Morphological Modular Computing

This paper introduces morphological modular computing, a new computational paradigm based on the principle of guided physical self-organization. It is proposed as a third model of computation, distinct from the sequential logic of the von Neumann architecture and the coherent superposition of the quantum paradigm. The core thesis is that the most efficient and robust form of computation is one that physically instantiates the intrinsic parallelism of modular arithmetic within an engineered substrate whose informational states are topologically protected. The architecture’s logical layer is based on residue number systems, enabling carry-free, parallel operations as guaranteed by the Chinese remainder theorem. Its dynamical layer redefines execution as the asynchronous relaxation of the physical substrate into a stable, low-energy ground state that represents the computational result. The information layer ensures data integrity by encoding residue classes as non-local, quantized topological invariants, providing intrinsic immunity to local errors. By unifying memory and processing into a single substrate, this “zero-transport” architecture directly addresses the thermodynamic limitations of the von Neumann bottleneck. We present the theoretical foundations, abstract architecture, and potential physical substrates for this paradigm, and outline a formal research program to address its primary theoretical and experimental challenges.