Adaptation and Control in the Allagmatic Method

Control was from its very beginning an important concept in Cybernetics. Later on, with the works of W. Ross Ashby, for example, biological concepts such as adaptation were interpreted in the light of cybernetic systems theory. Adaptation is the process by which a system is capable of regulating or controlling itself in order to adapt to changes of its inner and outer environment in order to maintain a homeostatic state. In earlier works we have developed a metamodel that on the one hand refers to cybernetic concepts such as structure, operation, and system, and on the other to the philosophy of individuation of Gilbert Simondon. The result is the so-called allagmatic method that is capable of creating concrete models of systems such as artificial neural networks and cellular automata starting from abstract building blocks. In this paper, we add to our already existing method the cybernetic concepts of control and especially adaptation. In regard to the metamodel, we rely again on philosophical theories, this time the philosophy of organism of Alfred N. Whitehead. We show how these new meta-theoretical concepts are described formally and how they are implemented in program code. We also show what role they play in simple experiments. We conclude that philosophical abstract concepts help to better understand the process of creating computer models and their control and adaptation. In the outlook we discuss how the allagmatic method needs to be extended in order to cover the field of complex systems and Norbert Wiener's ideas on control.