Displacement Calculation & RE: Jitter Calculation RE: ....

classic Classic list List threaded Threaded
66 messages Options
1234
Reply | Threaded
Open this post in threaded view
|

Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff


On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year


I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff


I've just realized that I was a bit sloppy when transitioning between two different comparisons:

Calendar date/time and solar ecliptic longitude

and

Calendar date/time and the progress of the Gregorian mean year.


I spoke about the relation between calendar date & time, and solar ecliptic longitude because it's observable. Though the progress of the 365.2425 day Gregorian mean-year isn't short-term observable, I suggest that the same principle applies when comparing calendar date & time to the progress of the 365.2425 day Gregorian mean year.

Michael Ossipoff


On Tue, Jan 17, 2017 at 3:33 PM, Michael Ossipoff <[hidden email]> wrote:


On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year


I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20



Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
If it were desired to stay with the comparison between calendar date/time and solar ecliptic longitude, then I'd emphasize (instead of Gregorian  jitter-range) the maximum calendar-displacemennt (with respect to solar ecliptic longitude, that occurs within a 400 year Gregorian cycle.

That amounts to about 2.5 days.

To me, that's the more directly relevant & interesting displacement value anyway.

Michael Ossipoff

On Tue, Jan 17, 2017 at 3:54 PM, Michael Ossipoff <[hidden email]> wrote:


I've just realized that I was a bit sloppy when transitioning between two different comparisons:

Calendar date/time and solar ecliptic longitude

and

Calendar date/time and the progress of the Gregorian mean year.


I spoke about the relation between calendar date & time, and solar ecliptic longitude because it's observable. Though the progress of the 365.2425 day Gregorian mean-year isn't short-term observable, I suggest that the same principle applies when comparing calendar date & time to the progress of the 365.2425 day Gregorian mean year.

Michael Ossipoff


On Tue, Jan 17, 2017 at 3:33 PM, Michael Ossipoff <[hidden email]> wrote:


On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year


I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20




Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
In reply to this post by Karl Palmen
Karl--

You wrote:

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

Yes. As of as soon as I found that wikipedia figure for the number of mean solar days currently in a mean tropical year.

You continued:

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

Certainly: I have no objection to 365.24215 instead of 365.24217,  if it would be better-preferred by calendarists. I'll change it in my calendar-wiki proposal, via the edit option.

Michael Ossipoff


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen
In reply to this post by Michael Ossipoff

Dear Calendar People

 

Thank you Michael for your reply.

 

Michael quoted me thus:

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year”

What I actually said was:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.”

 

Michael has ignored the part the he missed out. I’ll put that issue aside.

 

 

An important point emerged later on in my reply, which Michael did not address:

 

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

This implies that it is meaningful to say something such as “January 18, 12:00 is 0.25 days ahead of the year of 365.24215 days” (as suggested in another note). For this to be meaningful, there must be a point in the year of 365.24215 days that corresponds to January 18, 12:00 and also to be true, that point must occur at January 18, 18:00. This must also be so for other calendar dates. Hence I answered:

 

“KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 days as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.”

All this implies the existence of a correspondence between dates in the calendar year and dates in the mean calendar year.

 

For calculated displacements, we can have calculated solar ecliptic longitudes (CSEL)  these could occur at a constant rate of 360 degrees per calendar mean year (such as Y=365.24215 days).  The calendar year, whether a leap year or a common year would have ideal solar ecliptic longitudes(ISEL), these occur on a fixed date every year and some may occur in a leap day or leap week, so would be missed out of a common year.

Now the calculated displacement at the time of a given ISEL is equal to the time the same CSEL occurs after that ISEL.

Furthermore the actual displacement at the time of a given ISEL is equal to the time the same actual solar ecliptic longitude (ASEL) occurs after the ISEL.

Does Michael agree that for the purpose of measuring all year accuracy, the calendar needs Ideal Solar Ecliptic Longitudes (ISEL) defined for its dates?

The correspondence between the dates of the calendar year and the dates of the mean calendar year places the ISEL of the calendar year onto the CSEL of the mean calendar year and vice versa. In particular, the statement “January 18, 12:00 is 0.25 days ahead of the calendar mean year (of 365.24215 day)” means that the ISEL of January 18, 12:00 occurs 0.25 days before the same CSEL.

Now let’s suppose the ecliptic longitudes Michael refers to next are CSELs.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be true (a difference of up to 2 days may occur), but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

There is indeed no sudden change in the CSEL between February 28th and March 1st in a common year, but there is (for normally fixed displacements) a sudden change in the ISEL, because some ISELs occur on February 29th ; in fact 0.2425 days’ worth equalling 0.2425*(360/365.2425) = 0.2390… degrees. This leads to the sudden change of displacement at that time (either calculated or actual).

If Michael’s continuously changing displacement is used, the ISELs are squeezed uniformly into the non-leap days and on average further away from the equal CSELs, hence the larger displacement values, which would occur even if the LIP were at the end of the year. However the problems of having some ISELs on a leap day are eliminated.

Again I ask Michael to calculate continuously changing displacements in the vicinity of two leap days or leap weeks, if he still believes that moving the LIP to the end of the year would stop the continuously changing displacement range from being greater.

This is not an issue when taking displacements from one fixed time of year for a minimum displacement leap year rule nor does it have any effect on the CSELs (and of course the ASELs).

 

Karl

 

16(05(21

 

 

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen
In reply to this post by Michael Ossipoff

Dear Michael and Calendar People

 

I have more comments below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

KARL REPLIES: I disagree, because calendar date and ecliptic longitude of whatever type are quite different. There must be some fixed relationship between calendar date and ecliptic longitude defined to make such a displacement definable. I’ve called such a relationship the ideal ecliptic longitude (ISEL) of each date. You may think of each date such as January 18 12:00 has having an ecliptic longitude, which you want to be the ecliptic longitude of this date.

 

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

KARL REPLIES: An ecliptic longitude is measured in units of angle not time so cannot in principle change by 1/100 day. I think what is meant is that over 15 days, the difference in time between the current ISEL and the equal CSEL changes by 1/100 day. This would apply, if the ISELs were to increase at a uniform rate over 365 non-leap days and the leap day has no ISEL.

 

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

KARL REPLIES: To do such a calculation only the differences between ISELs matter, so it would apply to any such uniform 365-day ISEL definition. I.e. the ISEL of the new year does not matter here.

 

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

KARL REPLIES: This arises not because of any sudden change in CSEL, but because the leap day has no ISELs. This also indicates that the abrupt change is equal to one whole day. Because not every leap year has the same displacement just before the leap day, the range of displacement must exceed 1, even if the leap day occurs at the end of the year.

Karl

16(05(21

 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
I'd said:
 

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

KARL REPLIES: I disagree, because calendar date and ecliptic longitude of whatever type are quite different. There must be some fixed relationship between calendar date and ecliptic longitude defined to make such a displacement definable.

Yes, but I've addressed that. I said that any two annual cycles can be compared in a common unit: Percent completion.  ...or, over a longer period: Number of years (tropical years, or common years, or calendar mean-years Y days long, etc.) completed.

You pointed out that that causes a problem with regard to dates in a leap-year. I answered that I only use that percent-completion comparison when comparing a common year to a mean-year (of whichever kind).

While the 365-day common year is completing a day's worth of completion, a Gregorian mean year is completing (365/365.2425) times as much percentage of its annual completion.

In other words, in a day, the Gregorian mean year is having a completion-percentage equal to (365/365.2425) of the completion-percentage that the 365-day common year has in one day.

The difference is 1 - (365/365.2425) of a common-year's worth of percent-completion.

That's equal to .2425/365.2425.

That's how many days' worth of percent-completion the common year gains on the Gregorian mean-year each day.

So it's possible to put both years' annual progress in terms of the same unit, and express it in days.

So it seems to me that that units objection has an answer.

 

I’ve called such a relationship the ideal ecliptic longitude (ISEL) of each date. You may think of each date such as January 18 12:00 has having an ecliptic longitude, which you want to be the ecliptic longitude of this date.


Yes. When you mention that, and when you asked me if I agree that the notion of calendar-seasonal accuracy requires ISELs for the calendar years' dates, that reminded me that my accuracy-goal for the Minimum-Displacement Calendar is like that. ...and that it speaks of a certain one calendar-displacement for a whole year (a displacement-year starting on January 1, immediately after a LIP).

...which contradicts my notion of constantly-changing displacement during a year.

So, instead of saying that the Gregorian jitter-range is 2.44 days, I should say that it's arguably 2.44 days.

So I'm not asserting that the constantly-changing displacement is the most valid interpretation or definition of displacement.  It's just that I wanted to find the largest Gregorian jitter-range (2.44 days) and the largest Gregorian displacement during the 400-year cycle (2.5 days) that can be gotten by any interpretation or definition--even if that displacement interpretation or definition is different from the one that the accuracy-standard for the Minimum-Displacement Calendar's Dzero is based on.

 

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

KARL REPLIES: An ecliptic longitude is measured in units of angle not time so cannot in principle change by 1/100 day.

It can change by a completion-percentage equal to the completion-percentage achieved by the common year in one day or 1/100 of a day.

By that measure it's possible to say that the Roman-Gregorian common year gains a certain number of days with respect to the ecliptic-longitude or the  Gregorian mean year, in a certain amount of time.

That was what I meant.


 


16(05(21


Is that number quoted above the date in a certain calendar? What calendar?

I should more closely examine your definitions of your new terms before I try to answer statements involving those new terms.

Michael Ossipoff

 


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
In reply to this post by Karl Palmen
Continuing my preliminary reply:


On Wed, Jan 18, 2017 at 8:02 AM, Karl Palmen <[hidden email]> wrote:

 

Michael quoted me thus:

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year”

What I actually said was:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.”

 

Michael has ignored the part the he missed out.


I didn't quote "...and in his recent idea of the continuously changing displacement.”, because I don't disagree with it. I just wanted to emphasize that only one of my earlier proposals, the nonfixed Roman-months version, had its LIP other than at year-end.

As I mentioned, you you pointed out the Dzero problems that that caused, I decided that avoiding those problems is more important than maintaining the February 28 LIP tradition, with the nonfixed Roman-months version.

In fact, I decided that a proposal should only be one proposal, which why I now propose only the 30,30,31 Minimum-Displacement Calendar.

(But I like the ISO WeekDate Calendar too, and if that (due to its use-precedent & convenience) were what people want, that would be fine with me.)

 

 

An important point emerged later on in my reply, which Michael did not address:

 

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

This implies that it is meaningful to say something such as “January 18, 12:00 is 0.25 days ahead of the year of 365.24215 days” (as suggested in another note). For this to be meaningful, there must be a point in the year of 365.24215 days that corresponds to January 18, 12:00


At any time, those two years have different completion-percentages, and the 365-day year's completion-percentage is continually gaining on the 365.2425 year's completion-percentage.   ...with respect to some unstated arbitrary starting-time.

 



All this implies the existence of a correspondence between dates in the calendar year and dates in the mean calendar year.


Their completion-percentages, with respect to some unstated arbitrary starting-time, can be compared. And, on that basis, the 365-day year is continually gaining on the 365.2425-day year..

 

 


Does Michael agree that for the purpose of measuring all year accuracy, the calendar needs Ideal Solar Ecliptic Longitudes (ISEL) defined for its dates?


Yes. The choice of Dzero for my proposed calendar is based on one all-year displacement being the desired displacement for the calendar, and the center of its displacement-oscillation.

As I said in my other reply, a few minutes ago, that one displacement for all year contradicts my notion of constantly-changing calendar-displacement. The latter, I only use because I was looking for the largest Gregorian jitter-range (2.44), and the largest Gregorian Calendar displacement (2.5 days)that can be gotten in a 400-year cycle, by any interpretation or definition of calendar-displacement.

I realize that the notion of calendar displacement and accuracy by which I chose Dzero is different from the one that gives those large 2.44 & 2.5 day values.
 


Again I ask Michael to calculate continuously changing displacements in the vicinity of two leap days or leap weeks, if he still believes that moving the LIP to the end of the year would stop the continuously changing displacement range from being greater.

What you say wouldn't surprise me, because continuously-changing displacements give larger Gregorian jitter-range and larger maximum Gregorian displacement during a 400 year cycle, when measured between a time barely before a leapday, and a time barely after a leapday.

I don't mean for the continuously-changing displacement notion to replace the displacment interpretation that led to the choice of Dzero for my propsal. I just wanted to find the largest values that I could get for the Gregorian jitter-range and the maximum Gregorian Calendar displacement during a 400-year cycle--by whatever interpretation or definition of displacement would give that larges value.

 

This is not an issue when taking displacements from one fixed time of year for a minimum displacement leap year rule nor does it have any effect on the CSELs (and of course the ASELs).


I agree that displacements measured between days that are the same date in different years is better, because, as you pointed out, it doesn't give different answers that depend on conventions, definitions or interpretations of displacement.

Michael Ossipoff

 

Karl

 

16(05(21

 

 

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

 


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
Of course, if I wanted to (I don't) I could re-write the determination and justification of my proposal's Dzero value, in terms of constantly-varying instantaneous displacement (maybe arriving at a different Dzero value).

Here are some pros & cons:

Favoring constantly-varying instantaneous displacement:

1 It accords with the actual calculated &/or observed progress & completion-rates of whatever two years are being compared..

2. Its continuity reflects that of cycles in the physical world.

Favoring displacement constant over a DY, changing abruptly at LIP:

1. It's customary among calendarists.
2. It matches the way displacement, D, is dealt with in my proposal.
3. It's convenient to assign a constant displacement to a DY.
4. There's less of it. (exemplified by 2.2 vs 2.44, & 2.26 vs 2.5 max for Gregorian)

-------------------------------------------------------------

The determination, choice & justification of the Dzero value of my 30,30,31 Minimum-Displacement Calendar remains based on the displacement that is constant thoughout a DY, and abruptly changes at the LIP.

MIchael Ossipoff











On Wed, Jan 18, 2017 at 8:43 PM, Michael Ossipoff <[hidden email]> wrote:
Continuing my preliminary reply:


On Wed, Jan 18, 2017 at 8:02 AM, Karl Palmen <[hidden email]> wrote:

 

Michael quoted me thus:

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year”

What I actually said was:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.”

 

Michael has ignored the part the he missed out.


I didn't quote "...and in his recent idea of the continuously changing displacement.”, because I don't disagree with it. I just wanted to emphasize that only one of my earlier proposals, the nonfixed Roman-months version, had its LIP other than at year-end.

As I mentioned, you you pointed out the Dzero problems that that caused, I decided that avoiding those problems is more important than maintaining the February 28 LIP tradition, with the nonfixed Roman-months version.

In fact, I decided that a proposal should only be one proposal, which why I now propose only the 30,30,31 Minimum-Displacement Calendar.

(But I like the ISO WeekDate Calendar too, and if that (due to its use-precedent & convenience) were what people want, that would be fine with me.)

 

 

An important point emerged later on in my reply, which Michael did not address:

 

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

This implies that it is meaningful to say something such as “January 18, 12:00 is 0.25 days ahead of the year of 365.24215 days” (as suggested in another note). For this to be meaningful, there must be a point in the year of 365.24215 days that corresponds to January 18, 12:00


At any time, those two years have different completion-percentages, and the 365-day year's completion-percentage is continually gaining on the 365.2425 year's completion-percentage.   ...with respect to some unstated arbitrary starting-time.

 



All this implies the existence of a correspondence between dates in the calendar year and dates in the mean calendar year.


Their completion-percentages, with respect to some unstated arbitrary starting-time, can be compared. And, on that basis, the 365-day year is continually gaining on the 365.2425-day year..

 

 


Does Michael agree that for the purpose of measuring all year accuracy, the calendar needs Ideal Solar Ecliptic Longitudes (ISEL) defined for its dates?


Yes. The choice of Dzero for my proposed calendar is based on one all-year displacement being the desired displacement for the calendar, and the center of its displacement-oscillation.

As I said in my other reply, a few minutes ago, that one displacement for all year contradicts my notion of constantly-changing calendar-displacement. The latter, I only use because I was looking for the largest Gregorian jitter-range (2.44), and the largest Gregorian Calendar displacement (2.5 days)that can be gotten in a 400-year cycle, by any interpretation or definition of calendar-displacement.

I realize that the notion of calendar displacement and accuracy by which I chose Dzero is different from the one that gives those large 2.44 & 2.5 day values.
 


Again I ask Michael to calculate continuously changing displacements in the vicinity of two leap days or leap weeks, if he still believes that moving the LIP to the end of the year would stop the continuously changing displacement range from being greater.

What you say wouldn't surprise me, because continuously-changing displacements give larger Gregorian jitter-range and larger maximum Gregorian displacement during a 400 year cycle, when measured between a time barely before a leapday, and a time barely after a leapday.

I don't mean for the continuously-changing displacement notion to replace the displacment interpretation that led to the choice of Dzero for my propsal. I just wanted to find the largest values that I could get for the Gregorian jitter-range and the maximum Gregorian Calendar displacement during a 400-year cycle--by whatever interpretation or definition of displacement would give that larges value.

 

This is not an issue when taking displacements from one fixed time of year for a minimum displacement leap year rule nor does it have any effect on the CSELs (and of course the ASELs).


I agree that displacements measured between days that are the same date in different years is better, because, as you pointed out, it doesn't give different answers that depend on conventions, definitions or interpretations of displacement.

Michael Ossipoff

 

Karl

 

16(05(21

 

 

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

 



Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen
In reply to this post by Michael Ossipoff

Dear Michael and Calendar People

 

I can see how the percentage-completion idea can make the statement “January 18th 12:00 is 0.25 day ahead of the calendar mean year” meaningful. It means that the %completion of the common year (or leap year not counting the leap day) for January 18th 12:00 occurs 0.25 day later than  in the calendar mean year. Then one can say that the calculated displacement of January 18th 12:00 is 0.25 days. So the percentage completion idea gives rise to a definition of displacement. In this case the displacement rises constantly until February 29th when it drops by 1 day.

 

To generalise this, I’ll refer to the calendar common year here as the ideal year.

 

The displacement for a given date can be defined as how much later the %completion of the calendar mean year equal to the %completion of the ideal year at the date occurs after the date.

 

To minimize displacement, it is necessary to add the leap day (February 29th) to the ideal year, but at a reduced length of 0.2425 days, which corresponds to the average time spent in February 29th . Then the displacements change only at the LIPs as described earlier.

 

 

All this has been done without referring to solar ecliptic longitudes. This is because the percentage completion has served as solar ecliptic longitude. It can be converted to a solar ecliptic longitude by choosing an arbitrary angle as the ISEL of the start of the year and adding 3.6 degrees for each percent completed and if the result is 360 degrees or more subtracting 360 degrees. Then we get ISEL in the ideal year and CSEL in the mean calendar year. Note that the CSEL (calculated SEL) changes at a uniform rate equal on 360 degrees per calendar mean year and is independent of the ideal year.

 

The displacement for a given date can be defined as how much later the CSEL equal to the ISEL of the date occurs after the date.

 

 

I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

 

 

Karl

 

16(05(23

 

PS: The date I just quoted is in my Yerm Lunar Calendar

http://www.hermetic.ch/cal_stud/palmen/yerm1.htm

It too could be defined as a lunar minimum displacement calendar, but the yerms makes this unnecessary.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 19 January 2017 01:09
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

I'd said:

 

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

KARL REPLIES: I disagree, because calendar date and ecliptic longitude of whatever type are quite different. There must be some fixed relationship between calendar date and ecliptic longitude defined to make such a displacement definable.

Yes, but I've addressed that. I said that any two annual cycles can be compared in a common unit: Percent completion.  ...or, over a longer period: Number of years (tropical years, or common years, or calendar mean-years Y days long, etc.) completed.

You pointed out that that causes a problem with regard to dates in a leap-year. I answered that I only use that percent-completion comparison when comparing a common year to a mean-year (of whichever kind).

While the 365-day common year is completing a day's worth of completion, a Gregorian mean year is completing (365/365.2425) times as much percentage of its annual completion.

In other words, in a day, the Gregorian mean year is having a completion-percentage equal to (365/365.2425) of the completion-percentage that the 365-day common year has in one day.

The difference is 1 - (365/365.2425) of a common-year's worth of percent-completion.

That's equal to .2425/365.2425.

That's how many days' worth of percent-completion the common year gains on the Gregorian mean-year each day.

So it's possible to put both years' annual progress in terms of the same unit, and express it in days.

So it seems to me that that units objection has an answer.

 

I’ve called such a relationship the ideal ecliptic longitude (ISEL) of each date. You may think of each date such as January 18 12:00 has having an ecliptic longitude, which you want to be the ecliptic longitude of this date.

 

Yes. When you mention that, and when you asked me if I agree that the notion of calendar-seasonal accuracy requires ISELs for the calendar years' dates, that reminded me that my accuracy-goal for the Minimum-Displacement Calendar is like that. ...and that it speaks of a certain one calendar-displacement for a whole year (a displacement-year starting on January 1, immediately after a LIP).

...which contradicts my notion of constantly-changing displacement during a year.

So, instead of saying that the Gregorian jitter-range is 2.44 days, I should say that it's arguably 2.44 days.

So I'm not asserting that the constantly-changing displacement is the most valid interpretation or definition of displacement.  It's just that I wanted to find the largest Gregorian jitter-range (2.44 days) and the largest Gregorian displacement during the 400-year cycle (2.5 days) that can be gotten by any interpretation or definition--even if that displacement interpretation or definition is different from the one that the accuracy-standard for the Minimum-Displacement Calendar's Dzero is based on.

 

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

KARL REPLIES: An ecliptic longitude is measured in units of angle not time so cannot in principle change by 1/100 day.

It can change by a completion-percentage equal to the completion-percentage achieved by the common year in one day or 1/100 of a day.

By that measure it's possible to say that the Roman-Gregorian common year gains a certain number of days with respect to the ecliptic-longitude or the  Gregorian mean year, in a certain amount of time.

That was what I meant.

 

 

 

16(05(21

 

Is that number quoted above the date in a certain calendar? What calendar?

I should more closely examine your definitions of your new terms before I try to answer statements involving those new terms.

Michael Ossipoff

 

 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen
In reply to this post by Michael Ossipoff

Dear Michael and Calendar People

 

I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 19 January 2017 20:29
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

Of course, if I wanted to (I don't) I could re-write the determination and justification of my proposal's Dzero value, in terms of constantly-varying instantaneous displacement (maybe arriving at a different Dzero value).

Here are some pros & cons:

Favoring 365-day constantly-varying instantaneous displacement:

KARL REPLIES: I inserted ‘365-day’ to indicate that there is more than one possible form constantly-varying instantaneous displacement. For example we can have 366-day constantly varying instantaneous displacement (using a leap year as ideal year). For a leap week calendar, it would be 364-day or 52-week etc..

1 It accords with the actual calculated &/or observed progress & completion-rates of whatever two years are being compared..

KARL REPLIES: Only in a common year. In a leap year, the %completion is held constant  on the leap day, which is not counted.

2. Its continuity reflects that of cycles in the physical world.

KARL REPLIES: I disagree. There is a discontinuity at the leap day.

I do see two advantages:

1. Every ISEL occurs every year, because none of them occur on a leap day.

2. When the calendar mean year (Y) is changed, the ISELs do not change; whereas they must undergo a small change in “constant displacement over a DY” to fit the new calendar mean year.

 

Favoring displacement constant over a DY, changing abruptly at LIP:

1. It's customary among calendarists.

2. It matches the way displacement, D, is dealt with in my proposal.

3. It's convenient to assign a constant displacement to a DY.

4. There's less of it. (exemplified by 2.2 vs 2.44, & 2.26 vs 2.5 max for Gregorian)

-------------------------------------------------------------

The determination, choice & justification of the Dzero value of my 30,30,31 Minimum-Displacement Calendar remains based on the displacement that is constant thoughout a DY, and abruptly changes at the LIP.

Michael Ossipoff

 

Karl

 

16(05(23

 

 

 




 

 

On Wed, Jan 18, 2017 at 8:43 PM, Michael Ossipoff <[hidden email]> wrote:

Continuing my preliminary reply:

 

On Wed, Jan 18, 2017 at 8:02 AM, Karl Palmen <[hidden email]> wrote:

 

Michael quoted me thus:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year”

What I actually said was:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.”

 

Michael has ignored the part the he missed out.

 

I didn't quote "...and in his recent idea of the continuously changing displacement.”, because I don't disagree with it. I just wanted to emphasize that only one of my earlier proposals, the nonfixed Roman-months version, had its LIP other than at year-end.

As I mentioned, you you pointed out the Dzero problems that that caused, I decided that avoiding those problems is more important than maintaining the February 28 LIP tradition, with the nonfixed Roman-months version.

In fact, I decided that a proposal should only be one proposal, which why I now propose only the 30,30,31 Minimum-Displacement Calendar.

(But I like the ISO WeekDate Calendar too, and if that (due to its use-precedent & convenience) were what people want, that would be fine with me.)

 

 

An important point emerged later on in my reply, which Michael did not address:

 

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

This implies that it is meaningful to say something such as “January 18, 12:00 is 0.25 days ahead of the year of 365.24215 days” (as suggested in another note). For this to be meaningful, there must be a point in the year of 365.24215 days that corresponds to January 18, 12:00

 

At any time, those two years have different completion-percentages, and the 365-day year's completion-percentage is continually gaining on the 365.2425 year's completion-percentage.   ...with respect to some unstated arbitrary starting-time.

 

 

 

All this implies the existence of a correspondence between dates in the calendar year and dates in the mean calendar year.

 

Their completion-percentages, with respect to some unstated arbitrary starting-time, can be compared. And, on that basis, the 365-day year is continually gaining on the 365.2425-day year..

 

 

 

Does Michael agree that for the purpose of measuring all year accuracy, the calendar needs Ideal Solar Ecliptic Longitudes (ISEL) defined for its dates?

 

Yes. The choice of Dzero for my proposed calendar is based on one all-year displacement being the desired displacement for the calendar, and the center of its displacement-oscillation.

As I said in my other reply, a few minutes ago, that one displacement for all year contradicts my notion of constantly-changing calendar-displacement. The latter, I only use because I was looking for the largest Gregorian jitter-range (2.44), and the largest Gregorian Calendar displacement (2.5 days)that can be gotten in a 400-year cycle, by any interpretation or definition of calendar-displacement.

I realize that the notion of calendar displacement and accuracy by which I chose Dzero is different from the one that gives those large 2.44 & 2.5 day values.
 

 

 

Again I ask Michael to calculate continuously changing displacements in the vicinity of two leap days or leap weeks, if he still believes that moving the LIP to the end of the year would stop the continuously changing displacement range from being greater.

What you say wouldn't surprise me, because continuously-changing displacements give larger Gregorian jitter-range and larger maximum Gregorian displacement during a 400 year cycle, when measured between a time barely before a leapday, and a time barely after a leapday.

I don't mean for the continuously-changing displacement notion to replace the displacment interpretation that led to the choice of Dzero for my propsal. I just wanted to find the largest values that I could get for the Gregorian jitter-range and the maximum Gregorian Calendar displacement during a 400-year cycle--by whatever interpretation or definition of displacement would give that larges value.

 

This is not an issue when taking displacements from one fixed time of year for a minimum displacement leap year rule nor does it have any effect on the CSELs (and of course the ASELs).

 

I agree that displacements measured between days that are the same date in different years is better, because, as you pointed out, it doesn't give different answers that depend on conventions, definitions or interpretations of displacement.

Michael Ossipoff

 

Karl

 

16(05(21

 

 

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

 

 

 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff


On Fri, Jan 20, 2017 at 8:14 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 19 January 2017 20:29
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

Of course, if I wanted to (I don't) I could re-write the determination and justification of my proposal's Dzero value, in terms of constantly-varying instantaneous displacement (maybe arriving at a different Dzero value).

Here are some pros & cons:

Favoring 365-day constantly-varying instantaneous displacement:

KARL REPLIES: I inserted ‘365-day’ to indicate that there is more than one possible form constantly-varying instantaneous displacement. For example we can have 366-day constantly varying instantaneous displacement (using a leap year as ideal year). For a leap week calendar, it would be 364-day or 52-week etc..


But I only use the continuously-varying displacement to compare the common year's progress to that of the reference-year.

As regards the continuously-varying displacement,I consider the leap-day, with its resulting abrupt displacement, as something external that we ourselves do, to correct the gradual displacement that naturally occurs, given the interaction of the common year (fictitious) and the reference year (fictitious if it's the Gregorian mean year, real if it's a tropical year).
 

1 It accords with the actual calculated &/or observed progress & completion-rates of whatever two years are being compared..

KARL REPLIES: Only in a common year. In a leap year, the %completion is held constant  on the leap day, which is not counted.


The relation of the common year to the reference year is all that I define and use the continuously-varying instantaneous displacement for.
 

2. Its continuity reflects that of cycles in the physical world.

KARL REPLIES: I disagree. There is a discontinuity at the leap day.


Yes, but I regard the leap-day as external to the system consisting of the common year & the reference-year.   ...an external adjustment that we make to counter that system's natural change in the relation of the common & reference years.
 

I don't consider the leap-day to be part of the natural behavior of the relation of common and reference years. I regard the leap-day as something external to that naturally-operating system,...something added by us to compensate for that system's natural behavior.

Though I consider the continuously-varying instantaneous displacement as a perfectly valid way to describe the situation, I don't use it for determining or justifying my calendar's Dzero.

I only mention it as a curiosity of interest,and something that results in a different Gregorian jitter-range, and a different Gregorian maximum displacement in a 400 year cycle.


Michael Ossipoff

 

I do see two advantages:

1. Every ISEL occurs every year, because none of them occur on a leap day.

2. When the calendar mean year (Y) is changed, the ISELs do not change; whereas they must undergo a small change in “constant displacement over a DY” to fit the new calendar mean year.

 

Favoring displacement constant over a DY, changing abruptly at LIP:

1. It's customary among calendarists.

2. It matches the way displacement, D, is dealt with in my proposal.

3. It's convenient to assign a constant displacement to a DY.

4. There's less of it. (exemplified by 2.2 vs 2.44, & 2.26 vs 2.5 max for Gregorian)

-------------------------------------------------------------

The determination, choice & justification of the Dzero value of my 30,30,31 Minimum-Displacement Calendar remains based on the displacement that is constant thoughout a DY, and abruptly changes at the LIP.

Michael Ossipoff

 

Karl

 

16(05(23

 

 

 




 

 

On Wed, Jan 18, 2017 at 8:43 PM, Michael Ossipoff <[hidden email]> wrote:

Continuing my preliminary reply:

 

On Wed, Jan 18, 2017 at 8:02 AM, Karl Palmen <[hidden email]> wrote:

 

Michael quoted me thus:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year”

What I actually said was:

“One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year and in his recent idea of the continuously changing displacement.”

 

Michael has ignored the part the he missed out.

 

I didn't quote "...and in his recent idea of the continuously changing displacement.”, because I don't disagree with it. I just wanted to emphasize that only one of my earlier proposals, the nonfixed Roman-months version, had its LIP other than at year-end.

As I mentioned, you you pointed out the Dzero problems that that caused, I decided that avoiding those problems is more important than maintaining the February 28 LIP tradition, with the nonfixed Roman-months version.

In fact, I decided that a proposal should only be one proposal, which why I now propose only the 30,30,31 Minimum-Displacement Calendar.

(But I like the ISO WeekDate Calendar too, and if that (due to its use-precedent & convenience) were what people want, that would be fine with me.)

 

 

An important point emerged later on in my reply, which Michael did not address:

 

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

This implies that it is meaningful to say something such as “January 18, 12:00 is 0.25 days ahead of the year of 365.24215 days” (as suggested in another note). For this to be meaningful, there must be a point in the year of 365.24215 days that corresponds to January 18, 12:00

 

At any time, those two years have different completion-percentages, and the 365-day year's completion-percentage is continually gaining on the 365.2425 year's completion-percentage.   ...with respect to some unstated arbitrary starting-time.

 

 

 

All this implies the existence of a correspondence between dates in the calendar year and dates in the mean calendar year.

 

Their completion-percentages, with respect to some unstated arbitrary starting-time, can be compared. And, on that basis, the 365-day year is continually gaining on the 365.2425-day year..

 

 

 

Does Michael agree that for the purpose of measuring all year accuracy, the calendar needs Ideal Solar Ecliptic Longitudes (ISEL) defined for its dates?

 

Yes. The choice of Dzero for my proposed calendar is based on one all-year displacement being the desired displacement for the calendar, and the center of its displacement-oscillation.

As I said in my other reply, a few minutes ago, that one displacement for all year contradicts my notion of constantly-changing calendar-displacement. The latter, I only use because I was looking for the largest Gregorian jitter-range (2.44), and the largest Gregorian Calendar displacement (2.5 days)that can be gotten in a 400-year cycle, by any interpretation or definition of calendar-displacement.

I realize that the notion of calendar displacement and accuracy by which I chose Dzero is different from the one that gives those large 2.44 & 2.5 day values.
 

 

 

Again I ask Michael to calculate continuously changing displacements in the vicinity of two leap days or leap weeks, if he still believes that moving the LIP to the end of the year would stop the continuously changing displacement range from being greater.

What you say wouldn't surprise me, because continuously-changing displacements give larger Gregorian jitter-range and larger maximum Gregorian displacement during a 400 year cycle, when measured between a time barely before a leapday, and a time barely after a leapday.

I don't mean for the continuously-changing displacement notion to replace the displacment interpretation that led to the choice of Dzero for my propsal. I just wanted to find the largest values that I could get for the Gregorian jitter-range and the maximum Gregorian Calendar displacement during a 400-year cycle--by whatever interpretation or definition of displacement would give that larges value.

 

This is not an issue when taking displacements from one fixed time of year for a minimum displacement leap year rule nor does it have any effect on the CSELs (and of course the ASELs).

 

I agree that displacements measured between days that are the same date in different years is better, because, as you pointed out, it doesn't give different answers that depend on conventions, definitions or interpretations of displacement.

Michael Ossipoff

 

Karl

 

16(05(21

 

 

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 17 January 2017 20:34
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Tue, Jan 17, 2017 at 8:09 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar people

 

Thank you for your reply.

 

One thing I’ve been aware of since Michael first proposed his minimum displacement calendar is that he treated the common year as an ideal year. This showed up in his original proposal when the LIP was not at the end of the year

 

I want to emphasize that that was only for the non-fixed leap-day Roman version of my proposal at that time.

Other than that, I've specified a year-end LIP.

It seems to me that neither way of reckoning displacement is wrong . They just differ.

If we're using the Minimum-Displacement leapyear-system, it would be perfectly valid for someone to speak of, as the calendar's displacement, the leapyear-system's D value, which abruptly increases at the end of each common year, and then stays the same until the next year-end.

But we're talking about the Gregorian Calendar's jitter-range. The variable D isn't used in the Gregorian's leapyear-system, so there'd be less inclination to regard it that way.

You mentioned a problem that occurs between the percent-completion measure of year-progress, and the dates in a leap-year. Ok, but I only speak of percent-completion with regard to the comparison of common year and reference-year (mean-year) such as MTY or 365.2425, etc.

In this problem involving the Gregorian jitter-range, the mean year (I call it the "reference-year") is 365.2425 days, and that's just as fictitious as the 365-day common year. In fact, where the common-year is "observable", by calendar and clock, the 365.2425 year isn't short-term observable or noticeable at all. So, for the purpose of clarification, let's compare the Roman-Gregorian common-year, and a tropical-year, the MTY.

For simplification, let's say that the annual progress of the MTY approximates the actual solar ecliptic longitudes so well that we don't notice the difference when we make observations. That might not really be trues, but we're interested more in the principle.

You can "observe" the progress of the common year by means of a calendar & a clock. Maybe, for the best convenience, you refer to your computer, which tells both the date and the time.

Say your make those observations of your computer date/time on the night of February 28th of a common-year, at 11:59 p.m. and again 2 minutes later at 12:01 a.m. Say you're in phone contact with someone on the meridian opposite yours, and that person is making an astronomical observation to determine the exact solar ecliptic longitude.

In that way, you can literally observe the relation between the progress of the common-year's date & time, and the solar ecliptic longitude.

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

The 2.44 day value for the Gregorian jitter-range is convincingly observably supported in that way. In a meaningful sense, the calendar-displacement wouldn't (without a leap-day) change significantly between 2096, February 28th, 11:59 p.m., and 2096, March 1, 12:01 a.m.

There is a displacement that genuinely changes abruptly, and that's the displacement caused by a leap-day.  

During the 192 years from the LIP moment of 1904 to that of 2096, without any leapdays, the calendar-displacement, with respect to the Gregorian mean year, would be 192 X .2425.  From that product, subtract a day for each of the 49 leap-days between February 28, 1904, 11:59 and March 1, 2096, 12:01 a.m.

Taken between those two date-&-time points, there is 2.44 days of calendar-displacement, by the measure described above.

Michael Ossipoff

 

and in his recent idea of the continuously changing displacement.

 

I reply to individual points below. In some of these replies, I’ll point out an alternative convention of making the leap year ideal and the common year deficient in an attempt to make Michael aware of his choice of making a common year ideal. I do not of course, support the idea of making the leap year ideal, but show it as an alternative convention to make the idealisation of the common year visible.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 16 January 2017 19:08
To: [hidden email]
Subject: Re: Jitter Calculation RE: New Henry-Hanke calendar/website, old shortcomings

 

About having the LIP other than at the end of the year:

Originally, when I posted my Minimum-Displacement Calendar (multi-version) proposal last spring & summer, I wanted the nonfixed Roman version to be so true to tradition that its LIP is at the end of February 28th.

When you (Karl) pointed out the complexity that that would bring in, as regards the choice of Dzero, realized that having the LIP other than at the end of the year wouldn't be a good idea, even for a nonfixed Roman version.

Anyway, I've realized also that a multi-version proposal isn't such a good idea either. And so now my Minimum-Displacement Calendar proposal consists only of the 30,30,31 quarters, in the leapweek fixed version with the Minmum-Displacement leapyear rule.

When it's only one version, that allowed me to leave out a lot of definitions and terms that were complicating the proposal.

 

My only concession to multichoice is that I offer Dzero values of 0 or -.6288   ...with -.6288 as the recommendation.  ...with an epoch of Gregorian January 2nd, 2017.

KARL REPLIES: The Mean calendar year (Y) is again missing. Is it the 365.24217 days mentioned below?

I’d suggest 365.24215 days, which is a MTY not very far in the future and has the advantage of dividing by 7 to equal 52.17745 weeks enabling calculations to be done in weeks.

 

I've posted my 1-version Minimum-Displacement Calendar proposal at the Calendar Wiki, and it's shown at the recent-changes page, but (like the recently-posted Hanke-Henry proposal) it hasn't yet appeared at the Proposed Calendars page.

About displacement & jitter-calculation, it's more & more obvious that displacement isn't a simple topic.

As I was saying, it's a complex mix of difficultly-separated physical fact & conventional fiction.

KARL REPLIES: Yes. One could for example adopt a convention based on counting the vacant LIPs, where February 29 is missing, then the 194-year period from March 1, 1903 to February 28, 2097, excluding both the adjacent LIPs, would give an even larger value of jitter than 2.44 days:

194*0.7575 – 144 = 2.955 days

The 194 years contain 193 LIPs 49 of which are occupied by leap days and so 144 are vacant.

 

If I don't have an LIP other than at the end of the year, I hope that gets rid of some of the contradictions and incompatibilities.

We're using different definitions, and thereby getting different answers (2.2 & 2.44) for the Gregorian jitter-range.

Those definitions seem a matter of choice, not hard fact. Maybe my choices & definitions are contrary to accepted convention.

KARL REPLIES: I’ll continue to insist that the same dates (within a year) are used for calculating jitter, because values that use different dates depend on convention and so are not useful.



You mentioned that the notion of a constantly-increasing calendar-displacement can result in a calculation of greater max displacement, when the LIP isn't at year-end. But now I don't propose a calendar with LIP not at year-end.

KARL REPLIES: It would result in greater max displacement even if the LIP is at the end of the year and for exactly the same reasons, that it produces a larger calendar jitter.  Try calculating displacements just before and after a leap week or leap day for two different leap years.

 

But isn't it undeniable that, as the Roman-Gregorian common-year undergoes 1/365 of a year-completion, the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion?

KARL REPLIES: Yes, but also as the Roman-Gregorian leap-year undergoes 1/366 calendar year completion the Gregorian mean-year undergoes 1/365.2425 of a year-completion, and the MTY undergoes 1/365.24217 of a year-completion.

 



(A wikipedia page said that the MTY currently has about 365.24217 mean solar days.)

So isn't the Roman-Gregorian common year steadily, constantly gaining on those other 2 years every day, every minute?

KARL REPLIES:  It depends how you divide these other 2 years into days and months.

I’d divide them into normal length days, except by February 29, which is reduced to 0.2425 or 0.24217 day as applicable. Then the answer is no, except at the LIP, when there is a sudden gain of 0.2425 or 0.24217 days.

I think Michael would divide it into 365 equal stretched days, in which case there’d be the constant gain. This stretching of the days would increase displacement regardless of when the LIP occurs.

In Michael’s original proposal, he did not stretch the 365 days, but left a gap at the end of year. If the LIP were at the end of the year, the gap could be filled by a reduced leap day.

 

Sure, leapyear-rules, including my Minimum-Displacement leapyear-rule, at the end of a common-year, add (Y-365) days  to D. But that's just adding what has been accumulating all year, isn't it?

KARL REPLIES: Not necessarily, for reason just stated.

 

Of course the LIP is the time to find out what value the displacement has reached, for the purpose of determining if a leapweek is needed. That's a good reason for calculating the new D value at that time, at the LIP.

KARL REPLIES: Yes it would keep the calendar simple, if displacement were calculated at a fixed time of the year. For a constant increasing displacement, the time exactly half way between LIPs would be a good choice, because it would enable you to centre the displacements about 0.0.

Karl

16(05(20

 

 

 


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
In reply to this post by Karl Palmen
 


Karl--


You wrote:


I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.


[endquote]


But the system consisting of the 365-day common year, and the reference-year (be it the Gregorian mean year, or one of the tropical years) is more fundamental. The 365-day year is what our calendar year is, except when we need to make an exception, as a displacement-adjustment, ,to correct for what that common-year/reference-year system is doing.


So the common year does have special status, as a basis for a meaningful figure for the Gregorian jitter-range.


I consider both the 2.2 day value, and the 2.44 day value to be valid.


The 2.44 day value accords better with the actual calculated &/or observed relation in the progress of the common & reference years. The 2.2 day value matches how my leapyear-rule treats D, and is probably more practical and convenient. It remains the basis of my Dzero determination, choice & justification.


Michael Ossipoff




 


On Fri, Jan 20, 2017 at 8:01 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

I can see how the percentage-completion idea can make the statement “January 18th 12:00 is 0.25 day ahead of the calendar mean year” meaningful. It means that the %completion of the common year (or leap year not counting the leap day) for January 18th 12:00 occurs 0.25 day later than  in the calendar mean year. Then one can say that the calculated displacement of January 18th 12:00 is 0.25 days. So the percentage completion idea gives rise to a definition of displacement. In this case the displacement rises constantly until February 29th when it drops by 1 day.

 

To generalise this, I’ll refer to the calendar common year here as the ideal year.

 

The displacement for a given date can be defined as how much later the %completion of the calendar mean year equal to the %completion of the ideal year at the date occurs after the date.

 

To minimize displacement, it is necessary to add the leap day (February 29th) to the ideal year, but at a reduced length of 0.2425 days, which corresponds to the average time spent in February 29th . Then the displacements change only at the LIPs as described earlier.

 

 

All this has been done without referring to solar ecliptic longitudes. This is because the percentage completion has served as solar ecliptic longitude. It can be converted to a solar ecliptic longitude by choosing an arbitrary angle as the ISEL of the start of the year and adding 3.6 degrees for each percent completed and if the result is 360 degrees or more subtracting 360 degrees. Then we get ISEL in the ideal year and CSEL in the mean calendar year. Note that the CSEL (calculated SEL) changes at a uniform rate equal on 360 degrees per calendar mean year and is independent of the ideal year.

 

The displacement for a given date can be defined as how much later the CSEL equal to the ISEL of the date occurs after the date.

 

 

I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

 

 

Karl

 

16(05(23

 

PS: The date I just quoted is in my Yerm Lunar Calendar

http://www.hermetic.ch/cal_stud/palmen/yerm1.htm

It too could be defined as a lunar minimum displacement calendar, but the yerms makes this unnecessary.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 19 January 2017 01:09
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

I'd said:

 

Now, is or isn't the observed relation between the progress of the common year and the solar ecliptic longitude going to make a sudden +.24217 day jump, between 11:59 p.m. and 12:01 a.m.?

It's observable. It isn't in doubt.

I'd say that's a meaningful interpretation of what calendar-displacement means.

KARL REPLIES: I disagree, because calendar date and ecliptic longitude of whatever type are quite different. There must be some fixed relationship between calendar date and ecliptic longitude defined to make such a displacement definable.

Yes, but I've addressed that. I said that any two annual cycles can be compared in a common unit: Percent completion.  ...or, over a longer period: Number of years (tropical years, or common years, or calendar mean-years Y days long, etc.) completed.

You pointed out that that causes a problem with regard to dates in a leap-year. I answered that I only use that percent-completion comparison when comparing a common year to a mean-year (of whichever kind).

While the 365-day common year is completing a day's worth of completion, a Gregorian mean year is completing <a href="tel:(365)%20365-2425" value="+13653652425" target="_blank">(365/365.2425) times as much percentage of its annual completion.

In other words, in a day, the Gregorian mean year is having a completion-percentage equal to <a href="tel:(365)%20365-2425" value="+13653652425" target="_blank">(365/365.2425) of the completion-percentage that the 365-day common year has in one day.

The difference is 1 - <a href="tel:(365)%20365-2425" value="+13653652425" target="_blank">(365/365.2425) of a common-year's worth of percent-completion.

That's equal to .2425/365.2425.

That's how many days' worth of percent-completion the common year gains on the Gregorian mean-year each day.

So it's possible to put both years' annual progress in terms of the same unit, and express it in days.

So it seems to me that that units objection has an answer.

 

I’ve called such a relationship the ideal ecliptic longitude (ISEL) of each date. You may think of each date such as January 18 12:00 has having an ecliptic longitude, which you want to be the ecliptic longitude of this date.

 

Yes. When you mention that, and when you asked me if I agree that the notion of calendar-seasonal accuracy requires ISELs for the calendar years' dates, that reminded me that my accuracy-goal for the Minimum-Displacement Calendar is like that. ...and that it speaks of a certain one calendar-displacement for a whole year (a displacement-year starting on January 1, immediately after a LIP).

...which contradicts my notion of constantly-changing displacement during a year.

So, instead of saying that the Gregorian jitter-range is 2.44 days, I should say that it's arguably 2.44 days.

So I'm not asserting that the constantly-changing displacement is the most valid interpretation or definition of displacement.  It's just that I wanted to find the largest Gregorian jitter-range (2.44 days) and the largest Gregorian displacement during the 400-year cycle (2.5 days) that can be gotten by any interpretation or definition--even if that displacement interpretation or definition is different from the one that the accuracy-standard for the Minimum-Displacement Calendar's Dzero is based on.

 

Roughly every 15 days, that relation between common-year progress and ecliptic longitude will observably change by about 1/100 of a day. You can observe it gradually increasing by about +.24217 days from one LIP to the next, for example.

KARL REPLIES: An ecliptic longitude is measured in units of angle not time so cannot in principle change by 1/100 day.

It can change by a completion-percentage equal to the completion-percentage achieved by the common year in one day or 1/100 of a day.

By that measure it's possible to say that the Roman-Gregorian common year gains a certain number of days with respect to the ecliptic-longitude or the  Gregorian mean year, in a certain amount of time.

That was what I meant.

 

 

 

16(05(21

 

Is that number quoted above the date in a certain calendar? What calendar?

I should more closely examine your definitions of your new terms before I try to answer statements involving those new terms.

Michael Ossipoff

 

 


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff

Karl--

You wrote:

I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

[endquote]

But isn't there agreement that the common year is the primary calendar year, the 1st approximation to the desired average year, the closest integer (or 7-divisible integer) to the desired average year?

...whereas the leap-day, and the leapyear, is just a patch to correct the results of the length-mismatch between common & desired average years?

So the 365 (or 364) day common year has special status that the leap-year doesn't have.

Suppose that the desired average year were about 365.9

And say we want a leap-day calendar. What would the common year be then? It would be 366 days. And every so often, there'd be a leap-year in which a leap-day would be subtracted from the 366-day common year.


Michael Ossipoff





Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff
Karl--

As you pointed out, in terms of the continuously-varying instantaneous displacement, the Minimum-Displacement leapyear-rule doesn't keep calendar-displacement between -3.5 days and +3.5 days.

Yes, it certainly makes a lot more sense to measure a calendar's displacement by the same measure by which it's designed to limit displacement.

...instead of having to define two kinds of displacement, with mutually contradictory values:  one to define a leapyear-rule, and another, different one, to , measure its results..

Michael Ossipoff


On Sat, Jan 21, 2017 at 11:25 AM, Michael Ossipoff <[hidden email]> wrote:

Karl--

You wrote:

I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

[endquote]

But isn't there agreement that the common year is the primary calendar year, the 1st approximation to the desired average year, the closest integer (or 7-divisible integer) to the desired average year?

...whereas the leap-day, and the leapyear, is just a patch to correct the results of the length-mismatch between common & desired average years?

So the 365 (or 364) day common year has special status that the leap-year doesn't have.

Suppose that the desired average year were about 365.9

And say we want a leap-day calendar. What would the common year be then? It would be 366 days. And every so often, there'd be a leap-year in which a leap-day would be subtracted from the 366-day common year.


Michael Ossipoff






Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen

Dear Michael and Calendar People

 

Michael in an earlier note said

I don't consider the leap-day to be part of the natural behavior of the relation of common and reference years. I regard the leap-day as something external to that naturally-operating system,...something added by us to compensate for that system's natural behavior.

I’m glad Michael has made this explicit. I explains why Michael takes the 365-day year as the ideal year.

I don’t take that view and don’t see anything natural about a 365-day year.

I regard the leap day as an essential and integral part of the system and not something external to it. I see the ideal year to be the mean calendar year of either 365 days and a shortened leap day or 52 weeks and a shortened leap week. The length of each day in this ideal year is equal to the average time per year spent on this day. So the ideal year is really an average year.  A calendar cannot use this ideal year as a calendar year, because the calendar year must have a whole number of days. So instead it uses years of 365 AND years of 366 days or for a leap week calendar 52 AND 53 weeks, both are essential even though one occurs more often than the other. Therefore I consider it a deviation from the ideal year occurs whenever a leap day/week is inserted or omitted. I think this ideal year minimises displacements, because the calculated displacements are defined relative to a contiguous sequence of these ideal years. Note that the dates I defined in this ideal year can serve as a substitute for solar ecliptic longitude, just like %completion.

Michael has said that if the mean year were about 365.9 days, he’d regard the 366-day year as the ideal year.

However I have found another advantage 365-day ideal year. I have up to now deliberately not addressed the issue of the displacement value(s) in a leap day (or leap week), because I considered acceptable for the displacement not to be defined on a leap day for defining a minimum displacement calendar. However a leap day is just like any other day so for year round accuracy does merit a displacement and hence Ideal Solar Ecliptic Longitude (ISEL). There are several possible ways of defining displacement and hence ISEL on a leap day. I mention just one of these and it is that the displacement decreases over a leap day (or leap week) so there is no sudden change of displacement at the start of end of the leap day (or leap week). Then both displacement and ISEL are continuous within the 365-day system. The ISEL would be constant over a leap day (or leap week).

This would apply even if the mean year were about 365.9 days,  as would the advantage of every ISEL occurring in every year.

The advantage of not having to change the ISELs (by a few seconds) whenever the mean calendar year is changed, would apply to any fixed year as the ideal year such as 365 days, 366 days or 365.25 days. Note that one could get considerably smaller actual displacements, if one were free to change the ISELs whenever one changed the mean calendar year, but this could be seen as cheating as “moving the goal posts”. Ideally, the ISELs would not change at all, but if the ideal year changes, so must the ISELs. This change in ISELs can be minimised by fixing the ISEL exactly half way between the LIPs, then if the mean calendar year is reduced, then the ISELs would move by no more than half this reduction towards this fixed ISEL away from the LIPs to make space for the ISELs that can no longer be accommodated in the leap day or leap week, because of the shorter mean year.

Karl

16(05(26

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 22 January 2017 16:26
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

Karl--

As you pointed out, in terms of the continuously-varying instantaneous displacement, the Minimum-Displacement leapyear-rule doesn't keep calendar-displacement between -3.5 days and +3.5 days.

Yes, it certainly makes a lot more sense to measure a calendar's displacement by the same measure by which it's designed to limit displacement.

...instead of having to define two kinds of displacement, with mutually contradictory values:  one to define a leapyear-rule, and another, different one, to , measure its results..

Michael Ossipoff

 

On Sat, Jan 21, 2017 at 11:25 AM, Michael Ossipoff <[hidden email]> wrote:


Karl--

You wrote:


I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

[endquote]

 

But isn't there agreement that the common year is the primary calendar year, the 1st approximation to the desired average year, the closest integer (or 7-divisible integer) to the desired average year?

...whereas the leap-day, and the leapyear, is just a patch to correct the results of the length-mismatch between common & desired average years?

 

So the 365 (or 364) day common year has special status that the leap-year doesn't have.

 

Suppose that the desired average year were about 365.9

And say we want a leap-day calendar. What would the common year be then? It would be 366 days. And every so often, there'd be a leap-year in which a leap-day would be subtracted from the 366-day common year.

Michael Ossipoff




 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff


On Mon, Jan 23, 2017 at 8:15 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael in an earlier note said

I don't consider the leap-day to be part of the natural behavior of the relation of common and reference years. I regard the leap-day as something external to that naturally-operating system,...something added by us to compensate for that system's natural behavior.

I’m glad Michael has made this explicit. I explains why Michael takes the 365-day year as the ideal year.


The principle calendar year, as the best integer approximation to the desired average year.

I don’t take that view and don’t see anything natural about a 365-day year.


Sure, it's artificial, fictitious.

What I was referring to as natural was the interaction between the desired average year and the principle calendar year, the nearest approximation to the desired average year. For example, there's that .24217 day natural discrepancy between the principle calendar year and the mean tropical year..  ...natural only in the sense that it's the displacement between them that naturally results each year from the use of the 365-day principal calendar year. 

But sure, I recognize and admit that it could be looked at either way, and you could reasonably regard the common year and the leap-year as having equal status. It's just different ways of looking at it, and neither is wrong. But the common year is the one that's the nearest integer approximation to the desired average year.

Where this matter results in a more substantive difference of opinion is when the use of 365 days as the principle calendar year leads to 2.44 days as the alternative to 2.2 days, as the Gregorian Jitter-range.  ...by looking at the common-year's steady gain over the Gregorian average year, and not similarly comparing the rates of the leap-year and the Gregorian average year.

So you could say that I'm arbitrarily giving special status to the common year, in comparison to the leap-year. Your way of regarding the situation is more general and unbiased. The biased giving of preferential status to the common year indeed counts as an argument against 2.44 days as the Gregorian jitter-range.



I regard the leap day as an essential and integral part of the system and not something external to it. I see the ideal year to be the mean calendar year of either 365 days and a shortened leap day or 52 weeks and a shortened leap week. The length of each day in this ideal year is equal to the average time per year spent on this day. So the ideal year is really an average year.  

I never meant that 365 days is ideal. Just that I call it the principal calendar year. But I realize that arguably the 365 day year and the 366 day year could be regarded equally as parts of the system that approximates the desired average year, and therefore of equal status.

 

A calendar cannot use this ideal year as a calendar year, because the calendar year must have a whole number of days. So instead it uses years of 365 AND years of 366 days or for a leap week calendar 52 AND 53 weeks, both are essential even though one occurs more often than the other.

Sure, and that's the more general view that I referred to above, whose validity I don't deny.
 

Therefore I consider it a deviation from the ideal year occurs whenever a leap day/week is inserted or omitted. I think this ideal year minimises displacements, because the calculated displacements are defined relative to a contiguous sequence of these ideal years. Note that the dates I defined in this ideal year can serve as a substitute for solar ecliptic longitude, just like %completion.

Michael has said that if the mean year were about 365.9 days, he’d regard the 366-day year as the ideal year.


I'd say "the principal calendar year".
 
Anyway, I agree that the abruptly-varying displacement that's constant through a displacement-year (as opposed to the constantly-varying instantaneous displacment) is the one to use, for the various reasons I stated.

Maybe especially because it's the one by which D, in the Minimum-Displacement leapyear-rule is defined. So, if I were to speak of Minimum-Displacement's displacement in terms of the constantly-varying instantaneous displacement, I'd have to define two kinds of displacement when speaking of Minimum-Displacement--one in its definition, and a different one in its results-evaluation. I agree in preferring the displacement measure in which Minimum-Displacement keeps the displacement in the range of -3.5 days to +3.5 days.  ...the abruptly-varying displacement that's constant throughout each displacement year.

And if I want to compare the maximum displacements of Minimum-Displacement and the Gregorian leapyear-rule, then of course I have to measure them both by the same measure.  ...which means that 2.2 days is the Gregorian jitter-range, and 2.26 days is the Gregorian's maximum displacement during a 400-year cycle. (...as opposed to 2.44 & 2.5 days).

Michael Ossipoff

4 Monday

...by which I mean 2017W041.  But I realize that this is an international mailing-list, and that not everyone calls this day "Monday". I'd ordinarily only use "4 Monday" for local usage, within a same language-community.)

30,30,31 is my calendar proposal, because conversations have shown me that the bigger the change that a calendar-reform proposal makes, the fewer people would accept it. Eliminating the months is a bigger change, and fewer people would accept it.

But I feel that there's a strong case for saying that the WeekDate system would be more practical.

And the relation of month to season isn't close enough to justify an objection to WeekDate on those grounds.

Anyway, as I was saying, the week-number makes it pretty clear what the season is, as I was discussing before. Within a few weeks of week-52 or week-1 is obviously winter. After the 1st quarter, around week 14 is April, the usually-accepted beginning of Spring. July, the 1st of the two hottest (northern-hemisphere) months starts right after week 26, at mid-year.

Though I consider Minimum-Displacement to be better than Nearest-Monday, because of its deluxe adjustability of the parameters of oscillation-center and reference-year, I also recognize that people are more accepting of Nearest-Monday.  ...whose maximum displacement in a 400-year cycle is barely more than Minimum-Displacement's maximum displacement.

Because the week-number doesn't change as fast as the day-of-the-month, I suggest that WeekDate will result in fewer date-errors.

-------------------------------------------------

What does the number that I quoted immediately below represent? I assume that it's a date in an alternative calendar. What calendar?


16(05(26

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 22 January 2017 16:26
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

Karl--

As you pointed out, in terms of the continuously-varying instantaneous displacement, the Minimum-Displacement leapyear-rule doesn't keep calendar-displacement between -3.5 days and +3.5 days.

Yes, it certainly makes a lot more sense to measure a calendar's displacement by the same measure by which it's designed to limit displacement.

...instead of having to define two kinds of displacement, with mutually contradictory values:  one to define a leapyear-rule, and another, different one, to , measure its results..

Michael Ossipoff

 

On Sat, Jan 21, 2017 at 11:25 AM, Michael Ossipoff <[hidden email]> wrote:


Karl--

You wrote:


I don’t take the jitter of 2.44 days seriously, because it depends on the choice of the ideal year. Nor is it the largest value for all possible ideal years. One can have a leap year (with full length February 29th ) as an ideal year then the jitter would be 2.955 days as I showed in an earlier note.

[endquote]

 

But isn't there agreement that the common year is the primary calendar year, the 1st approximation to the desired average year, the closest integer (or 7-divisible integer) to the desired average year?

...whereas the leap-day, and the leapyear, is just a patch to correct the results of the length-mismatch between common & desired average years?

 

So the 365 (or 364) day common year has special status that the leap-year doesn't have.

 

Suppose that the desired average year were about 365.9

And say we want a leap-day calendar. What would the common year be then? It would be 366 days. And every so often, there'd be a leap-year in which a leap-day would be subtracted from the 366-day common year.

Michael Ossipoff




 


Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Karl Palmen

Dear Michael and Calendar People

 

Thank you Michael for your reply.

 

I don’t understand what Michael means by principal calendar year. I’ve never seen the term used anywhere. I have taken it to mean ideal year.

 

Does Michael agree that in whatever system he chooses, that for year-round accuracy to be meaningful, each date must have a solar ecliptic longitude assigned to it that is the solar ecliptic longitude most desired for that date?

 

If not, then he’ll have to explain in detail what he means by year-round accuracy and how the principal calendar year and how its relationship with the mean tropical year fit in with this.

 

Here I explain what I mean by the ideal year and Michael can then explain any differences between it and the principal calendar year.

Firstly I refer to that solar ecliptic longitude most desired for a date as the ideal solar ecliptic longitude of the date (ISEL).

The Ideal year is an abstract year of calendar dates in which all the ISELs occur evenly spaced. This ideal year can be a calendar common year of 365 days or 52 days or a calendar leap year of 366 days or 53 weeks or one may shorten the leap day or leap week and I do so to give the ideal year exactly the same length as the calendar mean year.

 

The Ideal year may be thought of as a projection of the calendar year onto the ISELs. Somewhat like a projection of a map of the globe onto a flat surface, but somewhat simpler, because only one dimension is involved.  For the examples we have considered, all the non-leap days are flat, but the leap day may slope, so appear shorter in the projection. It may be shortened to zero as Michael would do or to the fractional part of the mean year as I would. Also the projection is scaled to the 360 degree range of the ISELs.

 

Michael then considers defining two types of displacement, one for the minimum displacement calendar, which is constant within each DY and one using the 365-day ideal year. I don’t think this is necessary.

I believe these two displacements would be equal at one fixed time of the year. So one could use the 365-day ideal year displacement and then define the minimum displacement calendar by using only the displacement at that one time of year. One can then refer to this displacement as the displacement of the year and define it solely in terms of the displacements of other years. Note that the very idea of each date in a year having a displacement complicates the calendar definition and may be one reason Irv has rejected it.

 

I still don’t consider the 2.44 day Gregorian jitter range as any meaning, but might do if I can define it in terms of ISELs. I note the that Gregorian calendar has only one ISEL defined for it, which is the northward equinox and the exact date of this has not been specified.  So the fixing of this ISEL and the addition of other ISELs cannot be considered part of the Gregorian calendar, but something added to it.

 

Karl

 

16(05(27

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 23 January 2017 22:47
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Mon, Jan 23, 2017 at 8:15 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael in an earlier note said

I don't consider the leap-day to be part of the natural behavior of the relation of common and reference years. I regard the leap-day as something external to that naturally-operating system,...something added by us to compensate for that system's natural behavior.

I’m glad Michael has made this explicit. I explains why Michael takes the 365-day year as the ideal year.

 

The principle calendar year, as the best integer approximation to the desired average year.

I don’t take that view and don’t see anything natural about a 365-day year.

 

Sure, it's artificial, fictitious.

What I was referring to as natural was the interaction between the desired average year and the principle calendar year, the nearest approximation to the desired average year. For example, there's that .24217 day natural discrepancy between the principle calendar year and the mean tropical year..  ...natural only in the sense that it's the displacement between them that naturally results each year from the use of the 365-day principal calendar year. 

But sure, I recognize and admit that it could be looked at either way, and you could reasonably regard the common year and the leap-year as having equal status. It's just different ways of looking at it, and neither is wrong. But the common year is the one that's the nearest integer approximation to the desired average year.

Where this matter results in a more substantive difference of opinion is when the use of 365 days as the principle calendar year leads to 2.44 days as the alternative to 2.2 days, as the Gregorian Jitter-range.  ...by looking at the common-year's steady gain over the Gregorian average year, and not similarly comparing the rates of the leap-year and the Gregorian average year.

So you could say that I'm arbitrarily giving special status to the common year, in comparison to the leap-year. Your way of regarding the situation is more general and unbiased. The biased giving of preferential status to the common year indeed counts as an argument against 2.44 days as the Gregorian jitter-range.

 

I regard the leap day as an essential and integral part of the system and not something external to it. I see the ideal year to be the mean calendar year of either 365 days and a shortened leap day or 52 weeks and a shortened leap week. The length of each day in this ideal year is equal to the average time per year spent on this day. So the ideal year is really an average year.  

I never meant that 365 days is ideal. Just that I call it the principal calendar year. But I realize that arguably the 365 day year and the 366 day year could be regarded equally as parts of the system that approximates the desired average year, and therefore of equal status.

 

A calendar cannot use this ideal year as a calendar year, because the calendar year must have a whole number of days. So instead it uses years of 365 AND years of 366 days or for a leap week calendar 52 AND 53 weeks, both are essential even though one occurs more often than the other.

Sure, and that's the more general view that I referred to above, whose validity I don't deny.
 

Therefore I consider it a deviation from the ideal year occurs whenever a leap day/week is inserted or omitted. I think this ideal year minimises displacements, because the calculated displacements are defined relative to a contiguous sequence of these ideal years. Note that the dates I defined in this ideal year can serve as a substitute for solar ecliptic longitude, just like %completion.

Michael has said that if the mean year were about 365.9 days, he’d regard the 366-day year as the ideal year.

 

I'd say "the principal calendar year".
 

Anyway, I agree that the abruptly-varying displacement that's constant through a displacement-year (as opposed to the constantly-varying instantaneous displacment) is the one to use, for the various reasons I stated.

Maybe especially because it's the one by which D, in the Minimum-Displacement leapyear-rule is defined. So, if I were to speak of Minimum-Displacement's displacement in terms of the constantly-varying instantaneous displacement, I'd have to define two kinds of displacement when speaking of Minimum-Displacement--one in its definition, and a different one in its results-evaluation. I agree in preferring the displacement measure in which Minimum-Displacement keeps the displacement in the range of -3.5 days to +3.5 days.  ...the abruptly-varying displacement that's constant throughout each displacement year.

And if I want to compare the maximum displacements of Minimum-Displacement and the Gregorian leapyear-rule, then of course I have to measure them both by the same measure.  ...which means that 2.2 days is the Gregorian jitter-range, and 2.26 days is the Gregorian's maximum displacement during a 400-year cycle. (...as opposed to 2.44 & 2.5 days).

Michael Ossipoff

4 Monday

...by which I mean 2017W041.  But I realize that this is an international mailing-list, and that not everyone calls this day "Monday". I'd ordinarily only use "4 Monday" for local usage, within a same language-community.)

KARL REPLIES: Why not 4th Monday or Week 4, Monday?

 

Reply | Threaded
Open this post in threaded view
|

Re: Displacement Calculation & RE: Jitter Calculation RE: ....

Michael Ossipoff

Dear Michael and Calendar People

 

Thank you Michael for your reply.

Karl—


(After this, I'm not writing in Word, because now I have to re-insert all of the paragraph-spacings)

 

You wrote:


I don’t understand what Michael means by principal calendar year. I’ve never seen the term used anywhere. I have taken it to mean ideal year.


I only mean it with its usual informal meaning. I  just mean that 365 is the integer that best approximates the length of the desired average year (whether that be one of the various tropical years, or the Gregorian mean year).   …resulting in most years being 365 days long. Ask someone how long a year is, and they’ll say 365 days. That’s all I mean by “principle year”.  


Does Michael agree that in whatever system he chooses, that for year-round accuracy to be meaningful, each date must have a solar ecliptic longitude assigned to it that is the solar ecliptic longitude most desired for that date?


Yes.


If not, then he’ll have to explain in detail what he means by year-round accuracy and how the principal calendar year and how its relationship with the mean tropical year fit in with this.


I agree with your statement quoted above. But, when I spoke of “year-round accuracy”, I was talking about the choice of Y, the length of the reference tropical year (RTY).


The June solstice year has been suggested as the reference tropical year. Maybe there’s a misconception in this (something all too easy in calendar matters), but I felt that, with the June solstice year as the reference-year, the calendar’s date would be relatively stable or constant at the June solstice.   …that, for the June solstice, the date wouldn’t vary as much, if the June solstice year is the RTY.  But I felt that, with that RTY, the dates corresponding to other ecliptic longitudes would vary more greatly than they would if the MTY were chosen as the RTY. That was my motivation for suggesting the MTY as the RTY.


So, when I spoke of “year-round accuracy”, I was referring to the maximum, over the entire ecliptic, of the variation of date with respect to ecliptic longitude.


But, now that you mention it, that means that I was (then too) talking about a displacement that’s different throughout the year.  …even though I’ve agreed that a constantly-varying displacement isn’t the best way to define calendar-displacement.


So—contradicting myself.  But it just seems reasonable for the reference year (desired average year) to  have a length that’s the average of the lengths of the tropical years defined with respect to the various points of the ecliptic, instead of the reference year being the length of the tropical year defined with respect to one particular point of the ecliptic (such as the June solstice).


 Here I explain what I mean by the ideal year and Michael can then explain any differences between it and the principal calendar year.


Firstly I refer to that solar ecliptic longitude most desired for a date as the ideal solar ecliptic longitude of the date (ISEL).


Sure, if displacement means that the ecliptic longitude for a particular date is off, then there must be something that it’s off from.


The Ideal year is an abstract year of calendar dates in which all the ISELs occur evenly spaced. This ideal year can be a calendar common year of 365 days or 52 weeks or a calendar leap year of 366 days or 53 weeks or one may shorten the leap day or leap week and I do so to give the ideal year exactly the same length as the calendar mean year.


I’m not saying that I disagree with that, but I’m just saying that it isn’t how I speak of the situation. Maybe this means that I’m far from the conventional way of speaking of these things, but a shortened leap-day isn’t part of how I regard this matter.   …nor equally-spaced ISELs.  I think you’ll agree that, in these matters (a complex, difficultly-separated, mix of physical fact and conventional fiction), there’s lots of room for different descriptions and wordings.


I don’t claim that my wording, description or definition-system is the one that’s “right”.


The important thing is that we agree on what the various calendar-proposals mean—what today’s date is, in the various calendars. For example we agree that, today, on Gregorian January 24th, it’s January 23rd in my 30,30,31 Minimum-Displacement Calendar (because its epoch is on Monday Gregorian January 2nd) , and that in ISO WeekDate it’s 2017w042.


And I agree that a calendar-displacement that’s constant throughout a DY, and changes abruptly at the end of the DY, is the more useful definition of calendar-displacement. So there isn’t any significant disagreement.


The Ideal year may be thought of as a projection of the calendar year onto the ISELs. Somewhat like a projection of a map of the globe onto a flat surface, but somewhat simpler, because only one dimension is involved.  


Simpler? I wouldn’t call this subject simpler than map-projections. Map projections are a subject about straightforward co-ordinate transformations between lat,lon and X,Y. 


With calendars, there’s the  complex mix of physical fact & conventional fiction that I’ve been mentioning.

 

 You wrote:


Michael then considers defining two types of displacement, one for the minimum displacement calendar, which is constant within each DY and one using the 365-day ideal year. I don’t think this is necessary.


Yes:


One displacement that’s constant within each DY, varying abruptly at the end of each DY.


And...


An instantaneous, continuously-varying displacement.  …based on the variation between the completion-percentages of the common year and the desired mean-year.  …which gives the common year more status than the leap-year.


I don’t think this is necessary.


Sure, I don’t claim that it’s necessary.   …only that my 2nd displacement-definition above is one way to get a different value value (2.44 days) for the Gregorian jitter-range and (2.5 days) the Gregorian maximum displacement in a 400-year cycle.


The first of my two meanings for displacement, above is the one that we agree on.


You wrote:


I believe these two displacements would be equal at one fixed time of the year. So one could use the 365-day ideal year displacement and then define the minimum displacement calendar by using only the displacement at that one time of year. One can then refer to this displacement as the displacement of the year and define it solely in terms of the displacements of other years. Note that the very idea of each date in a year having a displacement complicates the calendar definition and may be one reason Irv has rejected it.


I myself rejected it too, in my previous posts.


 I still don’t consider the 2.44 day Gregorian jitter range as any meaning, but might do if I can define it in terms of ISELs. I note the that Gregorian calendar has only one ISEL defined for it, which is the northward equinox


The Gregorian mean year of 365.2425, as I understand it, was chosen because it’s close to the length of the March equinox year.

 

 

and the exact date of this has not been specified. 


Wasn’t it said that they wanted the March equinox to stay as close as possible to March 21st?


Michael Ossipoff 


Will you tell me what that number directly below stands for?


16(05(27

 

 

 


On Tue, Jan 24, 2017 at 8:05 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Thank you Michael for your reply.

 

I don’t understand what Michael means by principal calendar year. I’ve never seen the term used anywhere. I have taken it to mean ideal year.

 

Does Michael agree that in whatever system he chooses, that for year-round accuracy to be meaningful, each date must have a solar ecliptic longitude assigned to it that is the solar ecliptic longitude most desired for that date?

 

If not, then he’ll have to explain in detail what he means by year-round accuracy and how the principal calendar year and how its relationship with the mean tropical year fit in with this.

 

Here I explain what I mean by the ideal year and Michael can then explain any differences between it and the principal calendar year.

Firstly I refer to that solar ecliptic longitude most desired for a date as the ideal solar ecliptic longitude of the date (ISEL).

The Ideal year is an abstract year of calendar dates in which all the ISELs occur evenly spaced. This ideal year can be a calendar common year of 365 days or 52 days or a calendar leap year of 366 days or 53 weeks or one may shorten the leap day or leap week and I do so to give the ideal year exactly the same length as the calendar mean year.

 

The Ideal year may be thought of as a projection of the calendar year onto the ISELs. Somewhat like a projection of a map of the globe onto a flat surface, but somewhat simpler, because only one dimension is involved.  For the examples we have considered, all the non-leap days are flat, but the leap day may slope, so appear shorter in the projection. It may be shortened to zero as Michael would do or to the fractional part of the mean year as I would. Also the projection is scaled to the 360 degree range of the ISELs.

 

Michael then considers defining two types of displacement, one for the minimum displacement calendar, which is constant within each DY and one using the 365-day ideal year. I don’t think this is necessary.

I believe these two displacements would be equal at one fixed time of the year. So one could use the 365-day ideal year displacement and then define the minimum displacement calendar by using only the displacement at that one time of year. One can then refer to this displacement as the displacement of the year and define it solely in terms of the displacements of other years. Note that the very idea of each date in a year having a displacement complicates the calendar definition and may be one reason Irv has rejected it.

 

I still don’t consider the 2.44 day Gregorian jitter range as any meaning, but might do if I can define it in terms of ISELs. I note the that Gregorian calendar has only one ISEL defined for it, which is the northward equinox and the exact date of this has not been specified.  So the fixing of this ISEL and the addition of other ISELs cannot be considered part of the Gregorian calendar, but something added to it.

 

Karl

 

16(05(27

 

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 23 January 2017 22:47
To: [hidden email]
Subject: Re: Displacement Calculation & RE: Jitter Calculation RE: ....

 

 

 

On Mon, Jan 23, 2017 at 8:15 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael in an earlier note said

I don't consider the leap-day to be part of the natural behavior of the relation of common and reference years. I regard the leap-day as something external to that naturally-operating system,...something added by us to compensate for that system's natural behavior.

I’m glad Michael has made this explicit. I explains why Michael takes the 365-day year as the ideal year.

 

The principle calendar year, as the best integer approximation to the desired average year.

I don’t take that view and don’t see anything natural about a 365-day year.

 

Sure, it's artificial, fictitious.

What I was referring to as natural was the interaction between the desired average year and the principle calendar year, the nearest approximation to the desired average year. For example, there's that .24217 day natural discrepancy between the principle calendar year and the mean tropical year..  ...natural only in the sense that it's the displacement between them that naturally results each year from the use of the 365-day principal calendar year. 

But sure, I recognize and admit that it could be looked at either way, and you could reasonably regard the common year and the leap-year as having equal status. It's just different ways of looking at it, and neither is wrong. But the common year is the one that's the nearest integer approximation to the desired average year.

Where this matter results in a more substantive difference of opinion is when the use of 365 days as the principle calendar year leads to 2.44 days as the alternative to 2.2 days, as the Gregorian Jitter-range.  ...by looking at the common-year's steady gain over the Gregorian average year, and not similarly comparing the rates of the leap-year and the Gregorian average year.

So you could say that I'm arbitrarily giving special status to the common year, in comparison to the leap-year. Your way of regarding the situation is more general and unbiased. The biased giving of preferential status to the common year indeed counts as an argument against 2.44 days as the Gregorian jitter-range.

 

I regard the leap day as an essential and integral part of the system and not something external to it. I see the ideal year to be the mean calendar year of either 365 days and a shortened leap day or 52 weeks and a shortened leap week. The length of each day in this ideal year is equal to the average time per year spent on this day. So the ideal year is really an average year.  

I never meant that 365 days is ideal. Just that I call it the principal calendar year. But I realize that arguably the 365 day year and the 366 day year could be regarded equally as parts of the system that approximates the desired average year, and therefore of equal status.

 

A calendar cannot use this ideal year as a calendar year, because the calendar year must have a whole number of days. So instead it uses years of 365 AND years of 366 days or for a leap week calendar 52 AND 53 weeks, both are essential even though one occurs more often than the other.

Sure, and that's the more general view that I referred to above, whose validity I don't deny.
 

Therefore I consider it a deviation from the ideal year occurs whenever a leap day/week is inserted or omitted. I think this ideal year minimises displacements, because the calculated displacements are defined relative to a contiguous sequence of these ideal years. Note that the dates I defined in this ideal year can serve as a substitute for solar ecliptic longitude, just like %completion.

Michael has said that if the mean year were about 365.9 days, he’d regard the 366-day year as the ideal year.

 

I'd say "the principal calendar year".
 

Anyway, I agree that the abruptly-varying displacement that's constant through a displacement-year (as opposed to the constantly-varying instantaneous displacment) is the one to use, for the various reasons I stated.

Maybe especially because it's the one by which D, in the Minimum-Displacement leapyear-rule is defined. So, if I were to speak of Minimum-Displacement's displacement in terms of the constantly-varying instantaneous displacement, I'd have to define two kinds of displacement when speaking of Minimum-Displacement--one in its definition, and a different one in its results-evaluation. I agree in preferring the displacement measure in which Minimum-Displacement keeps the displacement in the range of -3.5 days to +3.5 days.  ...the abruptly-varying displacement that's constant throughout each displacement year.

And if I want to compare the maximum displacements of Minimum-Displacement and the Gregorian leapyear-rule, then of course I have to measure them both by the same measure.  ...which means that 2.2 days is the Gregorian jitter-range, and 2.26 days is the Gregorian's maximum displacement during a 400-year cycle. (...as opposed to 2.44 & 2.5 days).

Michael Ossipoff

4 Monday

...by which I mean 2017W041.  But I realize that this is an international mailing-list, and that not everyone calls this day "Monday". I'd ordinarily only use "4 Monday" for local usage, within a same language-community.)

KARL REPLIES: Why not 4th Monday or Week 4, Monday?

 


1234