did they practice politics?
Yes, there were states and chiefdoms which had fluctuating policies towards one another.
Maya civilization
Rather, throughout its history, the Maya area contained a varying mix of political complexity that included both states and chiefdoms. These polities fluctuated greatly in their relationships with each other and were engaged in a complex web of rivalries, periods of dominance or submission, vassalage, and alliances. At times, different polities achieved regional dominance, such as Calakmul, Caracol, Mayapan, and Tikal. The first reliably evidenced polities formed in the Maya lowlands in the 9th century BC.
how far back can we trace the mayan culture As far as circa 2000 BC what period of history is that? The Archaic period where were they located? The civilization encompassed areas of south-eastern Mexico, all of Guatemala and Belize, and the western portions of Honduras and El Salvador.
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Maya civilization [SEP] Politics
Unlike the Aztecs and the Inca, the Maya political system never integrated the entire Maya cultural area into a single state or empire. Rather, throughout its history, the Maya area contained a varying mix of political complexity that included both states and chiefdoms. These polities fluctuated greatly in their relationships with each other and were engaged in a complex web of rivalries, periods of dominance or submission, vassalage, and alliances. At times, different polities achieved regional dominance, such as Calakmul, Caracol, Mayapan, and Tikal. The first reliably evidenced polities formed in the Maya lowlands in the 9th century BC. During the Late Preclassic, the Maya political system coalesced into a theopolitical form, where elite ideology justified the ruler's authority, and was reinforced by public display, ritual, and religion.