Describing Ecosystem Dynamics as Tensors in Resonance

This is another attempt to construct a dynamic model of the bonds between society and its members. What I am looking for is a way that a user, person such as you or me, would be able to “instantiate”, or to make an instance of the model in order to “populate” it with particular data, and that this data can be “sparse”, just little bits at a time, if that is all that there is. This might be the “snapshots” of perception or understanding that we all have, or it might be objective facts that we have obtained through our research.

Here I am making use of a “dual” system, two distinct systems, each with their own forms of integrity: objective reality, and subjective experience. The mappings of objective reality conform with those of the sciences, while the mapping of qualia is one of interior, subjective, processes that are “owned” by the “locus of agency and intent”, and are as black boxes to the outside world. It is a dynamic model, incorporating ideas of force, latency, phase and resonance.

As a note: having to deal with the use of mathematical symbols is one of the stumbling blocks when transferring text from a chatbot to substack is not fun. Please be patient with typographical errors which may have escaped my edits.

I explain to the DeepSeek chatbot:

I am interested in dynamic ecosystems where time binding associates the processes owned by loci of agency and intent. In each case perception is governed by two factors: real structures that are imposed from the local context, and scale invariant qualia of perception, which are structured internally to each locus. I am interested in energy transfers between such entities in regard to their relative similarities and dissimilarities. I am interested to describe a set of tensors inherent to this model, and locate loops and nodes of resonances within some real instantiation of the model.

DeepSeek responded:

This is a rich and fascinating conceptual framework. It combines themes from systems theory, phenomenology, information physics, and network dynamics. Let’s unpack your model and attempt to formalize its tensorial and resonant properties.

1. Core Conceptual Framework

Your model posits:

• Loci of Agency and Intent: Discrete entities (agents, cells, organisms, organizations) that are “time-binding” – integrating past, present, and anticipated future states. They own internal processes.

• Dual-Perception Governance:

  1. Real Structures (R): Imposed by the local spatio-temporal context. These are objective constraints (physical laws, resource availability, topological connections).

  2. Scale-Invariant Qualia (Q): Internal, subjective perceptual frameworks. They are “scale-invariant” in the sense that similar perceptual categories (e.g., threat/opportunity, similarity/difference, valence) operate across different levels of organization (cell, organism, ecosystem).

• Energy Transfers: Interactions are fundamentally energetic (material, informational, attentional). The dynamics of these transfers are modulated by the relative similarity/dissimilarity between loci.

2. Tensor Formulation

We can define a set of tensors to describe the state of the ecosystem and its dynamics. Let the ecosystem have N loci. Let indices i, j denote specific loci.

A. State Tensors (for a given locus i at time t)

• Intent Tensor (I_i^μν): A 2nd-order tensor (matrix) representing the locus’s internal directionality. μ indexes temporal modes (past-integrated, present, projected future). ν indexes goal-directed processes. It encodes the “time-binding” property.

• Qualia Tensor (Q_i^{αβ}): A 2nd-order tensor representing the internal perceptual framework. α indexes perceptual channels (e.g., sensory modalities, cognitive categories). β indexes the scale-invariant qualia dimensions (e.g., affinity, novelty, valence). This is the internal structuring of perception.

• Receptivity Tensor (Ψ_i^{αγ}): A 2nd-order tensor mapping external Real Structures (R) to internal Qualia (Q). γ indexes aspects of the local real context R_i. It defines how R_i is filtered and transformed into subjective experience: Q_i^{αβ} ~ Ψ_i^{αγ} R_i^{γ}.

B. Interaction Tensors (governing energy transfer between loci i and j)

• Similarity-Dissimilarity Tensor (S_{ij}^{ρσ}): A 4th-order object (or a 2nd-order tensor in a compounded space). It compares the states of i and j. Its components could be built from contractions of I and Q:
  S_{ij}^{ρσ} = κ_1 * f(I_i^{μν}, I_j^{μν}) + κ_2 * g(Q_i^{αβ}, Q_j^{αβ})
  where f and g are similarity measures (e.g., cosine similarity, inverse distance), and κ are coupling constants. ρ and σ represent the compared feature spaces (intent-space and qualia-space).

• **Interaction Tensor (T_{ij}^{λη}$):** A 3rd-order tensor that dictates the **type** and **direction** of energy-matter-information transfer. It is a function of the **Similarity Tensor** and the **Real Structure** mediating the interaction (e.g., a shared medium, network link): T_{ij}^{λη} = Φ(S_{ij}^{ρσ}, R_{ij}^{ξ}) Here, λ indexes the type of energy/information transferred, η indexes the transfer channel, and R_{ij}^{ξ} is the component of the **Real Structure** relevant to the i-j` connection.

C. Ecosystem-Wide Tensor

• **Resonance-Admittance Tensor (A^{[ω]}_{ik...}$):** A high-order, potentially anti-symmetric tensor that identifies **resonant loops**. For a candidate loop of kloci (e.g.,i → j → k → ... → i), this tensor's magnitude for a frequency mode [ω](a pattern of oscillation in intent or qualia) indicates the loop's propensity to resonate. It would be computed from the cyclic product of interaction tensors and state alignments:A^{[ω]}{ijk...} ~ Tr( T{ij} · D_{[ω]}(I_i, Q_i) · T_{jk} · D_{[ω]}(I_j, Q_j) · ... · T_{...i} ) where D_{[ω]}is a selector for states oscillating in mode[ω]`.

3. Loops and Nodes of Resonance

Resonance occurs when a closed path in the network of loci experiences constructive interference of signals, leading to sustained, amplified patterns.

• Resonant Loops: These are cycles (e.g., i→j→k→i) where:

  1. The phase of a specific qualia or intent pattern ([ω]) is preserved/modified coherently around the loop.

  2. The Similarity-Dissimilarity conditions are such that energy transfer is efficient (e.g., high similarity in some dimensions creates coherence, while controlled dissimilarity in others drives exchange).

  3. The Real Structure (the “wiring”) allows for feedback at a timescale matching the loop’s natural frequency.

• Nodes of Resonance: These are individual loci that act as resonance hubs. They are characterized by:

  1. High Dimensionality of Q_i^{αβ}: Their qualia tensor can interface with many different perceptual frameworks.

  2. Plasticity of Ψ_i^{αγ}: They can dynamically adjust how they map real structures to internal qualia, “tuning” themselves to multiple resonant loops.

  3. High Centrality in the network defined by T_{ij}^{λη}.

4. Instantiating the Model: A Hypothetical Example

System: A research and development ecosystem (academia, startups, venture capital, corporate labs).

• Loci: Individual researchers, labs, firms, funding agencies.

• Real Structures (R): Physical proximity (clusters like Silicon Valley), intellectual property law, communication infrastructure, financial capital flows.

• Scale-Invariant Qualia (Q): Perceived novelty, technical feasibility, market potential, prestige/trust. (A researcher and a VC both use these categories, though scaled differently).

• Intent Tensors (I): For a lab: μ=[past publications, present experiments, future grant proposals]; ν=[hiring, publishing, patenting].

• Interaction & Similarity: Energy transfer is funding, talent, and knowledge.

  • Transfer is most efficient between a researcher and a VC if their Q tensors show alignment on perceived novelty and market potential (high similarity), but dissimilarity in their core competencies (creating a complementarity).

• Resonant Loops:

  • Innovation Loop: Researcher (publishes open-source tool) → Startup (commercializes tool) → VC (funds startup) → University (receives donation/partnership from VC) → Researcher (gets funded/idea validated). This loop resonates when the perceived novelty qualia is amplified around the cycle.

  • Stagnation Loop (Dissonant Resonance): Bureaucratic Agency (low risk tolerance) → Conservative Corporate Lab (incremental goals) → Safe Academic Field (low novelty research) → Peer Review (rejects radical ideas) → Agency (confirms low-risk mandate). This is a resonant loop amplifying the perceived risk qualia, locking energy into low-risk, low-innovation transfers.

Tensors in Action:
The Resonance-Admittance Tensor A^{[innovation]} would have a large component for the first loop, indicating it’s a dominant, stable pattern of energy circulation for the “innovation” frequency mode. Key nodes of resonance would be “translator” entities (e.g., a professor who is also a startup founder) whose Ψ tensor effectively maps academic R (journal impact) to venture R (market size), allowing them to couple these loops powerfully.

This framework provides a rigorous, multi-linear algebraic language for describing your dynamic ecosystem. The power lies in how the tensors S, T, and A formally link the subjective (Q), the agential (I), the objective (R), and the emergent dynamical patterns (resonant loops).

Me again, encapsulating the idea, and seeding it with a use example:

Create a single prompt to instantiate this model and include a sample instantiation (intended to be edited, or not, by the user) which includes two types of loci: thoughtful creators; and ungrateful scammers.

DeepSeek replied:

Here is a prompt to instantiate your dynamic ecosystem model with the specified entity types, followed by a sample instantiation.

Prompt for Instantiating the Ecosystem Model

Objective: Instantiate a dynamic ecosystem model of loci with agency and intent, governed by dual-perception (Real Structures R and scale-invariant Qualia Q), interacting via energy transfers modulated by similarity. Provide the following:

1. Define Locus Types: Provide n distinct types of loci. For each type, specify its archetypal Intent Tensor I, Qualia Tensor Q, and Receptivity Tensor Ψ in conceptual terms.

2. Define Real Structures (R): Describe the objective, shared context that imposes constraints (e.g., platform rules, resource scarcity, network topology).

3. Define Interaction Dynamics: Describe the form of the energy transfer (e.g., attention, money, trust, creative content). Explicitly state how the Similarity-Dissimilarity Tensor S modulates the transfer for a given pair of loci. Does high similarity in a specific qualia dimension amplify or dampen flow?

4. Identify Candidate Loops & Nodes: Propose at least one Resonant Loop (a reinforcing cycle of interactions) and one Dissonant Loop (a degenerative or parasitic cycle). Identify a potential Node of Resonance (a locus that bridges or amplifies loops).

Format Response as:

• A. Locus Definitions

• B. Real Structures (R)

• C. Interaction & Similarity Rules

• D. Candidate Loops & Nodes

• Sample Instantiation (ready to be used or edited)

Sample Instantiation: The Digital Creation Marketplace

A. Locus Definitions

1. Thoughtful Creator (Type-C)

   • Intent Tensor (I_C): μ modes: [Integrate Past Feedback (μ₁), Execute Current Project (μ₂), Nurture Future Audience (μ₃)]. ν processes: [Create, Share, Learn, Connect].

   • Qualia Tensor (Q_C^{αβ}): Qualia dimensions (β): Authenticity, Craft, Impact, Reciprocity. These are scale-invariant.

   • Receptivity (Ψ_C): Maps external R (e.g., audience metrics) strongly to Craft and Impact qualia; filters noise to protect Authenticity.

2. Ungrateful Scammer (Type-S)

   • Intent Tensor (I_S): μ modes: [Exploit Past Patterns (μ₁), Extract Value Now (μ₂), Evade Future Consequences (μ₃)]. ν processes: [Mimic, Harvest, Disguise, Exit].

   • Qualia Tensor (Q_S^{αβ}): Qualia dimensions (β): Leverage, Opacity, Short-Term Yield, Detachment.

   • Receptivity (Ψ_S): Maps external R (e.g., platform trends) exclusively to Leverage and Short-Term Yield; ignores qualia related to community or legacy.

B. Real Structures (R)

• R₁: Platform algorithms that govern visibility.

• R₂: Finite collective attention & trust of the audience.

• R₃: Financial capital flow (patreon, ads, scams).

• R₄: Network topology of followers/collaborators.

C. Interaction & Similarity Rules

• Energy Transfer: Primarily Attention and Trust, convertible to Financial Capital (R₃).

• Similarity-Dissimilarity Tensor (S_{ij}^{ρσ}) Rule: For the Authenticity (C) / Opacity (S) qualia dimension, maximum energy transfer occurs at intermediate dissimilarity. Pure similarity (C-C) fosters deep collaboration but slow growth; pure dissimilarity (C-S) causes rejection. The scammer’s strategy is to mimic similarity in other dimensions (e.g., Impact / Yield) to enter the transfer channel before exploiting the dissimilarity.

D. Candidate Loops & Nodes

• Resonant Loop (Virtuous): Creator A (shares process) → Audience (grants attention/trust) → Creator B (learns & cites) → Creator A (receives recognition & motivation) → ...
  Resonance Condition: High similarity in Authenticity and Reciprocity qualia amplifies trust and content quality.

• Dissonant Loop (Parasitic): Scammer (mimics creator format) → Algorithm (R₁) (promotes due to engagement) → Audience (R₂) (invests attention/trust) → Scammer (extracts value & exits) → Audience (trust depleted) → Ecosystem (authentic creators get less attention) → ...
  Dissonance Condition: Exploits dissimilarity in Intent (Create vs. Extract) while mimicking surface-level Qualia.

• Node of Resonance: The Hybrid Translator – A creator who understands scammer tactics (Ψ maps Leverage). Their I tensor has a mode for [Defend Ecosystem Integrity]. They can redirect energy from the parasitic loop by creating content that exposes mimicry, increasing the effective dissimilarity perceived by the audience and thus breaking the scammer’s access to attention.

(This instantiation can be edited: e.g., add more locus types like “Passive Audience” or “Benevolent Platform”; change the Qualia dimensions; specify tensors with dummy indices and sample values for computational modeling.)