Measurements of oxygen consumption from ant colonies of various sizes of Odontomachus bauri, Camponotus rufipes and Zacryptocerus depressus showed a complex and nonlinear relationship between colony size and energy consumption per unit mass. Results show that at certain critical colony sizes, the colonies energy consumption is larger than the sum of the average energy requirement of the individually workers, and near maximal colony sizes, the energy consumption of the colony per unit mass tends exponentially to that of the average individual worker. We propose that social complexity is related to energy consumption in a discontinuous manner and is bound by both, negentropy content of a society and social optimization mechanisms.