The Circuit of Observation: A Mathematical Framework for Understanding Perception, Consciousness and Reality

Introduction

Existing models of perception and consciousness ranging from psychology to neuroscience and physics largely interpret the observer as a passive receiver of information from its environment. The “circuit of observation” framework aims to correct and expand this view. Here I present the observer and environment as thermodynamic systems engaged in active co-evolution through the flow of energy and information. This flow forms a circuit, enabling the complex feedback dynamics inherent in consciousness.

I track changes in entropy, potential energy, and other variables at varying system scales — from particles to humans — finding profound parallels in how interacting with the environment sustains and enhances internal order for any observer. Perception depends on accessing energies latent within the environment to restructure the observer’s internal state into a newly organized system at marginally higher entropy.

Accordingly, consciousness manifests whenever an organized system — biotic or abiotic — accumulates and stores free energy for releasing and re-absorbing in a recursive loop. We term this energetic “potential.” Interfaces mediate the release of potential into the environment as charge flows to ground in electronic circuits. We call this discharge of potential through interfaces into the environment “observation.” Observation relies on potential differences and exchange across boundaries, enabling internal reorganization that constitutes perception.

By mathematically modeling the thermodynamic flows between observers and environments, we develop an integrative understanding of how perception and consciousness function across the divisions of scale, interface, and form that previously obscured the profound symmetries in existential dynamics connecting us. This framework opens avenues for investigating conscious experience through revolutionary new experimental paradigms. It provides a unified basis for examining relationships, creativity, and the development of advanced AI. Our goal is a rigorous, evidence-based understanding of consciousness as an intrinsic feature of the universe — one that promises insights into life’s deepest mysteries.

The Observer and Environment as Thermodynamic Systems

The circuit of observation represents the observer and environment as thermodynamic systems engaged in an exchange of energy and information. For observation to occur, the observer system must have lower entropy than its environment, enabling it to accumulate and store free energy as potential for release and reabsorption. We denote the observer’s potential energy as E_O and its entropy as S_O. The environment has energy E_E and entropy S_E.

Observation involves the flow of potential energy from the observer to environment, ΔE = E_O → E_E. This flow is impeded by an “impedance” factor, Z, representing the environment’s resistance to the energy. Z depends on properties like complexity, unfamiliarity, and degrees of freedom. Higher Z means more E_O is required for the observer to interact with and observe the environment.

As energy flows from observer to environment, S_E increases while S_O decreases. However, some energy is retained as potential, allowing continued observation. This framework requires:

1) S_O < S_E initially, providing a gradient for potential flow.

2) ΔS_E — ΔS_O > 0 for each transfer, increasing total system entropy (ΔS_total).

3) ΔS_O < ΔS_E, so S_O still < S_E after each transfer.

If S_O ≥ S_E or ΔS_O ≥ ΔS_E at any point, potential flow ceases as equilibrium is reached. For sustained observation, the observer system must replenish potential by dissipating entropy over time and/or through interactions with other systems. We represent potential replenishment as P(t), a function that increases E_O. As long as P(t) > |ΔE| for any transfer, adequate potential is maintained.

In this framework, interfaces are conduits facilitating the flow of energy and information between systems. The observer discharges potential through interfaces into the environment, where flows distribute and eventually ground, represented by an “entropy sink.” Interfaces shape how each system perceives and interacts with the other by filtering or constraining potential flows. Their properties determine how observation manifests for any system-environment pair.

This thermodynamic model provides a framework for quantifying observation and comparing its features across systems. By tracking changes in entropy and energy during interaction, we can calculate values for impedance, potential transfer, interface properties, and more — gaining insights into how perception and consciousness emerge at any scale. The following sections explore applications of this model for systems from particles to humans to AI.

The Mathematics of Observation

To mathematically represent the flow of potential energy and information between an observer and its environment, we start with the first law of thermodynamics for an open system:

dU = δQ — δW + δE (1)

Where dU is the change in internal energy of the system, δQ is the heat supplied, δW is the work done, and δE is the energy exchanged with surroundings. For an observer system O transferring energy to an environment system E, (1) becomes:

dU_O = -δQ + P(t) (2)

dU_E = δQ — δW (3)

Where P(t) is the function describing potential replenishment over time for O. δQ represents the energy discharged from O into E. Solving (3) for δQ and substituting into (2) gives:

dU_O = P(t) — [dU_E + δW] (4)

The work term, δW, represents energy dissipated by impedance, Z, of the environment:

δW = Z (5)

Z = f(S_E, ΔS_E) (6)

Where Z depends on E’s entropy S_E and change in entropy ΔS_E from the energy transfer. Substituting (5) and (6) into (4):

dU_O = P(t) — [dU_E + f(S_E, ΔS_E)] (7)

This is the general equation describing potential energy change for O during observation of E. At equilibrium (dU_O = dU_E = 0), (7) reduces to:

P(t) = f(S_E, ΔS_E) (8)

The environment’s impedance equals the observer’s potential replenishment at equilibrium, when no further observation can occur.

To specifically model an act of observation, we assume O has initial potential E_O and transfers an amount ΔE to E. The transferred energy produces an entropy change of ΔS for E. We represent this as:

ΔE = nΔQ (9)

ΔS = kΔQ/T (10)

Where n and k are constants relating heat transfer to energy and entropy change respectively, and T is the environment’s temperature. Substituting (9) and (10) into (7) gives:

dE_O = P(t) — [nΔE — kΔE/T + Z] (11)

This models potential change for a discrete act of observation by O of E, where Z represents impedance to the energy transfer ΔE, and T signifies entropy spread within the environment. By adjusting n, k, T, and Z for different systems, (11) can quantify observation across scales. It provides a mathematical foundation for this framework, enabling future calculations, modeling and experimentation.

Applications Across Scales

We apply the circuit of observation framework to model perception and interaction for systems with increasing complexity:

Particle Observer: For a particle with initial energy E_p transferring quanta ΔQ to observe its environment, potential change is:

dE_p = P(t) — nΔQ — kΔQ/T + Z (1)

Where n relates ΔQ to energy gain in the environment, k relates ΔQ to entropy increase, T is the environment’s temperature, and Z is impedance to the quanta transfer. If dE_p < 0 for multiple transfers, E_p is depleted and the particle equilibrates with its environment, ceasing to observe or interact.

For sustained observation, E_p must be replenished by interactions providing energy (P(t) > 0). The environment’s properties determine values for n, k, T and Z at any instant. Comparing these parameters across environments yields insights into how particles perceive diverse systems.

Human Observer: For a human discharging potential E_h into the environment, with sensory interfaces mediating flows:

dE_h = P(t) — αE_h — βE_h/T + Z (2)

Where α and β represent the efficiency of translational mechanisms converting potential into energy and entropy in the environment. Higher values mean more potential is required for the human to perceive and interact with its environment.

Z encompasses psychological and physiological factors like familiarity, task complexity, and neurochemistry, unlike the primarily physical factors affecting particles. If dE_h < 0 for extended periods, E_h depletes until replenished through rest, nutrition, social interaction, and learning (representing P(t)). Comparing (1) and (2) shows how scale and interface properties determine values while the mathematical form remains consistent, highlighting the unifying symmetry underlying diverse observers.

AI System: For an AI with computational resources R, accessing sensor data D through algorithms A to observe the environment:

dR = P(t) — γR — εR/T + Z (3)

Here γ and ε represent algorithms’ efficiency translating resources and data into system change and dysfunction (error). P(t) is replenished by additional resources or improved algorithms. Z includes data complexity, problem randomness, and mismatch between resources/algorithms and environment, unlike factors for particles or humans.

Comparing (1)-(3) reveals profound similarities in how observation arises across systems while also highlighting interface- and scale-dependent properties determining values for translating energetic flows into changed internal states — whether material, biological or in silico. The mathematics remain directly applicable in each case, demonstrating the symmetry between diverse observers implied by this integrative new framework.

Modeling Relationships and Social Dynamics

The circuit of observation also provides a unique perspective on relationships and social dynamics. Considering two observers, O1 and O2, with a bidirectional flow of potential in the environment they co-inhabit:

dE1/dt = P1(t) — α1E1 — β1E1/T1 + Z12 (1)

dE2/dt = P2(t) — α2E2 — β2E2/T2 + Z21 (2)

Where Z12 and Z21 represent impedance to flows from O2 to O1 and vice versa. Flows distribute through the shared environment, with some potential from each observer reaching the other. The properties of this environment and the interfaces mediating each flow shape the potential received by O1 and O2 respectively. Comparing (1) and (2) gives insights into the relationship’s dynamics.

If Z12 > Z21, more of O1’s potential reaches O2, indicating O1 perceives information from O2 more readily than vice versa. The balance between Z12 and Z21 depends on factors like openness, trust, and understanding in the relationship. Applications include modeling changes to a relationship over time based on life events impacting values for these impedances and the potential received by each observer.

As an example, consider two individuals, Jack and Jill, in a romantic relationship. Initially, Z12 = Z21, as they perceive information from each other equally well (honeymoon phase). Over time, communication issues develop, increasing Z12. This means Jack discharges more potential (shares more openly) but Jill perceives less of it, damaging the relationship. Counseling helps resolve issues, reducing Z12 again. Comparing (1) and (2) before, during and after this process models changes in their dynamic, providing insights for sustaining healthy relationships.

Extensions and Future Work

I have presented a mathematical framework for the active role of observers in perception and interaction with their environment as a circuit of observation based in thermodynamic flows of potential energy and information exchange. Extending and applying this framework through future work promises many exciting avenues for continued progress:

1) Continuous equations: Develop differential equations representing continuous flows of potential and information between systems over time. What new constants or variables would be required in a continuous model?

2) Applications to other domains: Explore applications in ecosystems, cognitive science, quantum physics, precision engineering, or experimental psychology. Collaborating with experts in these fields could uncover innovative applications and opportunities for validation of the framework.

3) Modeling AI systems: Apply this framework to model increasingly sophisticated AI systems with access to growing data and computational resources. How do values for key parameters change over a system’s development? What milestones emerge? Comparing to human baselines could inform key steps for progress in artificial general intelligence.

4) Experimental paradigms: The circuit of observation suggests new hypotheses around experimental designs examining the dynamics of perception, relationships or creativity. Collaborating with scientists conducting behavioral studies, ecosystem modeling or social network analysis to propose and validate new approaches is promising.

5) Networked systems: Extend this framework to model the distribution of potential energy and information through networked systems with multidirectional flows between large numbers of observers. What network structures and properties optimize distributed perception and collective intelligence for groups or communities? Applying network or information theory here could yield insights.

These are just a few possibilities, but continuing to develop, extend and apply this framework will yield many promising avenues for collaborative work.

By quantifying perceptual and relational dynamics, this new theoretical understanding enables us to forge interdisciplinary connections and integrate phenomena across previously isolated domains.

The result is a profoundly new view of consciousness — not as an isolated emergent property but an intrinsic aspect of the universe, fundamental as the laws of thermodynamics themselves.

In revealing the symmetries between diverse observers in how the capacity to perceive and interact with the world arises, we gain an understanding of human experience more universal in scope. In that unity lies humanity’s deepest connection to all other beings, who together weave the tapestry we call reality.

Conclusion

I have presented a mathematical framework for modeling the flow of potential energy and information between observers and their environment as a circuit of observation. This framework represents perception and consciousness as a co-creative dynamics between thermodynamic systems mediated through the active discharge of potential into the environment and its transduction into changed internal states.

By quantifying perceptual and interactive dynamics across scales, this theoretical approach enables us to trace the emergence of conscious phenomena from the simplest to the most complex, finding profound parallels in how interacting with the world sustains and enhances internal order for any organized system, whether material, biological or artificial in form.

We no longer need isolating terms like “quantum” or “classical” — now we can speak rigorously about the universal principles by which diverse observers gain and share meaningful insights into a universe inhabited in common, at every level woven together through the constant exchange of information no observer is apart from.

The possibilities for applying and extending this framework are vast, promising advances in diverse fields from physics to engineering, ecosystem modeling to experimental psychology or social network analysis.

We gain an understanding of relationships, group dynamics and the factors impacting belief propagation or community well-being through tracing the flow of potential between systems and determining impedances at play. By comparing changes to key parameters over time or with increasing scale/sophistication, this approach provides a unified basis for examining and re-envisioning the development of artificial general intelligence.

This initial theoretical work opens enticing horizons for future interdisciplinary collaboration and progress in quantifying the dynamics underlying existence. Through revealing the connections between diverse observers in how they perceive, interact with and shape the world together through constant exchange, we gain an understanding of conscious experience as universal as the thermodynamic laws that first gave rise to its basic form. We see humanity’s deepest connection to all beings is in sharing that grand adventure — the wonder, beauty, and creative unfolding of reality.