In Disney's "Aladdin", when the Genie is released from the lamp he makes a couple of interesting comments. One references that he's been imprisoned in the lamp for 10,000 years, and the other is that Aladdin's clothes are "so 3rd century." The only way for the Genie to know what the 3rd century was like is if he had been there, meaning the movie takes place at least 10,000 years later. As further proof, Genie also does impressions of celebrities who wouldn't have existed yet in ancient Arabia.
This theory also explains why there are so many strange technologies -- such as a talking cave, flying carpet, hypnotic staff, and an intelligent parrot.