Dissipative Arithmetic

Abstract

Large arithmetic expressions are dissipative: they lose information and are robust to perturbations. Lack of conservation gives resilience to fluctuations. The limited precision of floating point and the mixture of linear and nonlinear operations make such functions anti-fragile and give a largely stable locally flat plateau a rich fitness landscape. This slows long-term evolution of complex programs, suggesting a need for depth-aware crossover and mutation operators in tree-based genetic programming. It also suggests that deeply nested computer program source code is error tolerant because disruptions tend to fail to propagate, and therefore the optimal placement of test oracles is as close to software defects as practical.