Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

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Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Karl Palmen

Dear Michael and Calendar People

 

Michael said (first quoting me):

Karl said:

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

[endquote]

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

I apologize for using a difficult word.

KARL REPLIES: Please explain how this applies to a calendar.

 

Karl

 

16(06(06

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 01 February 2017 23:24
To: [hidden email]
Subject: Re: Year-Round Accuracy RE: Displacement Calculation & RE: Jitter Calculation RE: ....

 

(Instead of deleting or moving the intervening text, it's easier to just copy & paste Karl's new text at the top of this post, and leaving the previously-intervening text at the bottom of the post.)

 

KARL REPLIES: The problem is that if one defines year-round accuracy (or any other kind of accuracy) by only comparing year lengths (such as calendar mean year (Y) and tropical year lengths), one is not going see what effect any change in the D is going to have on the accuracy.

 

...but it will show what effect it has on the D1 displacement, which is what Karl advocates as the measure of calendar-displacement. And, in a recent post, I told how a mismatch between reference-year and an SEL's tropical year would affect the difference between that SEL's date of occurrence and its DD.

 

Karl wants to complicate the problem by bringing in a kind of "accuracy" different from his advocated D1 measure of displacement. That's fair, because I invoked accuracy for particular SELs, when I spoke of a reference-year's mean accuracy around the ecliptic.

 

I told how a mismatch between the lengths of the reference-year and a particular SEL's tropical-year would affect accuracy as measured by the difference between that SEL's DD and its actual date of occurrence. I said it in a recent post, and I shouldn't have to repeat it.

 

 

Karl said:

 

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

 

[endquote

 

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

 

I apologize for using a difficult word.

 

Karl should feel free to tell me if there are other words that he has trouble with.

 

 

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Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Michael Ossipoff


On Thu, Feb 2, 2017 at 11:25 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael said (first quoting me):

Karl said:

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

[endquote]

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

I apologize for using a difficult word.

KARL REPLIES: Please explain how this applies to a calendar.


Sure, gladly:

Whether the common-year is 365 days or 364 days (or anything else), it must be an integer number of days. That's why we need leapyears.

As an example, let's use the Minimum-Displacement Calendar. Its reference year is the MTY, whose length (according to Wikipedia) is currently about 365.24217 mean solar days.

But the Minimum-Displacement Calendar's common year is only 364 days.

For that reason, because 364 is different from 365.24217, every year, the date corresponding to a particular SEL is going to be different from what it was in the previous year.

In the leapyear-rule of the Minimum-Displacement Calendar, this "displacement" is represented by the variable "D". 

At the end of each calendar-year, D changes by an amount equal to Y (That's the assumed length of the reference-year) minus the length of the year that has just ended.

Because Y is larger than 364, therefore D is increased, at the end of each common-year, by +.24217.

This keeps happening every year, until the time comes when, if done as described above, that increase would result in D being greater than 3.5   If that would happen at the end of that year, then the length of that year is increased by 7 days, to make the calendar's length 371 days. So, at that particular year-end, then, D is changed by an amount equal to 365.24217 minus 371. 

That means that, this time, D is being decreased. It's being decreased to a negative value whose absolute value is less than 3.5  

As I said, the purpose of all this is to keep the absolute value of D from exceeding 3.5

This periodic back and forth changing of D, from increasingly positive values, to a negative value is called an "oscillation"

But the short answer to your question about what is oscillating is: "The value of D is oscillating."

Michael Ossipoff



 

 

Karl

 

16(06(06

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 01 February 2017 23:24
To: [hidden email]
Subject: Re: Year-Round Accuracy RE: Displacement Calculation & RE: Jitter Calculation RE: ....

 

(Instead of deleting or moving the intervening text, it's easier to just copy & paste Karl's new text at the top of this post, and leaving the previously-intervening text at the bottom of the post.)

 

KARL REPLIES: The problem is that if one defines year-round accuracy (or any other kind of accuracy) by only comparing year lengths (such as calendar mean year (Y) and tropical year lengths), one is not going see what effect any change in the D is going to have on the accuracy.

 

...but it will show what effect it has on the D1 displacement, which is what Karl advocates as the measure of calendar-displacement. And, in a recent post, I told how a mismatch between reference-year and an SEL's tropical year would affect the difference between that SEL's date of occurrence and its DD.

 

Karl wants to complicate the problem by bringing in a kind of "accuracy" different from his advocated D1 measure of displacement. That's fair, because I invoked accuracy for particular SELs, when I spoke of a reference-year's mean accuracy around the ecliptic.

 

I told how a mismatch between the lengths of the reference-year and a particular SEL's tropical-year would affect accuracy as measured by the difference between that SEL's DD and its actual date of occurrence. I said it in a recent post, and I shouldn't have to repeat it.

 

 

Karl said:

 

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

 

[endquote

 

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

 

I apologize for using a difficult word.

 

Karl should feel free to tell me if there are other words that he has trouble with.

 

 


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Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Karl Palmen

Dear Michael

 

Thank you Michael for your reply, I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 02 February 2017 19:25
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

 

 

 

On Thu, Feb 2, 2017 at 11:25 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael said (first quoting me):

Karl said:

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

[endquote]

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

I apologize for using a difficult word.

KARL REPLIES: Please explain how this applies to a calendar.

 

Sure, gladly:

Whether the common-year is 365 days or 364 days (or anything else), it must be an integer number of days. That's why we need leapyears.

As an example, let's use the Minimum-Displacement Calendar. Its reference year is the MTY, whose length (according to Wikipedia) is currently about 365.24217 mean solar days.

But the Minimum-Displacement Calendar's common year is only 364 days.

For that reason, because 364 is different from 365.24217, every year, the date corresponding to a particular SEL is going to be different from what it was in the previous year.

In the leapyear-rule of the Minimum-Displacement Calendar, this "displacement" is represented by the variable "D". 

At the end of each calendar-year, D changes by an amount equal to Y (That's the assumed length of the reference-year) minus the length of the year that has just ended.

Because Y is larger than 364, therefore D is increased, at the end of each common-year, by +.24217.

KARL REPLIES: Doesn’t Michael mean 365.24217 – 364 = +1.24217 days?

This keeps happening every year, until the time comes when, if done as described above, that increase would result in D being greater than 3.5   If that would happen at the end of that year, then the length of that year is increased by 7 days, to make the calendar's length 371 days. So, at that particular year-end, then, D is changed by an amount equal to 365.24217 minus 371. 

That means that, this time, D is being decreased. It's being decreased to a negative value whose absolute value is less than 3.5  

As I said, the purpose of all this is to keep the absolute value of D from exceeding 3.5

 

KARL REPLIES: So this D is the calculated displacement used to determine the leap years and not any other kind of displacement.

 

This periodic back and forth changing of D, from increasingly positive values, to a negative value is called an "oscillation"

But the short answer to your question about what is oscillating is: "The value of D is oscillating."

KARL REPLIES: Then the Calendar’s Centre of Oscillation is simply 0.00000. Is this what Michael really means?

My guess is that the D here is not the displacement DC used to define the leap year rule, but a different displacement DR defined relative to the reference year, which slowly changes in length. His words hint at this. Then the centre of oscillation would vary and if it’s value were C, then the range of DR would be C-3.5 to C+3.5 days. This C is also simply equal to DR – DC. Subtracting DC removes the oscillation.  Is this guess correct?

Subtracting DC is a good trick, because it removes the oscillation caused by the calendar. Then it varies by just a few minutes, caused by the gravity of the other planets, rather than 7 days for a leap week calendar.

Karl

16(06(07

Michael Ossipoff

 

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Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Michael Ossipoff


On Fri, Feb 3, 2017 at 7:50 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael

 

Thank you Michael for your reply, I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 02 February 2017 19:25
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

 

 

 

On Thu, Feb 2, 2017 at 11:25 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael said (first quoting me):

Karl said:

 I don’t understand what Michael means by “the calendar’s centre of oscillation”

[endquote]

When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".

I apologize for using a difficult word.

KARL REPLIES: Please explain how this applies to a calendar.

 

Sure, gladly:

Whether the common-year is 365 days or 364 days (or anything else), it must be an integer number of days. That's why we need leapyears.

As an example, let's use the Minimum-Displacement Calendar. Its reference year is the MTY, whose length (according to Wikipedia) is currently about 365.24217 mean solar days.

But the Minimum-Displacement Calendar's common year is only 364 days.

For that reason, because 364 is different from 365.24217, every year, the date corresponding to a particular SEL is going to be different from what it was in the previous year.

In the leapyear-rule of the Minimum-Displacement Calendar, this "displacement" is represented by the variable "D". 

At the end of each calendar-year, D changes by an amount equal to Y (That's the assumed length of the reference-year) minus the length of the year that has just ended.

Because Y is larger than 364, therefore D is increased, at the end of each common-year, by +.24217.

KARL REPLIES: Doesn’t Michael mean 365.24217 – 364 = +1.24217 days?


Yes, of course. I left out the "1", out of Gregorian habit.
 

This keeps happening every year, until the time comes when, if done as described above, that increase would result in D being greater than 3.5   If that would happen at the end of that year, then the length of that year is increased by 7 days, to make the calendar's length 371 days. So, at that particular year-end, then, D is changed by an amount equal to 365.24217 minus 371. 

That means that, this time, D is being decreased. It's being decreased to a negative value whose absolute value is less than 3.5  

As I said, the purpose of all this is to keep the absolute value of D from exceeding 3.5

 

KARL REPLIES: So this D is the calculated displacement used to determine the leap years and not any other kind of displacement.


Yes and no. Yes, D is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined. But no, that isn't all it is.

It's also a very good approximation to the actual displacement, by the D1 measure of displacement, specified with respect to a the 0 value, from which Minimum-Displacement's 2017 is displaced by -.6288

 

This periodic back and forth changing of D, from increasingly positive values, to a negative value is called an "oscillation"

But the short answer to your question about what is oscillating is: "The value of D is oscillating."

KARL REPLIES: Then the Calendar’s Centre of Oscillation is simply 0.00000. Is this what Michael really means?

Yes. But something else can be said about that "0":

It's the D value from which the D value of Minimum-Displacement's 2017 differs by -.6288

That Dzero value of -.6288, and the "0" that it implies, was chosen for reasons that I've already stated.
 

My guess is that the D here is not the displacement DC used to define the leap year rule

Incorrect guess.

The variable "D" is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined.

I've clarified that many times, Karl.

but a different displacement DR defined relative to the reference year, which slowly changes in length.

D is defined in the way that I've always defined it, when stating the Minimum-Displacement leapyear-rule.

That rule gives an initial value for D, referred to as "Dzero". Dzero =  -.6288

That rule tells how D changes at the end of each calendar year, as follows:

At the end of each calendar year, the value of D changes by an amount equal to Y minus the length of that calendar year.

It shouldn't be necessary to re-state that for you, Karl.

Yes, y is mentioned in defining D. But Y is a constant, the assumed value of the reference year, the MTY.


 

His words hint at this. Then the centre of oscillation would vary and if it’s value were C, then the range of DR would be C-3.5 to C+3.5 days. This C is also simply equal to DR – DC. Subtracting DC removes the oscillation.  Is this guess correct?


I don't know what Karl's other variable-names mean, but that's ok.

As the length of the MTY, in mean solar days, slowly changes, so that it differs slightly from Y, then the completion-percentage of the MTY, at the times of the extreme and middle points of D's variation, will change as well.

 In that sense, the calendar's "center of oscillation" drifts, with respect to the completion-percentage of the MTY. 

Yes, when I discussed the choice of the MTY, because I wanted to minimize the average difference between y and the lengths of the tropical years defined around the ecliptic, and when I spoke of how that reduces the average "drift of the centers of oscillation for the calendar with respect to various particular points of the ecliptic", the meaning of the words in quotes differ from the above in at least 2 ways:

1. I was talking about "displacement" for particular ecliptic longitudes, which admittedly isn't what D1 is about.

2. I was referring to displacement defined directly with respect to the ecliptic itself, rather than with respect to the completion-percentage of a reference-year.

I was doing so, even though it has nothing to do with the D1 measure of calendar-displacement that we agrees on.   ...just as an added benefit of a choice of reference-year.   ...not because I claim that it's relevant to D1 or to comparing the accuracy of different calendars.

Michael Ossipoff




 


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Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Karl Palmen
Dear Michael and Calendar People

I'm utterly confused by Michael's reply. Does any other calendar person understand?

Michael's seems to be referring to at least 2 different types displacement but won't say which one when.

Without further clarification, I'll not be able to continue this discussion.

Karl

16(06(11 till noon
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Michael Ossipoff [[hidden email]]
Sent: 03 February 2017 22:35
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....



On Fri, Feb 3, 2017 at 7:50 AM, Karl Palmen <[hidden email]<mailto:[hidden email]>> wrote:
Dear Michael

Thank you Michael for your reply, I reply below.

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]>] On Behalf Of Michael Ossipoff
Sent: 02 February 2017 19:25
To: [hidden email]<mailto:[hidden email]>
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....



On Thu, Feb 2, 2017 at 11:25 AM, Karl Palmen <[hidden email]<mailto:[hidden email]>> wrote:
Dear Michael and Calendar People

Michael said (first quoting me):
Karl said:
 I don’t understand what Michael means by “the calendar’s centre of oscillation”
[endquote]
When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".
I apologize for using a difficult word.
KARL REPLIES: Please explain how this applies to a calendar.

Sure, gladly:
Whether the common-year is 365 days or 364 days (or anything else), it must be an integer number of days. That's why we need leapyears.
As an example, let's use the Minimum-Displacement Calendar. Its reference year is the MTY, whose length (according to Wikipedia) is currently about 365.24217 mean solar days.
But the Minimum-Displacement Calendar's common year is only 364 days.
For that reason, because 364 is different from 365.24217, every year, the date corresponding to a particular SEL is going to be different from what it was in the previous year.
In the leapyear-rule of the Minimum-Displacement Calendar, this "displacement" is represented by the variable "D".
At the end of each calendar-year, D changes by an amount equal to Y (That's the assumed length of the reference-year) minus the length of the year that has just ended.
Because Y is larger than 364, therefore D is increased, at the end of each common-year, by +.24217.
KARL REPLIES: Doesn’t Michael mean 365.24217 – 364 = +1.24217 days?

Yes, of course. I left out the "1", out of Gregorian habit.

This keeps happening every year, until the time comes when, if done as described above, that increase would result in D being greater than 3.5   If that would happen at the end of that year, then the length of that year is increased by 7 days, to make the calendar's length 371 days. So, at that particular year-end, then, D is changed by an amount equal to 365.24217 minus 371.
That means that, this time, D is being decreased. It's being decreased to a negative value whose absolute value is less than 3.5
As I said, the purpose of all this is to keep the absolute value of D from exceeding 3.5

KARL REPLIES: So this D is the calculated displacement used to determine the leap years and not any other kind of displacement.

Yes and no. Yes, D is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined. But no, that isn't all it is.

It's also a very good approximation to the actual displacement, by the D1 measure of displacement, specified with respect to a the 0 value, from which Minimum-Displacement's 2017 is displaced by -.6288

This periodic back and forth changing of D, from increasingly positive values, to a negative value is called an "oscillation"
But the short answer to your question about what is oscillating is: "The value of D is oscillating."
KARL REPLIES: Then the Calendar’s Centre of Oscillation is simply 0.00000. Is this what Michael really means?
Yes. But something else can be said about that "0":

It's the D value from which the D value of Minimum-Displacement's 2017 differs by -.6288

That Dzero value of -.6288, and the "0" that it implies, was chosen for reasons that I've already stated.

My guess is that the D here is not the displacement DC used to define the leap year rule
Incorrect guess.

The variable "D" is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined.

I've clarified that many times, Karl.

but a different displacement DR defined relative to the reference year, which slowly changes in length.

D is defined in the way that I've always defined it, when stating the Minimum-Displacement leapyear-rule.

That rule gives an initial value for D, referred to as "Dzero". Dzero =  -.6288

That rule tells how D changes at the end of each calendar year, as follows:

At the end of each calendar year, the value of D changes by an amount equal to Y minus the length of that calendar year.

It shouldn't be necessary to re-state that for you, Karl.

Yes, y is mentioned in defining D. But Y is a constant, the assumed value of the reference year, the MTY.



His words hint at this. Then the centre of oscillation would vary and if it’s value were C, then the range of DR would be C-3.5 to C+3.5 days. This C is also simply equal to DR – DC. Subtracting DC removes the oscillation.  Is this guess correct?

I don't know what Karl's other variable-names mean, but that's ok.

As the length of the MTY, in mean solar days, slowly changes, so that it differs slightly from Y, then the completion-percentage of the MTY, at the times of the extreme and middle points of D's variation, will change as well.

 In that sense, the calendar's "center of oscillation" drifts, with respect to the completion-percentage of the MTY.

Yes, when I discussed the choice of the MTY, because I wanted to minimize the average difference between y and the lengths of the tropical years defined around the ecliptic, and when I spoke of how that reduces the average "drift of the centers of oscillation for the calendar with respect to various particular points of the ecliptic", the meaning of the words in quotes differ from the above in at least 2 ways:

1. I was talking about "displacement" for particular ecliptic longitudes, which admittedly isn't what D1 is about.

2. I was referring to displacement defined directly with respect to the ecliptic itself, rather than with respect to the completion-percentage of a reference-year.

I was doing so, even though it has nothing to do with the D1 measure of calendar-displacement that we agrees on.   ...just as an added benefit of a choice of reference-year.   ...not because I claim that it's relevant to D1 or to comparing the accuracy of different calendars.

Michael Ossipoff
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Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....

Michael Ossipoff


On Wed, Feb 8, 2017 at 4:26 AM, Karl Palmen <[hidden email]> wrote:
Dear Michael and Calendar People

I'm utterly confused by Michael's reply. Does any other calendar person understand?

Michael's seems to be referring to at least 2 different types displacement but won't say which one when.

Karl forgot to share with us an instance in which I neglected to say what kind of displacement I was referring to.

But that vagueness of Karls is typical. In fact it's so consistent that it can be regarded as a habitual tactic.

I've defined and spoken of two measures of displacement: D1 I& D2. I've stated their definitions so many times, that I'm not willing to do so again.

I've clarified the following:

In principle, displacement is a difference or change in the date at which a particular SEL occurs.

 But, in practice, when displacement is reckoned, the percent-completion of a reference-year usually stands in for ecliptic longitude. (That reference-year should of course be stated.)

For example,when I stated the D1 & D2 values (2.26 & 2.5) for the maximum displacement of the Gregorian Calendar during a 400 year cycle, it was reckoned with respect to the MTY.   ...and yes, I did say so.

When we spoke of Gregorian jitter-range, it was understood to be with respect to the Gregorian mean-year of 365.25 days.

When I spoke of the choice of a value for Y, for the Minimum-Displacement Calendar, and said that I chose the MTY for an overall reduction in the drift of the centers of oscillation of the dates of the SELs, I clarified that, for a particular jSEL, the oscillation I was referring to was the oscillation, from one leapyear to the next, of that SEL's calendar-date.

I couldn't have said it any more explicitly.

If Karl nevertheless has a problem with it, then he's welcome to say which part of it he doesn't understand.

But if Karl is going to discontinue his vague, unspecified complaints, that would be a welcome improvement. Thank you, Karl.

Michael Ossipoff

 (This post doesn't reply to any text below this point. I don't have a way to delete the large amount of text that Karl has included.)



 
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Michael Ossipoff [[hidden email]]
Sent: 03 February 2017 22:35
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....



On Fri, Feb 3, 2017 at 7:50 AM, Karl Palmen <[hidden email]<mailto:[hidden email]>> wrote:
Dear Michael

Thank you Michael for your reply, I reply below.

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]>] On Behalf Of Michael Ossipoff
Sent: 02 February 2017 19:25
To: [hidden email]<mailto:[hidden email]>
Subject: Re: Calendar's Centre Of Oscillation RE: Year-Round Accuracy RE: ....



On Thu, Feb 2, 2017 at 11:25 AM, Karl Palmen <[hidden email]<mailto:[hidden email]>> wrote:
Dear Michael and Calendar People

Michael said (first quoting me):
Karl said:
 I don’t understand what Michael means by “the calendar’s centre of oscillation”
[endquote]
When something moves back and forth, or in some way changes back and forth, we sometimes say that it "oscillates".  The middle of its range of oscillation can be called its "center of oscillation".
I apologize for using a difficult word.
KARL REPLIES: Please explain how this applies to a calendar.

Sure, gladly:
Whether the common-year is 365 days or 364 days (or anything else), it must be an integer number of days. That's why we need leapyears.
As an example, let's use the Minimum-Displacement Calendar. Its reference year is the MTY, whose length (according to Wikipedia) is currently about 365.24217 mean solar days.
But the Minimum-Displacement Calendar's common year is only 364 days.
For that reason, because 364 is different from 365.24217, every year, the date corresponding to a particular SEL is going to be different from what it was in the previous year.
In the leapyear-rule of the Minimum-Displacement Calendar, this "displacement" is represented by the variable "D".
At the end of each calendar-year, D changes by an amount equal to Y (That's the assumed length of the reference-year) minus the length of the year that has just ended.
Because Y is larger than 364, therefore D is increased, at the end of each common-year, by +.24217.
KARL REPLIES: Doesn’t Michael mean 365.24217 – 364 = +1.24217 days?

Yes, of course. I left out the "1", out of Gregorian habit.

This keeps happening every year, until the time comes when, if done as described above, that increase would result in D being greater than 3.5   If that would happen at the end of that year, then the length of that year is increased by 7 days, to make the calendar's length 371 days. So, at that particular year-end, then, D is changed by an amount equal to 365.24217 minus 371.
That means that, this time, D is being decreased. It's being decreased to a negative value whose absolute value is less than 3.5
As I said, the purpose of all this is to keep the absolute value of D from exceeding 3.5

KARL REPLIES: So this D is the calculated displacement used to determine the leap years and not any other kind of displacement.

Yes and no. Yes, D is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined. But no, that isn't all it is.

It's also a very good approximation to the actual displacement, by the D1 measure of displacement, specified with respect to a the 0 value, from which Minimum-Displacement's 2017 is displaced by -.6288

This periodic back and forth changing of D, from increasingly positive values, to a negative value is called an "oscillation"
But the short answer to your question about what is oscillating is: "The value of D is oscillating."
KARL REPLIES: Then the Calendar’s Centre of Oscillation is simply 0.00000. Is this what Michael really means?
Yes. But something else can be said about that "0":

It's the D value from which the D value of Minimum-Displacement's 2017 differs by -.6288

That Dzero value of -.6288, and the "0" that it implies, was chosen for reasons that I've already stated.

My guess is that the D here is not the displacement DC used to define the leap year rule
Incorrect guess.

The variable "D" is the calculated displacement by which the Minimum-Displacement leapyear-rule is defined.

I've clarified that many times, Karl.

but a different displacement DR defined relative to the reference year, which slowly changes in length.

D is defined in the way that I've always defined it, when stating the Minimum-Displacement leapyear-rule.

That rule gives an initial value for D, referred to as "Dzero". Dzero =  -.6288

That rule tells how D changes at the end of each calendar year, as follows:

At the end of each calendar year, the value of D changes by an amount equal to Y minus the length of that calendar year.

It shouldn't be necessary to re-state that for you, Karl.

Yes, y is mentioned in defining D. But Y is a constant, the assumed value of the reference year, the MTY.



His words hint at this. Then the centre of oscillation would vary and if it’s value were C, then the range of DR would be C-3.5 to C+3.5 days. This C is also simply equal to DR – DC. Subtracting DC removes the oscillation.  Is this guess correct?

I don't know what Karl's other variable-names mean, but that's ok.

As the length of the MTY, in mean solar days, slowly changes, so that it differs slightly from Y, then the completion-percentage of the MTY, at the times of the extreme and middle points of D's variation, will change as well.

 In that sense, the calendar's "center of oscillation" drifts, with respect to the completion-percentage of the MTY.

Yes, when I discussed the choice of the MTY, because I wanted to minimize the average difference between y and the lengths of the tropical years defined around the ecliptic, and when I spoke of how that reduces the average "drift of the centers of oscillation for the calendar with respect to various particular points of the ecliptic", the meaning of the words in quotes differ from the above in at least 2 ways:

1. I was talking about "displacement" for particular ecliptic longitudes, which admittedly isn't what D1 is about.

2. I was referring to displacement defined directly with respect to the ecliptic itself, rather than with respect to the completion-percentage of a reference-year.

I was doing so, even though it has nothing to do with the D1 measure of calendar-displacement that we agrees on.   ...just as an added benefit of a choice of reference-year.   ...not because I claim that it's relevant to D1 or to comparing the accuracy of different calendars.

Michael Ossipoff

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