A GENERAL TELEOLOGICAL PRINCIPLE FOR DYNAMICAL SYSTEMS

Abstract

We define a class of physical processes with a causal as well as a teleological component. A causal law generates a set of possible future states of a system when an initial state is given. If the law is deterministic, then different possible future states are obtained if minor variations of the initial state are taken. Possible futures are allowed to interfere with each other. Then, one possible future state is selected according to a deterministic or a nondeterministic selection criterion. The next state of the system is either the possible future state that has been selected, or an intermediate state taken by the system when it evolves to this state. This general scheme can be used to obtain teleological variations of many dynamical systems in which a function is maximized or minimized. We consider two concrete examples. As a first example, we consider a teleological variation of an algorithmic growth process. We show that a teleological algorithm leads to forms with higher values for a quality measure than the non-teleological process from which it is derived. The second example belongs to the cognitive domain. It is shown that a teleological variation of the connectionist backpropagation learning rule leads to significantly lower values for the error function of a network, and hence to a weight matrix of better quality than ordinary backpropagation. On a more basic level, it is conjectured that the type of teleology that is considered can be related to irreversibility in physics.