Three interesting points in Chapter 6:
1) Apparently a lot of Chinese technological innovations spread to Europe via the intermediary activity of Mongol merchants. Alas, too few examples are given, with most of the writing focusing on the geopolitics of European-Mongolian-Chinese interaction and too little on the specific innovations that made their way to Europe. That makes it hard for the reader to really appreciate the type or extent of Chinese influence.
2) Having already noted that the Arabs added a lot to what they received from the Greeks, Bala points out another problem with a narrative of Greek learning merely being passively held in reserve by the Arabs: It's just plain weird. It's almost a death and resurrection narrative. Europe reaches great heights under the Greeks, then there is a decline, the spirit of Greek learning is held in secret by the Arabs, then it is reborn in Europe. Even if we leave aside the lack of agency on the part of the Arabs, it's a good amount of self-abasement by the Europeans.
I've seen other writers argue that there was nothing particularly dark about the Dark Ages; Bala's analysis is that Europeans did this so that they could save face when they adopted Arab science and technology. Something went wrong after the fall of the Roman Empire, but eventually Europeans re-discovered their glorious heritage. They can claim a redemption, rather than admitting that they learned something from the Arabs.
3) In this chapter Bala emphasizes something that I also noted in an earlier post: It's kind of weird to claim that Western Europeans and Greeks were part of the same civilization. When the Greeks were doing philosophy the people of Western Europe were mostly illiterate farmers, herders, and fishermen. (Like most other people on earth for most of human history.) In fact, a lot of the Western Europeans of the Renaissance and early modern era were actually descended from people who had entered Europe as barbarian invaders. What, exactly, is the link between Western Europeans and ancient Greeks, beyond the fact that they both speak Indo-European languages and Greek writings eventually made their way to Western Europe?
Besides, as Bala notes, Hellenic civilization extended throughout much of the Mediterranean, especially the eastern Mediterranean, and into Egypt. And, what do you know, Arab/Muslim civilization is/was in those regions. The people of Egypt, Syria, and Turkey today are at least as connected to the Greeks as the people of the British Isles are. Yeah, the Turks, Egyptians, and Syrians got their religion from the Arabian peninsula, but Western Europeans mostly practice an Abrahamic faith as well. OK, a few eccentrics do rituals at Stonehenge, but the similarities between Christianity and Islam are at least as strong as the ancient Indo-European ties between Celtic and Greek mythologies.
One point Bala hasn't emphasized yet is that even if one wanted to make a narrative of Dark Ages, from an intellectual standpoint there was nothing very productive or enlightened about the Roman era. The Romans contributed comparatively little to math, science, or philosophy. The fall of the Roman Empire might have been a point of political, military, and economic decline for Europe, but the point of intellectual decline probably came with the integration of Hellenic civilization into the Roman Empire. Just sayin'. I love Italians, being a quarter dago and all, but we didn't contribute much to science until Galileo, you know? (Fortunately, Galileo was sufficiently awesome that for the remainder of time Italians can point to him and feel sufficiently justified, just as Newton did for the English.)