It was invented by Star Trek's creator, Gene Roddenberry, as a way to establish the events in the series as taking place far into the future without tying the episodes down to a particular time (as we know it) and place. He created it as an abstract idea without any thought to actual implementation, choosing to leave the idea up to the imaginations of the viewers.
As a result, little thought was given to the numbers used in stardates for episodes, except that the numbers for the dates generally increased. But so little care was exercised with the dates that sometimes times overlapped within a single episode. When pressed for an explanation, Roddenberry said:
Since Roddenberry did not really think about a specific implementation of stardates, his explanation above notwithstanding, many fans have attempted to develop such a system that would be universally applicable. Some of these systems have been proven unreliable and no general consensus has been reached as to what the implementation of a "real" stardate should be.
Fans of the series who attempt to develop a stardate system go to great lengths to reverse engineer such a system that makes the dates used in the series logical. Many critics find this attempt farcical since the writers of the original series picked dates almost at random, not cohering to any type of standard with the exception that dates should generally increase. Critics feel that it would be far more useful to invent a real standard—one that can be used practically in everyday life without trying to back-legitimize fictional events.
In TNG, a slightly more systematic system of stardates was used. They were 5-digit numbers, initially starting with 4 (symbolically to represent the 24th century), and followed by the season number. Within these thousand-unit ranges, sub-ranges were allocated to writers of episodes to use. After the first season, these increased monotically between episodes. In Deep Space Nine and Voyager the same system was kept, incrementing to 48xxx in what would have been TNG season 8, and wrapping round to 50xxx and beyond in season 10. It is generally assumed that a season is a year.
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