CALLIOPE · BCOM

This note develops a compression-based perspective on time at two levels. First, in fundamental physics, time can be treated as an emergent parameter that simplifies the description of change---a viewpoint associated with Machian/relational approaches and emphasized by Barbour. Second, in an explicitly algorithmic formulation, a time coordinate (and, jointly, an embedding notion of space) can be rediscovered as latent structure that yields maximal compression of relational observations. We then extend the same compression lens to subjective time flow: perceived duration is hypothesized to track the density of internal model updates and counterfactual simulation, predicting systematic time dilation under pain (high planning/search) and in youth (high learning rate). Empirical anchors are reviewed from time-perception work linking duration judgments to predictability, sensory change, and pain.

Time is just the coordinate that makes your description of the world shortest — and that same idea explains why pain feels slow and childhood feels fast.

The paper starts from a simple but radical claim: time isn't a fundamental ingredient of reality, it's a bookkeeping trick that earns its place by making things compressible. Julian Barbour's relational physics already says something like this — that "time" is just whatever parameter makes the laws of motion look simple. Ruffini sharpens this into an information-theoretic criterion: the best time coordinate is the one that minimizes total description length (in the MDL sense — Minimum Description Length, a formalism where the "best" model is the one that compresses data most). A "good clock" isn't metaphysically special; it's just a parameterization that keeps the equations short.

The algorithmic move is the interesting one. Imagine you have a pile of relational observations — pairwise distances between particles at various moments, with no timestamps attached. The paper proposes that you can discover both a time coordinate and a spatial embedding simultaneously, by searching for whatever latent structure lets you encode that pile as "law + initial conditions" rather than a brute-force list. Time and space aren't assumed; they fall out of compression. This connects naturally to modern equation-discovery methods (like sparse regression on dynamical systems), but extends the search space to include the time axis itself as something to be inferred.

The second half applies the same lens to subjective experience. The hypothesis is that perceived duration tracks the rate of internal model updates — how fast your brain's generative model is being revised. Two things drive this up: high prediction error (novelty, learning) and counterfactual search (planning, threat, pain). The paper formalizes this as subjective time being proportional to model-update density plus planning load. This predicts time dilation under pain (you're running a lot of "what do I do next?" simulations) and in youth (your model is updating rapidly because everything is new). It also predicts time contraction in flow states, where planning load drops and attention drifts away from timing. Empirical support is cited from several time-perception studies linking duration judgments to predictability and sensory change.

The paper is explicitly a speculative note — it doesn't present new experiments or proofs, and the subjective-time equation is a hypothesis rather than a derived result. But it does propose falsifiable hooks: manipulate prediction error and measure prospective duration; show that pain-induced dilation scales with planning demands rather than raw arousal; look for trial-wise correlations between representational change in cortex and duration reports. The unifying payoff is conceptual: physical time and felt time are both compression artifacts, one in the structure of the world, one in the dynamics of the agent modeling it.