One of the things you have to appreciate about change is that it can be non-linear. So, for 100's of millennia humans wandered around the world chipping stones, hunting, and gathering. During this ENTIRE TIME there was cultural change, undoubtedly, but the effectiveness of the instrumentalities of society didn't change much. An early modern human from 250,000 YA and one from 40,000 YA probably had fairly similar kit. It undoubtedly got somewhat refined and adapted to a wider range of environments, but progress was slow, almost non-existent.
At some point, people began to grow food. Nobody is entirely sure when this happened, certainly it became a prevalent practice some 12,000 YA in the Fertile Crescent (headwaters of the Tigris and Euphrates rivers in eastern Anatolia most likely). It isn't clear exactly how long the transition period was, but at some point some people reached a critical threshold and in that region society rapidly transformed. Now, rapid might mean it took 20,000 years to go from "I planted a seed, look something grew that I can eat, this is a good idea." to Katal Huyuk. This is part of the point being made by Hodgson in
@pemerton's quotation.
So, this is an uneven process. It is probably analogous to a phase transition in physics. Nothing seems to change as water gets colder and colder, but at some point one location, due to some variation in local state, begins to freeze. Once the change starts, it can proceed quite rapidly, the new ordering of molecules spreads throughout the system. This phase change may start in multiple locations too, and the resulting ice might have boundaries between crystals, each organized in a different orientation. Likewise agriculture happened in one or a few specific locations and then spread.
When you compare cultural change or diffusion during a period when the 'state' of society didn't change much, vs a situation where such rapid change did happen, you are talking about two different processes which happen at different timescales. Not only that, but if society A is in the new and more rapidly changing state, then obviously society B, which is still in the old state, hardly changes at all by comparison. So Sumer leaped to an urbanized state, but Europe remained in the old state for another several thousand years until agriculture was established there, and its own internal rate of progress was still stone age, which by comparison is basically no change at all on the timescales in question.
Likewise with sub-saharan Africa. Its technology was probably not that much different from Medieval Europe. They had iron, cities, roads, public works, etc. (at least in some areas), state structures, etc. Meanwhile Europe, by 1600 had started a rapid transformation. So we see that it changed radically from 1600 to 1800, but Africa changed maybe as much as Europe did from 1000 to 1200, which is not a heck of a lot in overall terms. There need not be much other explanation. Diffusion takes centuries, so when you say agriculture diffused to Europe, yes, over 2000 years or more. It might take 500 or 1000 more years for Africa to achieve what Europe has now by diffusion alone. But at our accelerated rate of change, we will be (perhaps, if you are optimistic) vastly more advanced still, and one would assume that the gap would only ever grow, and not shrink. This isn't an indictment of one society vs another, it is just the nature of non-linear change, aka phase changes.
Another thing to consider in terms of 'advancement' is that you only have, or are considering, one yardstick and one possible sequence by which 'progress' might happen. We don't know how many possible pathways there are which could lead to similar phase changes in society. Not all of them may be technological, or it may be possible to base them on entirely different aspects of technology. However, once one society stumbles upon a scenario in which they achieve non-linear phase changing transformation, then if that change involves an increase in means, improved instrumentality, it is likely to abort progress on all other paths. Thus it is easy to imagine that European civilization was 'superior' or 'more advanced' in some fashion, but it is equally likely that, given time, any society might have emerged into a new form of some kind and entered into a non-linear rate of change scenario. We just don't know, and will perhaps never know.
So, here's an alternate way of looking at 'progress'. Imagine it is a lot like a maze. Each society wanders through the maze, and once in a while one reaches a location where they can find a brushhog. From that point on, the maze is no obstacle to them, they go on in whatever direction circumstances dictate at a much more rapid rate, and pretty soon the whole maze is nothing but pathways leading wherever they were going. Any other solutions to the maze that might have existed are now moot.
