NapoleonXIV said:
As I understand it, the Greco-Roman aversion to technology had to do with slavery. Slave work was despised and anything even slightly allied with it was very much beneath anyone of intelligence. The intelligent went into politics, law and the military, in about that order.
An example I read about was supposed to be illustrated in the construction method they had surmised for a Roman ship they dug up. The ship was constructed by laying the boards first and then building the frame inside it, instead of making it over the frame. This much more laborious method was employed because noone went to the trouble to improve it as it would only save time for a slave.
Actually, if you get to look at boats made by this method you will find that while they are harder to build and ciostlier than the 'modern-style' ones, they are also more flexible, take greater strain and leak less. Shell-building a ship is highly skilled craftsmanship, which, BTW, was a reason it was often left to slaves. Would you trust a free worker with the knowledge investment? He'll just walk away from you...
However, I think the upper-class attitude to crafts would have been a problem (though one easy to overstate: there was considerable pride in workmanship and respect for Skill in the Roman world, just the top 1% chose to look down on craftsmen).
My problem is that I still can't see a plausible incentive. THe Romans did not have the twechnology for true mass-manufacturing on the scale of the machine age, and their metals were rarer and more expensive to make (though just as good as anything prior to 1800). Why would they be particularly interested in steam power? In Britain, a unique constellation of deep-shaft mining needed to meet the demand for iron ore and coke required by the new ironworks that, in turn, could provide the cheap high-quality iron and coal needed by the steam engines that drained the mines touched things off. 'Atmospheric engines' had been around quite some time. Someone even built an experimental steamship in the 1690s.
What would the Romans' excuse be? Maybe they discover canal navigation as a cheap mode of transport and build steam tugs? Their mines were a lot shallower.