The Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message (l) and its frequency (p), for rational communication systems—all of which were fully based on fundamental ideas of Information Theory—are all incorporated into the findings of our long-term experimental study on the "language" and intelligence of ants in this review. The following significant findings regarding the intelligence and communication of ants were made possible by this strategy: i) to demonstrate ants' "distant homing," or their capacity to transmit information about distant events; ii) to estimate the transmission rate of information; iii) to demonstrate that ants can recognize regularities and use them for information "compression "iv) to uncover that insects can move to one another the data about the quantity of articles; (v) to learn that ants can add and subtract relatively small amounts. The outcomes demonstrate that information theory is not only a superior mathematical theory but also that many of its outcomes are comparable to natural laws.
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