The atheist argument--often trotted out, and frequently rebutted--is that scientific progress ground to a halt during the medieval period (of the "dark ages"). The argument basically says that the Christian religion ruled Europe during the dark ages, that scientific progress ceased during the dark ages, and that the first thing is the cause of the second thing: the Christians came to power and immediately started to suppress scientific progress by suppressing anyone who would have been a scientist. Call it, the gap in scientific progress argument.
There are a number of problems with the argument. For one, religious authorities were often not so powerful as we like to paint, and indeed many of the actual monarchs (and princes, and lords, etc) lacked such complete power to suppress science. For another, very few rulers--weather clerical or noble--actually went about suppressing science (whether technological or speculative), and indeed often embraced technological advances: the stirrup, the horse collar, the water-wheel, the printing press, spectacles, etc. were rather quickly embraced by those to whom they were introduced.
Also overlooked is the fact that much of what made the dark ages so bleak was not the relevant rulers and other authorities, but rather the constant invasions from without. There were Huns, Goths, Vikings, Mohhamedans, Franks, Vandals, and Saxons who are various times were invading one part or another of what once was the Roman Empire (and each other). The western half of said empire had basically collapsed, and the Eastern half was often besieged. Manichaenism from the east took popular piety beyond the bounds of Christianity, and (especially in its Cathar/Albigensian phase) often laid waste to the areas where it took hold.
|Not shown: Saracens, Normans, Norsemen, Lombards, Mohammedans....|
Travel is dangerous, trade is dangerous, thanks to the brigands, and yet these are basically the only way for information to be passed from one town to the next.
The fact that any widespread developments are possible at all becomes something of a miracle in that scenario, no? Sure, the occasional inventor or genius might pop up here or there, though in such a setting simply rediscovering forgotten knowledge is perhaps more important that making new discoveries. Further, I can't imagine that paper to write down observations come cheaply in such a world.
This is basically the world shortly after the fall of the Roman Empire (at least in the west), sans radioactive fallout. This lasted a while, in part because of the invasions (build a monastery, it becomes a center of study and learning, and in a couple of generations it's been sacked and razed). The occasional renaissance becomes possible, often when one leader unites a large area under his rule (e.g. Charlemagne), but then he dies and his descendants squabble over the empire and it falls back to pieces: it's a story older than Christianity, and indeed had gone on even during the "glory day" of Rome. The big difference is that after Rome, there was a Church which worked to reunite society and rekindle civilization. It took a few hundred years to do the latter, and the former never has really happened (the closest to it might be the rule of Charles V, or possible the British Empire during its heyday). Thanks to the Church, some parts of civilization survived; thanks to the monks, often in unpopulated and thus relatively un-endangered areas, some of the learning of the old world remained with us, and eventually some new inventions caught on, then spread.
As Ye Olde Statistician notes in commenting on this,
"In part, this was self-promotion; in part, a humanist reaction against science and reason. There was virtually no progress in the natural sciences during the humanist Renaissance -- which was really about art and architecture. In part, too, the medieval era was rejected because it was too Catholic. The Age of Reason, another self-congratulatory name now rejected by more objective historians, was an age of demolition of philosophy. The Scientific Revolution was less revolutionary than many suppose. Most of its features were present in the 14th century. The most revolutionary feature, the restriction of science to the metrical properties of physical bodies, shifted natural science from a sort of art criticism (understanding how it all fits together) to a servant of business and industry (knowing how to apply it to useful products).As we learn more and more about the real history of the middle ages (as distinguished from the Enlightenment's propaganda of that era), we see fewer and fewer places in which the Catholic religion can legitimately be called a suppressor of science, to say nothing of civilization.
This was all primarily a consequence of demographics achieving a critical mass of inquiring minds, the medieval printing press accelerating the distribution of new knowledge, the employment of late medieval mathematical notation, and new measuring devices. The medievals knew there was a difference between a form and its quantitative extension -- between say 'heat' and 'temperature,' but they had no instrument with which to measure the latter."