Did they ever trade or talk with each other at any point in history. If so what would they have traded?
Thanks!
They definitely knew of each other and referred to each other, although it is worth noting that the Chinese seem to have had significantly better understanding of Rome than the reverse (a link to many relevant texts). The Chinese had a more or less recognizable sense of who the Romans were and the basics of Roman society, while it is very difficult at times to see who, exactly, Roman authors are referring to (for example, "Seres" often seems to refer to a confusion between central Asians and Chinese). In terms of direct meetings, the only precisely recorded one is an "embassy" to the Chinese court by the ruler "An Dun of Da Qin" (that is, Marcus Aurelius Antoninus of Rome). This was almost certainly a group of merchants who either pretended to be or were confused for ambassadors.
Now this was probably not the only meeting between Chinese individuals and Roman individuals. There was likely contact between private individuals before this, but not exactly common.
In terms of goods, Roman goods found in China include beads, glass, and high quality silver plate. There has been no Chinese material found on a Roman site, but we have abundant reference to silk.
To follow up on /u/Tiako's comment, one thing to keep in mind about the "hearing" of their respective civilizations, is much of it was clouded in, if not poor communication and understanding, but in outright projected fantasy.
Keep in mind too, linguistically, the meanings of the words "Seres" and "DaQin" to the Romans and the Chinese respectively, mean worlds different things than "Chinese Empire" and "Roman Empire" to us now, even though we are choosing to overlay those as definitions.
For example, the Romans thought of China as more of the "land where silk comes from", i.e. "Seres." This is pretty straightforward, and while the records to describe their depictions of China as a vast populous country, it gives no inclinations to their thoughts of China as a universal empire equal to theirs.
Whereas for the Chinese, Rome as "DaQin" or "Great Qin" (Qin being the dynasty of the first Chinese emperor), Rome was thought as a sort of fantastical "nega-empire", a sort of mirror/opposite one to China. Considering the Chinese philosophy regarding the barbarian-ness of worlds as they radiated outward past the Central Kingdom, the conception to them of a vast civilized empire beyond all the barbarians, would be an indication as to its distance in perceived limits of conceivable imagination.
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