Attention as Measurement Selection

Attention as Measurement Selection

Compression determines what can be perceived. But a second operation determines what is perceived: attention. Even within the compressed representation, the system must allocate processing resources selectively—it cannot respond to all viability-relevant features simultaneously. Attention is this allocation.

In any system whose dynamics are sensitive to initial conditions—and all nonlinear driven systems are—the choice of what to measure has consequences beyond what it reveals. It determines which trajectories the system becomes correlated with.

The claim is that attention selects trajectories. Let a system $\mathcal{S}$ inhabit a chaotic environment where small differences in observation lead to divergent action sequences. The system’s attention pattern $\alpha: \mathcal{O} \to [0,1]$ weights which observations are processed at high fidelity and which are compressed or discarded. Because subsequent actions depend on processed observations, and those actions shape future states, the attention pattern $\alpha$ selects which dynamical trajectory the system follows from the space of trajectories consistent with its current state.

This is not metaphor. In deterministic chaos, trajectories diverge exponentially from nearby initial conditions. The system’s attention pattern determines which perturbations are registered and which are ignored, which means it determines which branch of the diverging trajectory bundle the system follows. The unattended perturbations are not “collapsed” or destroyed—they continue to exist in the dynamics of the broader environment. But the system’s future becomes correlated with the perturbations it attended to and decorrelated from those it did not.

The mechanism admits a precise formulation. Let $p_0(\mathbf{x})$ be the a priori distribution over states—the probability of finding the environment in state $\mathbf{x}$, governed by physics. Let $\alpha(\mathbf{x})$ be the system’s measurement distribution—the probability that it attends to, and therefore registers, a perturbation at state $\mathbf{x}$. The effective distribution over states the system becomes correlated with is:

The system does not control $p_0$—that is physics. But it controls $\alpha$—that is attention. If $\alpha$ is sharply peaked (narrow attention), the effective distribution concentrates on a small region of state space regardless of the prior. If $\alpha$ is broad (diffuse attention), the effective distribution approximates the prior. The system’s trajectory through state space follows from the sequence of effective distributions it generates, each conditioned on the previous.

This has a consequence for agency that deserves explicit statement. A system whose trajectory depends on its attention pattern is a system whose future depends, in part, on what it chooses to measure. Every branch it follows is fully deterministic—no physical law is violated. But which deterministic branch it follows is selected by the attention pattern, which is itself a product of the system’s internal dynamics (its world model, its self-model, its policy). This is not “free will” in the libertarian sense of uncaused choice. It is something more precise: trajectory selection through measurement, where the selecting mechanism is the system’s own cognitive architecture. Determinism is preserved. Agency is real. Both are true because “agency” does not require violation of physical law—it requires that the system’s internal states (including its values, its goals, its attention distribution) causally influence which trajectory it follows. They do.

This trajectory-selection mechanism operates at the population level too. In evolutionary experiments (V31), different seeds follow different trajectories through the same dynamical landscape — not because their initial conditions differ (all start identically) but because the drought-recovery measurement distribution differs: which agents survive each bottleneck selects which evolutionary path the population follows. The correlation between post-drought recovery and mean integration across seeds is $r = 0.997$. The measurement distribution — which perturbations are survived rather than which are attended to — selects the trajectory. The equation is the same; the scale is different.

This trajectory selection has a temporal depth. Once measurement information is integrated into the system’s belief state, its future must remain consistent with what was observed. Registered observations constrain the trajectory: the system cannot “un-observe” a perturbation. However, if entropy degrades the information—if the observation is forgotten, overwritten, or lost to noise—the constraint dissolves. The system’s trajectory is no longer pinned by that measurement, and the space of accessible futures re-expands. Sustained attention to a particular feature of reality functions as repeated measurement: it continuously re-constrains the trajectory, stabilizing it near states consistent with the attended feature. This is analogous to the quantum Zeno effect, where repeated measurement prevents a system from evolving away from its measured state—but the classical version requires no quantum mechanics, only the sensitivity of chaotic dynamics to which perturbations are registered.