  The theoretical limits of 'lossy' data compression algorithms are considered.
The complexity of an object as seen by a macroscopic observer is the size of
the perceptual code which discards all information that can be lost without
altering the perception of the specified observer. The complexity of this
macroscopically observed state is the simplest description of any microstate
comprising that macrostate. Inference and pattern recognition based on
macrostate rather than microstate complexities will take advantage of the
complexity of the macroscopic observer to ignore irrelevant noise.
