Although great progress in neuroanatomy and physiology has occurred lately, we still cannot go directly to those levels to discover the neural mechanisms of higher cognition and consciousness. But we can use neurocomputational methods based on these details to push this project forward. Here we describe vector subtraction as an operation that computes sequential paths through high-dimensional vector spaces. Vector-space interpretations of network activity patterns are a fruitful resource in recent computational neuroscience. Vector subtraction also appears to be implemented neurally (...) in primate frontal eye field activity, which computes dimensions of saccadic eye movements. We use this apparent neural implementation as a model and construct from it a general neurocomputational account of an important type of sequential cognitive and conscious process. We defend the biological plausibility of all components of the general model and show that it yields testable anatomical and physiological predictions. We close by suggesting some interesting consequences for consciousness if our model characterizes correctly the neural mechanisms producing a common type of episode in our conscious streams. (shrink)