Posted: September 15, 1999 at 13:50:19: by Olorin
I'm not that well informed in ancient history or in the size of cities related to standing armies. But I am well-versed in mathematics. If I correctly understand what you did, then you compared the size of Constantinople to the size of the Byzantine Empire, then scaled it (using a ratio) to the size of Gondor's army.
This makes a very large assumption. The assumption is not necessarily invalid (though I think it is), but you may not realize that you're even making it. You are assuming that a capital's population as a function of army size is a linear function. I find this highly unlikely. Ratios only work in the case of a direct proportion (a very specific form of linear functions), so if it isn't a direct proportion then all of your calculations are totally invalid.
When dealing with populations, the best functions are not linear at all, they are exponential, or (usually even better) logistic. Depending on which model fits our function best, a (linear) ratio will either be an underestimate (in the case of an exponential model) or an overestimate (in the case of a logistic model).
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