Quantum Models of the Recognition Process — On a Convergence Theorem

Abstract

One of the main activities of the brain is the recognition of signals. As it was pointed out in [22, 25] the procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an "expected view of the world". Then the brain compares a signal arising from our senses with the signal chosen from the memory. That changes the state of both signals in such a manner that after the procedure the signals coincide in a certain sense. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from "excited" to "nonexcited". For that reason a statistical model of the recognition process should reflect both — the change of the signals and the loss of excited neurons. Now, [5] represents the first attempt to explain the process of recognition in terms of quantum statistics. According to the general conception of quantum theory, the procedure of recognition should be described by an operator on a certain Hilbert space. In [5] we proposed two candidates for such an operator. One of them reflects in a clear sense the mentioned change of the signals. The other one reflects the loss of excited neurons. We will prove (cf. Theorem 4) that for sufficiently high intensities of the signals both operators are approximately equal.