Industrialized Rome

More to the point you need a huge degree of capability in metallurgy that the Roman's didn't have. People were not asleep during the Middle Ages! They were doing stuff.
A capability in metallurgy (if by that you mean better quality metals and more metal in use) that was in the most part developed in answer to the need of more canon, bigger canon and canon that didn't blow up and kill the crew.
 
Hope 3 month necromancy is still tolerated, but I wanted to chime in about the printing press idea that everyone was going on about. And also to egg Scott on in his various trolling.

The historian James Burke posits that for a printing industry to take off, a ready source of cheap paper is first needed. Before cheap paper, there exists a relative equilibrium in the long term between the production of material (the paper) and the script. Once there's more material than can economically be enscribed by various clerics, the impetus to replace them is enough to develop a printing press.

Papyrus and parchment are both too scarce to meet that threshold. Historically speaking, it was the medieval expansion of the textile industry and the byproduct of waste cloths that provided the necessary raw materials to supply the fledgling paper industry into high enough efficiency to produce enough paper to outstrip the scribes.

At that point, it helps to have an enterprising goldsmith, say, with experience in a mint, puttering around.
 
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