The Hierapolis stone sawmill shows the use of gear train, crank and connecting rods, if they just could have paired that with Heron's steam engine they might have had an industrial revolution.
I think the Roman Empire was more sophisticated and urbane than the Hollywood portrayal we’ve been feed.
The old saying in show business is, write about what you know. That’s why so many shows are about struggling artists (or have a character who’s trying to make it as a performer; The Big Bang Theory has Penny, Friends had Joey, Seinfeld had Seinfeld...), and why their portrayals of ancient Rome go immediately to orgies and bulemia.
All right, but apart from the sanitation, medicine, education, wine, public order, irrigation, roads, the fresh water system and public health, what have the Romans ever done for us?
Glass windows: the Romans used glass windows even in the most remote parts of the Empire like Hadrian's wall.
Stone buildings: In Italy, by the 2nd century even remote peasants liven in masonry houses with fine tile roofs.
Extensive trade: even the poor had access to very highly quality terracotta vessels and plates that were produced en masse in a few sites and distributed throughout the Empire.
Medicine: We make fun of Galen's theories today but even if he didn't understand the causes of infectious disease he had a decent understanding of epidemiology, disease transmission, anatomy and surgery. His reforms of the Roman army's medical corps made army physicians highly sought after, and they probably provided the best level of care and surgery available until the invention of chloroform and carbolic acid in the 19th century.
Fresh running water and sewers: even without modern chemistry, the Romans knew how to test the pH of water to make sure it had a healthy mineral content without so many minerals that it clogged the aqueducts too quickly.
Chemical electroplating: there's good evidence from ships built by Caligula that someone figured out how to chemically electroplate iron nails with copper for ship building.
Roads, bridges: many are still used in Europe today with a thin layer of blacktop.
In brief, the level of material life (even for common people) was not probably equaled in Europe until sometime in the 19th century. The collapse of the Western Empire can even be seen in ice cores from Greenland, where traces of lead and arsenic from smelting fall dramatically in the 5th century.
The Hierapolis stone sawmill shows the use of gear train, crank and connecting rods, if they just could have paired that with Heron's steam engine they might have had an industrial revolution.