After I wrote about the problem of restrictive guild rules in Meereen some readers asked if I thought this could account for the generally slow pace of technological innovation across the multi-thousand year history of the world portrayed in A Song of Fire and Ice.
This is a complicated issue that I plan to continue thinking about, but as a first observation I would say that the technological level of Westeros is in some ways more advanced than it initially appears. One's first instinct is to describe it as featuring a "medieval" level of technology since you have knights in armor, castles, no guns or cannons, and no printing press. But in other respects Westeroi technology is much more advanced than the technology of medieval Europe. This is particularly true in the life sciences. Their "moon tea" appears to be a highly effective abortifacient or perhaps some kind of equivalent to our so-called "morning after pill." They also appear to understand a fair amount about the problem of infected wounds and how to treat them. This science is less advanced than post-WWII antibiotics but seems to be at-or-beyond 19th century medical science. There's also indication that thanks to the exigencies of extra-long winters they've figured out how to treat scurvy properly.
In other domains Westeroi progress is a bit less clear, but raven-based communication is pretty impressive and their seafaring capabilities may compare favorably with medieval ships (this isn't really described very clearly). Last but by no means least there's "magical" technology like wildfire that certainly seems cool.
All of which is to say that the "medieval" look and feel (as opposed to merely preindustrial) of the fictional universe stems pretty overwhelmingly from a lack of gunpowder. Without gunpowder castles, swords, and suits of armor are still the key modalities of warfare. But there's more to life than gunpowder, and in a lot of other ways it's a technologically sophisticated society.
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