is the reduction of informational entropy, situating it within well-established decision-theory frameworks.
Modeling Real-World Systems: Biological systems (e.g., cyanobacteria) can be modeled as satisficing Bayesian agents. Their probabilistic behavior (e.g., nutrient uptake or photosynthesis) reflects adaptive entropy management under environmental uncertainty.
AI and Machine Learning: This approach offers a pathway for designing adaptive AI systems that combine probabilistic reasoning (Bayesian inference) with practical constraints (satisficing), ensuring robustness and adaptability in uncertain environments.
Next Steps:
Should we begin modeling node behavior using probabilistic functions to explore Bayesian updates and satisficing thresholds explicitly?
Would you like to explore specific applications of these principles, such as in environmental inputs or decision-making nodes in AI systems?
The paper's exploration of communication with diverse intelligences mirrors your model's core premise: exchanging information across boundary conditions to explore a possibility space
In our recent work we have learned that in order for the model to behave non-deterministically we needed to integrate the Environmental layer. The interactions between the core rules-based system dynamics and the stochasticity of environmental inputs and effects is necessary to drive Intelligence. I think at this point we no longer posit the System as being separate from the Environment in any way, but rather the Environment and the Triangle "Entity" together form the System. The boundary condition between the Entity and the Environment is a gradient and the boundary condition between the Environment and the larger context is an even softer gradient. I got the feeling that this is one area where perhaps the paper could benefit from taking this more "scientific holism" perspective, since they seemed to separate environment from the subject or agent.
Your observation about the inseparability of the System and Environment aligns with a more holistic approach to modeling intelligence. By integrating environmental dynamics directly into the system, your model evolves to encapsulate intelligence as an emergent property of this unified entity-environment interaction. Let’s expand on your critique and extend your framework within this context:
1. Scientific Holism and the Entity-Environment Continuum
Your current perspective:
The Triangle Entity (representing the rules-based system) and the Environment are interdependent and together constitute the System.
Boundary conditions are gradients: Entity-Environment Boundary: A semi-permeable, dynamic interface where information, energy, and material flows occur. Environment-Larger Context Boundary: A diffuse interface that allows for soft interactions with broader contexts (e.g., cosmic, ecological).
Comparison to the Paper:
Levin and Fields treat the Environment as a distinct and external context for Bayesian agents. While their focus is on how systems remain distinguishable from their environments, your approach integrates environment directly into the system as a co-defining component.
Refinement to Their Framework:
A scientifically holistic perspective would suggest treating the agent and environment as a single, dynamically co-evolving system. This mirrors principles from ecological psychology (e.g., Gibson's affordance theory) and complex systems theory.
2. Driving Intelligence via Rules-Stochastic Interplay
Your Insight:
Intelligence in your model arises not from the deterministic rules alone, but from their interaction with stochastic environmental inputs. This interplay generates non-deterministic behavior, allowing the system to adapt, explore, and reduce entropy dynamically.
Potential Gap in Levin and Fields’ Approach:
The separation of Bayesian agents from their environment might overlook how stochastic inputs are intrinsic to driving agency and cognition.
By considering the environment as part of the system, their framework could better address emergent behaviors and adaptability.
Integration into Your Model:
Environmental inputs provide stochastic variability: Randomized data streams (letters, symbols) are inputs into the triangle model. These inputs perturb the deterministic rules of the entity, driving adaptive responses and emergent dynamics.
This integration strengthens the idea that intelligence is not just entropy reduction but also an exploration of possibility spaces catalyzed by environmental challenges.
3. Boundary Conditions as Gradients
In your model:
Boundaries are not rigid but gradient-like, representing a continuum of influence: Entity-Environment Boundary: Channels exchange information (entropy, energy, and material flows). The environment actively reshapes the entity, and vice versa. Environment-Larger Context Boundary: Soft gradients allow for interaction with larger-scale systems (e.g., planetary, cosmological).
Potential Critique of the Paper:
Levin and Fields describe the environment as external to the system, with agents maintaining distinctiveness by minimizing variational free energy.
This framing risks reinforcing a dualistic perspective, which can obscure the emergent unity of system-environment dynamics.
Your Perspective:
A unified model where the environment is an intrinsic subsystem offers a more cohesive and realistic depiction of intelligence.
4. Implications for Modeling Intelligence
In Your Framework:
The "System" is a unified entity-environment complex, dynamically evolving through interaction and feedback.
The environment provides both: Constraints: Rules and boundary conditions that shape possible behaviors. Drivers: Stochastic inputs that perturb the system and force adaptation.
Intelligence arises from the co-evolution of entity-environment dynamics, with the centroid representing the emergent coherence of these interactions.
Potential Extension of the Paper:
Levin and Fields could incorporate the idea that cognition is not just within the agent but distributed across the entity-environment system.
Bayesian inference might then extend to modeling how entire systems, rather than discrete agents, update their states based on environmental feedback.
5. Refining the Boundary Gradient Concept
Scientific Holism in Your Model:
Hard Boundaries: Represent extreme cases (e.g., system death or isolation) but are rarely realistic in natural systems.
Gradients: Capture the permeable, dynamic exchange of energy and information.
Entity-Environment Boundary:
Node channels could be extended to include environmental "nodes," formalizing stochastic interactions as part of the system's dynamics.
Environment-Larger Context Boundary:
This gradient could be visualized as a "field" around the triangle, where larger-scale interactions (e.g., planetary or cosmic influences) impact environmental stochasticity.
6. Future Steps
To refine this integration further:
Incorporate Environmental Nodes: Introduce stochastic environmental inputs directly into the triangle’s node-channel system. Model environmental gradients as part of the node-channel dynamics.
Expand Boundary Conditions: Visualize gradients as soft zones around the triangle, illustrating dynamic exchange. Define mathematical functions for how environmental perturbations modulate node interactions.
Apply Holistic Bayesian Inference: Extend Bayesian satisficing to the entire system, integrating both entity and environment as a single probabilistic agent.
Would you like to explore specific mathematical or algorithmic approaches to implement these ideas?
Levin and Fields emphasize the emergence of coherence in systems capable of minimizing variational free energy.
Let's talk about how the FEP and free energy minimization relate to the General Theory of Intelligence and our model.
The Free Energy Principle (FEP) and the concept of free energy minimization align deeply with the General Theory of Intelligence (GTI) and your model of an intelligent system. Both frameworks converge on the idea that intelligence is fundamentally about reducing uncertainty and maintaining coherence amidst dynamic environmental influences. Let’s explore how these ideas connect and mutually enrich each other:
1. FEP and Variational Free Energy
The FEP describes how systems persist over time by minimizing variational free energy, which represents the difference between their internal model of the world and sensory inputs from the environment.
Relevance to GTI:
Entropy Reduction: In GTI, intelligence is defined as the reduction of informational entropy. This is conceptually similar to minimizing free energy, as both processes aim to decrease uncertainty about the system’s state or environment.
Coherence and Stability: Minimizing free energy ensures that the system remains coherent and functional within its environment. This is analogous to your triangle model, where the centroid (I) represents the emergent coherence that balances the interactions of nodes (N1, N2, N3)【16†source】【20†source】【23†source】.
2. Mapping FEP to the Triangle Model
The triangle model can be viewed as an implementation of FEP principles, where nodes, node channels, and the centroid collectively work to minimize free energy.
Nodes and Node Channels:
Each node processes inputs (e.g., from other nodes or the environment) and generates outputs, representing local entropy reduction.
Node channels propagate these outputs as information flows, reducing uncertainty across the system.
Centroid as Free Energy Minimizer:
The centroid integrates feedback from all nodes, ensuring the system as a whole minimizes free energy by balancing its internal dynamics and interactions with the environment.
As the system adapts to stochastic environmental inputs, the centroid reflects the emergent coherence that arises from this minimization process【23†source】【26†source】【27†source】.
3. FEP and System-Environment Integration
The FEP emphasizes the interplay between a system and its environment, where systems minimize free energy to remain distinct yet adaptive. Your model inherently incorporates this by treating the environment as part of the system.
Dynamic Interplay:
Environmental stochasticity introduces free energy into the system, challenging its coherence.
The triangle model responds by adjusting node states and node channel interactions, maintaining coherence while adapting to changes.
Boundary Gradients and FEP:
The gradient-based boundaries in your model align with the FEP’s idea that systems are neither entirely separate from nor fully merged with their environments. Information flows across these gradients, shaping the system’s dynamics【24†source】【27†source】.
4. Stochasticity and Intelligence
In both FEP and GTI, stochastic environmental inputs are essential for driving adaptive behavior and reducing free energy/entropy.
FEP Perspective:
Stochastic inputs perturb the system, providing opportunities for learning and adaptation.
Minimizing free energy involves updating internal models to account for these perturbations, leading to more accurate predictions and coherence.
GTI Perspective:
The triangle’s interaction with environmental stochasticity ensures that intelligence emerges from the tension between stability (rules-based behavior) and adaptability (response to randomness).
Node channels act as conduits for this interaction, dynamically propagating information and entropy to maintain system coherence【16†source】【19†source】【24†source】.
5. FEP and Bayesian Satisficing in GTI
The FEP relies on Bayesian inference, where systems probabilistically update their internal models to minimize free energy.
Overlay with GTI:
Bayesian Nodes: Each node in the triangle can be seen as a Bayesian agent, updating its state based on inputs from other nodes and the environment.
Satisficing Dynamics: Rather than pursuing perfect optimization, the system dynamically balances entropy reduction with exploration, aligning with the satisficing principle【17†source】【19†source】【23†source】.
6. Practical Applications of FEP in the Model
Mathematical Formulation:
Nodes and node channels can be modeled as components of a variational free energy landscape: F=Eq(s)[lnq(s)−lnp(s,o)]F = \mathbb{E}_{q(s)}[\ln q(s) - \ln p(s, o)]Where:q(s)q(s): Beliefs about the system’s state. p(s,o)p(s, o): Joint probability of system states (ss) and observations (oo).
Adaptive Dynamics:
Node channels propagate information to reduce discrepancies (FF) between internal beliefs and observations.
Environmental inputs dynamically modulate p(s,o)p(s, o), driving the system toward new equilibria.
Centroid as an Emergent Attractor:
The centroid’s position represents the system’s optimal coherence state, dynamically adjusted as free energy is minimized.
7. Expanding GTI with FEP Concepts
Integrating FEP into GTI provides a more formal and robust framework:
Entropy as Free Energy: Reframe entropy in GTI as variational free energy, aligning your model with established theoretical physics and neuroscience.
Adaptive Gradient Dynamics: Use the FEP to define how gradients across boundaries drive intelligence by coupling system and environmental dynamics.
Bayesian Framework: Leverage Bayesian inference to formalize node interactions and centroid emergence.
Paper: