Because Game of Thrones is set in a medieval timeline, there is no form of digital communication that allows information to be exchanged. This means the show resorts to classical methods used at that time. These methods are:
Spying is a highly efficient communication method in Game of Thrones. Each spymaster has “little birds”, which is a term for children who provide the spy with valuable information. These children are usually enticed into serving their masters, such as by luring them with candies (as shown by Qyburn offering candies in exchange for gossip).
Intelligence gathered from spying is usually restricted to a few people with lots of connections. Varys is shown to be the most popular spymaster, being the King’s official spymaster. He seems to know updates on every important person and situation in Westeros as well as Essos. There are, however, others as well, such as Cersei and Littlefinger.
The method of spying is bound to be factually inaccurate, as each time the information is passed down to another person, it is subject to being changed slightly. This is why information from spies is normally referred to as a rumor, possibly being incorrect.
It is, however, a fast method, as shown by instances where spymasters already know what happened across the world very recently.
Thinking differently since 2000
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