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For a definition of civilisation we can turn to an early Spanish observer of Mexican society, known as the "Anonymous Conquistador."  The Anonymous Conquistador has nothing to say about himself and his companions, and instead gives us a sober, matter-of-fact description of early sixteenth-century Mexican society.
Like the Old World society from which our conquistador stemmed, the New World society he describes is based on farming. For example, he speaks of the grain from which the people make their bread (clearly maize). This is accordingly a sedentary society with large cities. These cities have streets and squares that he compares favorably to those of his own country; the main square of Tenochtitlan is about three times the size of that of Salamanca. They hold markets at regular intervals, with an orderly arrangement of wares; their most commonly used currency is the cacao bean (he provides a rate of exchange). Society is stratified, with lords at the top. Unlike the people at large, the lords dine sumptuously. The men hold women in lower esteem than do any other people on earth; they are polygamous, like the Moors (i.e., Muslims). Organized political power is a salient feature of the society: at the summit there is a ruler resembling an emperor, and there are kings and such (not to mention some cities with non- monarchic governments). War is waged by armies, which are divided into companies, with officers in command of them; the Aztec ruler has a special guard of ten thousand warriors. Weapons include bows and arrows, spears, swords, and slings. Religion plays a prominent part in the life of the society, which our conquistador describes as very devout. It is associated with special buildings (he calls them temples or mosques), special personnel (he compares them to bishops and canons), idols or gods, and rituals that he compares to Christian ones (one ritual reminds him of matins). The sons of lords are trained in the temples. In short, the basic categories that our conquistador brought with him from the Old World (Christian and Muslim) seem to have worked well enough for him, even though in the New World he was confronted with a civilization that had evolved quite separately from his own.
He seems to have had no difficulty describing polytheism, cannibalism, and human sacrifice, features of the society not paralleled in early modern Spain, though attested at that time to the outermost fringes of the Old World. If there was an aspect of Mexican society that was totally opaque to him, he does not mention it. Mexican society was indeed sedentary, stratified, and endowed with cities, markets, kings, armies, religion, and the like.
The most striking differences between the two societies in fact have to do with things that were commonplace in the Old World but largely absent from the New. Our conquistador tends not to remark on these absences, but we can easily supply them. Mexican farming (in contrast to that of the Andes) lacked pastoralism. Mexican technology lacked a whole string of things. For example, it made no use of the wheel in transport or in pottery making, and its metalworking was limited in character and impact. This in turn explains why Ethic technology was so highly developed. Our conquistador, who was greatly impressed by this, remarks on the stone spearheads and wooden swords with inset stone blades; Old World societies had little need for such things. All this can broadly be attributed to the less favoured environment of the New World.
The first civilisations based on agriculture emerged around 3000 B.C. The first was probably that of Mesopotamia or, more specifically, of the Sumerians (the earliest people we can call after a name they used themselves). The second, in the northeast corner of Africa, was that of Egypt. From the Near East we move to northwestern India, where the Indus Valley civilization makes its appearance in the middle of the third millennium B.C. The second millennium B.C. then takes us east to China and west to Crete. Finally, the first millennium B.C. brings us to Mesoamerica, in the first instance to the culture we know as Olmec.
One thing worth noting about the cultural sequence of the invention of farming followed by civilisation is its geographical unevenness. In terms of continents, we have one instance from Africa, one from Europe, one from the Americas, and no fewer than three from Asia. In another way it is even more uneven: only China and Mesoamerica take us outside the Near East and the regions adjoining it.