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Vid, Baharad and the 6 days of creation
According to Rebbi Eliezer the world was created over the six days from the 25th of Ellul until the first of Tishrei , 5765 years ago (according to Rebbi Yehoshua this happened 6 months earlier) as discussed in the Talmud (Rosh Hashana 8, Tosefos, and Pirush to Rambam as below). The first man, Adam HaRishon, proclaimed the first new moon (the molad) in the 9th hour of the sixth day (the day of his creation) and the new moon first appeared 6 hours earlier in the second hour of the 6th day (this is called Vid, or the 14th hour of the 24 hour 6th day) of year 2 which started on that Friday, the first day of Tishrei, the day Adam was created. Since creation actually started 5 days earlier on the 25th of Ellul, the previous year, year 1, is extrapolated back to an imaginary Tishrei, and its new moon is called Baharad (second day, fifth hour, 204 chalakim).
Now, calculate forward from Baharad and Vid to the new moon for Tishrei of this year -- and you get Tuesday 1:15 and 17 chalakim -- precisely the time that appears in the luach! Our calendar is consistent with the 6 days of creation down to a chelek (3.5 seconds)!
Thanks to AB for the calculations below.
Ramba"m KHC 6:8 says: "And the first molad from which you should start is
the molad that was in the first year of Creation. It was ... at BaHaRad,
and from there is the beginning of the calculation."
The "Peirush" on the side of the Rambam there gives the description similar
to the Tosafot as above, and then goes on to explain at length
the three acceptable possibilities as to which year is the year known as
year number one, from which we start counting. Towards the end, it says
"... Each one of these three opinions has the truth, because they all make
the leap years at the same time [they just label the years differently] ...
The one who starts the calendar at BaHaRaD will have the leap years numbered
3, 6, 8, 11, 14, 17, 19, whereas the leap years according to the second
starting point (Vav-yud-dalet) are the years numbered 2, 5, 7, 10, 13, 16,
18, and according to the third starting point the leap years are 1, 4, 6, 9,
12, 15, 17. According to all versions, the leap years are at the same time
because year 3 from BaHaRad is the same year as year 2 from VY"D which is
year number 1 from the [third starting point]. Most of the calendar
scholars chose to start from BaHaRaD so as not to discard even one day of
the Creation days from being part of a counted year."
Now, for the calculations to the present year, showing that BaHaRaD is the
correct starting point:
All calculations are taken mod 7 days, because we are only concerned with
the position in the week.
We know the offset for a month (ignoring full weeks) is:
1 day 12 hours 793 chalakim (where 793 chalakim = 44 minutes + 1 chelek).
Offset for a 12-month year is 12 times the above, which is:
4 days 8 hours 876 chalakim (= 48 minutes 12 chalakim).
Offset for a 13-month year is 13 times the one-month offset, which gives:
5 days 21 hours 589 chalakim (= 32 minutes 13 chalakim).
Offset for a complete 19-year cycle is 12 times the offset for a 12-month
year + 7 times the offset for a 13-month year, which is:
2 days 16 hours 595 chalakim.
Now, if we start from the assumption that year 1 was BaHaRaD, i.e. the molad
of Tishrei at year 1 was:
Day 2, 5 hours 204 chalakim
Then we proceed as follows.
303 full 19-year cycles give a total offset of:
303 times (2 days 16 hours 595 chalakim) = 606 days 4848 hours 180285
chalakim = 606 days 5014 hours 1005 chalakim = 814 days 22 hours 1005
chalakim = (mod 7 days) 2 days 22 hours 1005 chalakim.
Add this to BaHaRad and we get a molad of:
Day 5, 4 hours 129 chalakim. This should be the molad for Tishrei after 303
cycles have been completed, i.e. 303*19 = 5757 full years after the
beginning of year 1, i.e. Tishrei of year 5758. Which is correct - if you
check a luach for 5758, the molad for Tishrei was at that time, Wednesday
night at 10:07 and 3 chalakim. (And so Rosh HaShana 5758 was on Thursday
according to the usual rules.)
Moving forward, to our year 5765, we can add the offsets for 5 12-month
years and 2 13-month years (total of 5 days 15 hours 158 chalakim) and get:
Day 3, 19 hours 287 chalakim. This was the molad for Tishrei 5765, which is
correct according to the luach - Tuesday 1:15 and 17 chalakim. (Rosh
HaShana was postponed to Thursday because of molad zaken on Tuesday.)