Why did civilization appear everywhere simultaneously?

Homo Sapiens had appeared and populated Africa, Europe, Asia and Australia by 50,000 BC, and the Americas by 12,000 BC (perhaps much earlier). After that not much happens for tens of thousands of years.
Then, after tens of thousands of years, literate civilizations suddenly appear in Mesopotamia (3000 BC), China (1700 BC), and Central America (as early as 1000 BC)

Why did they all emerge at once?

Implausible suggestions

Isolationism: the Sumerians, Shang Chinese, and Olmecs/Mayans independently became civilized and invented writing at the same time.
This seems inconceivable. Why did they all do it within 3000 years of each other, after 50,000+ years of wandering around hunter-gathering?

UFOs, Earth created in 4000 BC, etc.
Just mentioning the possibilities.

Conceivable scenarios

Diffusionism: agricultural techniques spread from Mesopotamia, leading to civilization and literacy as far away as China and Central America.
The order of appearance of literate civilization is consistent with this, but the actual transmission seems like a major problem. Even assuming that agriculture naturally leads to writing, how did agricultural techniques spread across the infertile wastes between these regions?
[It has recently been suggested that some early Americans may have come from Europe. Stone cutting techniques and some genetic evidence points to it (Discover magazine, Feb 1999). This would make diffusion at least possible.]

Climate: before about 5000 BC civilization was trying to emerge wherever there were people, but something in the global climate stymied it. At some recent time that suddenly changed, and within a few thousand years civilization developed independently wherever conditions were suitable.
This is conceivable, although it is hard to believe that for 40,000+ years there was nowhere on earth that was suitable for raising crops. Interestingly, there is evidence from ice cores (see, for example, this paper, esp Fig. 1) that 10,000 years ago the earth's climate suddenly became not only warmer but more stable. Was this the starting gun for the global race to civilisation?

Believable solutions

Suggestions welcome.

alford(at)physics.wustl.edu