Alternative conceptions of the time-line

Summary form only given. It is often assumed that if time is continuous, then the standard mathematical account of the continuum, the real line, is the appropriate model of the local structure of the timeline. However, another popular account of the timeline which provides the basis for Allen´s famous 13 interval relations does not seem naturally compatible with the real line. This paper sharpens the differences between these two accounts and offers a unified account which retains some advantages of both, at the cost of making the continuum a slightly more complicated structure. The end result, which allows intervals to have negative and zero lengths, might be seen as a re-invention of arithmetic