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There's something infantile about these post-Dark Age rulers' relationship with Rome. They seem to have only the sketchiest idea of what the Roman Empire actually was, but a strong sense that it was enormous and official and that the route to looking like you're allowed to be in charge of stuff was via affecting to be extremely Roman.
It's a bit like some nursery-school children trying to dress up as astronauts. There's lots of glue and glitter but it's all a bit crumpled. The whole business of having crowns was borrowed from the later Roman emperors' habit of wearing diadems. The objects were then infused with some handy religious significance when the Eastern Romans invented coronations based on some biblical references to crowns and anointing. What looks to us like an archetypically medieval ceremony caught on across Europe because of its associations with the mystique of classical antiquity – this ancient pagan superpower that was also somehow where Christianity came from.
Then Charlemagne decided he was going to have a bit of that. He had the brilliant idea of announcing he was the Roman emperor — or as the office was later referred to with garish hyperbole "Holy Roman Emperor!" […] So, having put together an extremely large early medieval kingdom (albeit still much smaller than the Western half of the Roman Empire had once been), Charlemagne twigged that a key part of becoming an emperor was saying you were one.
There's a pleasing irony to this. The first actual Roman emperors […] always pretended not to be emperors. They still went along with the notion that Rome was a republic run by elected consuls, sometimes not troubling to become consuls themselves.
In fact, the term "emperor" started as a euphemism. Rome, having become a republic, loathed the notion of kings. "Emperor" derived from imperator, which means a "military commander" — they weren't horrible kings, just trusty commanders, in the same way that Stalin was just a nice reliable general secretary rather than anything showy or threatening like a president or tsar.
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(David Mitchell, Unruly)