The baghdad batteries are nothing compared to the antikythera mechanism, which comes from a similar time frame. This timeframe is after Jayne's hypothesized breakdown of the bicameral mind, though, so it's not quite the same.

Jaynes suggests that a different state of mind... one of essentially hypnosis allowed civilization to expand up to a certain point. In this type of civilization... dubbed "bicameral", both the left and right hemispheres' linguistic areas were active. The right hemisphere essentially provided our "internal monologue" but in the form of auditory hallucinations. These hallucinations provided the basis for remote governance and were ultimately interpreted as gods by people, but these civilizations would fall apart beyond a certain size because the hallucinations would start to fade.

The elaborate rituals that became more elaborate as time went on was attributed to these hallucinations starting to fade as the world became more crowded with these types of civilizations. The part that gave me chills was his description of depictions of gods: up until a certain time, people were always depicted conversing with gods face to face. The gods were present, and the ruler described conversations with them. Until one point in Sumeria, when a frieze was made where god was simply a dot. Depictions of god as a dot or a symbol became more and more common, as did the deference that rulers had. Rather than conversing, they were kneeling and pleading. There were recorded complaints that the voice of the gods were fading. Eventually the voices became associated with demons. The bible records systematic purges of people who heard voices like these.

It's a pretty crazy yet weirdly hard to dismiss theory, and I wish there were more ways to find evidence to support it or debunk it.

An alternative theory for why there were so many "false starts" so to speak, is described by Joseph Tainter in "the collapse of complex societies"... which I find pretty interesting. It's much more mainstream. Basically he turns the question on its head and says "why does civilization exist at all?" That complexity takes energy. That energy wouldn't be wasted unless there were a reason... a positive return on investment in complexity. He says societies break down when the marginal returns on that investment inevitably decrease. So for instance a Native American tribe which developed around a water-sparse area and fluorished by creating cisterns and presumably trading water for other supplies developed, but as the created more cisterns, each new cistern provided less 'bang for the buck'. Eventually they hit the point where building more cisterns was actually counterproductive. The cisterns were too close together so they were cannibalizing each other's trade, and their source of water was starting to dry up, but that's what their society was organized around. Those with influence gained more wealth by creating more, even though the net benefit to the civilization was negative, so they kept doing it. You could say the society existed by virtue of a surplus-generating algorithm. But those algorithms eventually eat through the source of the surplus, and then you need something else.