So just how accurate is the Mayan Haab calendar compared to the
Julian and the Gregorian? It is not very accurate. Here are
the results using the actual number of days per year from one
vernal equinox to the next as being 365.242374
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Mayan Haab:
===========
Method: 13 equal periods of 20 days each and 5 days at
the end that are not part of any period.
Calculation: 1 / (365 - 365.242374) = -4.125855
Accuracy: It falls a day behind about every four to five
years.
Regularity: Very regular unless you don't like the five extra
days which does not bother me. The alternative
is to lose five more days every year except for
Gregorian leap years when it loses six days.
That is FAR LESS PALATABLE to me. We are losing
too much as it is anyway! If you added six every
Haab year that was evenly divisible by 4 then
you would have the Julian calculations that errs
in the oppossite direction of too much but not
by very much.
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Julian:
=======
Method: if year evenly divisible by 4
then
it IS a leap year
else
it is NOT a leap year
endif
Calculation: 1 / (365.25 - 365.242374) = 131.13034
Accuracy: It gains only one day every 131 to 132 years
That is much improved over the Mayan Haab.
Regularity: Other than the extra day being part of the
second month it is highly regular. But religions
with their seventh day are driving that decision.
But it is so regular that light years are given
in Julian years, not Gregorian even though the
Julian years aren't as accurate.
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Gregorian:
==========
Method: if year evenly divisible by 4
then
if year evenly divisible by 100
then
if year evenly divisible by 400
then
it IS a leap year
else
it is NOT a leap year
endif
else
it IS a leap year
endif
else
it is NOT a leap year
endif
---
Note - the Y2K bug occurred because the
programmers did not use this code - basically
they forgot to make the 400 year divisibility
check and just marked all century years as
non-leap years because they didn't understand
how it works or thought that we won't have to
worry about it more often than every 400 years.
E.g., their code looked like this because they
thought it was cleaner and more like the simple
but Julian calculation even if it is wrong:
---
if year evenly divisible by 4
then
if year evenly divisible by 100
then
it is NOT a leap year
else
it IS a leap year
endif
else
it is NOT a leap year
endif
---
OR they had just two digits for years. Mostly
it was only the two digits for years. But if
they can't get this right, how much chance is
there in fouling up on DST? IT IS VERY HIGH!
Calculation: 1 / (365.2425 - 365.242374) = 7936.5079
Acccuracy: It gains only one day every 7936.508 years.
It is so much more accurate than the Mayan Haab
calendar there is no comparison. It is also
a dramatic improvement over even the next most
accurate calendar which is the Julian.
Regularity: Not very. They had to skip 10 days in October
1582 in most Catholic countries and 13 days in
Russia in the 20th century. It is not the
algorithm that poses the problem. It is this
drop of days that is the weak point. If we
adopted it going forwards and backwards from Nov
1582 and ignored the Julian dates it would be
just as regular as the other calendars. Would
that foul up the BC / AD divide point? No. The
Julian and Gregorian would be in sync if we used
the Nov 1582 jump date going back to year 1 AD
and the days for both Julian and Gregorian would
align perfectly in the year 1 AD. But we would
have to recalculate all dates. I think this
should be done since the 10 day drop in 1582 has
repercussions in the seventh day argument. But
so does Phileas Fogg traveling eastward around
the globe, gaining an entire day. If he had
gone westward he would have lost a day. So which
is the real seventh day? Maybe we should
reconsider that calendar proposed by the US
Congress in the 1950s:
http://www.securemecca.com/public/NoMoreDST/US_Congress_Calendar.txt
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GREGORIAN RED HERRING:
Now is the time to throw in the red Herring. The older GMT was
fairly rigid, and didn't have as accurate a clock to measure time
as the UTC standard does. Most of the time you can consider GMT
and UTC as being congruent but they really aren't the same thing
underneath the hood. The UTC provides leap seconds for finer
granularity to make sure the vernal equinox as measured by our
clocks is a close as possible the actual vernal equinox.
http://www.timeanddate.com/time/leapseconds.html
http://www.timeanddate.com/time/leap-seconds-background.html
Ergo, 7400 years from now maybe nothing will need to be done.
The leap seconds may be able to do away with the day that would
have been added. Note that I am NOT saying this is what they
are doing. You just need to know that all efforts are being
made to extend the Gregorian as far as possible into the future
with minimal days lost or gained. With leap seconds it is done
without anybody but somebody involved in maintaining a highly
accurate Cesium Atomic clock even being aware it is happening.
Actually, we have been ADDING leap seconds, not subtracting
them. It is more likely we would have needed to subtract a
day in 13,000 years or so instead. But by adding (all adds
so far) or subtracting a leap second every few years and
split seconds in between under UTC we will never need a
correction of a day every few thousand years since it will never
happen.
What a contrast to Daylight Saving Time! EVERYBDDY is aware
when we have our leap hour in either a positive or negative
direction. We get it twice a year whether we want it or not!
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