The origin of the Julian Period: An application of congruences and the Chinese Remainder Theorem

Abstract

In 1583, Joseph Justus Scaliger introduced the Julian Period of 7980 years, which is the basis of the Julian Day system of counting days sequentially from 1 January 4713 BC. It is not commonly known how this date was chosen as the origin of the system. This paper formulates the problem as an application of the theory of congruences and the Chinese Remainder Theorem. Scaliger’s interesting original solution to the problem is also reviewed.

Calculation of Elapsed Decimal Time for Tracing Studies

“…Counting time since tracer release is most easily achieved when injection and sampling dates and times are converted to decimal time where the injection date and time is taken as time zero. Decimal times are preferred because, although the Gregorian calendar serves quite well for recording events (e.g., injection date and time and sampling dates and times), it is not readily adaptable to computer programming (Ohms 1986), which is required if large or numerous data files are to be processed rapidly and efficiently (see Vallado [2001, 179–205] and Reese et al [1981, 1983, 1991] for a more thorough discussion of time systems and conversions).…”

Mathematical Methods in the Study of Historical Chronology

“…Scaliger also intuitively applied congruences and the Chinese Remainder Theorem to fix the Julian epoch to noon on Monday, January 1, 4713 BC, which thus became a convenient reference point for all his computations [13]. A method he then devised, based on the twelfth-century work of Roger of Hereford and used extensively by Scaliger's follower Dionysius Petavius, was that of combined cycles.…”