In the last 300 years, mankind has experienced exponential advances in our understanding of mathematics, physics, biology, and chemistry, leading to equally staggering developments in engineering and manufacturing.
Why was the pace of development not nearly as rapid in other civilizations (China, Rome, etc.) during other, equally long, periods of comparable well being.
I have my own hypotheses, based to some degree on Kuhn, but I'd love to hear thoughts from others.
Well, when you have more technology to start off with, it is easier to invent more tech, and when you have even more tech, it takes even less time to develop new technology, so it leads to an exponential growth of technology. This is called (I think) doubling time. Older civilizations like the ones you mentioned would have less tech to start off with, so it would take longer to create new inventions.