The idea of traveling through time is one which is natural to our modern sensibilities. While there is some debate as to how possible such an exercise may be, most everyone at least acknowledges it as a popular concept in fictional literature.
However the idea of time travel as a plot possibility is one which is not found much in human culture throughout the ages. We have a few ancient stories that have a rough inclination towards traveling forward in time, but there are no recorded mentions of even a vague idea of backward time travel found in any written form until at least the 1700's.
One of the earliest mentions we have of time travel at all comes from an ancient Hindu text called the Mahabharatha. This story dates back to around 700 BCE - 300 CE and involves King Revaita traveling to heaven to meet Brahma. Upon returning home he finds that several hundred years have passed.
In 720 CE we see the tale of Urashima Taro described in the Nihongi, which describes the adventure of a fisherman who travels to an undersea palace for three days. When he returns home he finds that 300 years have actually passed, and his house has collapsed and his family has all passed and everything he owned in life is gone. This is quite similar to Washington Irving's story Rip Van Winkle.
A more modern version of the time travel story comes from Louis-Sebastien Mercien's book "The Year 2440, A Dream If Ever There Were One". This extremely popular book depicts the tale of a man who has a fight with a philosopher friend of his about the problems with Parisian society. He then falls asleep, and when he awakes he is in a Paris of the future. While the story was fictional the author actually intended the book to be a guideline for people to follow to create a utopian society.
The first story that even toys with the notion of backwards time travel is "Memoirs of the Twentieth Century" by Samuel Madden. This is comprised mostly of a series of letters sent by British Ambassadors regarding the state of the nation in 1997, and 1998. The overlying story is that the narrator of the book was given the letters by a guardian angel in 1733, although there is no explanation of how the angel acquired those letters.
Later time travel novels include A Christmas Carol, by Charles Dickens, and the Time Machine, by HG Wells. The latter book, The Time Machine, is really the novel that popularized time travel as a literary concept, and has been the guideline for all time travel novels that have come since.
previous post