  Recent observation for scale invariant neural avalanches in the brain have
been discussed in details in the scientific literature. We point out, that
these results do not necessarily imply that the properties of the underlying
neural dynamics are also scale invariant. The reason for this discrepancy lies
in the fact that the sampling statistics of observations and experiments is
generically biased by the size of the basins of attraction of the processes to
be studied. One has hence to precisely define what one means with statements
like `the brain is critical'.
  We recapitulate the notion of criticality, as originally introduced in
statistical physics for second order phase transitions, turning then to the
discussion of critical dynamical systems. We elucidate in detail the difference
between a 'critical system', viz a system on the verge of a phase transition,
and a 'critical state', viz state with scale-invariant correlations, stressing
the fact that the notion of universality is linked to critical states.
  We then discuss rigorous results for two classes of critical dynamical
systems, the Kauffman net and a vertex routing model, which both have
non-critical states. However, an external observer that samples randomly the
phase space of these two critical models, would find scale invariance. We
denote this phenomenon as 'observational criticality' and discuss its relevance
for the response properties of critical dynamical systems.
