alt Hacker News> they invented a steam engine[0]
The Aeolipile was not a functional steam engine - it was essentially an unpressurised two-spouted kettle that span on an axle. It had no way of maintaining enough pressure (no valves) to do useful work and the metal working techniques of the day weren't good enough to contain useful pressure without exploding. Real steam engines only came about after people had spent centuries building cannons that didn't explode.
The first practical application of steam engines was pumping water out of deep coal mines (which the Romans didn't have or need) where it didn't matter if the engine was both underpowered and massive. Even after these engines became commercially viable, it took another 70 years or so for the engines to become small enough to be mounted on vehicles.
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There was this synergistic interaction between coal and iron ore deposits, trains and the steam engine. Having a portable steam engine meant that you could build trains, which meant that you could transport coal and iron ore to the steel mills, which meant you could build more steam engines, which meant that you could build more trains and expand the rail network. The fact that these things followed one another wasn't a coincidence.
> steam engines only came about after people had spent centuries building cannons that didn't explode
That's an interesting insight. I had not thought about the possibility of a scientific understanding of pressure developing prior to the steam engine. If you have some pointers to read up on this, I'd love to learn more.
Also, there were demands for pumps in antiquity, particularly in hydraulics. Lot's of labor was invested in building aqueducts and underground waterways. I always saw the Aeolipile as a tech demo showing that heat can be used as a power source for mechanical motion, but this is probably because I live after the steam machine, knowing it's true potential. I've long wondered why the idea wasn't expanded upon by the Romans or later the Greeks or Egyptians, but I suppose it wasn't convincing enough on its own.