Nonlinear Computing

The Nonlinear Computing program investigates whether a single formal criterion can distinguish systems capable of nontrivial information processing from those that are not, regardless of physical implementation. Building on the integration-differentiation balance metric developed in the Existence Threshold program, this work addresses not pattern persistence but the capacity for computation itself. The central hypothesis is that a system computes when its integration-differentiation ratio falls within a bounded regime: sufficiently integrated to propagate signals across the medium, sufficiently differentiated to represent distinct states.

Empirical validation has proceeded across three domains chosen for maximal diversity in physical medium. Neural systems, both biological (EEG recordings) and artificial (transformer attention layers), exhibit integration-differentiation ratios that track computational load. Financial time series display regime transitions between noise-dominated and structure-dominated phases that align with the predicted thresholds. Geomagnetic field data, drawn from solar-terrestrial interaction records, provide a test case for systems whose computational status is genuinely uncertain, offering ground for falsification rather than confirmation.

The program's longer-term trajectory concerns the relationship between the physical properties of a computing medium and its computational expressiveness. If integration-differentiation balance governs computational capacity, then limits on that balance in a given medium should predict what classes of computation it can and cannot support. This connects the program to questions in unconventional computing, neuromorphic engineering, and the physical limits of non-von-Neumann information processing.