The Online Dictionary of Language Terminology (ODLT)

gestural theory
Definition - The theory that human language developed from gestures that were used for simple communication.

According to the Wikipedia, "Two types of evidence support this theory:
(1) Gestural language and vocal language depend on similar neural systems, and the regions on the cortex that are responsible for mouth and hand movements border each other.
(2) Nonhuman primates can use gestures or symbols for at least primitive communication, and some of their gestures resemble those of humans, such as the 'begging posture.'"

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