The 10 bits/s bottleneck as error-correcting redundancy: an information-theoretic theory of cognitive reserve

Among individuals with equivalent Alzheimers pathology, cognitive outcomes can diverge by decades, a phenomenon termed cognitive reserve that remains descriptive after thirty years of research. We propose that the [~]109-to-10 bits/s gap between sensory input and behavioral output functions as error-correcting redundancy in the sense of Shannons channel coding theorem. Progressive neuronal loss maps to symbol erasure in a redundant code, and the critical damage fraction at which cognition fails is dc = 1 - k/n, where k {approx} 10 bits/s is the behavioral channel requirement and n is the effective number of coding units. We evaluate this threshold across three channel models (binary erasure, Gaussian, and Erd[o]s-Renyi percolation) and show that all produce a sharp phase transition from reliable to unreliable decoding. The framework makes four testable predictions: (i) dc scales with the measurable redundancy ratio{rho} = n/k, which accounts for clinical heterogeneity; (ii) information-theoretic redundancy from resting-state fMRI should predict time-to-conversion beyond structural atrophy; (iii) the decline trajectory near dc is sharp, consistent with the "cognitive cliff"; and (iv) motor circuits, operating at higher bandwidth, have lower reserve than cognitive circuits. Significance StatementCognitive reserve (why some brains resist dementia pathology better than others) has been described for thirty years but never given a quantitative, information-theoretic foundation. We propose that the roughly hundred-million-fold gap between sensory input ([~]109 bits/s) and behavioral output ([~]10 bits/s) functions as error-correcting redundancy in the Shannon coding-theoretic sense. This yields a closed-form critical damage threshold, dc = 1 - k/n, below which cognitive function is preserved and above which it collapses; this is consistent with the clinically observed plateau-then-cliff pattern of dementia. The framework unifies cognitive reserve with channel coding theory, accounts for individual heterogeneity in disease onset, and generates falsifiable predictions that link information-theoretic redundancy measures to time-to-clinical-conversion.