  As neuroscientists we want to understand how causal interactions or
mechanisms within the brain give rise to perception, cognition, and behavior.
It is typical to estimate interaction effects from measured activity using
statistical techniques such as functional connectivity, Granger Causality, or
information flow, whose outcomes are often falsely treated as revealing
mechanistic insight. Since these statistical techniques fit models to
low-dimensional measurements from brains, they ignore the fact that brain
activity is high-dimensional. Here we focus on the obvious confound of common
inputs: the countless unobserved variables likely have more influence than the
few observed ones. Any given observed correlation can be explained by an
infinite set of causal models that take into account the unobserved variables.
Therefore, correlations within massively undersampled measurements tell us
little about mechanisms. We argue that these mis-inferences of causality from
correlation are augmented by an implicit redefinition of words that suggest
mechanisms, such as connectivity, causality, and flow.
