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Re: Tropical vs. Vernal Equinox year

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  • John Hynes
    The differences were well within their capability to distinguish with sufficient accuracy, and had, in fact, been known for a long time. However, the so-called
    Message 1 of 13 , Jan 13, 2005
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      The differences were well within their capability to distinguish with
      sufficient accuracy, and had, in fact, been known for a long time.
      However, the so-called mean tropical year, as defined by ROG, was
      probably not something that they used, because it is not a measurement
      of anything, but an average of several measurements. But you are
      right that the Gregorian reform was closer to the tropical years of
      all the seasons than the Julian calendar.

      I know that everyone is not Christian. I am not Christian. But the
      whole Gregorian reform was done for Christian reasons. If we were
      going to fix it for non-Christian reasons, we would need to remove 2
      more days, and use a different formula for leap-years. The whole
      point of the century rule was to synchronize the reckoning of Easter
      with the 4th century Church council. As I said before, if we ignore
      religious motivations, then why should we care at all if it changes
      over the course of generations? Why not simply keep the Julian
      calendar and have spring start on March 8? The change is too subtle
      to be observed in a single lifetime. What's the benefit of "fixing"
      the seasons at all? When the Julian calendar was introduced, spring
      started around March 25 and winter around December 25, so shouldn't
      that be what we fix them to? Why should we care that something occurs
      on exactly the same date every year? The Muslims don't.

      It's not about who's right and who's wrong. I am not in favor
      changing the calendar one way or the other, merely stating the
      historical facts. In fact, I'd probably prefer using stardates, or
      Julian Dates, which are what astronomers actually use to date star
      observations.

      John Hynes


      --- In ISO8601@yahoogroups.com, John Steele <johnmsteele@y...> wrote:
      > You have succinctly expressed the opposing point of view. I doubt
      that either view is 100% right or wrong and ultimately become a matter
      of opinion. A few points:
      >
      > *I'm sure it was Pope Gregory's intent to stabilize the spring
      equinox. From the POV of Christianity, the date of Easter was screwed
      up and that is what they were trying to fix. The difference between
      it and the other equinox, solstices (or their average, the tropical
      year) is pretty subtle, and most likely beyond the capability of their
      time to distinguish with any accuracy. To first order, fix one, you
      have fixed them all. Certainly from Julian to Gregorian, all were
      tremendously improved.
      >
      > *Not everybody is Christian and emphasizing that it fixes Easter is
      probably not conducive to worldwide adoption of the Gregorian
      calendar. Just think of it as a subtle side benefit. I think it is
      consistent with worldwide adoption to focus on the benefits of fixing
      the tropical year, and allowing it to become a multicultural calendar.
      >
      > *To an agricultural society, the spring equinox is most important
      (and the origin of Jewish Passover, which undoubtedly affected the
      date of Christ's crucifixition). But back to planting, the spring
      equinox tends to fix the agricultural cycle. But the other seasons are
      important to somebody too. If you fix the start of one of the seasons,
      the others vary by a larger amount. If you fix the average, all the
      seasons move a little bit, plus and minus.
      >
      > *The change in length of season varies with a 26000 year cycle
      involving precesion in the tilt of earth's axis relative to its
      orbital plane. The Gregorian calendar best fits stabilization of the
      current date for spring equinox at the present point in the cycle.
      Halfway through the cycle, it will be the season that varies the most
      relative to the calendar. Rather than chasing this cycle with calendar
      changes, it is better to fix an average, the tropical year. Humans are
      now capable of conceiving a calendar scheme that, on average, is good
      over multiple precession cycles, and planning for some contingency
      adjustments as observations require them, rather than requiring major
      overhaul every couple of thousand years.
      >
      > This is not to say I'm right and you're wrong, but merely to assert
      some points that favor the tropical year argument.
      >
      > John Hynes <john@h...> wrote:
      >
      > I don't know how it favors the northern hemisphere, since the northern
      > vernal equinox is also the southern autumnal equinox.
      >
      > Pope Gregory's decree is called Inter Gravissimas, and it specifically
      > refers to the vernal equinox, even though almost everyone thinks it's
      > the so-called mean tropical year. The purpose was not to keep the
      > seasons in sync, but religion. The date of Easter is determined from
      > the vernal equinox and the moon, according to the Nicene Council of
      > 325 CE. The Gregorian reform removed 10 days so that the vernal
      > equinox returned to what it was in 325, instead of the 12 days that
      > the Julian calendar has gained since 1 CE. The average period between
      > vernal equinoxes is 365.2424, so the Gregorian calendar should be
      > accurate until 10,000 CE, although the margin of uncertainty makes
      > that moot. The seasons, themselves, are not stable but vary over time
      > even in relation to each other, although the vernal equinox is more
      > stable than the others.
      >
      > Other than religious reasons, I don't know why people thousands of
      > years from now would care if the seasons are a day or two off from the
      > time of their distant ancestors.
      >
      > A 4000-year rule was proposed for the French Republican Calendar, but
      > they stopped using it before it was adopted.
      >
      > In Outlines of Astronomy, John Herschel wrote:
      >
      > "The actual value of the tropical year, (art. 383.) reduced into a
      > decimal fraction, is 365•24224, so the error in the Gregorian rule on
      > 10000 of the present tropical years, is 2•6, or 2d 14h 24m; that is to
      > say, less than a day in 3000 years; which is more than sufficient for
      > all human purposes, those of the astronomer excepted, who is in no
      > danger of being led into error from this cause. Even this error is
      > avoided by extending the wording of the Gregorian rule one step
      > farther than its contrivers probably thought it worth while to go, and
      > declaring that years divisible by 4000 should consist of 365 days.
      > This would take off two integer days from the above calculated number,
      > and 2•5 from a larger average; making the sum of days in 100000
      > Gregorian years, 36524225, which differs only by a single day from
      > 100000 real tropical years, such as they exist at present."
      >
      >
      > John Hynes
      >
      > --- In ISO8601@yahoogroups.com, John Steele <johnmsteele@y...> wrote:
      > > There is no 4000 year rule. It was not part of Pope Gregory's
      > decree. It has been proposed but it has never been agreed on by any
      > body or standard organization. The length of the year keeps shortening
      > (very slowly) so no fixed schema can be right forever. Even if a
      > "year 4000" rule helped in the year 4000, it would be out of whack by
      > 8000.
      > >
      > > Actually, a 500 year rule is now closer to correct than a 400 year
      > rule. If we could agree prior to 2400 that 2500, not 2400, should be
      > the next centennial leap year, we could use the 500 year rule to
      > around 8000 then change to a 600 year rule. If we generalize the
      > Gregorian scheme, every 4 years, except centennials, except every
      > "n-hundred" years, it would work to 30,000 (more or less) when we
      > would have to drop more than centennial leap years. (Note than any
      > predictions of validity for thousands of years are just predictions
      > and that accumulated error has to be taken into account closer to any
      > proposed changes. At best, we can only get it right for awhile.)
      > >
      > > NOTE: There is a debate over whether the calendar should stabilize
      > just the spring equinox or the mean tropical year. Since not everyone
      > lives in the Northern Hemisphere, and some people care about seasons
      > other than spring, I think that the correct answer is "obviously" mean
      > tropical year, but be aware the debate exists.
      > >
      > > The Orthodox Church also has a proposal to observe 2 of 9 centennial
      > leap years. I'm unclear if that has been officially adopted. They
      > seem fragmented. Some branches still use the Julian calendar, some use
      > Gregorian, but use Julian for selected holidays.
      > > hjwoudenberg@a... wrote:
      > > The Gregorian Calendar leap year rules.
      > > If devisable by 4
      > > Not if divisible by 100
      > > If divisible by 400
      > > Not if divisible by 4000
      > >
      > > Everywhere I see the formulas for converting Gregorian to Julian day
      > ignoring the 4000 rule.
      > >
      > > Why?
      > >
      > > hjw
    • John Steele
      I think fixing the seasons is a very desirable attribute of a calendar and the lack of that is a severe deficiency of the Islamic calendar. Julius Caesar was
      Message 2 of 13 , Jan 13, 2005
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        I think fixing the seasons is a very desirable attribute of a calendar and the lack of that is a severe deficiency of the Islamic calendar. Julius Caesar was out to "fix" the seasons in 45 BC, and not for religious reasons; granted he was off by a little bit.
         
        Not sure about the March 25. There is such a legend and also a legend that after Caesar was assassinated, the priests screwed up and had leap years every three years instead of ever four until Augustus fixed it by cancelling three. Those legends don't quite reconcile with known equinox dates in early AD years. I don't think the actual usage of the Julian calendar is known to a Julian day prior to 4 or 8 AD, although several theories exist.
         
        The Gregorian calendar has fairly well fixed the spring equinox around March 21 since 1583. I'm prepared to let it be. It already varies on the order of a day or two because the calendar is an integer approximation.  The debate about whether to stabilize the average of all seasons or just spring can continue, but a calendar where dates drift continuously through the seasons seems chaotic and unacceptable. Random variation about a mean is not much of a problem,unchecked drift is.
         
        Frankly Christians can fix Easter by using the actual moment of equinox, the actual (following) full moon, and the following Sunday. These events can be calculated far enough ahead to eliminate the need for cumbersome tables used in the Gregorian calendar to calculate Easter. Nobody really cares about the date more than 100-200 years into the future as long as they know some one is continuing to advance the calculation.
         
        Since the Gregorian calendar has become a world calendar and international standard, it should serve the needs of that broader audience (if we can agree on what those needs are)

        John Hynes <john@...> wrote:


        The differences were well within their capability to distinguish with
        sufficient accuracy, and had, in fact, been known for a long time.
        However, the so-called mean tropical year, as defined by ROG, was
        probably not something that they used, because it is not a measurement
        of anything, but an average of several measurements.  But you are
        right that the Gregorian reform was closer to the tropical years of
        all the seasons than the Julian calendar.

        I know that everyone is not Christian.  I am not Christian.  But the
        whole Gregorian reform was done for Christian reasons.  If we were
        going to fix it for non-Christian reasons, we would need to remove 2
        more days, and use a different formula for leap-years.  The whole
        point of the century rule was to synchronize the reckoning of Easter
        with the 4th century Church council.  As I said before, if we ignore
        religious motivations, then why should we care at all if it changes
        over the course of generations?  Why not simply keep the Julian
        calendar and have spring start on March 8?  The change is too subtle
        to be observed in a single lifetime.  What's the benefit of "fixing"
        the seasons at all?  When the Julian calendar was introduced, spring
        started around March 25 and winter around December 25, so shouldn't
        that be what we fix them to?  Why should we care that something occurs
        on exactly the same date every year?  The Muslims don't.

        It's not about who's right and who's wrong.  I am not in favor
        changing the calendar one way or the other, merely stating the
        historical facts.  In fact, I'd probably prefer using stardates, or
        Julian Dates, which are what astronomers actually use to date star
        observations.

        John Hynes


        --- In ISO8601@yahoogroups.com, John Steele <johnmsteele@y...> wrote:
        > You have succinctly expressed the opposing point of view. I doubt
        that either view is 100% right or wrong and ultimately become a matter
        of opinion. A few points:

        > *I'm sure it was Pope Gregory's intent to stabilize the spring
        equinox. From the POV of Christianity, the date of Easter was screwed
        up and that is what they were trying to fix.  The difference between
        it and the other equinox, solstices (or their average, the tropical
        year) is pretty subtle, and most likely beyond the capability of their
        time to distinguish with any accuracy. To first order, fix one, you
        have fixed them all. Certainly from Julian to Gregorian, all were
        tremendously improved.

        > *Not everybody is Christian and emphasizing that it fixes Easter is
        probably not conducive to worldwide adoption of the Gregorian
        calendar. Just think of it as a subtle side benefit. I think it is
        consistent with worldwide adoption to focus on the benefits of fixing
        the tropical year, and allowing it to become a multicultural calendar.

        > *To an agricultural society, the spring equinox is most important
        (and the origin of Jewish Passover, which undoubtedly affected the
        date of Christ's crucifixition). But back to planting, the spring
        equinox tends to fix the agricultural cycle. But the other seasons are
        important to somebody too. If you fix the start of one of the seasons,
        the others vary by a larger amount. If you fix the average, all the
        seasons move a little bit, plus and minus.

        > *The change in length of season varies with a 26000 year cycle
        involving precesion in the tilt of earth's axis relative to its
        orbital plane.  The Gregorian calendar best fits stabilization of the
        current date for spring equinox at the present point in the cycle.
        Halfway through the cycle, it will be the season that varies the most
        relative to the calendar. Rather than chasing this cycle with calendar
        changes, it is better to fix an average, the tropical year. Humans are
        now capable of conceiving a calendar scheme that, on average, is good
        over multiple precession cycles, and planning for some contingency
        adjustments as observations require them, rather than requiring major
        overhaul every couple of thousand years.

        > This is not to say I'm right and you're wrong, but merely to assert
        some points that favor the tropical year argument.
        >
        > John Hynes <john@h...> wrote:
        >
        > I don't know how it favors the northern hemisphere, since the northern
        > vernal equinox is also the southern autumnal equinox.
        >
        > Pope Gregory's decree is called Inter Gravissimas, and it specifically
        > refers to the vernal equinox, even though almost everyone thinks it's
        > the so-called mean tropical year.  The purpose was not to keep the
        > seasons in sync, but religion.  The date of Easter is determined from
        > the vernal equinox and the moon, according to the Nicene Council of
        > 325 CE.  The Gregorian reform removed 10 days so that the vernal
        > equinox returned to what it was in 325, instead of the 12 days that
        > the Julian calendar has gained since 1 CE.  The average period between
        > vernal equinoxes is 365.2424, so the Gregorian calendar should be
        > accurate until 10,000 CE, although the margin of uncertainty makes
        > that moot.  The seasons, themselves, are not stable but vary over time
        > even in relation to each other, although the vernal equinox is more
        > stable than the others.
        >
        > Other than religious reasons, I don't know why people thousands of
        > years from now would care if the seasons are a day or two off from the
        > time of their distant ancestors.
        >
        > A 4000-year rule was proposed for the French Republican Calendar, but
        > they stopped using it before it was adopted.
        >
        > In Outlines of Astronomy, John Herschel wrote:
        >
        > "The actual value of the tropical year, (art. 383.) reduced into a
        > decimal fraction, is 365�24224, so the error in the Gregorian rule on
        > 10000 of the present tropical years, is 2�6, or 2d 14h 24m; that is to
        > say, less than a day in 3000 years; which is more than sufficient for
        > all human purposes, those of the astronomer excepted, who is in no
        > danger of being led into error from this cause. Even this error is
        > avoided by extending the wording of the Gregorian rule one step
        > farther than its contrivers probably thought it worth while to go, and
        > declaring that years divisible by 4000 should consist of 365 days.
        > This would take off two integer days from the above calculated number,
        > and 2�5 from a larger average; making the sum of days in 100000
        > Gregorian years, 36524225, which differs only by a single day from
        > 100000 real tropical years, such as they exist at present."
        >
        >
        > John Hynes
        >
        > --- In ISO8601@yahoogroups.com, John Steele <johnmsteele@y...> wrote:
        > > There is no 4000 year rule. It was not part of Pope Gregory's
        > decree.  It has been proposed but it has never been agreed on by any
        > body or standard organization. The length of the year keeps shortening
        > (very slowly) so no fixed schema can be right forever.  Even if a
        > "year 4000" rule helped in the year 4000, it would be out of whack by
        > 8000.
        > > 
        > > Actually, a 500 year rule is now closer to correct than a 400 year
        > rule.  If we could agree prior to 2400 that 2500, not 2400, should be
        > the next centennial leap year, we could use the 500 year rule to
        > around 8000 then change to a 600 year rule. If we generalize the
        > Gregorian scheme, every 4 years, except centennials, except every
        > "n-hundred" years, it would work to 30,000 (more or less) when we
        > would have to drop more than centennial leap years. (Note than any
        > predictions of validity for thousands of years are just predictions
        > and that accumulated error has to be taken into account closer to any
        > proposed changes. At best, we can only get it right for awhile.)
        > > 
        > > NOTE: There is a debate over whether the calendar should stabilize
        > just the spring equinox or the mean tropical year. Since not everyone
        > lives in the Northern Hemisphere, and some people care about seasons
        > other than spring, I think that the correct answer is "obviously" mean
        > tropical year, but be aware the debate exists.
        > > 
        > > The Orthodox Church also has a proposal to observe 2 of 9 centennial
        > leap years.  I'm unclear if that has been officially adopted. They
        > seem fragmented. Some branches still use the Julian calendar, some use
        > Gregorian, but use Julian for selected holidays.
        > > hjwoudenberg@a... wrote:
        > > The Gregorian Calendar leap year rules.
        > >     If devisable by 4
        > >     Not if divisible by 100
        > >     If divisible by 400
        > >     Not if divisible by 4000
        > > 
        > > Everywhere I see the formulas for converting Gregorian to Julian day
        > ignoring the 4000 rule.
        > > 
        > > Why?
        > > 
        > > hjw
        >
        >
        >
        >
        >
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      • John Hynes
        ... Actually, it was for religious reasons, partially, and partially for political reasons, too. He was the Pontifex Maximus, after all, the high priest, and
        Message 3 of 13 , Jan 13, 2005
        • 0 Attachment
          --- In ISO8601@yahoogroups.com, John Steele <johnmsteele@y...> wrote:
          > I think fixing the seasons is a very desirable attribute of a
          > calendar and the lack of that is a severe deficiency of the Islamic
          > calendar. Julius Caesar was out to "fix" the seasons in 45 BC, and
          > not for religious reasons; granted he was off by a little bit.

          Actually, it was for religious reasons, partially, and partially for
          political reasons, too. He was the Pontifex Maximus, after all, the
          high priest, and religious celebrations in Rome were also determined
          by the calendar.

          > Not sure about the March 25. There is such a legend and also a
          > legend that after Caesar was assassinated, the priests screwed up
          > and had leap years every three years instead of ever four until
          > Augustus fixed it by cancelling three. Those legends don't quite
          > reconcile with known equinox dates in early AD years. I don't
          > think the actual usage of the Julian calendar is known to a
          > Julian day prior to 4 or 8 AD, although several theories exist.

          The first day of spring was said to be March 25 in the time of Numa,
          and Caesar was supposedly restoring that date, although it might be
          that March 25 was the first FULL day of spring, i.e. the day after the
          actual equinox, which was counted as the last day of winter. Then
          again, it is uncertain exactly how many leap-days were observed before
          the year 8 CE, as you point out.

          However, I think that the Gregorian calendar is accurate enough,
          whether as measured by the vernal equinox or Newcomb's tropical year,
          that it won't affect anyone if it gains or loses a day in 4000 or 8000
          years. The Christians can decide what to do about Easter. The
          equinox already fluctuates between March 20 and March 22.

          John Hynes
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