Metric Tensor as Degree of Coherence in the Dynamical Organization of the Central Nervous System

The mechanism by which neuronal networks dynamically organize and differentiate during development is a salient issue concerning neurogenesis. This central event reflects a topological order and its metrizability. One important parameter in this process concerns the role of tremor and intrinsic electrical properties of neurons [Llinàs 1988] from a different in the developmental organization of Central Nervous System (CNS), which we now would like to develop more formally. While tremor is usually considered an undesirable parameter in the generation of coordinated movement it is actually essential in efficient motor execution and reflects fundamental intrinsic neuronal electrophysiological oscillation. In addition, we propose, such intrinsic properties contribute to organize the neuronal connectivity that results in the development of internal coordinate reference systems. Thus the degree of coherence in the oscillatory activities of neuron can be interpreted as embodying a metric tensor of non-Euclidean space that produce topological order associated to CNS development.