# What calendar is Mathematica using for dates in the distant past?

It appears that Mathematica treats all dates as proleptic Gregorian dates by default, a hypothesis that can be easily tested by using AbsoluteTime to compute the Julian Day:

jd[t_] := AbsoluteTime[t]/86400 + 2.4150205*^6


but, while this works for recent dates and for some older ones, it yields results that differ from the correct result for some older dates by exactly a day

jd[{2012, 11, 24, 12}] - 2456256
0
jd[{1100, 11, 24, 12, 0, 0}] - 2123154
0
jd[{-3000, 11, 24, 12, 0, 0}] - 625660
1


notably for the reference date, 12:00 Universal Time on January 1, 4713 BCE in the proleptic Julian calendar (-4713-11-24 in the proleptic Gregorian calendar):

jd[{-4713, 11, 24, 12, 0, 0}]
1


What calendar is Mathematica using for these older dates, if not the proleptic Gregorian calendar?

Here, perhaps is another clue:

DateList[{-4713, 11, 24, 12, 0, 0}]
{-4713, 11, 25, 12, 0, 0}
DateList[{-3000, 11, 24, 12, 0, 0}]
{-3000, 11, 25, 12, 0, 0}


I'm no calendar expert, but this "canonicalization" doesn't map to any calendar I'm familiar with. Is this a bug?

Update: Version 9, behaves differently:

jd[{2012, 11, 24, 12}] - 2456256
0.
jd[{1100, 11, 24, 12, 0, 0}] - 2123154
0.
jd[{-3000, 11, 24, 12, 0, 0}] - 625660
365.

jd[{-4713, 11, 24, 12, 0, 0}]
366


and

DateList[{-4713, 11, 24, 12, 0, 0}]
{-4713, 11, 24, 12, 0, 0.}
DateList[{-3000, 11, 24, 12, 0, 0}]
{-3000, 11, 24, 12, 0, 0.}

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I'm guessing it's just a bug. Similarly, AbsoluteTime[{2009,01,01,0,0,0}]-AbsoluteTime[{2008,12,31,23,59,59}] gives 1 instead of the correct 2, assuming the standard UTC+Gregorian. –  Mechanical snail Nov 25 '12 at 8:24
@Mechanicalsnail: Yes, that's an additional issue, with leap seconds. –  raxacoricofallapatorius Nov 25 '12 at 15:01
@Mechanicalsnail: AbsoluteTime[{2009, 01, 01, 0, 0, 0}] - AbsoluteTime[{2008, 12, 31, 23, 59, 59}] still gives 1, in version 9.0, rather than 2. –  raxacoricofallapatorius Nov 29 '12 at 18:28
Wolfram support has confirmed that change of date by DateList was a bug in version 8. It remains to be seen why AbsoluteTime added a day in 8 and a year in 9. –  raxacoricofallapatorius Dec 8 '12 at 18:01
Still there in version 10.0.0.0 –  rhermans Aug 1 '14 at 10:05

In version 10, I think that much of the behavior is simply a difference between how the year 0 is handled by astronomers (and therefore the page you were getting Julian Dates from) and everybody else.

For example, take this calculation:

jd[{-3000, 11, 24, 12, 0, 0}] - 625660


I believe that you have actually pulled the wrong number from the website due to a year 0 issue. Consider this:

(AbsoluteTime[{1, 1, 1, 12}] - AbsoluteTime[{-1, 1, 1, 12}])/86400


366

Note that Mathematica will return a result consistent with the Gregorian/Julian calendars where there is no year 0. But, your link reports that the Julian Day of 1,1,1,12 is:

1721426

and the Julian day of -1,1,1,12 is:

1720695

a difference of 2 years. This is consistent with how an astronomy specific app should work. If you account for this difference in years, I believe that the results will be consistent (in Mathematica 10, past results were just incorrect, as noted in comments).

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