  In this review we integrate results of long term experimental study on ant
"language" and intelligence which were fully based on fundamental ideas of
Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and
the Shannon's equation connecting the length of a message ($l$) and its
frequency $(p)$, i.e. $l = - \log p$ for rational communication systems. This
approach, new for studying biological communication systems, enabled us to
obtain the following important results on ants' communication and intelligence:
i) to reveal "distant homing" in ants, that is, their ability to transfer
information about remote events; ii) to estimate the rate of information
transmission; iii) to reveal that ants are able to grasp regularities and to
use them for "compression" of information; iv) to reveal that ants are able to
transfer to each other the information about the number of objects; v) to
discover that ants can add and subtract small numbers. The obtained results
show that Information Theory is not only wonderful mathematical theory, but
many its results may be considered as Nature laws.
