Gillespie acknowledged that the Olmecs established a vibrant culture and that their accomplishments were extraordinary. She also agreed that they were innovative and that their leaders presided over a political system capable of mobilizing labor for public works. It was no easy task raising an artificial plateau or hauling heavy blocks of basalt 40 miles to San Lorenzo from volcanic fields and fashioning them into the stone heads that stand as high as 10 feet.

Olmecs also contributed games with rubber balls, which became popular and were fiercely played by later regional cultures. The Aztecs, much later, used the name in their own language for "rubber people" — Olmec — to describe the culture that was by then long vanished but not forgotten. No one knows what the ancient Olmecs called themselves.

"But others in the area were doing things equally complex, though different," Gillespie said. "Other areas were also taking steps on their own toward the development of Mesoamerican civilization."

That, and an active interchange of ideas and beliefs among various neighboring societies, is the essence of the argument advanced by sister-culture proponents. They further contend that the concept of the Olmecs as a mother culture grew out of 19th-century ethnocentrism, in which the construction of stone sculptures is a sign of civilization because that is a hallmark of early Western civilizations.

Many of these archaeologists have concentrated their research and excavations on non-Olmec areas with evidence of ancient complex societies, like the Valley of Oaxaca, the central basin of Mexico and the Pacific coastal sites of Chiapas in southwestern Mexico. Gillespie, though, has studied Olmec workshops that were operating in the culture's heyday, mainly producing stone artifacts thought to be altar thrones.

Blomster cited recent excavations by Dr. Ann Cyphers, of the National University of Mexico, that "emphasize the higher sociopolitical level that the Olmecs achieved relative to contemporaneous groups in Mesoamerica," a view contrary to the sister-culture position. Cyphers said the rulers of San Lorenzo appear to have lived in a palace with huge basalt columns and sculptures, while leaders in the adjacent Valley of Oaxaca had places not much better than the wattle-and-daub huts of commoners.

Dr. Michael D. Coe, an archaeologist at Yale who is an authority on the Olmec and the Maya cultures, sides more with the mother-culture school, saying that "much of the complex culture in Mesoamerica has an Olmec origin."

In the new edition of his book "The Maya," Coe writes that during four centuries of San Lorenzo's prime, ending about 900 B.C., "Olmec influence emanating from this area was found throughout Mesoamerica, with the curious exception of the Maya domain — perhaps because there were few Maya populations at that time sufficiently large to have interested the expanding Olmecs."