We see civilizations with great levels of centralization and organization seem to pop up all over the world, in Mesoamerica, West Asia, China, and the Indian subcontinent. Why is it that they seem to have come about almost at the same time but probably had little contact with each other? (Especially Mesoamerica to the rest of them)
I'm not sure if we're talking about neolithical, bronze age, or iron age cultures; or rather what exactly do you mean by 'great levels of centralization and organization'.In any case, given the neolithical transition from the hunter-gatherer society to an agrarian society, centralization and organization are a necessity to make the sedimentary lifestyle work. Are we talking about the development of agriculture, or development of language and script? What is the exact criteria?
In any case, the timeframes considered a 'start' for the locales you mentioned :
*Neolithic*
Mesoamerica : 3500 BC, Tehuacan culture
West Asia : 10000 BC, Jericho culture
China : 7000 BC, Peigligang culture
India : 9000 BC, Bhimbetka culture
*Bronze age*
Mesoamerica : 1200 BC, Olmec culture
West Asia : 3000 BC, Mesopotamia and Egypt
China : 1600 BC, Shang dynasty
India : 2200 BC, Harappan culture
* Iron age*
Mesoamerica : never happened on its own, until the arrival of europeans around 1500 CE
West Asia : 1600 BC, Hittite culture
China : 1000 BC, Zhou dynasty
India : 600 BC, late Vedic period
As you can see, it's very hard to say they come about almost at the same time, as practically none of these 'age starting' periods coincide ( the Olmecs and Shang Dynasty being whole 400 year aparts being the closest, and a huge stretch) with West Asia clearly leading the way in terms of technological development and mesoamerican cultures staying in Bronze age for 2700 years. Also, if we rearrange this table to be locale specific instead, we can see completely different time-technology development curve, with West Asia and India going through the neolithic period in some 7000 years, and Mesoamerica in 2300.
Societal and technological development is an effect of a million of factors ( like geography, climate, local flora, fauna, and so on), so even in a hypothetical situation that the developments of certain cultures would've coincided to be almost in temporal parallel, it couldn't be surmounted to anything more than a coincidence.