  Standard neuroimaging techniques provide non-invasive access not only to
human brain anatomy but also to its physiology. The activity recorded with
these techniques is generally called functional imaging, but what is observed
per se is an instance of dynamics, from which functional brain activity should
be extracted. Distinguishing between bare dynamics and genuine function is a
highly non-trivial task, but a crucially important one when comparing
experimental observations and interpreting their significance. Here we
illustrate how the ability of neuroimaging to extract genuine functional brain
activity is bounded by the structure of functional representations. To do so,
we first provide a simple definition of functional brain activity from a
system-level brain imaging perspective. We then review how the properties of
the space on which brain activity is represented allow defining relations
ranging from distinguishability to accessibility of observed imaging data. We
show how these properties result from the structure defined on dynamical data
and dynamics-to-function projections, and consider some implications that the
way and extent to which these are defined have for the interpretation of
experimental data from standard system-level brain recording techniques.
