I'm talking about which language is the most popular second language used in international dialogue, especially research.
And the relevant speed there is not population growth but how fast the interconnections and traditions of science change. On the one hand, you have a lot of new scientists coming online, but on the other hand, the bigger the network of scientists, the harder it is to change -- e.g. the lockin effects are bigger.
Rather, I think today a lingua franca is much more sticky than it was in the past, when you were talking about scientists from just a handful of nations communicating with each other. It was mostly just Europe and North America. Now, it's global. The best chance of another language displacing english isn't today, it was in the past. Now, even if China, India, and Japan all ban English and adopt, say, Japanese as their Lingua France, the rest of the world will continue with English and they'll be pulled back into the orbit. Also, there is much more trade today than in the past, so you have a network that is bigger and more interconnected, that has settled on a lingua franca, and that system has much more inertia.
It's hard to imagine what could shift this trend, especially to Mandarin. China's population is probably not going to get dramatically larger than the current 1.4 bn, which is only 20% of the world total. Maybe some sort of civilization-destroying world cataclysm like a meteor impact, pandemic, or nuclear warfare.
If I could live long enough to see the payout, I'd be willing to bet that far future humans will speak only one language, and that language will have evolved primarily from English.
But even if that language is almost certain to be English, because english changes and has so many loan words, it would probably be unrecognizable to the english we speak today.
That Latin persisted for 1300 hundred years after the fall of Rome has more to do with the Roman Church than the Roman Empire. European universities were essentially religious institutions until the renaissance.
To me, it was a very interesting time. For example, that's the period of time in which we built the most beautiful and livable town squares in the world. Even today, when you go to Europe to visit a city, the city square was probably designed in the middle ages (Paris being a notable exception) and the "old city" dating back to the middle ages, is more beautiful than the newer stuff around it. It was a period of beauty in urban design.
Also, the patterns of Feudalism were incredibly stable, compared to previous economic models, so a lot of the rich cultural traditions that were necessary to catapult Europe forward in the Enlightenment were rooted in the middle ages, and wouldn't have existed without Feudalism. If you tried to skip Feudalism and go straight into the 17th Century, Europe would have turned into a horror show -- just think of the French Revolution reign of terror, but assume it just never ends, because at the reciprocal commitments that became established in the middle ages tempered the radicalism of the enlightenment.
And although the pace of learning wasn't as fast as before, there were huge advances made in architecture and construction, culminating with the beautiful Gothic Cathedrals that are still wonders today, and survive today. How many buildings built today will stand for 800 years in the same splendor as the Cathedrals built in the middle ages?
It was also a time of great flowering of crafts and craftsmen, working in guilds scattered across small city-states and distributed political organizations. Distribution, rather than centralization, was the mantra.
For a more nuanced view especially of the cult of crafts, I recommend reading John Ruskin's essay "On the Nature of the Gothic" from his series "The Stones of Venice"
And the dark ages aren't called that because human nature was "dark" during that time. They're called that because we know very little about them.
The Middle Ages is in the "middle" of the Roman Empire and Modernity. It's further divided into "early", "middle", and "late" middle ages. People don't use "dark ages" any more, you want to say "early middle ages". And while we don't know as much about that period as about other periods, we do still know quite a bit.
The point being that with the fall of the Roman Empire and these roving bands of germanic tribes coming in from the east, as well as Arab invaders coming in from the south, ND Viking Invaders coming in from the North, you had full blown race wars being fought all across Europe. People needed to form protective associations, and this created feudalism. If there is anything that defines the middle ages, it is Feudalism, and its remarkably stable system of reciprocal obligations. The lord had to protect the people working the land from the hostile world outside, and in return, they paid rent. This created a patchwork of little city-states, manors, and fiefdoms which collectively pacified Europe by creating a common sense of identity ("Christendom") as well as deterring invaders since there was no great Prize to sack anymore, there were thousands of little Prizes each defended with their own little perimeter. Across this patchwork there were large informal networks of guilds, monastic orders, etc. This is not to say that there were no wars, but the wars were between nobility, they were not race wars, which is huge. Race wars tend to be gruesome wars of extermination or enslavement because you don't view the other side as being human. When the whole continent shared the same faith and followed similar customs, and was connected by the same set of monastic orders and guilds, you couldn't fight a race war anymore.