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> Please do, this is very interesting.
Well, many of the similarities originate from a set of fundamentals which were very close between the two races. Worship of a patriarchal sky deity is probably the most fundamental, and from this a more or less analogous pair of worldviews evolves. This worldview places great importance on the principles of family relations, ancestor relations and defines a social hierarchy. Men saw God as a father, and themselves as children. The devotion a man shows to his god was therefore analogous to the devotion a son shows to his father. And this model of fidelity ("fides") was basically extrapolated to the entire body of society. For instance, both races HEAVILY emphacized the relation between a guest and host, seeing the two positions as reciprocal in their owing fidelity to one another (in original Proto Indo-European, the word for "guest" and "host" were the same). For example, Mongols had the custom that it was a great sin to kill a man, even a mortal enemy, while he is a guest (Genghis Khan's father was killed this way, which is why he eventually retaliated so brutally).
This is why both traditional Indo-European and traditional Asian societies had such rigid social hierarchies, such as the Indian caste system (an extreme example), analogous to the Simin (四民, four categories of people) in China. The choice of four is not insignificant either, as it corresponded to four directions and four seasons. Those that worshipped Heaven placed heavy importance upon the movement of celestial bodies in order to calibrate their calendars. The swastika, a holy symbol in both Asian and Aryan civilizations, came from this. Many think that it was Aryan Buddhism that brought the swastika to East Asia, but the symbol had actually been there much longer. It comes from observing the Big Dipper rotate about Polaris, the Dipper with Polaris forming an L shape, which, repeated four times radially, generates a swastika.
We can also see where many Asian and IE societies converged in political and philosophical thought. For instance, it is significant to note that both societies had a concept of a "warrior-scholar". It was the Greek Thucydides who said "The Nation that makes a great distinction between its scholars and its warriors will have its thinking done by cowards and its fighting done by fools." There was some other Greek (can't remember who off the top of my head) who said that those who focus solely on physical strength are "too vulgar" and those who focus solely on mental strength "too girly", that the ideal man sought to increase both. We know the Chinese had the same line of thought, as their language actually had a word (士, shi) that refered to a man that possessed both warrior and scholar qualities. Later on the word lost its original meaning, however, and just came to refer to a "scholar" (as a social class).
Of course, for every one similarity I can find there are probably about ten differences. What's important though is that a lot of the religious, social and philosophical foundations of IE and East Asian societies contained several similarities such as these, even though specific details might have differed and eventually diverged throughout history.