alt Hacker NewsThis kind of fiction is pretty popular in Russia. So there are websites and forums that discuss the kind of hand-waving needed to make the stories interesting (I recommend https://www.popadancev.net/ ).
And one thing that really stands out is that there are really not that many shortcuts. To build something like a steam engine, you need to invent advanced steelmaking, casting, advanced tooling (lathes, drills, etc.), and so on.
In general, ancient people were able to exploit the tech available to them with great efficiency.
There are some technologies that were overlooked longer than they should have, but not that many. For example, rubber could have been invented 400 years earlier. Hooke had a microscope capable of resolving micro-organisms in 1665, but the germ theory of diseases took 300 more years to develop.
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It should have been possible to create electricity with waterwheels. You ”only” need copper.
I actually disagree a bit. The whole premise of the story is that there are shortcuts indeed, when someone has the entire tech tree available at the push of a button.
The Romans were very capable engineers. If you give them a few key ideas and steer them away from dead ends, progress can compress a lot.