The objective of this research is to advance significantly Artificial Intelligence by developing the first ever, brain-like Super-Turing system. The approach is to build a computational system that is much more powerful (Super) than digital computation. Alan Turing, a WWII code breaker, developed a conceptual (Turing) machine that has been basic to the digital computation revolution of the last 70 years. This project will develop a Super-Turing mathematical model and implement it on an Optical Analog Neural Network Computer. The project will focus on understanding system abilities and differences between Super-Turing and Turing systems. Natural and artificial time-series will be compared to those of Super-Turing models and modeled Super-Turing processes will be compared with those of the brain. Intellectual Merit Super-Turing Computation is a novel, transformative technology that will rewrite computational limits and lay a new foundation for Artificial Intelligence. Broader Impact Increasing the capabilities of machine intelligence will profoundly influence society; Intelligent Super-Turing systems are expected to be capable of improving quality of life, e.g. providing intelligent robotic assistants, improving individualized education, creating new industries and medical technologies producing great economic benefit. Further, a deepened understanding of Super-Turing computation as it relates to living systems is likely to bring new insights into brain function - fundamentally impacting neuroscience and brain-related medical technologies. Graduate and undergraduates will be trained in the interdisciplinary areas of advanced mathematics, physics, and computer science.