User:Someone the Person/citylists/chrono2

A sortable table of historical populations of settlements, organized so that you can find out what the largest cities were at a given time in history.

About the numbers
(I know these explanations are a bit hard to process when I write them in words; I'll give some examples once I get this table off the ground.)

Exponential growth
These figures are based on the assumption that populations grow and shrink exponentially. While this is a drastic oversimplification, it is far more realistic than a linear model, but not too much harder to work with. Here is a description of how it works:

Interpolation
Imagine I have a source, that gives the population of a city every hundred years or so. Let's say I want to estimate the city's population sometime between 100 and 200 CE. Over this hundred-year time period, the city's population increased by a certain fraction of itself. The 100th root of this fraction is the number that the city's population multiplied by in one year (if you multiply by the 100th root 100 times, you get the original proportion). If I multiply the population in 100 CE by the 100th root, I get the population in 101 CE. If I do this 32 times (or raise my root to the 32nd power), I get the population in 132 CE.

Extrapolation
For numbers that lie outside the range of my sources, I will take the two nearest ones, and use the ratio between them to get my root. In other words, I will assume that the population grew at the same rate as it did within the bounds. Be warned that these numbers can only decrease in accuracy the farther they are from a sourced number.

If a settlement starts / stops existing, I will not extrapolate for fear of overestimating. Instead, I will place a "1" at the time when the settlement started / stopped existing, and interpolate based on that. This is based on the assumption that if a settlement existed, its population was at least 1. Usually, these numbers are massive underestimates, but I prefer this to overshooting.

Combining sources
Sources often disagree with each other, especially in the case of ancient cities. My method for integrating multiple sources is this: I take each source, and interpolate its data using the exponential growth method. Then, for each year, I take the average of the numbers I get (whether sourced or interpolated), and this number is my estimate. These appear within the main tables in bold, without any citations. I provide the original numbers in separate tables in the bottom half of the page. They are organized alphabetically by city, so that you can find them easily.

When font is normal, the data comes from a single source, or two sources that provide data for exactly the same years (just averaged). If cited, it comes directly from the source. If not, it is an interpolation/extrapolation.

N.B.: Sources often do not coincide in time. When I am extrapolating one source and interpolating others (one source "runs out" of data), I find the nearest year with at least one sourced number, and use my average for that year as a placeholder in the row for the source that ran out. Then I interpolate based on that. You will see these placeholders in bold italic font.

Rounding
All non-integer estimates are truncated (always rounded down, not up, to the nearest one). All averages are rounded to the nearest whole.

Integrations of multiple sources
Chang'an see Xi'an