Joining list. Calendar reforms.

[MIKE OSSIPOFF]

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Dear Yiping and Calendar People,
 
Before I went offline for a few days, I acknowledged that, in your alternative universe, in which people have a differfent perception and definition of summer, Subjective Seasonal would be, accordingly, different from what it is in our own universe. It isn't clear to me why you think that is a problem for Subjective Seasonal, or, in some way, a contadiction or fault.
 
But there is something else that I'd like to mention to day, in reply to your displaced-year criticism:
 
I've been generous in going along with your assumption that people would always perceive and define summer as beginning at the beginning of a month. And your assumption that, therefore, if the Gregorian year and its months were displaced about half a month, people would
resultingly still say that summer arrives with June (or maybe May?).
 
You need to understand that that is only an assumption. To treat an assumption as fact is unscientific. Of course there is no way to test the correctness of your assumption, and therefore it must remain an assumption, a guess.
 
For all you know, in your alternative universe, Leigh Hunt would have (instead) written "Full summer begins sometime in May".
 
Mike Ossipoff
 
 

---

Date: Thu, 13 Aug 2009 13:29:40 +0000
From: yipingzeng@...
Subject: Re: Yiping's displaced Gregorian New Year's Day
To: CALNDR-L@...

Dear Mike and calendar people,
Today I only reply you about one problem.
I wrote:
From moving new year's day foreward to Jan 14th,I deduce to that your winter's length is 90,not 117. it is right or wrong?
You reply:
It is wrong?
I reply you again:
Why?
According your step I show you as follow:
new year's day as Jan 1st          new year's day as Jan 14th
North's start     Jun 1st          North's start     Jun 14th
north solstice    Jun 21st         north solstice    Jun 21st
distance          21-1=20          distance          21-14=7
timelag           38               timelag           38
half of North    20+38=58          half of North    7+38=45
length of season  58*2=116         length of season  45*2=90
Where wrong?

Yiping Zeng 13/Aug/2009

> Date: Wed, 12 Aug 2009 22:28:31 +0000
> From: nkklrp@...
> Subject: Yiping's displaced Gregorian New Year's Day
> To: CALNDR-L@...
>
>
> Dear Yiping and Calendar People,
>
> You wrote:
>
> > I say that if the new year's day move forward 13 days .......only want to show Mike's winter length 117 days is a random number,which relate to random new year's day of Gregorian calendar.Moving 13 days is not neccessary.Moving 1 day or 2 days or....also can show 117 is a random number.
>
> I reply:
>
> Ok, now I believe that I know what your point is. I wasn't trying to evade answering you before--I just didn't understand your point. Now I do. So I'll reply now:
>
> Here's what you're saying:
>
> Consider an alternative universe differing from ours in only one respect: The Gregorian calendar's New Year's Day, January 1, occurs on a day that has a different name (such as January 14th) in our own Gregorian Calendar.
>
> You point out that if the displacement from our Gregorian calendar is part of a month, then the solar ecliptic longitude corresponding to our June 1 won't occur at the beginning of a month.
>
> You point out that, when defining the beginning of summer according to a month, people tend to use a whole month, saying, for instance that "June is full summer". In other words, the public perception will be that summer starts when some particular month starts.
>
> Therefore, with this alternate universe's displaced Gregorian Calendar, people are going to have a different notion of when summer starts.
>
> And, if I based my Subjective Seasonal Calendar proposal on that public perception, then of course my calendar would be different from how it is in our own universe. In particular, the length of North would be different.
>
> My answer: So what?
>
> In your alternate universe, people have a different definition of summer. A Subjective Seasonal Calendar designed for that universe would be based on that definition of summer. Yes, it would be different from how it is in our universe, with our Gregorian Calendar. So what?
>
> Mike Ossipoff
>
>
> _________________________________________________________________
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[MIKE OSSIPOFF]

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Dear Yiping and Calendar People,
 
You wrote:

Your today's reply  said that if we live in a universe which new year is on our Jan 14th,our North season of Subjectical Calendar would be 90 days.
 
I reply:
 
No, I didn't say that. But it's probably true, at least roughly.
 
You continued:
 
But we realy live
in our universe which new year is Jan 1st,
 
I reply:
 
Yes, I think most here would agree with that statement.
 
You continued:
 
so our North season of Subjective Calendar must be 116 days(then change to 117 or 118 or 119 for fixed or non-fixed goals).
 
I reply:
 
I get 117 or 118 days for nonfixed, depending on whether method #1 or method #2 is used to determine the length of North. For the fixed version, it's 119 days, because that contains a whole number of weeks.
 
But please, we needn't quibble about the exact number of days (but or course we could if you want to).
 
You continued:

If your meaning is this,I would say that you are wrong.
 
I reply:
 
I have no idea what you're saying. If my meaning is what?
Do you mean, if my meaning is that North is 116 days long? But I never said that, and it very likely is wrong. But you said it, I didn't.
 
You continued:
 
We can contininue argue if you want.
 
I reply:
 
No, that's okay, we don't have to continue to argue. And you don't have to say what statement of mine you think is wrong. (if you even know what statement of mine you think is wrong).
 
You continued:

Now I reply your last posts:
In chinese languege word "scientific" means a thing has nature which has definite definition in special domain of science.In common speaking it is saying that something
has sufficient reason for being. A random thing can't be a sufficient reason for other thing or matter.
 
I reply:
 
Randomness has a significant legitimate role in science.
 
And, anyway, the fact that Subjective Seasonal's North would have a different length in a different universe where people had a different perception and definition of summer doesn't mean that Subjective Seasonal is "random".
 
You continued:

If you don't like this word,I can avoid it and restead it with another word such as "having sufficient reason."

I reply:
 
I understand and accept that public perception isn't sufficient reason for Yiping.
 
You continue:
 
You wrote:
Summer is what we perceive or define it to be.Simple as that.Science hasnothingto do with that.
I reply:
You had said that subjective seasons are thermal seasons. wasn't it? Can or can't give a quantitative definition (temperature range) for four seasons?
 
I reply:
 
It would be ridiculous to define the seasons in terms of fixed temperature limits, applicable worldwide.
 
You continued:
You coninued:

You wrote that for getting the North length the first step is "given that starting date for North and given the typical midrange seasonal timelag.
I reply:
The ending date for North is the result of next step. I want ask:if given ending date for first step
 
#1 and #2 are not steps. They are two separate and distinct ways of defining the end of North.
 
You continued:
 
,what result would be gotten and cann't you give ending date
for forst step?
 
I have no idea what that means. Methods #1 and #2 both specify ways of defining the end of North.
 
You continued:

Will answer your other comments later.
 
Mike Ossipoff
 

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[MIKE OSSIPOFF]

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I understand that, if there is one particular point on the ecliptic that is of interest, and if one wants to keep the solar ecliptic longitude on a certain date in a proposed calendar near to that particular value, then, instead of the mean tropical year, a particular specific tropical year length, for that particular point on the ecliptic, would be more accurate.
 
But what if, though the ecliptic positioning of the calendar is based on that point on the ecliptic (As my calendars seek to keep North-I/1 as close as possible to some particular solar ecliptic longitude), maybe one wants to minimize the overall annual ecliptic displacement of the calendar at its various dates throughout the year? Then, wouldn't the mean tropical year be justified as the relevant year-length?
 
I believe that Irv said that the difference in the length of the tropical year, with respect to various solar ecliptic longitudes, varies by about a minute and a half, over the ecliptic. But the overall average Gregorian year is within about 26 seconds of 365.2422 days.
So then, wasn't the Gregorian leapyear system designed to keep pace with the mean tropical year, for the reason that I mentioned in the 2nd paragraph of this message?
 
Judging by the fact that the mean tropical year's length decreased by about a millionth of a day during the past half-century, I'd expect that its length at the time of the Gregorian reform might have been close to that rounded figure above, 365.2422 days.
 
Of course more detailed or accurate information about the mean tropical year length's rate of decrease, and the rate of change of that decrease-rate, would be welcome, as would information about what causes those rates.
 
I understand that the lengthing of the day due to lunar and solar tides is maybe the main reason for the decreasing of the number of days per mean tropical year. Are there other influences on that decrease rate? If the rate is changing, how is it changing, and what causes its changing?
 
Mike Ossipoff
 
 
 

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[Irv Bromberg]

On 2009 Aug 24, at 16:50 , MIKE OSSIPOFF wrote:

But what if, though the ecliptic positioning of the calendar is based on that point on the ecliptic (As my calendars seek to keep North-I/1 as close as possible to some particular solar ecliptic longitude), maybe one wants to minimize the overall annual ecliptic displacement of the calendar at its various dates throughout the year? Then, wouldn't the mean tropical year be justified as the relevant year-length?

Irv replies:

How would you verify the calendar drift if there isn't a specific event relative to which to evaluate its astronomical drift?

Also, the choice of epoch affects the calendar performance in a manner that is cumbersome to evaluate (requires a lot of least squares regression analysis).

In addition, the units of time are different:  calendars need mean solar days, whereas the so-called mean tropical year is in terms of atomic days.  Although there seems to be little difference today, that is just because we happen to be quite close to the epoch when the length of the atomic day was defined, but as time moves on the difference will grow exponentially.

I developed an average year length in terms of mean solar days, which I called the Mean Orbital Year (MOY), having Delta T implicitly embedded in it (correction for tidal slowing of the Earth rotation rate).  I published the calendar arithmetic for finding the New Year Day using the MOY leap rule, but numerous participants in this LISTSERV objected to it because of problems verifying drift, and because the embedded Delta T is unlikely to be accurate enough (unknown future).

Therefore I separated the Delta T and developed the Rotation Adjusted Year (RAY), which employs a fixed year length of 365+31/128 atomic days, and then the user's preference of Delta T correction is subtracted.  This math is "future-proof" because the Delta T function can be corrected as necessary.  I published the calendar arithmetic for finding the New Year Day using the RAY leap rule, but again numerous participants in this LISTSERV objected to it because of the drift verification problem and because allowing the Delta T function to vary would make calendar dates unpredictable.  Also, different users whose Delta T functions don't match exactly could obtain mismatching dates.

My freeware calendar calculator Kalendis continues to offer both MOY and RAY as experimental leap rule alternatives that can be applied to the Symmetry454 or Symmetry010 calendars or their quarter-structure variants, but I have withdrawn the documentation of their arithmetic, so as not to distract from the simplicity of the preferred fixed leap rule with symmetrically distributed smoothly spread leap year intervals.

I believe that Irv said that the difference in the length of the tropical year, with respect to various solar ecliptic longitudes, varies by about a minute and a half, over the ecliptic. But the overall average Gregorian year is within about 26 seconds of 365.2422 days.
So then, wasn't the Gregorian leapyear system designed to keep pace with the mean tropical year, for the reason that I mentioned in the 2nd paragraph of this message?

Irv replies:  No, regardless of how large or small the difference seems, the explicitly stated objective of the Gregorian calendar reform was to keep the vernal equinox on March 21st.  That means that the relevant astronomical mean year is the mean vernal equinoctial year, or to be hemisphere neutral, the mean northward equinoctial year, which in terms of mean solar days is currently within a fraction of a second of 365 days 5 hours 49 minutes.

Judging by the fact that the mean tropical year's length decreased by about a millionth of a day during the past half-century, I'd expect that its length at the time of the Gregorian reform might have been close to that rounded figure above, 365.2422 days.
  
Of course more detailed or accurate information about the mean tropical year length's rate of decrease, and the rate of change of that decrease-rate, would be welcome, as would information about what causes those rates.
 
I understand that the lengthing of the day due to lunar and solar tides is maybe the main reason for the decreasing of the number of days per mean tropical year. Are there other influences on that decrease rate? If the rate is changing, how is it changing, and what causes its changing?

Irv replies:  You will find answers to the above 3 points / questions in my analysis of the mean tropical year, which actually varies quasi-sinusoidally in relationship to the Earth axial tilt, on my web page about the Lengths of the Seasons at <http://www.sym454.org/seasons/>.

Also note that from the charts posted there, in the distant future when the Earth orbital eccentricity will be very small (for a number of millennia), all of the equinoctial and solstitial year lengths will be getting shorter in parallel with the tidal slowing of the Earth rotation rate.  In that far distant future era a leap rule like MOY or RAY might be the best option.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

<http://www.sym454.org/kalendis/>

[MIKE OSSIPOFF]

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Thanks for the answers.
 
How would I judge the calendar's drift? For any particular date of the year that one is looking at, one would be interested in how much, at that date, the solar ecliptic longitude varies. A person might be interested in how much it varies cyclically, during the leapyear cycle, or how much it has drifted unidirectionally during a particular period.
 
Of course, with all my current proposals, NorthI/1 is the date of principle interest for me. But I was just wondering if basing the leapyear rule on the mean tropical year would be a compromise that would be equally fair to all parts of the year, trying to keep down the variation of solar ecliptic longitude for all dates of the year. Of course the mean tropical year's length is easier to look up, and can be found in all sorts of sources, so laziness comes into it a little too.
 
About the units, I know this is naive, but surely  the length of the mean tropical year, expressed in atomic days, could be converted into mean solar days. I understand that, because the length of the solar day is gradually increasing, the mean tropical year length expressed in terms of those days decreases correspondingly.
 
What you've mentioned is something that I'd never heard about: I'd always assumed that 365.242190 days referrred to the solar days whose length is graduallly increasing due to lunar and solar tides. I don't want to seem too lazy to look this up (and of course I'll look for it at the 454symmetry website that you posted), but what is the definition of an atomic day? Obviously I should read more about year and day definitions, and I'll start at the website that you posted. But, aside from that, sometimes the information is difficult or impossible to find, leading me to ask questions on the list. Anyway, this is an immediate reply, before I read the websites that you and Karl have posted; of course the less I say before I read more, the better.
 
I always assumed that a calendar's leapyear rule would just be based on a tropical-year length correct for the time when the calendar comes into use, and then, over the millenia, it will lose accuracy as the day-length changes and maybe as the orbit changes. When it loses too much accuracy, the leapyear rule is changed. That isn't such a nuisance if it only happens each millenium or each few millenia. I know that it would make it impossible to accurately extend the calendar into the very distant future, but I expect that's an unavoidable problem. Anyway, calendars are pretty much always used for looking at times that are so near that the changing number of days-per-year isn't a problem. I mean, the mean tropical year's length has apparently changed by something on the order of 1/10 of a second since 1955.
 
Now, to check the websites.
 
Mike Ossipoff
 
 
 
 
 
 
 

 

---

Date: Mon, 24 Aug 2009 18:04:04 -0400
From: irv.bromberg@...
Subject: Re: Mean tropical year sometimes relevant for calendars?
To: CALNDR-L@...

On 2009 Aug 24, at 16:50 , MIKE OSSIPOFF wrote:

But what if, though the ecliptic positioning of the calendar is based on that point on the ecliptic (As my calendars seek to keep North-I/1 as close as possible to some particular solar ecliptic longitude), maybe one wants to minimize the overall annual ecliptic displacement of the calendar at its various dates throughout the year? Then, wouldn't the mean tropical year be justified as the relevant year-length?

Irv replies:

How would you verify the calendar drift if there isn't a specific event relative to which to evaluate its astronomical drift?

Also, the choice of epoch affects the calendar performance in a manner that is cumbersome to evaluate (requires a lot of least squares regression analysis).

In addition, the units of time are different:  calendars need mean solar days, whereas the so-called mean tropical year is in terms of atomic days.  Although there seems to be little difference today, that is just because we happen to be quite close to the epoch when the length of the atomic day was defined, but as time moves on the difference will grow exponentially.

I developed an average year length in terms of mean solar days, which I called the Mean Orbital Year (MOY), having Delta T implicitly embedded in it (correction for tidal slowing of the Earth rotation rate).  I published the calendar arithmetic for finding the New Year Day using the MOY leap rule, but numerous participants in this LISTSERV objected to it because of problems verifying drift, and because the embedded Delta T is unlikely to be accurate enough (unknown future).

Therefore I separated the Delta T and developed the Rotation Adjusted Year (RAY), which employs a fixed year length of 365+31/128 atomic days, and then the user's preference of Delta T correction is subtracted.  This math is "future-proof" because the Delta T function can be corrected as necessary.  I published the calendar arithmetic for finding the New Year Day using the RAY leap rule, but again numerous participants in this LISTSERV objected to it because of the drift verification problem and because allowing the Delta T function to vary would make calendar dates unpredictable.  Also, different users whose Delta T functions don't match exactly could obtain mismatching dates.

My freeware calendar calculator Kalendis continues to offer both MOY and RAY as experimental leap rule alternatives that can be applied to the Symmetry454 or Symmetry010 calendars or their quarter-structure variants, but I have withdrawn the documentation of their arithmetic, so as not to distract from the simplicity of the preferred fixed leap rule with symmetrically distributed smoothly spread leap year intervals.

I believe that Irv said that the difference in the length of the tropical year, with respect to various solar ecliptic longitudes, varies by about a minute and a half, over the ecliptic. But the overall average Gregorian year is within about 26 seconds of 365.2422 days.
So then, wasn't the Gregorian leapyear system designed to keep pace with the mean tropical year, for the reason that I mentioned in the 2nd paragraph of this message?

Irv replies:  No, regardless of how large or small the difference seems, the explicitly stated objective of the Gregorian calendar reform was to keep the vernal equinox on March 21st.  That means that the relevant astronomical mean year is the mean vernal equinoctial year, or to be hemisphere neutral, the mean northward equinoctial year, which in terms of mean solar days is currently within a fraction of a second of 365 days 5 hours 49 minutes.

Judging by the fact that the mean tropical year's length decreased by about a millionth of a day during the past half-century, I'd expect that its length at the time of the Gregorian reform might have been close to that rounded figure above, 365.2422 days.
  
Of course more detailed or accurate information about the mean tropical year length's rate of decrease, and the rate of change of that decrease-rate, would be welcome, as would information about what causes those rates.
 
I understand that the lengthing of the day due to lunar and solar tides is maybe the main reason for the decreasing of the number of days per mean tropical year. Are there other influences on that decrease rate? If the rate is changing, how is it changing, and what causes its changing?

Irv replies:  You will find answers to the above 3 points / questions in my analysis of the mean tropical year, which actually varies quasi-sinusoidally in relationship to the Earth axial tilt, on my web page about the Lengths of the Seasons at <http://www.sym454.org/seasons/>.

Also note that from the charts posted there, in the distant future when the Earth orbital eccentricity will be very small (for a number of millennia), all of the equinoctial and solstitial year lengths will be getting shorter in parallel with the tidal slowing of the Earth rotation rate.  In that far distant future era a leap rule like MOY or RAY might be the best option.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

<http://www.sym454.org/kalendis/>

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[Irv Bromberg]

On 2009 Aug 24, at 20:56 , MIKE OSSIPOFF wrote:

How would I judge the calendar's drift? For any particular date of the year that one is looking at, one would be interested in how much, at that date, the solar ecliptic longitude varies. A person might be interested in how much it varies cyclically, during the leapyear cycle, or how much it has drifted unidirectionally during a particular period.

Irv replies:  When I developed MOY, I chose its epoch and slope by least squares minimization of the deviation for each equinox and solstice evaluated over many millennia. Each equinox and solstice inevitably had to be allowed to vary by +/- 4 days from the mean, so the same would hold true for any selected point in the solar cycle.  One could evaluate more points, such as every 10 degrees or every degree of ecliptic solar longitude, but that greatly increases the scale of the data analysis for relatively little gain.

Of course, with all my current proposals, NorthI/1 is the date of principle interest for me. But I was just wondering if basing the leapyear rule on the mean tropical year would be a compromise that would be equally fair to all parts of the year, trying to keep down the variation of solar ecliptic longitude for all dates of the year. Of course the mean tropical year's length is easier to look up, and can be found in all sorts of sources, so laziness comes into it a little too.

Irv replies:  It is unavoidable that "how fair" it is to various parts of the year will vary over the millennia.

Your question suggests to me another way of charting the solar cycle, by plotting a 3D chart showing years on the x-axis, mean length of solar year on the y-axis, and the ecliptic solar longitude for which the calculation is made on the z-axis.  More simply, one could plot mean length of solar year on the y-axis against the ecliptic solar longitude for which the calculation is made on the x-axis for just the present era, or any chosen era.  Hmm, it would be neat to make an Excel spreadsheet macro that lets the user vary the choice of era and watch what happens to the lengths of the solar year throughout the solar cycle.  Calculation for every 10-15 degrees of solar longitude with linear interpolation ought to suffice for plotting the curves reasonably smoothly.  If the choice of era was constrained to century years only (for example), then it would not be unwieldy to base it on a pre-calculated list of moments generated by SOLEX numerical integration.

About the units, I know this is naive, but surely  the length of the mean tropical year, expressed in atomic days, could be converted into mean solar days. I understand that, because the length of the solar day is gradually increasing, the mean tropical year length expressed in terms of those days decreases correspondingly.

Irv replies:  As I explained in my previous message, after one carries out calculations in terms of atomic time (Terrestrial Time), one simply subtracts the Delta T value for the calculated moment to obtain the mean solar time moment (Universal Time).  The figure that I suggested of 365+31/128 days is based on the very long-term averaging in terms of atomic time.  If one were to look at just a few millennia near the present era, the appropriate length of Tropical Year will be slightly different, as it varies with a period of about 41000 years.  See the chart in row #9 of the "Graphical Analyses of Length of the Solar Year" at <http://www.sym454.org/seasons/>.

What you've mentioned is something that I'd never heard about: I'd always assumed that 365.242190 days referrred to the solar days whose length is graduallly increasing due to lunar and solar tides. I don't want to seem too lazy to look this up (and of course I'll look for it at the 454symmetry website that you posted), but what is the definition of an atomic day? Obviously I should read more about year and day definitions, and I'll start at the website that you posted. But, aside from that, sometimes the information is difficult or impossible to find, leading me to ask questions on the list. Anyway, this is an immediate reply, before I read the websites that you and Karl have posted; of course the less I say before I read more, the better.

Irv replies:  In general, whatever anybody assumes in astronomy is most likely wrong.  Intuition will almost always mislead us, especially when special and general relativity come into the picture.

1 atomic day = exactly 24 x 60 x 60 = 86400 s.i. seconds (international seconds)

1 s.i. second = the duration of exactly (by definition) 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom in an atomic clock.

I always assumed that a calendar's leapyear rule would just be based on a tropical-year length correct for the time when the calendar comes into use, and then, over the millenia, it will lose accuracy as the day-length changes and maybe as the orbit changes. When it loses too much accuracy, the leapyear rule is changed. That isn't such a nuisance if it only happens each millenium or each few millenia. I know that it would make it impossible to accurately extend the calendar into the very distant future, but I expect that's an unavoidable problem. Anyway, calendars are pretty much always used for looking at times that are so near that the changing number of days-per-year isn't a problem. I mean, the mean tropical year's length has apparently changed by something on the order of 1/10 of a second since 1955.

Irv replies:  Fine, but there often are points in the solar cycle that exhibit exceptional mean year stability for many millennia.  At present the mean northward equinoctial year is stable and will remain quite stable for the next 4-5 millennia, and the mean north solstitial year is stable and will remain so for the next 10-11 millennia.  Thus a calendar having a calendar mean year that is close to the mean northward equinoctial year will not drift appreciably relative to the northward equinox for 4-5 millennia, or a calendar having a calendar mean year that is close to the mean north solstitial year will not drift appreciably relative to the north solstice for 10-11 millennia.  By contrast, the Tropical Year is essentially never stable, when expressed in terms of mean solar days, always getting shorter due to tidal slowing of the Earth rotation rate.  See row #6 of the web page cited above.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[Mark J. Reed]

Originally, the day was divided into 12 hours and the night into 12
hours.  In general, day hours and night hours were different lengths,
depending on the season.  With the development of water clocks and
other timekeeping devices that functioned independent of the sun, we
defined a single hour for both day and night, 24 from noon to noon,
and day and night were no longer exactly 12 hours each (except
approximately, near the equinoxes).

These hours were divided into 60 minutes of 60 seconds, effectively
defining the "second" as 1/86400th of the Earth's mean rotational
period.   As we needed more and more precise time measurements, and
built more and more precise clocks to make them, we redefined the unit
in more readily-measurable terms; most recently, in terms of
Cesium-133 emissions. The unit so defined is the 'atomic' or 'SI'
second, and International Atomic Time (TAI) measures time in such
units.

The atomic second was originally based on the "ephemeris second"; as a
result, even though it was defined more recently, it matches the speed
of the Earth's rotation as it was around the year 1820.   At the
present time the mean rotational period of the Earth is about 2
milliseconds longer than that, so on average every 500 days the Earth
falls another full second behind atomic time.  And of course the
rotation continues to slow down, so the discrepancy will grow faster
as time goes on.

Atomic time is not affected by this, as it's wholly divorced from the
actual rotation of the Earth. But civil timekeeping still tries to
track the Earth's rotation.  We therefore use something called
Coordinated Universal Time (UTC).  UTC also ticks in atomic seconds
(because you can't measure the Earth's actual rotation in real time
with sufficient speed and accuracy to run a clock), but periodically
we insert a leap second to keep it in synch with the rotation of the
Earth. Currently there's a 34-second difference between UTC and TAI.

When measuring time out to the distant past and far future,
astronomers use Terrestrial Time, which differs from TAI, but still
uses the units of atomic time.  This is because a constantly-changing
time scale is of little practical use; when examining the changes in
the length of the earth's rotation, it's not very helpful to say "it's
still 24 hours, but the hours are longer". :)

So when speaking of the length of the Earth's year in days, it's
important to note if those are mean solar days as of the reference
time, or atomic days (of exactly 86,400 atomic seconds no matter when
you're measuring).

[MIKE OSSIPOFF]

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Irv--
 
Yesterday I missed the point of your question. Later I understood the problem, and that I hadn't answered it:
 
You wrote:
 

How would you verify the calendar drift if there isn't a specific event relative to which to evaluate its astronomical drift?

 

I reply:

 

 

 

If I were using the mean tropical year's length to judge the calendar's annual displacement:

 

1. I start by determining the initial "d", as I was describing, and choosing, as the calendar's 1st New Year's Day, the Monday in 2000 that minimizes it by positioning North-I/1 as close as possible to the desired solar ecliptic longitude (for a Monday in 2000 A.D.). Therefore, that also positions the year as a whole as close as possible to where it should be. All of the year's dates are, at that time, displaced by "d" from where they should be.

 

2. I'd use 1.24219 as the year's annual displacement with respect to the ecliptic, and have a leapyear system that corrects for that. So I'm using an average displacement for the various dates of the year, instead of for any one particular date. When, immediately after a non-leap-year ends, I add 1.24219 to d, I'm taking into account the average amount by which the year's various dates' displacement are increased annually. In years after the epoch, the ecliptic displacement of different dates of the year aren't the same, but the annual increment of 1.24219 gives an average of how much their various displacements have increased each year. And that average displacement is what the leapyear rule would then be correcting for, trying, as a round-the-year compromise, to keep the year as a whole, all of its dates, close to where they shoiuld be (where they'd all be at the epoch, if North-I/1 were at the desired solar eclliptic longitude). It's a round-the-year compromise, rather than an effort to keep one particular date close to a particular longitude.

 

That approach seems perfectly ok. The goal is different from my initial goal. I'll stick with my initial goal. I only mention this mean-tropical-year approach as a possibility. One advantage is that it's easier for anyone to look in an ordinary encyclopedia to find the year's length, given as the mean tropical year's length, so that they can easily see why the calendar proposal uses 1.24219   Otherwise someone might say, "Hey where do you get that annual year displacement. I thought the year was 365.242190 days." So it would simplify the proposal and its explanation.

 

But my initial intention was to keep North-I/1 close to a particular solar ecliptic longitude. Keeping one particular date close to a certain solar ecliptic longitude seems to be the approach preferred by calendarists. In fact, now I understand that the Gregorian leapyear system was designed with such a purpose. So, for those reasons, and because it was my initial intention anyway, I'll stick with the goal of keeping North-I/1 as close as possible to the desired solar ecliptic longitude. You and Karl have pointed out that, for that goal, I need something other than the mean tropical year--I need a particular tropical year relevant to the particular solar ecliptic longitude that I want to keep North-I/1 close to. So I'll look that up at the websites that have been posted here.

 

Mike Ossipoff

 

 

 

.org/kalendis/>

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[MIKE OSSIPOFF]

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Irv--
 
You wrote:
 
When I developed MOY, I chose its epoch and slope by least squares minimization of the deviation for each equinox and solstice evaluated over many millennia.
 
I reply:
 
A choice of epoch based on that sophisticated future-looking optimization hadn't occurred to me at all.
 
I was just choosing the epoch to minimize the calendar's displacement from ideal in the calendar year beginning at the epoch (which felt adequate, because the epoch was in 2000, only about 9 years ago).
 
Aside from the fact that that simple approach it was all that occurred to me, it has the appeal of instant gratification and postponement of adverse consequences.
 
But, of course, if a new calendar were adopted, it might be a long time from now, and so minimizing its displacement for 2000 might not be best, even by those standards.
 
So maybe, optimistically assuming that a new calendar will be adopted before too many decades, it might be best to use a future displacement minimizing approach like yours, but doing the optimization only for the next century. And then let corrections be made as needed in future millennia. That postponement of consequences seems ok.
 
(I'll start saving space and writing-time by using the term epoch, if it's a briefer way of saying "date of the new calendar's first New year". It will be a relief not to have to write all that out.)

You wrote:
 

It is unavoidable that "how fair" it  [a leapyear rule based on mean tropical year] is to various parts of the year will vary over the millennia.

 

I reply:

 

Yes, from what you say below on this page, I can see that. Well, the declination calendar's important date is around April 23, only about a month away from the northward equinox, and Subjective Seasonal's important date is around June 1, less than a month from the North solstice, so maybe both of those calendars would benefit some from the stability that you describe below.

 

You wrote:

 

At present the mean northward equinoctial year is stable and will remain quite stable for the next 4-5 millennia, and the mean north solstitial year is stable and will remain so for the next 10-11 millennia.  Thus a calendar having a calendar mean year that is close to the mean northward equinoctial year will not drift appreciably relative to the northward equinox for 4-5 millennia, or a calendar having a calendar mean year that is close to the mean north solstitial year will not drift appreciably relative to the north solstice for 10-11 millennia.  By contrast, the Tropical Year is essentially never stable, when expressed in terms of mean solar days, always getting shorter due to tidal slowing of the Earth rotation rate.  See row #6 of the web page cited above.

 

I reply:

 

So then, basing the leapyear rules of Subjective Seasonal and the declination calendar on keeping their respective important  date (close to Gregorian April 23 and June 1) close to its desired solar ecliptic longitude, by use of the specific tropical-year length appropriate for that important date,  might give a leapyear system that would be useful and meaningful for longer than one based on the mean tropical year compromise. That's another good reason for doing their leapyear systems in that way. Subjective Seasonal and the declination calendar are fortunate in that way, with their important dates being close to those stable dates. Well, I've been assuming that April 23 and June 1 are close enough to the stable equinox and solstice, for those two calendars to benefit significantly, but of course I don't know that.

 

Mike Ossipoff

 

 

 

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[MIKE OSSIPOFF]

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Mark--
 
Thanks for the information.
 
If they updated the definition of the ephemeris second and atomic second, from the ephemeris second's 1820 value, to a value equal to 1/86400 of today's solar day, then wouldn't we need a lot less frequent leap-seconds, for quite some time into the future?
 
Mike Ossipoff
 

 

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[Mark J. Reed]

The small difference with solar time is a minor inconvenience compared
to redoing all the arithmetic in scientific literature that has used
the SI second since its definition. :)  Anyway, for most applications
that need accurate solar time, mean time at the reference meridian of
the time zone isn't good enough, regardless of units.  They need
actual local solar time at a particular longitude, so you'd still have
to do a conversion, even from your modified atomic time.

There have been formal proposals to abolish leap seconds, and let the
drift accumulate (at least until it reaches an hour - which will take
almost 5000 years).   But one has yet to be put to a vote.


On Tue, Aug 25, 2009 at 7:16 PM, MIKE OSSIPOFF<nkklrp@...> wrote:

> Mark--
>
> Thanks for the information.
>
> If they updated the definition of the ephemeris second and atomic second,
> from the ephemeris second's 1820 value, to a value equal to 1/86400 of
> today's solar day, then wouldn't we need a lot less frequent leap-seconds,
> for quite some time into the future?
>
> Mike Ossipoff
>
>
>
>
> ________________________________
> Get back to school stuff for them and cashback for you. Try BingT now.

--
Mark J. Reed <markjreed@...>

[Irv Bromberg]

On 2009 Aug 25, at 19:05 , MIKE OSSIPOFF wrote:

So maybe, optimistically assuming that a new calendar will be adopted before too many decades, it might be best to use a future displacement minimizing approach like yours, but doing the optimization only for the next century. And then let corrections be made as needed in future millennia. That postponement of consequences seems ok.

Actually, I found that the short-term deviations are very misleading.  The long-term calculation was necessary to obtain a good average.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[MIKE OSSIPOFF]

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Calendars are interesting, and so is the time-of-day naming system, and so are maps.
 
We use calendars a lot more often than we use maps, and that's much of what makes them especially worth studying (and reforming). Of course we use the time-of-day naming system more often than the calendar, but it's already quite rational, not in need of reform (I take Mark's word for it that updating the 1820 second would be more inconvenient than the frequent leap-seconds). Of course the calendar currently in use doesn't share the rationality of our time-of-day naming system, with a month-system that had its relevance 2000 years ago. As I said before, our current calendar cries out for replacement. The Roman months were fine for the Romans. But we don't have to keep copying them. We could replace the Roman month system with something environmentally relevant.
 
So why have we reformed time-of-day naming, and not touched the old calendar? Because, with the calendar, there's no practical accuracy issue. _Any_ calendar can name the days, and be used for appointments, and for running all of our business.
 
Of course there's one different good thing about maps: You can use any map you want to, even for practical purposes. That isn't true of the calendar. Of what interest is an alternative calendar, one different from the one officially in use?
 
Well, I wouldn't say that no alternative calendars can be of interest. For instance, what if there were an alternative calendar whose year-divisions and their naming tells something about the seasonally-relevant time of year?
 
That's true of any seasonal calendar, including the longitude calendars that divide the year (as nearly as practically possible) into quarters divided by equinoxes and solstices. They're of interests because they tell you how far we are between equinoxes and solstices. Likewise of interest is the declination calendar whose month-naming refers to the amount of the declination. 
 
And, similarly, the Subjective Seasonal Calendar, which represents the astronomical seasons, or attempts to represent the terrestrial seasons as we perceive them.
 
I haven't forgotten that I said that I was going to post the numerical facts about Subjective Seasonal--epoch, initial d, and a date-conversion. I haven't done so yet only because it requires getting to the necessary almanac.
 
But, till then, I can make a good reasonable, and probably close, maybe correct, guess about a date conversion:
 
Today, August 26th, 2009, is close to, and may likely actually be (pending a check of the almanac)
 
North-III/24
 
That tells you that, today, in the northern hemisphere's temperate zone, it's fairly late summer, but not quite into the last month of summer. Of course you already knew that about August 26th. But the difference is that North-III/24 tells that, not just from your experience and prior familiarity with the months, but directly, explicity from the date's name.
 
A longitude calendar would tell you that we're about 2/3 of the way from north solstice to southward equinox. The declination calendar would tell you that the north solar declination has just dropped below its half-maximum value. And the Subsctive Seasonal calendar tells you what I said in the paragraph before this one.
 
Some have objected that seasons and their timing differ different parts of the north or south temperate zone.
 
I've answered those objections, but I'd like to summarize some of the answers here:
 
1. Even if the calendar's seasonal indication is a week, or even two weeks, off, where you reside, it's still informative. And a simple fairly small time-lag correction can adjust its seasonal indication for your local time-lag.
 
2. If, as seems to be so, people thoughout the north and south temperate zones feel that northern summer and southern winter arrive with June, and that northern winter and southern summer arrive with December, then that constitutes those people's definition of summer and winter. If time-lag causes similar conditions to arrive at slightly different times here and there, then that merely means that people's definitions of summer here and there differ a little. But the fact remains that, if people in some particular northern-hemisphere country feel that summer arrives with June, then, by their definition of summer, Subjective Seasonal is accurate when it indicates the beginning of the North season (northern summer) as close as possible to June 1.
 
3. As I said, today's guessed, but likely, Subjective Seasonal date of North-III/24 says that today it's fairly late summer, but not into the last month of summer. Exactly how much seasonal precision do you need? If an astronomical table were off by a week or two, you'd have good reason to be outraged. But I suggest that what Subjective Seasonal says about today is valid and informative.  ...And shows that Subjective Seasonal's date-naming is relevant and un-arbitrary.
 
Environmental relevance is what would make a new calendar un-arbitrary.
 
(Forgive the guessed date-conversion. I'll do better when I get a chance to check the necessary almanac.)
 
Mike Ossipoff
 
 
 
 
 

 

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[Irv Bromberg]

On 2009 Aug 26, at 20:28 , MIKE OSSIPOFF wrote:

Environmental relevance is what would make a new calendar un-arbitrary.

The Earth environment is itself arbitrary, as it varies between locales, hemispheres, and over time.

It seems especially arbitrary if one asks what will space travelers use to track the long-term passage of time, or colonists on other planets?

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[MIKE OSSIPOFF]

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Irv--
 
You wrote:
 
The Earth environment is itself arbitrary, as it varies between locales, hemispheres, and over time.
 
I reply:
 
But, for one thing, it's unusual for the seasonal time-lag in the north and south temperate zones to differ from 1.25 months by more than about half a month.
 
Besides, aside from that, North-I/1 is tied to a time that temperate-zone inhabitants tend to perceive as the arrival of summer in the northern hemisphere, or of winter in the southern hemisphere, even if, in north-temperate countries that share the perception of summer arriving with June,  similar conditons actually arrive in different countries at varying times. Then, as I was saying, that just means that "summer" or "winter" doesn't mean exactly the same thing in those diffent countries.
 
For instance, you know that if today is North-III/25th, and North, the norther-hemisphere summer calendrical season, has 4 months, then that date's suggestion of fairly late summer, toward the last month of summer, is remarkably close to what we actually perceive about August 27th.
 
Is that just because that calendar is intentionally set to dates that we regard in that way? Of course.

 

Subjective Seasonal is ambitious, an ambitious attempt at environmental relevance. This may be an issue without an objective yes/no answer, but it seems to me that Subjective Seasonal represents the perceived temperate-zone seasons pretty well.

 

And, aside from all that, if, somewhere in the temperate zones, there _were_ a feeling that the calendar was ahead or behind, then with that knowledge taken into account, and the time-lag difference corrected for, the calendar's seasonal indications would still be informative.

 

Can a calendar be more than just a numbering of days and months? I think it can, and I suggest that Subjective Seasonal shows that.

 

You wrote:

 

It seems especially arbitrary if one asks what will space travelers use to track the long-term passage of time, or colonists on other planets?

 

I reply:

 

Not fair--I'm only proposing an Earth calendar.

 

Mike Ossipoff

 

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

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[MIKE OSSIPOFF]

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I'd like to add a little to my previous reply:
 
Irv said:
 

The Earth environment is itself arbitrary, as it varies between locales, hemispheres, and over time.

 

I reply:

 

This is identically the same argument that anti-seasonalists, Irv included, on this list have been stating and re-stating since I first suggested a terrestrial-seasonal calendar.

 

I've posted many answers to that objection. Anti-seasonalists have never addressed those answers, but, instead, have just continued to re-use the same already-answered argument.

 

Re-use is very important for conserving the environment's resources, but it is less useful or productive to continue re-using an argument that has already been answered.

 

In fact, some discussion mailing-lists specifically ask their members to not do that.

 

I won't re-post the answers that I've posted in my most recent message, but I'll re-mention something that I mentioned much earlier in the discussison:

 

No matter where you live, the solar declination varies in exactly the same way. Likewise, the declination's delayed terrestrial consequences follow the recognizably same pattern.

 

The solar declination changes more and more slowly as it approaches its north and south maxima. That's where the term "solstice" comes from, referring to the fact that the declination's value stands still at those maxima. Additionally, in the declination's extreme excursions, it must go out and back, doubling its time in those extreme regions. In contrast, the solar declination rapidly and unidirectionally speeds through its transition between those extreme regions. 

 

The north solar declination spends about 1/3 of the year in the top half of its range, as does the south solar declination. The transitions between those periods are each of only about 1/6 of a year.

 

There is a time of year when people perceive that the terrestrial consequences of the solar declination have settled into an extreme-declination mode. We call that summer and winter. Those are periods during which the change has pretty much ended, because the solar declination, one seasonal time-lag ago, has arrived in the region where it changes only relatively little.

 

Yiping has suggested that maybe people tend to define a season as starting with a particular month, and that, therefore, the time of the month-beginnings have influenced people's perception of when summer starts. Maybe, but it doesn't matter, because I'm interested in what their perception is, more than in why they have it. Anyway, another thing that strongly influences that perception is the fact that, as I've been saying here, there are times of year when high-declination conditions have set in and remain relatively unchanged (summer and winter), in contrast to the intervening transitional periods of rapid change (spring and fall).

 

And yes, that pattern, which follows the pattern of variation of the declination itself, is global, not local.

 

In equatorial regions the temperature varies less, but in the regions with significant temperature variation, the pattern described above is distinctly recognizable everywhere.

 

Months have to have some sort of names. We could just just number them. But the calendar is more relevant if they're named for the time of year, and the conditions that characterize the times of year. That's obvious, isn't it?

 

Mike Ossipoff

 

 

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[Irv Bromberg]

On 2009 Aug 28, at 16:55 , MIKE OSSIPOFF wrote:

This is identically the same argument that anti-seasonalists, Irv included, on this list have been stating and re-stating since I first suggested a terrestrial-seasonal calendar.

I am outraged (OK, maybe just peeved) that you would denigrate me with the descriptive "anti-seasonalist" when in fact I have done so much work to analyze the lengths of the seasons, the lengths of the equinoctial and solstitial years, and the lengths of the solar years measured from arbitrary points in Earth's orbit, with so much of my web site dedicated to these efforts.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[MIKE OSSIPOFF]

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Numerical facts for Subjective Seasonal Calendar, fixed version:
 
First:  Leapweek, in my fixed calendars, including Subjective Seasonal, is in the last month of the year. For Subjective Seasonal, that's Southward-II.
 
Therefore, in leapyears, Southward has 10 weeks instead of 9. Both of its months, then, have 35 days.
 
Epoch: Midnight UT, Gregorian November 29th, 1999
 
Midnight Gregorian November 29th, 1999, is midnight,
South-I/1, 2000, in the Subjecive Seasonal Calendar. That's  the beginning of New year's Day in Subjective Seasonal.
 
Initial d: 2.8585
 
Date Conversion:
 
Today, August 29th, 2009, is North-III/27th, 2009 in the Subjective Seasonal Calendar.
 
Because I hadn't access to an almanac a few days ago, and because June 1, 2009 is a Monday, I guessed, at that time, that North-I/1, 2009 would be on Gregorian June 1, 2009, and that, therefore, Gregorian August 26, 2009 would be Subjective Seasonal North-III/24. That guess was correct.
 
How these numerical facts were arrived at:
 
South-I/1, the New Year's Day of Subjective Seasonal, occurs around December 1 Gregorian. I wanted the epoch to be close to the beginning of Gregorian 2000 A.D., and so I chose, as the epoch, the Monday in 1999 that minimizes initial d.
 
I calculated d as I described when I defined these calendars.
 
Gregorian 1999 and 2000 are in the 1996-2000 Gregorian leapyear cycle, which I define as January 1, 1997 to December 31, 2000.
 
The midpoint of the variation of the solar ecliptic longitude at midnight June 1, over that leapyear cycle, is 70.6829 degrees.
 
That, then, is the desired solar eclptic longitude for midnight, UT, North-I/1.
 
To minimize the magnitude of initial d, the Monday at which, at midnight UT, the solar ecliptic longitude is closest to 70.6829 was chosen as North-I/1.
 
That determined the Gregorian date for South-I/1,  2000, which is New Year's Day, 2000 of Subjective Seasonal.
 
From today's date conversion, and the fact that North has 4 months, you can't say that the name of Subjective Seasonal's date today doesn't agree with what you already know about August 29th, from your prior experience with the Gregorian calendar and its months and the time-of-year significance of its dates. According to Subjective Seasonal's date-naming, today is fairly late summer, about a month from the end of summer, something that you already know about August 29th.
 
Contrary to what we sometimes hear on this list, there is nothing unfeasible about a useful and seasonally meaningful terrestrial seasonal calendar. Subjective Seasonal is one.
 
 
Mike Ossipoff
 
 
 
 

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[Brillig]

I skipped over most of your post, which seemed more words than substance.

On Sat, Aug 29, 2009 at 3:37 PM, MIKE OSSIPOFF<nkklrp@...> wrote:

> Contrary to what we sometimes hear on this list, there is nothing unfeasible
> about a useful and seasonally meaningful terrestrial seasonal calendar.
> Subjective Seasonal is one.

I think you got it wrong. That should be:

There is little useful or advantageous about such a feasible scheme.
At least that's my position. In other words, there is nothing
compelling about the scheme that would prompt me to want to use it.

Victor

[MIKE OSSIPOFF]

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Victor said:
 
I skipped over most of your post, which seemed more words than substance.

I reply:
 
My post was, admittedly, mostly words, though it did contain a few numbers. Sorry, no pictures. But many or most of the words were about the numerical facts regarding the Subjective Seasonal Calendar, fixed version. Forgive me, but numerical facts are about as substantial as it gets.
 
Victor continued:
>

> On Sat, Aug 29, 2009 at 3:37 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
>
> > Contrary to what we sometimes hear on this list, there is nothing unfeasible
> > about a useful and seasonally meaningful terrestrial seasonal calendar.
> > Subjective Seasonal is one.
>
> I think you got it wrong. That should be:
>
> There is little useful or advantageous about such a feasible scheme.
> At least that's my position.

 
I reply:
 
Ok, Victor has changed his position. Now a seasonally-meaningful terrestrial-seasonal calendar is feasible, but just is not useful or advantageous.
 
As for practical usefulness, suppose you moved to Australia tomorrow. (Or, if you already live there, suppose you moved to Europe or the U.S.). The Gregorian months (last-version Roman months--Let's call a spade a spade) would have no seasonal meaning to you. But Subjective Seasonal's month-names would, because Subjective Seasonal's months are explicitly named for the seasons that people throughout the world's temperate zones identify with the corresponding solar ecliptic longitudes. That's useful and advantageous.
 
You've seen how Subjective Seasonal's naming of dates agrees with what you already know, from long experience, about the seasonal meaning of the months we use now. If you moved across the equator, the same Subjective Seasonal Calendar would continue to have the same seasonal relevance, though our last-version Roman months (or any month system not explicitly terrestrial-seasonal) would lose their seasonal meaning for you.
 
Now, if you don't move across the equator, then, because you already are familiar, over your entire lifetime, with the seasonal connotations of our latest-version Roman months that are in use now, Victor would claim that it isn't "useful" to change calendars, because, under those conditions, any kind of numbering of months and days would work for you--if you've been using it all your life.
 
And maybe that's why we're still using that ancient month system that is without any modern meaning or explicit seasonal relevance.
 
Does anyone else find that shabby, and an embarrassment?
 
Besides, for one thing, not everyone has lived for many years with the last-version Roman months. Perhaps it's easy to forget that not everyone has been around for as long as Victor or you or me.
 
Change to a neater, less arbitrary , but not terrestrial-seasonally-explicit, numbered month system, such as one that measures time between equinoxes and solstices, without the irrationally odd month-lengths? Well, then it would be similar to how it would be if you moved across the equator, because the month-names would lack obvious seasonal connotation--unlike the month names of Subjective Seasonal.
 
Admittedly, a calendar based on equinoxes and solstices, with rational month-lengths, would be an aesthetic improvement over the calendar we're using now, but it wouldn't achieve the improvement that Subjective Seasonal achieves.
 
As I said, the months have to be named something. So name them for what most defines the year and affects our daily life--the seasons.
 
The Monday that is tomorrow is the Monday that starts North-IV, calendrical (northern  hemisphere) summer's last month, in the fixed Subjective Seasonal Calendar. If you were vacationing in Australia, that date-name would automatically explicitly tell you that it was the beginning of Winter's last month.
 
Mike Ossipoff
 
 

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