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In the 1st century AD, Heron of Alexandria created the aeolipile, a basic steam engine. Using the technology he created 'automated' doors for an Apollian temple, but little else. The engine was known to be pretty inefficent but what if Heron or one of his proteges had continued to work on it, seeing more to the technology than entertaining worshippers?
Could a practical steam engine have been developed. The idea of railways existed at the time, I'm not suggesting an Industrial Revolution 1500 years early but what effect would it have had on the Empire and beyond?