The Orthodox Interpretation of quantum mechanics, as developed by many physicists, particularly John von Neumann, addresses the role of measurement, available choices and response of the quantum system to questions posed by an observer in specific quantum laboratory experiments. As such, it is, more consistent and clearer than other interpretations of quantum mechanics and it provides an account of the interactions of observers with the external world. However, in order to explore whether quantum mechanics plays a role in the brain, (...) which is the primary issue, one has to examine the applicability of Hilbert space structure as a valid geometric description of neurodynamics. Here, we re-visit previous work involving the orientation selectivity of neurons, which constructed a type of statistical distance function, in agreement with quantum formalism. This is proportional to the usual distance between orientations of the neurons. The equivalence between the statistical distance and the Hilbert-space distance was developed before. As such, it gives rise to the possibility of reanalyzing the issue of measurement and information processing in the brain function, what is termed geometroneurodynamics. Several issues of this geometrical approach are examined and work that needs further development identified, such as measurement and observation, what is Nature and who the observer is, all of course relevant to functions of the brain. Extending Orthodox quantum mechanics to neurodynamics may be the ontological opening to the relevance of universal non-dual Awareness, examined in previous works. (shrink)