''Interpretatio graeca'' (Latin, "Greek translation" or "interpretation by means of Greek ()") is a discourse〔Characterized as "discourse" by Mark S. Smith, ''God in Translation: Deities in Cross-Cultural Discourse in the Biblical World'' (Wm. B. Eerdmans, 2008, 2010), p. 246.〕 in which ancient Greek religious concepts and practices, deities, and myths are used to interpret or attempt to understand the mythology and religion of other cultures. It is thus a comparative methodology that looks for equivalencies and shared characteristics. The phrase may describe Greek efforts to explain others' beliefs and myths, as when Herodotus describes Egyptian religion in terms of perceived Greek analogues, or when Dionysius of Halicarnassus and Plutarch document Roman cults, temples, and practices under the names of equivalent Greek deities. ''Interpretatio graeca'' may also describe non-Greeks' interpretation of their own belief systems by comparison or assimilation with Greek models, as when Romans adapt Greek myths and iconography under the names of their own gods.
''Interpretatio romana'' is comparative discourse in reference to ancient Roman religion and myth, as in the formation of a distinctive Gallo-Roman religion. Both the Romans and the Gauls reinterpreted Gallic religious traditions in relation to Roman models, particularly Imperial cult.
Jan Assmann considers the polytheistic approach to internationalizing gods as a form of "intercultural translation":
The great achievement of polytheism is the articulation of a common semantic universe. …The meaning of a deity is his or her specific character as it unfolded in myths, hymns, rites, and so on. This character makes a deity comparable to other deities with similar traits. The similarity of gods makes their names mutually translatable. … The practice of translating the names of the gods created a concept of similarity and produced the idea or conviction that the gods are international.〔''Moses the Egyptian: The Memory of Egypt in Western Monotheism'' (Harvard University Press, 1997), pp. 44–54 (quotation p. 45), as cited by Smith, ''God in Translation,'' p. 39.〕
Pliny the Elder expressed the "translatability" of deities as "different names to different peoples" ''(nomina alia aliis gentibus).''〔Pliny, ''Natural History'' 2.5.15.〕 This capacity made possible the religious syncretism of the Hellenistic era and the pre-Christian Roman Empire.
Herodotus was one of the earliest authors to engage in this form of interpretation. In his observations regarding the Egyptians, he establishes Greco-Egyptian equivalents that endured into the Hellenistic era, including Amon/Zeus, Osiris/Dionysus, and Ptah/Hephaestus.
Some pairs of Greek and Roman gods, such as Zeus and Jupiter, are thought to derive from a common Indo-European archetype (Dyeus as the supreme sky god), and thus exhibit shared functions by nature. Others required more expansive theological and poetic efforts: though both Ares and Mars are war gods, Ares was a relatively minor figure in Greek religious practice and deprecated by the poets, while Mars was a father of the Roman people and a central figure of archaic Roman religion.
Some deities dating to Rome's oldest religious stratum, such as Janus and Terminus, had no Greek equivalent. Other Greek divine figures, most notably Apollo, were adopted directly into Roman culture, but underwent a distinctly Roman development, as when Augustus made Apollo one of his patron deities. In the early period, Etruscan culture played an intermediary role in transmitting Greek myth and religion to the Romans, as evidenced in the linguistic transformation of Greek ''Heracles'' to Etruscan ''Her()cle'' to Roman ''Hercules''.
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