There is evidence of a medeival decline, even in those areas, although obviously not as bad.
In "Why The West Rules, For Now", Ian Morris defines "The West" very broadly, and definately includes everything you are talking about. He then comes up with various metrics which are not averages, but which focus the most successful part of the region (e.g. population of the biggest city).
Not surprisingly, the most successful parts of the west by his reckoning, were in the Islamic world during the middle ages. But even then his overall metric shows a medeival dip for the west, which his "east" (aka China) did does not see.
How is that the New York art scene? It’s equivalent to “privatize profits, socialize losses”. You’re saying when The West succeeds it’s because of its Westiness, and when The East succeeds it’s because it was having a Westy period.
This data would surprise me too, but the author is fairly well credentialed and has done reasonable work at estimating this kind of thing before. He is one of the authors of https://classics.stanford.edu/publications/cambridge-economi...
His work on city size seems to be in this PDF, pages 109-117: http://www.ianmorris.org/docs/social-development.pdf
I'm far from an expert on this. The only thing I noted was that his estimate of 125K in 1000CE Baghdad is lower than I expected. He argues it may actually have been lower given the documented size, and he notes the 500K-700K estimates for Baghdad imply a much higher density to anywhere else at that time.
I'd note that I don't see the OP's point (that population declined in the Muslim cities during this period) reflected in the numbers I'm seeing in this document. That is mostly because it isn't clear about the whole area population as opposed to the largest cities.