In chemistry in general, a lot of times, minute impurities can have a massive role on the properties of materials (this is especially apparent in food, were flavors are basically entirely defined by chemicals found in ppm quantity). Modern process control essentially works by having the needed and acceptable impurities measured in precise amounts, and relying on chemists and metallurgists to monitor how these impurities come about, but this kind of control has only really been possible for a century or maybe two.
In more ancient times, the process control instead basically relied on "get your ingredients from this well/mine/whatever". So while we actually have a decent idea of what Greek fire is (it's a kind of napalm), we don't have any way of knowing what their actual source of naphtha was, so we don't know what the precise impurities that gave it its best kick were. (I'll also opine that there were probably several different formulas in use, and we may be ascribing properties of different kinds of Greek fire to the same one, which would mean that the search for "the" formula for Greek fire could only ever be a failure.)
The real secret to Greek fire was the Byzantine's unusually advanced "siphon," which heated the mixture in a pressure vessel to allow it to spray fairly long distances. The main use was on ships of course, but there was also a man-portable flamethrower version, which is quite strange to think about someone in AD 900 wielding.
This ship-borne version only worked in calm conditions, otherwise fireships were just as likely to set themselves on fire. However, it did do pretty well in the sheltered Sea of Marmara around Constantinople. The fireships probably saved the empire from the Caliphate during the 719 siege of Constantinople by destroying the much large Muslim fleet. That occurred at a nadir of Byzantine power and the height of Caliphate power. Western Eurasian history would have looked very different if the Caliphate got control of the Bosporus then, as opposed to the Turks 700 years later.
Yes, exactly, the same story is with the Damascus steel. We now know that the secret to it, beside the cool look, was that it contained many carbon nanotubes in steel that greatly improved the performance of the blade. That was achieved by a combination of special properties of the iron ore (supposedly sourced from somewhere in India) and the technology itself that got lost over the time. Of course, modern steel is way better and we now actually understand the tech behind the carbon nanotubes, but the old masters were achieving it all by simply conducting many, many experiments.
Something curious to me in materials science/pharmaceuticals/etc. is how difficult it is to replicate the natural laboratory in an artificial one. This is another way in which humanity is losing knowledge, but here it's even dressed up to look like the accumulation of knowledge!
In more ancient times, the process control instead basically relied on "get your ingredients from this well/mine/whatever". So while we actually have a decent idea of what Greek fire is (it's a kind of napalm), we don't have any way of knowing what their actual source of naphtha was, so we don't know what the precise impurities that gave it its best kick were. (I'll also opine that there were probably several different formulas in use, and we may be ascribing properties of different kinds of Greek fire to the same one, which would mean that the search for "the" formula for Greek fire could only ever be a failure.)