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Safeholdian Leap Years and Calendar Creep

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Safeholdian Leap Years and Calendar Creep
Post by wingfield   » Wed Mar 27, 2019 5:41 am

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Edited to acknowledge the howler (now with blue text) in my initial post.

[Corrected information posted further down in the thread]

In a thread entitled “Anybody Know Anything About Solar or Geothermal Energy?”, reply No 90, on about January 2, 2015, fallsfromtrees suggested that the Safeholdian calendar would be suffering from some noticeable creep, gaining about one day every 75 years.

I have looked at the figures and the creep is more dramatic than that. I make it that a day is gained every 24 years (or every eight leap years). Assuming that the calendar was “correct” in YOG 1, it would be over 38 days ahead by YOG 916.

The simple expedient to resolve this would be to omit every eighth leap year, which, miraculously, leaves the calendar exact to the day with no gain whatsoever.

Our esteemed author must have calculated this very carefully. However, there is no mention of this anywhere in the text or on the forum. A safe assumption would have been that the “Archangels” would have provided for this correction right from the beginning.

For those who would like to check, here are the numbers:

• 26 hours and 31 minutes (in a Safehold day) amount to 1591 minutes.
• 1591 minutes in a 30 day month amount to 47730 minutes, or 795.5 hours (not 795, as appears in the Note on Safeholdian Timekeeping.
• There are 479400.12 minutes in a Safeholdian year of 301.32 local days and 478891 minutes in a non-leap year day of 301 local days.
• The difference in the number of minutes between a full orbit of 301.32 days and 301 days is 509.12. A Safeholdian day of 1591 minutes is exactly 3.125 times this difference. Adding a day every third Safeholdian year puts the calendar 0.125 days ahead of the orbital period every leap year, or one eighth of a day. In eight leap years, 25 days would have been added instead of the 24 days actually required.

I also note that equinoxes are set on specific dates in the Note on Safeholdian Timekeeping. I don’t know whether they were on different dates originally, gradually drifting with calendar creep. Even if there were the correction every 24 years to bring the calendar exactly into line, I suggest that the dates were probably always roughly as stated by the author. Of course, there would be a bit of a wobble over each three year cycle of two normal and one leap year, just as there is on Earth with the normal four year cycle.
Last edited by wingfield on Fri Mar 29, 2019 3:55 am, edited 1 time in total.
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Re: Safeholdian Leap Years and Calendar Creep
Post by isaac_newton   » Wed Mar 27, 2019 1:05 pm

isaac_newton
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wingfield wrote:In a thread entitled “Anybody Know Anything About Solar or Geothermal Energy?”, reply No 90, on about January 2, 2015, fallsfromtrees suggested that the Safeholdian calendar would be suffering from some noticeable creep, gaining about one day every 75 years.

I have looked at the figures and the creep is more dramatic than that. I make it that a day is gained every 24 years (or every eight leap years). Assuming that the calendar was “correct” in YOG 1, it would be over 38 days ahead by YOG 916.

The simple expedient to resolve this would be to omit every eighth leap year, which, miraculously, leaves the calendar exact to the day with no gain whatsoever. Our esteemed author must have calculated this very carefully. However, there is no mention of this anywhere in the text or on the forum. A safe assumption would have been that the “Archangels” would have provided for this correction right from the beginning.

For those who would like to check, here are the numbers:

• 26 hours and 31 minutes (in a Safehold day) amount to 1591 minutes.
• 1591 minutes in a 30 day month amount to 47730 minutes, or 795.5 hours (not 795, as appears in the Note on Safeholdian Timekeeping.
• There are 479400.12 minutes in a Safeholdian year of 301.32 local days and 478891 minutes in a non-leap year day of 301 local days.
• The difference in the number of minutes between a full orbit of 301.32 days and 301 days is 509.12. A Safeholdian day of 1591 minutes is exactly 3.125 times this difference. Adding a day every third Safeholdian year puts the calendar 0.125 days ahead of the orbital period every leap year, or one eighth of a day. In eight leap years, 25 days would have been added instead of the 24 days actually required.

I also note that equinoxes are set on specific dates in the Note on Safeholdian Timekeeping. I don’t know whether they were on different dates originally, gradually drifting with calendar creep. Even if there were the correction every 24 years to bring the calendar exactly into line, I suggest that the dates were probably always roughly as stated by the author. Of course, there would be a bit of a wobble over each three year cycle of two normal and one leap year, just as there is on Earth with the normal four year cycle.



Maybe they called it "Langhorn's Day" similiar to Langhorn's watch? or has that been takne for something else?
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Re: Safeholdian Leap Years and Calendar Creep
Post by wingfield   » Wed Mar 27, 2019 9:24 pm

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isaac_newton wrote:Maybe they called it "Langhorn's Day" similiar to Langhorn's watch? or has that been takne for something else?

As it would involve dropping a day every 24 years, there would be no need to name it anything!
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Re: Safeholdian Leap Years and Calendar Creep
Post by wingfield   » Fri Mar 29, 2019 3:48 am

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Posts: 107
Joined: Sat Apr 25, 2015 11:15 pm
Location: Melbourne, Australia

wingfield wrote:
isaac_newton wrote:Maybe they called it "Langhorn's Day" similiar to Langhorn's watch? or has that been takne for something else?

As it would involve dropping a day every 24 years, there would be no need to name it anything!

Actually, I did the math again and note that in a 25 year cycle with no messing with the leap years, the 25th year brings us exactly to the 7533 days required. Doing that over three sets of 25 years, or 75 years, gives us 22599 but the additional (25th) leap year in this time brings the total to 22600 days. The cycle begins again and in another 75 years the calendar is two days ahead, and so on.

The cycle is (8 x 3) + 1, which leaves a hanging day once there are 25 sets of leap years.

So my neat little fix argued above is useless! :oops:

My apologies to fallsfromtrees, who was correct in the basic calculation.

After 900 years, the calendar would be 12 days ahead. This doesn't seem to fit with any movement of solstice and equinox dates.

This leaves the problem of how to adjust to drop that extra day every 75 years. On Earth, having a leap year every FOUR years makes adjustments of three days every four hundred years (as per the Gregorian Calendar) relatively easy. On Safehold, tinkering with a leap year that falls every three years is not easy in a hundred year period.

However, the 75th year IS actually a leap year and is the ideal candidate in which to omit the extra day, thus bringing the calendar back into line.

With EVERYTHING under Church guidance, there would be no problem mandating such and adjustment and teaching the mechanics to all priests as part of their seminary training. There would have been very little difficulty in prescribing that the three-quarter, half and one-quarter century years (as applicable), namely YOG 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825 and 900 as those in which the leap year was to be skipped.

No doubt the culmination of the jihad in 899 would have allowed (or not prevented) a long scheduled calendar adjustment to proceed.
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Re: Safeholdian Leap Years and Calendar Creep
Post by isaac_newton   » Mon Apr 01, 2019 8:26 am

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isaac_newton wrote:Maybe they called it "Langhorn's Day" similiar to Langhorn's watch? or has that been takne for something else?

wingfield wrote:
wingfield wrote:As it would involve dropping a day every 24 years, there would be no need to name it anything!

Actually, I did the math again and note that in a 25 year cycle with no messing with the leap years, the 25th year brings us exactly to the 7533 days required. Doing that over three sets of 25 years, or 75 years, gives us 22599 but the additional (25th) leap year in this time brings the total to 22600 days. The cycle begins again and in another 75 years the calendar is two days ahead, and so on.

The cycle is (8 x 3) + 1, which leaves a hanging day once there are 25 sets of leap years.

So my neat little fix argued above is useless! :oops:

My apologies to fallsfromtrees, who was correct in the basic calculation.

After 900 years, the calendar would be 12 days ahead. This doesn't seem to fit with any movement of solstice and equinox dates.

This leaves the problem of how to adjust to drop that extra day every 75 years. On Earth, having a leap year every FOUR years makes adjustments of three days every four hundred years (as per the Gregorian Calendar) relatively easy. On Safehold, tinkering with a leap year that falls every three years is not easy in a hundred year period.

However, the 75th year IS actually a leap year and is the ideal candidate in which to omit the extra day, thus bringing the calendar back into line.

With EVERYTHING under Church guidance, there would be no problem mandating such and adjustment and teaching the mechanics to all priests as part of their seminary training. There would have been very little difficulty in prescribing that the three-quarter, half and one-quarter century years (as applicable), namely YOG 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825 and 900 as those in which the leap year was to be skipped.

No doubt the culmination of the jihad in 899 would have allowed (or not prevented) a long scheduled calendar adjustment to proceed.


I'll glad bow to your calcs. :-)

I guess what confused mewas the phrase 'leap year' - since to my mind that always means adding something in.

perhaps we should call it a 'drop year' or a 'fall year' :-)
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Re: Safeholdian Leap Years and Calendar Creep
Post by Louis R   » Mon Apr 01, 2019 7:09 pm

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Why. There isn't anything being dropped, it's just not being added - something familiar to anybody using the Gregorian calendar. Which does the same thing, but only needs to do it every 400 years rather than every 75. And we don't have any special name for the leap-year that wasn't.


isaac_newton wrote:
wingfield wrote:Actually, I did the math again and note that in a 25 year cycle with no messing with the leap years, the 25th year brings us exactly to the 7533 days required. Doing that over three sets of 25 years, or 75 years, gives us 22599 but the additional (25th) leap year in this time brings the total to 22600 days. The cycle begins again and in another 75 years the calendar is two days ahead, and so on.

The cycle is (8 x 3) + 1, which leaves a hanging day once there are 25 sets of leap years.

So my neat little fix argued above is useless! :oops:

My apologies to fallsfromtrees, who was correct in the basic calculation.

After 900 years, the calendar would be 12 days ahead. This doesn't seem to fit with any movement of solstice and equinox dates.

This leaves the problem of how to adjust to drop that extra day every 75 years. On Earth, having a leap year every FOUR years makes adjustments of three days every four hundred years (as per the Gregorian Calendar) relatively easy. On Safehold, tinkering with a leap year that falls every three years is not easy in a hundred year period.

However, the 75th year IS actually a leap year and is the ideal candidate in which to omit the extra day, thus bringing the calendar back into line.

With EVERYTHING under Church guidance, there would be no problem mandating such and adjustment and teaching the mechanics to all priests as part of their seminary training. There would have been very little difficulty in prescribing that the three-quarter, half and one-quarter century years (as applicable), namely YOG 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825 and 900 as those in which the leap year was to be skipped.

No doubt the culmination of the jihad in 899 would have allowed (or not prevented) a long scheduled calendar adjustment to proceed.


I'll glad bow to your calcs. :-)

I guess what confused mewas the phrase 'leap year' - since to my mind that always means adding something in.

perhaps we should call it a 'drop year' or a 'fall year' :-)
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