Joining list. Calendar reforms.

[MIKE OSSIPOFF]

(I wanted to post this yesterday, Sunday, but I didn't get a chance to do e-mail yesterday)
 
After I left the computer on Saturday, I realized that the two leapyear rules that I'd posted, "4-or-5" and "First-Low", don't minimize the drift. They only minimize what the drift will be after the next leapyer, which isn't the same thing. The rule that I state in the next paragraphs minimizes the drift and is the leapyear rule that I suggest. I'm not changing the determination of "d", the initial drift expressed in days. I'm only changing the subsequent determination of which years will be leapyears.
 
Minimum Drift leapyear rule:
 
A year is a leapyear if, for that year's d, abs(d-5.75781) < abs(d+1.24219)
 
After the end of a year that isn't a leapyear, add 1.24219 to d. After the end of a leapyear, subtract 5.75781 from d.
 
[end of Minimum Drift leapyear rule definition]
 
Minimum Drift is my only leapyear rule suggestion.
 
I don't claim that I'm the first to mention this obvious leapyear rule.
 
In fact, surely someone has pointed out my error with the two leapyear procedures I posted on Saturday. And it's a sure thing that someone has already posted, since Saturday, the obvious leapyear rule described above in this posting.
 
Of course I'm going to re-post "Vol.1, fixed Subjective Seasonal", with "Minimum Drift", instead of "4-or-5" and "First-Low". I'll also fix a typo or two. That will be my final posting of "Vol.I, fixed Subjective Seasonal".
 
Because the sun's speed along the ecliptic isn't exactly the same from day to day, of course I don't claim that Minimum Drift _perfectly_ minimizes drift measured in degrees along the ecliptic. Its accuracy could be very slightly further improved, at great cost in complexity. Minimum Drift is more than accurate enough for practical purposes.
 
Minimum Drift's natural and obvious simplicity is unmatched.
 
Some might complain about the fact that I've offered several alternative ways of doing some things. As I said, I believe that a proposal, at this stage, should be open, flexible and broad. But if there's complaint about too many choices, then let me say which choices I call my main fixed proposal:
 
Initial Date Alignment:
 
I would use Centered Initial Date Alignment. Matched Initial Date alignment could shorten the time till the first leapyear. Because the calendar only tries to keep NorthI/1 as close as possible to the middle of the designated lyc, and doesn't claim that NorthI/1 will always be on June 1, I feel that Centered Initial Date Alignment better demonstates that goal from the start.
 
Choice of designated lyc:
 
I'd use current lyc. (The lyc containing the first year of the new calendar's use). It gives the best accuracy. If 2004-2008 is designated, and the reform is being considered in 2050, the proposal will look out-of-date. And even though the .7 day error possible towards the end of this century isn't serious, it would be better to not have so much avoidable error.
 
Months:
 
I'd use Mike Months, for simplicity, and so that the month containing the important Christmas holiday and the northern hemisphere's winter solstice would be a long month.
 
Mike Ossipoff
 
 
 
 
 
 
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[MIKE OSSIPOFF]

 
Mark--
 
I'd said:
 
>> Because, in the perceptions of everyone in the north and south temperate regions, summer arrives with June and lasts into September.

You replied:

> You keep making unsupportably broad assertions.
>
> Even assuming you mean only the north temperate regions, since June is
> winter in the south temperate zone, it's clear that not "everyone"
> perceives things that way, or there would not have been a long thread
> in which nearly "everyone" on the list disagreed with your statement.
> :)
 
I reply:
 
Two or three people have disagreed, apparently on "general principle" rather for some stated reason.
 
Yes, I was referring, in that sentence, to the north temperate region. In Australia, it's been said that summer arrives with December.
 

> There are various different ideas of when summer starts and ends, but
> I can't find any definition that makes it 17 weeks long.
 
I reply:
 
17 weeks is a good approximation to the 117 or 118 days that I determined for North, based on the widespread perception that northern-hemisphere summer arrives with June, and based on the 1.25 midpoint of the usual ranage of variation of the seasonal timelag in the temperate regions. The resulting end of northern summer near the end of September is also in accord with opinions that I've heard.
 
You continued:
 
At most 15,
> usually 13-14.
 
I reply:
 
Unlike me, you give no hint about where you got those figures.
 
You continued:
 
I can see making summer and winter longer than spring
> and autumn rather than equal quarters, but a factor of two difference
> in length seems excessive.
 
I reply:
 
How so? Are most people, who, when stating their own perceptions, say that northern summer arrives with June or that southern summer arrives with December, so unreasonable? Did it seem to you, this year, that it wasn't summer until June 21? As I said, the June 1 starting date and the 1.25 month usual midrange timelag imply a northern summer of 117 or 118 days. I don't know what you want to base a definition of summer on, if it's something different from widespread perceptions.
 
The north and south declinations that (about 1.25 months later) lead people to say it's summer are very nearly the high half of the solar declination's north and south ranges. As I mentioned before, if the Earth's orbit were circular, sin(abs(dec)) would be in the top half of its range for periods exactly twice the length of the transitionary periods between those high-declination periods.
 
Why? For one thing, the declination changes quite a bit more slowly when in the high part of its north or south range. That's where the term "solstice" comes from. It refers to the sun's declination having zero rate of change when at its north or south maximum. Additionally, during the high-declination periods, the declination must go out and back, retracing and reversing its movement. For both of those reasons, it's hardly surprising that the solar declination spends about twice as much time in the top half of its north and south range as in the intermediate periods, and that the corresponding perceived terrestrial seasons are correspondingly long.
 
Mike ossipoff
 
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[MIKE OSSIPOFF]

 
Mark--
 
You said:

> So what about the centennial 8-year gaps between leap years?

I was assuming that we won't begin using a new calendar during such a period. But let me specify a rule for if we do: When beginning the use of the new fixed calendar other than during a 4-year Gregorian lyc, then "Current lyc" specifies that the preceding 4-year Gregorian lyc shall be the designated lyc.
 
You continued:
 
> You're using the scare-quotes around "Gregorian" again. Could you
> please not do so? It's distracting and inappropriate.
 
1. If the quotes bother you, then sure, I'll adopt the conventional language and will misleadingly and incorrectly call our current calendar the Gregorian Calendar even though Gregorius had nothing to do with its month system. So I'll copy that conventional language.
 
2. Yes, the quotes are probably distracting.
 
3. No, the quotes are not inappropriate. What's inappropriate is calling our current calendar the Gregorian Calendar when Gregorius's only role was in its leapyear system.
 
You continued:

>
>> Two ways to determine the relionship of NorthI/1 to June 1 in the first year:
>
> "NorthI"?

I reply:
 
Yes, I'd previously said several times that I would divide each calendar season into months named for their place in that season. So North would contain NorthI, NorthII, NorthIII, and NorthIV.
 
I'd said:
 
 
>
>> Have a leapyear when necessary, to minimize the distance of the position of NorthI/1 from the middle of the designated lyc.

[the Minumum Drift leapyear rule that I posted today accomplishes that goal very well]
 
You replied:
 
>
> Given the wobble inherent in a leap-week-based calendar, it might be
> overkill to have a precise astronomical rule for when to insert the
> leap week. A simple arithmetic rule would be a better fit.
 
I reply:
 
Not more accurate. But I agree that great accuracy isn't essential. That's one reason why I only mention Minimum Drift as a suggestion, not as a stipulation. But Minimum Drift is also the simplest, most obvious and natural leapyear rule for leapweeks.
 
You continued:
 
There> have been several proposals for such; none of them is quite as
> straightforward as the Gregorian system, given the need to alternate
> between 5- and 6-year gaps fairly frequently.
 
I reply:
 
Yes, and does any of them even come close to the natural and obvious simplicity of Minimum Drift?
 
But yes, especially because no leapweek rule can be as simple as when, till the end of each century, every year divisible by 4 is a leapyear, a fixed calendar has a complexity disadvantage. That's why a nonfixed calendar reform proposal may very well be more winnable.
 
 
Mike Ossipoff
 
 
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[Irv Bromberg]

On 2009 Jun 29, at 10:39 , MIKE OSSIPOFF wrote:

Minimum Drift leapyear rule:
A year is a leapyear if, for that year's d, abs(d-5.75781) < abs(d+1.24219)
After the end of a year that isn't a leapyear, add 1.24219 to d. After the end of a leapyear, subtract 5.75781 from d.

Dear Mike and Calendarists:

Where are the above-quoted numbers coming from?  Is this still intended to parallel the Gregorian mean year?

On the one hand Mike seems to want his calendar to have a summer seasonal alignment (for northern temperate regions), which implies an approximation to the mean north solstitial year (an excellent choice for the present era, because of its very long-term stability >10 millennia), but on the other hand he keep falling back onto a fixed relationship in parallel to the Gregorian leap cycle.  These are incompatible, because the Gregorian mean year is 365 days 5 hours 49 minutes 12 seconds whereas presently the mean north solstitial year is about 365 days 5 hours 47 minutes 56 seconds, a difference of 1 minute 16 seconds per year, which will accordingly cause his calendar to drift relative to the solstice.

A 389-year leap cycle with either 94 leap days or 69 leap weeks would have a much more accurate mean year of 365d 5h 47m 58+58/389s, and will also be an excellent choice for at least the next 10 millennia, because the mean north solstitial year will get slightly longer over the coming millennia, and then will return to its present slightly shorter mean year.  See:

http://individual.utoronto.ca/kalendis/leap/index.htm#ns

http://individual.utoronto.ca/kalendis/leap/Solar_Year_Range.pdf

Therefore, I urge Mike to let go of the Gregorian leap rule.  To minimize solstice wobble, I also suggest spreading out the leap year intervals as smoothly as possible, and why not make the distribution of leap years symmetrical while you're at it, because of the astronomical / calendrical design advantages that that will afford?  See:

http://individual.utoronto.ca/kalendis/leap/index.htm#slc

-- Irv Bromberg, Toronto, Canada

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

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

[MIKE OSSIPOFF]

             <677CE4DD24B12C4B9FA138534E29FB1D06781EFA@...>
                        <BLU134-W134A28713230F738DC8929CF340@...>
             A<f60fe000906251843k6988190k2acd50fa22d685e@...>
 <677CE4DD24B12C4B9FA138534E29FB1D06782052@...>
Content-Type: text/plain; charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
MIME-Version: 1.0
X-OriginalArrivalTime: 29 Jun 2009 15:55:30.0782 (UTC) FILETIME=[076797E0:01C9F8D2]


=20
=20
Karl wrote:

>
> No Mark=2C I've been receiving plenty of messages from Mike that are muck=
ed up.
>
> I think Mike needs to reconfigure his E-mailer to make it compatible with=
 CALNDR-L or use a different format for his E-mails (e.g. plain text or HTM=
L).
=20
I reply:
=20
Sorry--I didn't know about the problem till now. I do try to remember to us=
e plaintext=2C because they say that it's compatible everywhere. Hopefully =
if I make sure to use plaintext there won't be a problem.
=20
Mike Ossipoff
=20
=20

>
> I deliberately sent an E-mail in plain text to attempt to avoid this prob=
lem=2C but it hasn't worked.
>
> Karl
>
> 10(10(03 till noon
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List [mailto:CALNDR-L@=
LISTSERV.ECU.EDU] On Behalf Of Mark J. Reed

> Sent: 26 June 2009 02:44
> To: CALNDR-L@...
> Subject: Re: June-September season
>
> Am I the only one getting messages where the mailing list reflector
> seems to have decided to cut off the headers and start treating them
> as body text? It always seems to be Mike's messages=2C and they're
> very hard to read this way...
>
> On Thu=2C Jun 25=2C 2009 at 7:29 PM=2C MIKE OSSIPOFF wrote:
>>=20
>>=20
>>=20
>>=20
>> A
>>=20
>> Content-Type: text/plain=3B charset=3D"Windows-1252"
>> Content-Transfer-Encoding: quoted-printable
>> MIME-Version: 1.0
>> X-OriginalArrivalTime: 25 Jun 2009 23:29:33.0135 (UTC) FILETIME=3D[CB75C=

5F0:01C9F5EC]
>>
=20
I don't know why it's saying I wrote that.






Mike continues to take this attitude
>> =3D20
>> I reply:

I have no idea where "=3D20" is coming from. I hope it won't do that if I m=
ake sure to always use plaintext.
=20
Mike Ossipoff
=20
=20
_________________________________________________________________
Hotmail=AE has ever-growing storage! Don=92t worry about storage limits.=20
http://windowslive.com/Tutorial/Hotmail/Storage?ocid=3DTXT_TAGLM_WL_HM_Tuto=
rial_Storage_062009=

[Karl Palmen]

Dear Mike and Calendar People

This E-mail is an example. Please read other notes on this topic before
replying.

Karl

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
Sent: 29 June 2009 16:56
To: CALNDR-L@...
Subject: Re: Some of Mike's Messages are Mucked Up RE: June-September
season


 
<677CE4DD24B12C4B9FA138534E29FB1D06781EFA@...>
                        <BLU134-W134A28713230F738DC8929CF340@...>
             A<f60fe000906251843k6988190k2acd50fa22d685e@...>

 <677CE4DD24B12C4B9FA138534E29FB1D06782052@...>
Content-Type: text/plain; charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
MIME-Version: 1.0
X-OriginalArrivalTime: 29 Jun 2009 15:55:30.0782 (UTC)
FILETIME=[076797E0:01C9F8D2]


=20
=20
Karl wrote:

>
> No Mark=2C I've been receiving plenty of messages from Mike that are
muck=
ed up.
>
> I think Mike needs to reconfigure his E-mailer to make it compatible
with=
 CALNDR-L or use a different format for his E-mails (e.g. plain text or
HTM=
L).
=20
I reply:
=20
Sorry--I didn't know about the problem till now. I do try to remember to
us=
e plaintext=2C because they say that it's compatible everywhere.
Hopefully =
if I make sure to use plaintext there won't be a problem.
=20
Mike Ossipoff
=20
=20

>
> I deliberately sent an E-mail in plain text to attempt to avoid this
prob=
lem=2C but it hasn't worked.
>
> Karl
>
> 10(10(03 till noon
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@=
LISTSERV.ECU.EDU] On Behalf Of Mark J. Reed

> Sent: 26 June 2009 02:44
> To: CALNDR-L@...
> Subject: Re: June-September season
>
> Am I the only one getting messages where the mailing list reflector
> seems to have decided to cut off the headers and start treating them
> as body text? It always seems to be Mike's messages=2C and they're
> very hard to read this way...
>
> On Thu=2C Jun 25=2C 2009 at 7:29 PM=2C MIKE OSSIPOFF wrote:
>>=20
>>=20
>>=20
>>=20
>> A
>>=20
>> Content-Type: text/plain=3B charset=3D"Windows-1252"
>> Content-Transfer-Encoding: quoted-printable
>> MIME-Version: 1.0
>> X-OriginalArrivalTime: 25 Jun 2009 23:29:33.0135 (UTC)

FILETIME=3D[CB75C=
5F0:01C9F5EC]
>>
=20
I don't know why it's saying I wrote that.






Mike continues to take this attitude
>> =3D20
>> I reply:

I have no idea where "=3D20" is coming from. I hope it won't do that if
I m=
ake sure to always use plaintext.
=20
Mike Ossipoff
=20
=20
_________________________________________________________________
Hotmail=AE has ever-growing storage! Don=92t worry about storage
limits.=20
http://windowslive.com/Tutorial/Hotmail/Storage?ocid=3DTXT_TAGLM_WL_HM_T
uto=
rial_Storage_062009=

--
Scanned by iCritical.

[MIKE OSSIPOFF]

 
Christopher VAnce wrote:
 
> Summer starts in December and lasts until February.
> It's winter that starts in June, and it only lasts until August.
>
> By definition I am part of 'everyone' and am therefore a counter example.
>
> -- Christopher

I reply:
 
Thank you, Christopher, for confirming that, in the southern hemisphere, summer arrives with December.
 
As for summer ending in February, are you sure that you aren't just basing that on the assumption of four equal seasons?
 
For summer to begin with December, and end when February ends, implies a seasonal timelag much shorter than that which I found average for Australia in the worldwide temperature records book. The Australian temperature records in the book indicated that, in Australia, the seasonal timelag varies between .75 and 1.75, as is typical in the north and south temperate zones. A summer lasting from December 1 to February 28, when its timelag is calculated from the amount by which its middle lags behind the summer solstice there, implies a seasonal timelag of only about .79 months, near the very low end of the range of variation in Australia.
 
Using the 1.25 month usual midrange, that, according to the worldwide record-book, as valid in Australia as anywhere else, you get a summer that, when beginning on December 1, lasts into the last few days of March.
 
Mike Ossipoff
 
 
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[Irv Bromberg]

On 2009 Jun 29, at 10:39 , MIKE OSSIPOFF wrote:

Minimum Drift leapyear rule:
A year is a leapyear if, for that year's d, abs(d-5.75781) < abs(d+1.24219)
After the end of a year that isn't a leapyear, add 1.24219 to d. After the end of a leapyear, subtract 5.75781 from d.

Irv replies:  The above is not a stand-alone leap rule, it is a serial one.  The only way to know if a year is a leap year or not, following the above instructions, is to serially check every year from the epoch to the target year, to find out the cumulative value of d.  Instead, a properly leap rule should allow direct stand-alone calculation of the leap status of any year.  That is not to say that the leap rule can't use an accumulator, but the expression involving the accumulator has to allow direct evaluation, preferably in one step.  Examples follow below.

On 2009 Jun 29, at 11:27 , MIKE OSSIPOFF wrote:

But yes, especially because no leapweek rule can be as simple as when, till the end of each century, every year divisible by 4 is a leapyear, a fixed calendar has a complexity disadvantage. That's why a nonfixed calendar reform proposal may very well be more winnable.

Irv replies:  The direct expression for the Gregorian leap rule is more complex than a properly implemented smoothly spread leap rule:

Boolean isGregorianLeapYear(Year)

    // return True if Year is a leap year on the Gregorian calendar

    If modulus(Year, 100) = 0 Then

        // century year is leap year only if year is divisible by 400

        return modulus(Year, 400) = 0

    Else

        // non-century year is leap if year is divisible by 4

        return modulus(Year, 4) = 0

    End If

End Function

Compare with the much simpler single-step direct function for a symmetrical, smoothly spread leap rule (this can work for a leap day or leap week calendar, provided appropriate coefficients are used (C=years per cycle, L=leap years per cycle, K=any constant but I recommend the one that gives a symmetrical distribution of leap year intervals for the given number of years per cycle, as explained in my discussion about that, linked to in my previous message):

Boolean isLeapYear(Year)

    // return True if Year is a leap year, based on accumulator

     return modulus( L * Year + K, C ) < L

        

End Function

As the above function definitions show, the smoothly spread leap rule is a single step expression, whereas the Gregorian leap rule has two steps plus an IF...THEN...ELSE branch.

Although the Gregorian leap rule may seem more familiar, very few people "on the street" actually know the details of the leap rule (even though we are <10 years past the "Y2K" crisis), and it is flatly incorrect to describe it as simpler than smoothly spread alternatives that offer the advantages of reduced equinox or solstice wobble, reduced long-term astronomical drift, and, with appropriate choice of K, a symmetrical distribution of leap years.  Making a leap week calendar that parallels the Gregorian leap rule is even more complicated, and for most people there is essentially no hope of carrying out such a calculation in their head, even if they know the steps to execute.

For a 389-year leap cycle (an excellent approximation to the mean north solstitial year), L=94 for leap day or L=69 for leap week, and for symmetrical arrangement of leap years K=(389-1)/2=194.  Choose your desired solstice-relative alignment in year 1 of a near-present era calendar cycle (such as year 1168, 1557, or 1946, all of which are the first year of a 389-year cycle), and the symmetry of the leap year distribution will ensure that that mean alignment will be preserved to very good approximation for the next 10-11 millennia.

-- Irv Bromberg, Toronto, Canada

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

[Mark J. Reed]

On Mon, Jun 29, 2009 at 11:27 AM, MIKE OSSIPOFF<nkklrp@...> wrote:
>> You're using the scare-quotes around "Gregorian" again. Could you
>> please not do so? It's distracting and inappropriate.
>
> 1. If the quotes bother you, then sure, I'll adopt the conventional language and will misleadingly and incorrectly call our current calendar the Gregorian Calendar even though Gregorius had nothing to do with its month system. So I'll copy that conventional language.
> 3. No, the quotes are not inappropriate. What's inappropriate is calling our current calendar the Gregorian Calendar when Gregorius's only role was in its leapyear system.

Oy.  That is exactly the sort of superior, "the whole world is wrong
and I'm right" attitude that puts people off of reform efforts.

The conventional language is not incorrect.  The calendar we use is
called the Gregorian calendar because it was decreed by Pope Gregory.
Yes, the only aspect of it that differs from the Julian calendar for
everyday use is the leap year rule (although that's ignoring the very
significant change to the Easter calculation), but that's enough.  If
you change any detail in a calendar's definition, you have created a
new calendar.

If we were to adopt Herschel's proposed change that makes every 4000th
year common (in order to bring the mean year closer to the "mean of
mean tropical years" value), while leaving every other detail of the
Gregorian calendar the same, that would no longer be the Gregorian
calendar. We could call it the Herschelian.

Incidentally, the name of the various Popes Gregory is written
"Gregory" in English text, including in official Church documents in
that language.  It's only "Gregorius" when writing in Latin.

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

[Mark J. Reed]

On Mon, Jun 29, 2009 at 12:09 PM, Irv Bromberg<irv.bromberg@...> wrote:
> Irv replies:  The direct expression for the Gregorian leap rule is more
> complex than a properly implemented smoothly spread leap rule:

It's more complex to write code to calculate, yes.  But it is much
simpler for a human to determine.  That's the trade-off.  Any sort of
evenly-spread rule would make the leap/common status of a year (is
there a word for that quality, btw?) nearly impossible to determine
mentally.

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

[Mark J. Reed]

On Mon, Jun 29, 2009 at 12:08 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
> As for summer ending in February, are you sure that you aren't just basing that on the assumption of four equal seasons?

Who cares what he's basing it on?  Your statement was that everyone
perceives things a certain way.  That statement has been proven false
many times over.

> For summer to begin with December, and end when February ends, implies a seasonal timelag much shorter than that which I found average for Australia in the worldwide temperature records book.

I still don't understand how you're defining this "lag".

Take Amberley as an example.  Its high temperature of the year falls
in January; that should presumably be midsummer.  The low temperature
of the year falls in July, so that should presumably be midwinter.
The temperature midpoints between those extremes, presumably the
middle of the transitional seasons, fall in April/May and Sept/Oct.
Which looks pretty darn close to equal quarters to me.

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

[MIKE OSSIPOFF]

 
I'd said:

> Minimum Drift leapyear rule:
> A year is a leapyear if, for that year's d, abs(d-5.75781) < abs(d+1.24219)
> After the end of a year that isn't a leapyear, add 1.24219 to d. After the end of a leapyear, subtract 5.75781 from d.

> Irv replies:
 
The above is not a stand-alone leap rule, it is a serial one. The only way to know if a year is a leap year or not, following the above instructions, is to serially check every year from the epoch to the target year, to find out the cumulative value of d.
 
I reply:
 
No argument there. If a "stand-alone leap rule" is defined as one that isn't a serial leap rule, then my serial leap rule isn't a stand-alone rule.
 
But I don't know if "stand-alone" is a good descriptive term. Maybe "single-step-evaluation" would be better.
 
The need for a single-step-evaluation rule hadn't occurred to me, but, now that you mention it, it could sometimes be useful to have one.  As I said, I merely was making a suggestion. But I still say that Minimum Drift, as I specified it, is as simple as a leapyear rule can be. And machine computation of as many future leapyears as you want to print out and publish wouldn't be any problem. Most people aren't going to use the single-step-evaluation formula for a leapyear rule, any more than they're going to repeatedly apply my rule to find out if some distant future year is a leapyear.
 
Irv continued:
 
Instead, a proper leap rule should allow direct stand-alone calculation of the leap status of any year.
 
I reply:
 
Yes, it could sometimes be more convenient if the leap rule is, or can be expressed as, a single-step-evaluation rule. But you're exaggerating a lot when you say that it's "improper" for it to not be.
 
I claim that the great simplicity and obviousness of Minimum Drift outweighs the computational convenience advantage of a single-step-evaluation leap rule, especially when most people aren't going to use either, and since either can be quickly machine-calculated and printed out for any number of years into the future.
 
Irv continued:
 
That is not to say that the leap rule can't use an accumulator, but the expression involving the accumulator has to allow direct evaluation, preferably in one step.
 
I reply:
 
Again, I suggest that "has to" is a bit of an exaggeration. Sure, more convenient when you want to find out if some distant future year is a leapyear, and aren't using a computer program.
 
 
Irv wrote:
 
The direct expression for the Gregorian leap rule is more complex than a properly implemented smoothly spread leap rule
 
I reply:
 
But how often, in anyone's lifetime, is it a year divisible by 100? For nearly all of anyone's life, we have a leapyear every fourth year. Every year divisible by four is a leap year, for nearly all of anyone's life.  That's what I meant. That simplicity is unmatched till there's a century year (something we needn't worry about for a while). And, when there is one, people can simply be told, "This year is an exception--it isn't a leapyear. This happens for most century years. You won't have to worry about it again for another century".
 
Sure, for a fixed calendar we need a new leapyear system, one that works with leapweeks (because blank days are out of the question). I too wouldn't consider a Gregorian-style leapyear rule for leapweeks.
 
I know that you, Irv, don't have any use for a nonfixed calendar reform, but, if the calendar is not a fixed calendar, then I suggest that proposal-simplicity dictates keeping the Gregorian leapyear system unchanged. Its wobble isn't a problem (How could it be? The wobble of a leapweek calendar isn't a problem.) Another advantage of keeping the Gregorian leapyear system for a nonfixed calendar is that, then, it's possible to ensure that NorthI/1 is _always_ on Gregorian June 1.
 
As I was saying, it never occurred to me to look for a 1-step way to find out if a distant future year is a leapyear. I haven't looked at that problem at all. Again, I would have no objection to Minimum Drift being written in such a 1-step-evaluation form, or for some other 1-step-evaluation rule to be used instead, if it does a reasonable job of minimizing drift. And I'm sure that any reasonable symmetrical leapyear rule would do a fine job of minimizing drift.
 
Mike ossipoff
 
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[MIKE OSSIPOFF]

 
Mark--
 
Ok, so I'll call it the Gregorian Calendar. Fair enough--Gregorius made a new calendar. But do we have to also call it the Gregorian month system too?
 
You wrote:
 
> Incidentally, the name of the various Popes Gregory is written
> "Gregory" in English text, including in official Church documents in
> that language. It's only "Gregorius" when writing in Latin.
 
I reply:
 
Did he call himself Gregory or Gregorius? Did his contemporaries call him Gregory or Gregorius? If there's a historical person who was named Dionysius, do we have to call him Dennis?
 
If you say "Hay-lee's comet", people will correct you and say that the "Ha-" must be pronounced as in "Hack". Wrong. Halley himself pronounced it more like "Holly". Why not go by what the person himself used?
 
Mike Ossipoff
 
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[Brillig]

On Mon, Jun 29, 2009 at 11:29 AM, Mark J. Reed<markjreed@...> wrote:
> On Mon, Jun 29, 2009 at 12:08 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
>> As for summer ending in February, are you sure that you aren't just basing that on the assumption of four equal seasons?
>
> Who cares what he's basing it on?  Your statement was that everyone
> perceives things a certain way.  That statement has been proven false
> many times over.
>

Here in Texas, I dare say a typical division of the seasons might look
something like this:

Summer: May through September
Fall: October through December
Winter: December through February
Spring: Feburary through May

Some bases for these divisions:

If summer months are those months where it's possible for temperatures
to exceed 100 degrees fahrenheit, then summer is from February through
September.
If fall starts when the first frost is possible, then it's not until
the end of October.
If spring starts on the average last day of frost, then it starts in
March. If it starts when the first wildflowers bloom, then it's in
Feburary.

Having lived in Texas since 1980, I'll disagree with the notion that
if you don't like the weather then wait a while and it will change.
That is certainly true for springtime weather, but summer is typically
monotonously hot -- usually from sometime in mid-May until the end of
September.

Winter is those few days that usually are between December and
February when it freezes and you have to bring tender plants in. In
1993 or thereabouts, winter didn't arrive until late March. Then it
was over a couple days after it started. Spring was already well under
way by the time winter arrived.

There's a huge overlap in the seasons here. The best growing season
for vegetables depends upon which vegetables you grow. Some do best in
fall. Others do best in winter. Very few do best in summer. Trees drop
their leaves in fall -- except those that drop their leaves in spring.

People have various ways to denote the start of a season. Usually it's
springtime that people comment about. Sometimes the comments will be
about the first bluebonnets blooming. Others will note when pecan
trees sprout. Pecan trees, it seems, are rarely fooled by late frost,
so winter is not truly over until pecans sprout. The last few years
I've paid attention to the pecans, they sprouted around March 25-28.

Victor

[Mark J. Reed]

On Mon, Jun 29, 2009 at 12:53 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
> But do we have to also call it the Gregorian month system too?

Well, it's the month system used by the Gregorian calendar.  You can
call it the Julian month system if you prefer.  But calling it the
Roman month system is confusing, since that usually refers to the
pre-Julian Roman calendar.

> Did he call himself Gregory or Gregorius? Did his contemporaries call him Gregory or Gregorius? If there's a historical person who was named Dionysius, do we have to call him Dennis?
>
> If you say "Hay-lee's comet", people will correct you and say that the "Ha-" must be pronounced as in "Hack". Wrong. Halley himself pronounced it more like "Holly". Why not go by what the person himself used?

Because common practice is not based on any such airtight principle;
it's all convention. There was a Genoese man born Christoffa Corombo,
who went by Cristóbal Colón in his everyday life in Spain, and
published his works in Latin as Christophorus Columbus.  But what do
we call him in English?  None of the above.

I know you have no respect whatsoever for tradition or common
practice, but adhering to conventional norms keeps people from getting
distracted by irrelevancies so they can focus on the point you're
actually trying to make.  In this case, we're talking about reforming
the calendar.  You can reform historical nomenclature later.

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

[Brillig]

On Mon, Jun 29, 2009 at 11:53 AM, MIKE OSSIPOFF<nkklrp@...> wrote:

> Did he call himself Gregory or Gregorius? Did his contemporaries call him Gregory or Gregorius?

I think it was Ugo Boncompagni -- at least until he became pope. What
name he used while pope is largely irrelevant, I think. The forum
we're using now is an English forum, so using English names is
appropriate. You can see a listing of English pope names here:

http://en.wikipedia.org/wiki/Popes

Victor

[MIKE OSSIPOFF]

 
Mark--
 
I'd said:

>> As for summer ending in February, are you sure that you aren't just basing that on the assumption of four equal seasons?

You replied:

> Who cares what he's basing it on? Your statement was that everyone
> perceives things a certain way.
 
If he's basing it on the conventional notion of equal seasons, quarters as seasons, then he isn't basing it on his own perceptions. I was talking about perceptions, not official conventions.
 
But his statement that summer begins on December more reasonably qualifies as a genuine perception (one that I've heard from another Australian too), because it _contradicts_ the official statement that summer and winter begin on solstices.
 
You continued:
 
That statement has been proven false
> many times over.
 
I reply:
 
Well, it wasn't proven false this time, or by expressions, that I've heard, of people's own perceptions.

>
>> For summer to begin with December, and end when February ends, implies a seasonal timelag much shorter than that which I found average for Australia in the worldwide temperature records book.
>
> I still don't understand how you're defining this "lag".

In general, "lag" is the delay by which one event or change process follows another.
 
I've given two definitions of the lag of a calendar season behind the solar declination that causes the seasons. I'll repeat that definition at the end of this posting.
 
You wrote:
 
>
> Take Amberley as an example. Its high temperature of the year falls
> in January; that should presumably be midsummer. The low temperature
> of the year falls in July, so that should presumably be midwinter.
> The temperature midpoints between those extremes, presumably the
> middle of the transitional seasons, fall in April/May and Sept/Oct.
> Which looks pretty darn close to equal quarters to me.

I reply:
 
I disagree. The fact that the _middles_ of the seasons are equally-spaced doesn't mean that the seasons are equal in length.
 
 
Two definitions of a calendar season's timelag:
 
1. Middle-after-Solstice:
 
The lag of (say) a calendar summer is the delay by which its middle follows the summer solstice.
 
 
2. Equal bounding lagged declinations:
 
Find a number, N, such that the solar declination N days before the end of calendar summer is the same as the solar declination N days before the beginning of calendar summer. Then, N days is the timelag of that calendar summer.
 
[end of two lag definitions]
 
When you're starting with an assumed timelag, such as 1.25 months, or 38 days, and using it, in conjunction with North's starting date, to find the length of North, I think that #2 is a better way. But #1 is simpler and easier to describe. For that reason, my favorite nonfixed proposal uses #1 to find the length of North, given its starting-date and estimated timelag.
 
 
Mike Ossipoff
 
 
 
 
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[MIKE OSSIPOFF]

 
Mark--
 
You wrote:
 
...but adhering to conventional norms keeps people from getting
> distracted by irrelevancies so they can focus on the point you're
> actually trying to make. In this case, we're talking about reforming
> the calendar. You can reform historical nomenclature later.
 
I reply:
 
Ok, true enough. But I just felt that "Gregory" sounds too modern, if he and his contemporaries used "Gregorius". Gregory sounds like just some modern Joe, not a history-making 16th century pope. Sure, if everyone else here is calling him Gregory, or Greg, and if Gregorius is distracting because it brings up a separate issue, a historical naming issue, then I'll go by what's conventional here.
 
Anyway, since I'm no longer protesting "Gregorian Calendar", I probably won't be mentioning Gregory again.
 
Mike Ossipoff

 
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[MIKE OSSIPOFF]

----------------------------------------
> Date: Mon, 29 Jun 2009 12:17:58 -0500
> From: brillig@...
> Subject: Re: June-September season
> To: CALNDR-L@...
>
> On Mon, Jun 29, 2009 at 11:53 AM, MIKE OSSIPOFF wrote:
>
>> Did he call himself Gregory or Gregorius? Did his contemporaries call him Gregory or Gregorius?
Victor wrote:

> I think it was Ugo Boncompagni -- at least until he became pope.
 
I reply:
 
But he was pope when he reformed the leapyear rule.
 
Anyway, if I mention him again, I'll call him Gregory--I've had my little protest.
 
Mike Ossipoff
 
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[Irv Bromberg]

On 2009 Jun 29, at 12:40 , MIKE OSSIPOFF wrote:

I'd said:

Minimum Drift leapyear rule:

A year is a leapyear if, for that year's d, abs(d-5.75781) < abs(d+1.24219)

After the end of a year that isn't a leapyear, add 1.24219 to d. After the end of a leapyear, subtract 5.75781 from d.

Irv replied: 

The above is not a stand-alone leap rule, it is a serial one. The only way to know if a year is a leap year or not, following the above instructions, is to serially check every year from the epoch to the target year, to find out the cumulative value of d.

No argument there. If a "stand-alone leap rule" is defined as one that isn't a serial leap rule, then my serial leap rule isn't a stand-alone rule.
The need for a single-step-evaluation rule hadn't occurred to me, but, now that you mention it, it could sometimes be useful to have one.  As I said, I merely was making a suggestion. But I still say that Minimum Drift, as I specified it, is as simple as a leapyear rule can be. And machine computation of as many future leapyears as you want to print out and publish wouldn't be any problem. Most people aren't going to use the single-step-evaluation formula for a leapyear rule, any more than they're going to repeatedly apply my rule to find out if some distant future year is a leapyear.

Mike, you aren't thinking about how calendars are used.  You are focused only on the design of a printed calendar that people will follow this year and next year.

What about the millions of dated database transactions that take place every day?  What about calendrical calculations that go on "behind-the-scenes" to determine the duration of a loan, or a contract, or when a product will expire, how many days until or since such-and-such, and so on?  All such calculations need efficient calendrical calculations that work directly, efficiently and unambiguously.

Irv wrote:  Instead, a proper leap rule should allow direct stand-alone calculation of the leap status of any year.

Mike replied:  Yes, it could sometimes be more convenient if the leap rule is, or can be expressed as, a single-step-evaluation rule. But you're exaggerating a lot when you say that it's "improper" for it to not be.

Irv replies:  No, I'm not exaggerating at all.  Without publishing such a simple direct calculation, any calendar reform has no hope of being adopted, because computer systems account for almost all of the date-related transactions and records in our societies, and the implementors of such systems will demand efficient algorithms.  Also, "list lookup" is not efficient and not future-proof.  In addition, you are focused only on the present era or near future.  What about people who need to carry out calendrical calculations for the distant past or remote future?  Even to calculate a person's age you need to be able to go back >100 years in some cases (hey, there's that pesky century leap year calculation, can't ignore that, not now, not ever).  Do a little bit of planning for a major project and you are calculating dates that are potentially decades into the future.  My favorite future calculation, hopefully near future = date of global eradication of malaria.  (But I'll accept global eradication of poliomyelitis as an interim step.)

Mike continued:  I claim that the great simplicity and obviousness of Minimum Drift outweighs the computational convenience advantage of a single-step-evaluation leap rule

Irv replies:  If you say so, but frankly I don't understand your Minimum Drift rule at all, so I'll have to take your word on how simple and obvious it is.  I previously asked where the numeric coefficients came from and you didn't answer that question.  I don't really care, because it is flatly inappropriate to use a serial calculation to determine leap status.

Irv continued:  That is not to say that the leap rule can't use an accumulator, but the expression involving the accumulator has to allow direct evaluation, preferably in one step.

Mike replied:  Again, I suggest that "has to" is a bit of an exaggeration. Sure, more convenient when you want to find out if some distant future year is a leapyear, and aren't using a computer program.

Irv replies:  Again, no, I'm not exaggerating at all, as explained above.

irv wrote:  The direct expression for the Gregorian leap rule is more complex than a properly implemented smoothly spread leap rule

Mike wrote:  But how often, in anyone's lifetime, is it a year divisible by 100? For nearly all of anyone's life, we have a leapyear every fourth year. Every year divisible by four is a leap year, for nearly all of anyone's life.  That's what I meant. That simplicity is unmatched till there's a century year (something we needn't worry about for a while). And, when there is one, people can simply be told, "This year is an exception--it isn't a leapyear. This happens for most century years. You won't have to worry about it again for another century".

Irv replies:  Mike, you are not looking beyond the end of your nose.  The century leap vs. non-leap years need to be taken account of in every calendrical calculation.  Say you want the Julian Day number for today's date, or any other ordinal day numbering system, to a necessary step whenever one is carrying out a calendrical calculation.  In calculating that number, you need to account for all elapsed days since the epoch of the Gregorian calendar, including the leap status of all elapsed centurial years.  There are relatively simple expressions to do that in only a few steps, but the number of steps are fewer and the expression much more direct when the leap years are at intervals that are as smoothly spread as possible, as I explained in my discussion of symmetrical leap cycles at:

http://individual.utoronto.ca/kalendis/leap/index.htm#slc

Mike continued:  I know that you, Irv, don't have any use for a nonfixed calendar reform, but, if the calendar is not a fixed calendar, then I suggest that proposal-simplicity dictates keeping the Gregorian leapyear system unchanged. Its wobble isn't a problem (How could it be? The wobble of a leapweek calendar isn't a problem.)

Irv replies:  The wobble of the Gregorian calendar leap rule is what is responsible for the fact that this century the northward equinox never falls on March 21st.  It mostly falls on March 20th, and later in this century it will often fall on March 19th.  That is short-term drift, due to the wobble, not long-term drift indicating excessive mean year.  That short term drift is identical to the drift of the Julian calendar, but it gets "corrected", with a big step, the next time that a leap year is skipped, because year 2100 will not be a leap year.

Who says that wobble isn't a problem?  Has the Catholic Church said that it is of no concern?  If so, then have they said how far out it would have to be before they do get concerned?

Who says that the greater wobble due to the leap week (which is much shorter term than the Gregorian wobble discussed above) is acceptable?  Or not?

The much greater seasonal wobble (±15 days) of the traditional oriental and Hebrew lunisolar calendars doesn't bother anybody, so on that basis I would say that yes, the ±3 day wobble (ignoring the middle day because any wobble within that day is no worse than a leap day calendar having the minimum possible wobble) due to a leap week ought to be culturally acceptable.

It comes down to how the seasons matter for ritual purposes.  If Easter is reckoned using March 21st as the ecclesiastical equinox date (or the equivalent date on your calendar), then increasing the wobble causes Easter to wobble too (on top of its inherent lunisolar wobble).  If the calendar is a leap week calendar, but Easter is reckoned using the leap day equivalent cycle then the increased wobble is of no ritual concern.  Or, if Uniform Easter is reckoned astronomically as recommended by the World Council of Churches then the calendrical wobble and calendrical mean year are also of no ritual concern.

(By the way, the Gregorian Easter computus has a mean year that is identical to that of the Gregorian calendar, so if you use a different calendar mean year then Gregorian Easter will drift through your calendar.)

Mike continued:  Another advantage of keeping the Gregorian leapyear system for a nonfixed calendar is that, then, it's possible to ensure that NorthI/1 is _always_ on Gregorian June 1.

Irv replies:  I can't imagine why that would be an advantage in any way.  If you are going to reform the calendar, then why would you want the Gregorian still around?  Sure, it is desirable to be able to convert Gregorian to other calendars and other calendars to Gregorian in connection with converting old database records or accessing old records without updating their representations of dates, but there is no need to make such conversions "easy" by aligning month starts.  Such alignment is of no consequence to any computer system converting or accessing such records.  All such calendrical calculations and conversions come down to Gregorian-to-ordinal-day-number, ordinal-day-number-to-other-calendar, other-calendar-to-ordinal-day-number, and ordinal-day-number-to-Gregorian.  The same steps would be mindlessly carried out every time, no short cuts, don't care how the months line up.  It is faster to just execute the standard algorithm than checking whether a "simpler" conversion might be possible in some circumstances.

I highly recommend the book "Calendrical Calculations" by Dershowitz and Reingold, see:

http://emr.cs.iit.edu/home/reingold/calendar-book/third-edition/

-- Irv Bromberg, Toronto, Canada

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