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This paper reframes neural computation through the lens of observational resolution, analogous to Mandelbrot's coastline paradox, by introducing a scale-indexed decomposition to disentangle information from direct dependencies versus residual structure. Exact constructions reveal that projection can convert higher-order dependencies into pairwise interactions, paradoxically increasing the fraction of information captured by direct dependencies while potentially decreasing total predictive information. This scale-dependent information availability and access, grounded in local coincidence detection and saturating integration, implies that point-neuron or direct population models provide scale-specific descriptions rather than uniquely identifying the underlying finer computation.
Neural computation's apparent complexity and information content are artifacts of observational resolution, with projection revealing how higher-order interactions can be misrepresented as simpler pairwise dependencies.
Mandlebrot's coastline paradox reframes measurement as a joint property of an object and its ruler. Here we ask how observational resolution shapes the apparent structure of neural computation. We introduce a scale-indexed decomposition that separates the predictive information captured by direct dependencies from the residual outside that model family. Exact constructions show that projection can convert higher-order dependence into pairwise structure. Projection can increase the direct fraction of surviving information even as total predictive information decreases. A schematic branch-to-soma cascade grounds these effects in local coincidence detection, saturating integration and somatic mixing. Resolving organized nonlinear subunits improves approximation and raises effective representational rank. In a nested hierarchy, these gains occur without increasing information about the target. This distinction separates information availability from access by a restricted readout. A point-neuron or direct population model therefore establishes an effective description at a specified scale. It does not uniquely identify the finer computation that generated the observed relation. Which resolution is adequate depends on the observable and perturbation of interest.