Artificial neural network research is one of the new directions for new generation computers. Current research suggests that open box artificial higher order neural networks (HONNs) play an important role in this new direction. HONNs will challenge traditional artificial neural network products and change the research methodology that people are currently using in control and recognition areas for the control signal generating, pattern recognition, nonlinear recognition, classification, and prediction. Since HONNs are open box models, they can be easily accepted and used by individuals working in information science, information technology, management, economics, and business fields.