  This paper is about the meaning of understanding in scientific and in
artificial intelligent systems. We give a mathematical definition of the
understanding, where, contrary to the common wisdom, we define the probability
space on the input set, and we treat the transformation made by an intelligent
actor not as a loss of information, but instead a reorganization of the
information in the framework of a new coordinate system. We introduce,
following the ideas of physical renormalization group, the notions of relevant
and irrelevant parameters, and discuss, how the different AI tasks can be
interpreted along these concepts, and how the process of learning can be
described. We show, how scientific understanding fits into this framework, and
demonstrate, what is the difference between a scientific task and pattern
recognition. We also introduce a measure of relevance, which is useful for
performing lossy compression.
