The limits of falsifiability: Dimensionality, measurement thresholds, and the sub-Landauer domain in biological systems

Karl Popper's falsifiability criterion assumes that scientific hypotheses can be reduced to binary tests. We show this assumption is scale-dependent and can saturate in high-dimensional biological systems operating near physical measurement limits, especially near criticality. In neural networks, much relevant information exists as patterns below the Landauer threshold for irreversible bit recording-signals too weak for individual neurons to detect but detectable when pooled across populations. These sub-threshold patterns cannot be projected into binary outcomes without destroying their causal structure. We develop a framework connecting dimensionality, thermodynamic measurement limits, and biological epistemology, showing that Popperian logic represents a special case applicable only to low-dimensional systems with strong signals. Our analysis has implications for neuroscience, where aspects of conscious processing may in part depend on sub-threshold coherence patterns that resist binary measurement, motivating a shift from single-case hypothesis tests to multi-scale, ensemble-based inference. The framework extends to other complex biological systems including ecological networks, protein folding dynamics, and evolutionary processes where causal relationships exist as irreducible multi-dimensional structures operating below classical measurement thresholds.