Current Equation
T = αI + γΦ + δE − βK
A clean, interpretable linear objective in which informational contribution, local organisation, and viability are balanced against complexity or crowding cost.
Future Development · Telos v2
Coupled Objective Functions and Nonlinear Telic Dynamics
This page outlines the next major development direction for Telos: extending the current linear telic model into a nonlinear formulation where information, structure, energy, and complexity do not merely accumulate but interact.
The aim is to deepen the simulator's capacity to produce sharper attractors, richer phase transitions, and more meaningful emergent organisation while preserving the clarity and interpretability of the original framework.
Minimal Extension
Preserve the elegance of the current model while introducing a single nonlinear coupling term.
Sharper Attractors
Expected to produce clearer stable regimes, stronger convergence, and more informative trajectory separation.
Research Instrument
Supports parameter sweeps, archive comparison, and behavioural phase mapping across different coefficients.
Implementation Ready
The proposed change requires only a modest extension to the objective calculation and experiment logs.
From Linear Telos to Coupled Telos
The current Telos formulation treats information, local structure, energy, and complexity as independently weighted contributors. The proposed extension introduces a coupling term so the value of information rises when it is embedded inside organised local structure.
Proposed Telos v2 Equation
T = αI + γΦ + δE − βK + λ(IΦ)
The new coupling term rewards coherent organised information, allowing structure and information to reinforce each other rather than acting as isolated signals.
Why Coupling Matters
In many real complex systems, order becomes meaningful when components interact. Information on its own is weak. Structure on its own can be rigid. Together, they create coherent, persistent organisation.
What λ Controls
The coupling coefficient λ determines how strongly informational content and local structure reinforce one another. Small values preserve continuity with the linear model while still revealing richer geometry in the telic landscape.
Expected Result
The landscape becomes more rugged and expressive, with clearer basins, stronger regime separation, and more distinctive attractor-like outcomes across repeated runs.
Research Direction
The nonlinear extension turns Telos into a stronger laboratory for exploring how organised information stabilises, collapses, or transitions under local pressure, mutation, and resource constraints.
Research Questions
- Does coupling information and structure produce stronger attractor formation?
- Does symbolic convergence become sharper under nonlinear telic pressure?
- Do clearer phase boundaries appear across λ, γ, and temperature sweeps?
- Are metastable states more persistent than under the linear formulation?
Useful Outputs
- population trajectories
- average telic score and coupling contribution
- Φ stability under changing population size
- symbol entropy and symbolic collapse timing
- archived experiment logs with λ tracking
Optional Extended Form
A further development path introduces a second interaction term to discourage brittle, overly dense structural states and preserve adaptive flexibility.
Extended Telos v2
T = αI + γΦ + δE − βK + λ(IΦ) − μ(KΦ)
Here, λ rewards coherent organised information while μ penalises rigid structure when complexity or crowding becomes excessive. This creates a stronger balance between coordination and flexibility.
Implementation Path
The proposed development is intentionally incremental. Telos can adopt the nonlinear extension without losing continuity with its current formulation or archive structure.
1
Add λ to the parameter set
Introduce a configurable coupling coefficient to the simulator interface and archive schema.
2
Compute the interaction term
During telic evaluation, calculate IΦ and include it in the score calculation for each agent decision.
3
Log the nonlinear contribution
Record the coupling contribution alongside existing metrics so archived runs can be compared rigorously.
4
Run comparative sweeps
Compare the current linear model against Telos v2 across λ, γ, temperature, and mutation ranges.
5
Map behavioural regions
Use the archive to identify regimes such as chaotic exploration, structured clustering, symbolic monoculture, and metastable diversity.
Future Development Reference
This page can be linked directly from the Telos landing page as a living reference for model evolution, research direction, and implementation priorities inside Blue Whale.