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“Recursion” is understood in two ways: 1) “hierarchical embedding” as a structure and 2) “self-reference / self-invocation of a function” as an operation. The former refers to structure itself, and the latter refers to an operation to create the structure. In research of language and comparative cognition between humans and non-human animals, these two kinds of “recursion” were sometimes confused and misunderstood (Martins, 2012). In the current talk, we demonstrate that the conceptual essence of recursive operation is not the existence and generation of a certain hierarchical embedded structure, but a function which calls itself to create a new embedded structure indefinitely. Additionally, we suggest that the ecological environment of humans is likely to have made the latter adaptive, and the human brain has neural infrastructure that realizes recursive operation. Finally, from research on bird songs, human uniqueness of the recursive operation is discussed. Goal-directed behavior in human beings includes not only non-recursive operation which is generally observed in non-human animals but also recursive operation in which parts of sequence are maintained so that it can be combined with other parts of sequence and arranged to have a particular form. However, the recursive operation requires a higher cognitive load to hold temporal processes. An evolutionary simulation study showed that the adaptive significance of self-

Difference of two recursions, “hierarchical embedding” and “selfreference”: From view of adaptive functions and implementations