DU: There are multiple examples of medieval mechanical computation devices, if not actually programmable computers, being built and none of that era was really beyond the Romans in a materials or manufacturing way. They might not have had all the mathematical concepts, though.
Foosnark: Not discussed: software. More specifically, math.
They didn't have zero. They had horrible awkward notation in which you cannot even do algebra. They had no interest in pure mathematics, and failed to advance mathematics in the slightest.
The best they could have done is maybe an electric abacus, and I have my doubts there.
DU: Yeah, the Romans were actually pretty terrible at math. You know their famous water system? You could get nozzles installed in your house for that. Guess how they charged you for water usage? Cross-sectional area of the nozzle, not flow-rate. (Of course, they didn't have clocks either, but you can still time it against a calibrated-drip bucket or something.) So you buy a nozzle, put it in there at an angle to maximize flow-rate and other tweaks and get like twice the water for the money.
DU: The antikythera mechanism was not a general-purpose programmable computer.
None of which is needful for creating a computer
Maybe. Smedlyman has outlined why they wouldn't have bothered.
DU: round pipe diameter at a perpendicular = flow rate
You seem to have forgotten about pressure. In a city with multiple-story houses, this is an issue.
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