| Summary: | 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 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 excellent mathematical theory, but many of its results may be considered as Nature laws.
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