Information processing organs,mathematical mappings and self-organizing systems

A self-organizing system, which may be biological or man-made, adjusts itself in response to inputs from the surroundings. The input information is processed and transformed, so as to guide the system in accordance with a desired final state. The visual nervous system is considered, to illustrate some possible transformations or mappings, which may be employed by self-organizing systems. The mappings given as examples are linear, but there is evidence also for nonlinear mappings to explain the action of biological systems. The successive stages of adjustment in a self-organizing system can be treated as a feedback control process. Mathematically, feedback control of linear as well as nonlinear systems can be handled by using the principle of contraction mapping. The kind of control considered is flexible in the sense that a desired state of the system as a whole can be achieved through a variety of states of the individual parts. This leads to such questions as equivalence and classification which are also discussed in this paper.