As a matter of fact it's very hard to figure out why and how much a city grew, if you don't have any quantitative sources. That's exactly our problem: there is no ancient source that tells us how many people lived in the city. The reason for a comparative study is this: if you can find a city with a comparable (supposed) number of inhabitants, in a comparable position in the world (i.e. capital of an empire), you might be able to base some conclusions on those facts.
For example, most people believe Rome had about 1 million inhabitants. My study so far shows that this is by no means certain and that it could easily have been half that number. A comparison might support either a higher or a lower number. No, it's not solid science, but it's the best we've got in terms of ancient demography.
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