Morphogenetic Sources in Quantum, Neural and Wave Fields: Part 2

Abstract

Neural network and quantum computer have the same conceptual structure similar to Huygens sources in the wave field generation. Any point of the space is a source with different intensity of waves that transport information in all the space where are superposed in a complex way to generate the wave field. In wave theory this sources are denoted Huygens sources. The morphogenetic field is the wave field generate by computed sources that are designed in a way to transform the original field in a wanted field to satisfy wanted property. The morphogenetic computation is this type of global computation by sources like Huygens sources that in parallel and synchronic way give us the designed field. So the intensity of the sources must be computed a priory before the morphogenetic effective computation in a way to have an entanglement of the sources that in the same time compute the field. If we cannot design the sources a priory and we want generate the field by a recursion process we enter easily in a deadlock state for which one source generate local wanted field that destroy the generation of another local field. So we have a contradiction between the action of different non entangled sources that cannot generate all the wanted field. In neural network we have the superposition of the input vectors in quantum mechanics we have the superposition of the states. In the neural network the intensity of the sources are the neural weights and the threshold. In quantum mechanics the intensity of the sources are the coefficients of the quantum states superposition. To design neural sources intensity (weights) we use the matrix of all possible inputs by which we can define all possible outputs. In the design neural network we cannot use the simple theory of input output but all the past or future input output are used. Space and time is not important in the design the network more important is to use the space of all possible input and output. The same in the quantum computer where we must design the unitary transformation for which only one wanted state coefficient is different from zero all the other coefficients are put to zero. In this way we can select among a huge possible states any one wanted state solution of our problem. In this scheme we include Deutsch problems, Berstein Varizani theorem and Nagata parallel function computing. The difference between quantum computer and neural network is that in quantum computer the basis is the oracle square matrix without any threshold and contradiction. In neural network the basis is a rectangular matrix of possible input with possible contradiction and threshold. So in neural network is necessary first to enlarge the basis in a way to solve with the minimum enlargement the contradiction and after use the threshold to reduce the complexity of the input basis. In the one step neural method we compute the parameters in one step as in quantum computer we use one query is used to generate the wanted result by a unitary matrix. To select wanted result in quantum computer and to obtain the wanted function in neural network, we use the projection operator method for non orthogonal states as oracle and inputs in quantum computer and neural network. Coker Specher theorem is revised in the light of the projection operator. In fact projection operator can select in a superposition one and only one element. Now when we have many basis with elements in common the local projection can enter in conflict with other connected basis projections. This put up in evidence that quantum computer and neural computer include contradiction or conflict. So before any computation we must solve the contradiction itself by the entangled projection method.