Overview
Information theory characterises what can be transmitted through a channel, but does not explain how communication structure arises. The inaccessible game (Lawrence, 2025) derives a dynamical system from information-theoretic axioms in which the Fisher information matrix acts as a state-dependent conductance tensor — an information topography. Existing demonstrations from the inaccessible game are largely descriptive: GENERIC-like structure appears, bottlenecks can be visualised. This project asks the sharper question required for a generative theory: does the conductance geometry predict where bottlenecks form and how the topography reorganises under controlled interventions? The project builds on the open-source companion library tig-code and on the classical equivalence between steepest entropy ascent and GENERIC dissipation (Montefusco, Consonni and Beretta, 2015). Success means pre-registered predictions from the Fisher geometry that outperform naive baselines.
Prerequisite
L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
FAQs
- What are the prerequisites?
L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
- What will I learn in this Project?
You will learn information geometry (Fisher metric as a Riemannian structure on probability manifolds), constrained maximum-entropy dynamics, and the GENERIC / steepest-entropy-ascent (SEA) frameworks for non-equilibrium systems. You will gain experience implementing nontrivial dynamical systems in Python, designing pre-registered intervention experiments, and evaluating geometric predictions against null models.
- What is the objective of the project?
(1) Reproduce the Curie–Weiss and harmonic-oscillator GENERIC analyses from tig-code, verifying the symmetric/antisymmetric decomposition $M = S + A$. (2) Design three to four interventions (constraint hardness, coupling strength, external forcing, resolution $\varepsilon$) with predictions, written before running dynamics, for bottleneck location, reorganisation timing, and $|A|/|S|$ regime. Predictions must be derived from local conductance / eigenvectors of $G(\theta)$. (3) Evaluate hit rate against null models (random metric, Euclidean gradient ascent under the same constraints). (4) Write a short theory note arguing when Fisher conductance is necessary versus any SEA metric (Beretta’s generic-metric formulation). Deliverables: reproducible experiment suite, prediction log, and a thesis chapter suitable for conversion to a workshop paper.
- How does this fit into the bigger picture?
This project contributes to the mathematical foundations of information topography: communication structure as an endogenous outcome of constrained information dynamics. It connects directly to the IEI module (Fisher geometry, $I+H=C$, MaxEnt) and to talks on the inaccessible game and information topography. A successful project strengthens the claim that topography is predictive, not merely metaphorical.
