obliquity.com table discrepancy

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obliquity.com table discrepancy

Lance Latham
Group -

Regarding Karl's query concerning the absence of a
Blue Moon date for 1961 in the obliquity.com page, I
must have deleted the original e-mail, so I will reply
to what I can recall.

First, it seems that one explanation might be that the
assertion of an astronomical BM for November 1961 is
simply incorrect. I find no other 'no Blue Moon' entry
in the tables covering 2 centuries.

Second, the original explanation still seems valid to
me. Suppose that, owing to a slight difference in the
length of the seasons under the 2 different
definitions, the November 1961 FM happened to qualify
as the 3rd FM of 4 for the 'astronomical'  season, but
failed to qualify under the almanac definition. That
would account for the discrepancy observed.

Looking at this case in more detail, imagine that
under the 'astronomical' season definition, a FM just
manages to squeak by, and is counted as the first FM
of a season. Successive lunations work out so that 4
FMs are counted in that season. This is possible,
since one must allow for 3 periods of 29.53 days on
average, plus some slop, that could squeeze them in.

Now imagine an RAMS-defined season that starts only
slightly later, missing the first FM that was counted
under the 'astronomical' definition. That first FM
would have to occur before the RAMS autumnal equinox.
Then a fourth FM will not be counted for that
RAMS-defined season, and ergo, the November 22 FM is
not counted as the 3rd FM of 4 in that season. For
that to happen, the RAMS-defined season of fall would
have to start slightly later than the FM date. These
relations could be checked for November 1961.

Regarding the logical consequences of that difference,
the FM did not go missing in any sense; it simply
qualified as a 3rd FM of 4 under one definition, and
did not qualify under another. I do not understand
that a total of FMs for a century would be affected in
this case.

In one sense, it doesn't matter anyway for the larger
question of Blue Moon definition, since the almanac
clearly states the definition that it uses (RAMS). But
an explanation of the difference in the two tables
perhaps would illuminate the nature of the definition
in some way. Exceptions are generally more instructive
than regular cases.

I have not had time to return to the Blue Moon
mini-project that I started several years ago, so I
don't have reliable code that might help to resolve
this matter. Perhaps some code could be obtained that
produces the RAMS season dates, and a look into the
code and results might supply an answer to the
difference in the table.

-Lance


Lance Latham
[hidden email]
Phone:    (518) 274-0570
Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
 





               
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Re: obliquity.com table discrepancy

VictorEngel
Dear Lance, Karl, and Calendar People,

> Regarding Karl's query concerning the absence of a
> Blue Moon date for 1961 in the obliquity.com page, I
> must have deleted the original e-mail, so I will reply
> to what I can recall.

It was Victor's comment, not Karl's.
 
> First, it seems that one explanation might be that the
> assertion of an astronomical BM for November 1961 is
> simply incorrect. I find no other 'no Blue Moon' entry
> in the tables covering 2 centuries.

Right. And if there is one, the one of the following must be true:

* There is another one in the other column.
* There is a season with only two full moons.
* The total number of full moons for the century is different for the
century for the two calculations.
 
> Second, the original explanation still seems valid to
> me. Suppose that, owing to a slight difference in the
> length of the seasons under the 2 different
> definitions, the November 1961 FM happened to qualify
> as the 3rd FM of 4 for the 'astronomical'  season, but
> failed to qualify under the almanac definition. That
> would account for the discrepancy observed.

But it's more than that. It's the third of four for the season. The
astronomical season reckons 4 FMs.

> Looking at this case in more detail, imagine that
> under the 'astronomical' season definition, a FM just
> manages to squeak by, and is counted as the first FM
> of a season. Successive lunations work out so that 4
> FMs are counted in that season. This is possible,
> since one must allow for 3 periods of 29.53 days on
> average, plus some slop, that could squeeze them in.

OK so far.

> Now imagine an RAMS-defined season that starts only
> slightly later, missing the first FM that was counted
> under the 'astronomical' definition. That first FM
> would have to occur before the RAMS autumnal equinox.
> Then a fourth FM will not be counted for that
> RAMS-defined season, and ergo, the November 22 FM is
> not counted as the 3rd FM of 4 in that season. For
> that to happen, the RAMS-defined season of fall would
> have to start slightly later than the FM date. These
> relations could be checked for November 1961.
>
> Regarding the logical consequences of that difference,
> the FM did not go missing in any sense; it simply
> qualified as a 3rd FM of 4 under one definition, and
> did not qualify under another. I do not understand
> that a total of FMs for a century would be affected in
> this case.

But here is the point. If the RAMS defined season omits the first FM that
the corresponding astronimical season starts with, then the PREVIOUS RAMS
defined season must contain that same FM. This would imply that that
previous season on the RAMS table would have a blue moon where the
astronimical table does not (for the previous season), UNLESS, the same
condition happened to be the case for the season before that. At some point,
there is eventually a season where the two have the same starting FM. That
is why I mentioned the unambiguity of the endpoints of the century.

The other alternative, of course, is for it to be possible to have only 2
FMs in a season. Then the table could represent 3 FMs in each of the
consecutive seasons for the RAMS case and 2 and 4, respectively, for the
astronomical case.

I suspect that either:

* a RAMS blue moon has been omitted from the table.
* an astronomical blue moon has been included in error.
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Re: obliquity.com table discrepancy

VictorEngel
In reply to this post by Lance Latham
Dear Lance and Calendar People,

> The other alternative, of course, is for it to be possible to
> have only 2 FMs in a season. Then the table could represent 3
> FMs in each of the consecutive seasons for the RAMS case and
> 2 and 4, respectively, for the astronomical case.

It looks like this is actually the case. Consider the following:

Full Moon        Equinox/Solstice
1961-12-22 00:42 1961-12-22 02:20
1962-03-21 07:55 1962-03-21 02:30

In other words, this season has only two full moons, hence the table
discrepancy. So, shall we call the third full moon of such a season an
invisible moon?

Victor
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Re: obliquity.com table discrepancy

Lance Latham
RE:

> > The other alternative, of course, is for it to be
> possible to
> > have only 2 FMs in a season. Then the table could
> represent 3
> > FMs in each of the consecutive seasons for the
> RAMS case and
> > 2 and 4, respectively, for the astronomical case.
>
> It looks like this is actually the case. Consider
> the following:
>
> Full Moon        Equinox/Solstice
> 1961-12-22 00:42 1961-12-22 02:20
> 1962-03-21 07:55 1962-03-21 02:30
>
> In other words, this season has only two full moons,
> hence the table
> discrepancy. So, shall we call the third full moon
> of such a season an
> invisible moon?

Lance replies:
Hmm, I'm still working on my first cup of coffee this
morning, so bear with me.

If I err not, the season of autumn starts with the
autumnal equinox. The November 1961 Blue Moon is
therefore the 3rd full moon of 4 in the season of
autumn in 1961. Victor identifies the 4th, which
appears just before the winter solstice; we assume the
first occurs just after the autumnal equinox in 1961.

Victor's data presumably pertain to 'astronomical'
full moons; and we infer that the astronomical winter
of 1961-2 contains only 2 full ones, in January and
February.

Frankly, I had considered that case, but decided it
was not possible, since it would require lunations
with extreme duration values that exceeded Meeus's
16-hour slop figure. But that may not be the case,
assuming these data are correct.

Clearly, Victor is on the right track in solving this
little conundrum. Running out date/times for solstices
and equinoxes for both schemes, then comparing them to
full moon date times for the period of September 1961
to March 1962 would answer that question completely.

As it is, we are left to infer that the RAMS method
would produce values for the equinox and solstice that
would suffice to shift the seasonal definitions just
enough to produce the effect Victor mentions. That
certainly looks plausible, even very probable, but to
nail it down, we'll need those RAMS figures.

Regarding the nomenclature, if this explanation pans
out, then the moon could be called Spoils moon.
Actually, it seems odd to have a name for something
that does not exist, but then we're fussing over Santa
Claus at the moment.

-Lance


Lance Latham
[hidden email]
Phone:    (518) 274-0570
Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
 




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Re: obliquity.com table discrepancy

Victor Engel
Dear Lance and Calendar People,

Lance Latham wrote:

> Regarding the nomenclature, if this explanation pans
> out, then the moon could be called Spoils moon.

Can you explain?

> Actually, it seems odd to have a name for something
> that does not exist, but then we're fussing over Santa
> Claus at the moment.

My best friend in high school told me that when he was a kid he had a
conundrum about Santa Claus. The way he figured it, either one of the
following virtually impossible things had to be true:

* Santa Claus really could travel around the world visiting every
household in just one night.
* The entire human race of adults were able to agree on something, a
conspiracy successfully kept secret from children.

Victor
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Re: obliquity.com table discrepancy

Lance Latham
In reply to this post by VictorEngel
RE:

> It was Victor's comment, not Karl's.

Lance replies:
Apologies. I was working from memory, intending to
return to an e-mail that I had already inadvertently
deleted.

-Lance


Lance Latham
[hidden email]
Phone:    (518) 274-0570
Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
 




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Re: obliquity.com table discrepancy

Lance Latham
In reply to this post by Victor Engel
RE:

>then the moon could be called Spoils moon.
>
> Can you explain?

Lance replies:
To the Victor belong the Spoils.
 

> ...one of the
> following virtually impossible things had to be
> true:
>
> * Santa Claus really could travel around the world
> visiting every
> household in just one night.
> * The entire human race of adults were able to agree
> on something, a
> conspiracy successfully kept secret from children.

Lance replies:
Hmm. Given that adults can't even agree on the color
of the seat cushions in their church, the second
explanation seems highly implausible. That's as close
to a definitive proof of the existence of Santa Claus
as we're ever going to get. I like it!

-Lance


Lance Latham
[hidden email]
Phone:    (518) 274-0570
Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
 




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Santa Claus RE: obliquity.com table discrepancy

Palmen, KEV (Karl)
In reply to this post by Lance Latham
Dear Victor and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Victor Engel
Sent: 08 December 2005 15:52
To: [hidden email]
Subject: Re: obliquity.com table discrepancy


> Actually, it seems odd to have a name for something
> that does not exist, but then we're fussing over Santa
> Claus at the moment.

My best friend in high school told me that when he was a kid he had a
conundrum about Santa Claus. The way he figured it, either one of the
following virtually impossible things had to be true:

* Santa Claus really could travel around the world visiting every
household in just one night.

KARL SAYS: This may be because Santa Claus is a timelord and the chameleon circuit of his TARDIS makes it look like a sleigh pulled by reindeer. The TARDIS also has plenty of room inside for the presents. I expect it also has flexible tube that is bigger inside than outside to get Santa down a narrow chimney while remaining red and cheery.

Karl

07(15(08

07(15(24 on Santa night.
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Re: obliquity.com table discrepancy

VictorEngel
In reply to this post by Lance Latham
Dear Calendar People,

I received the following email from Dr. David Harper:

Dear Victor,

Greetings from Cambridge, England and thank you for your query
which you sent via our web site at www.obliquity.com

Victor's query:

> Your table at http://www.obliquity.com/astro/seasonal.html contains
> an impossibility or another interesting phenomenon.

> There are no full moons at the endpoints of the 20th century that are
> ambiguous with respect to whether they should be included in the
> total count of full moons for the century. Therefore, both tables
> should have the same count of full moons.

> The only way to make the count add up would be to have only 2 full
 > moons in a season for some seasons.

That's correct, and congratulations on spotting this. I confess that it
had escaped me!

The answer is that the Winter of 1961/2, defined by the astronomical
seasons, had only two Full Moons.

There were Full Moons just a few hours before the 1961 Winter Solstice
and a few hours after the 1962 Spring Equinox:

1961 Dec 22 00:42    Full Moon
1961 Dec 22 02:19    Winter Solstice
1962 Jan 20 18:16    Full Moon
1962 Feb 19 13:18    Full Moon
1962 Mar 21 02:30    Spring Equinox
1962 Mar 21 07:55    Full Moon

Both the preceding Autumn and the subsequent Spring had four Full Moons,
resulting in "seasonal" Blue Moons in two consecutive years.

When I next revise the web page, I'll add a footnote to point out this
interesting phenomenon, and I'll be sure to credit you with the discovery.

Yours sincerely,

Dr David Harper

> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Lance Latham
> Sent: Thursday, December 08, 2005 9:03 AM
> To: [hidden email]
> Subject: Re: obliquity.com table discrepancy
>
>
> RE:
>
> > > The other alternative, of course, is for it to be
> > possible to
> > > have only 2 FMs in a season. Then the table could
> > represent 3
> > > FMs in each of the consecutive seasons for the
> > RAMS case and
> > > 2 and 4, respectively, for the astronomical case.
> >
> > It looks like this is actually the case. Consider
> > the following:
> >
> > Full Moon        Equinox/Solstice
> > 1961-12-22 00:42 1961-12-22 02:20
> > 1962-03-21 07:55 1962-03-21 02:30
> >
> > In other words, this season has only two full moons,
> > hence the table
> > discrepancy. So, shall we call the third full moon
> > of such a season an
> > invisible moon?
>
> Lance replies:
> Hmm, I'm still working on my first cup of coffee this
> morning, so bear with me.
>
> If I err not, the season of autumn starts with the
> autumnal equinox. The November 1961 Blue Moon is
> therefore the 3rd full moon of 4 in the season of
> autumn in 1961. Victor identifies the 4th, which
> appears just before the winter solstice; we assume the
> first occurs just after the autumnal equinox in 1961.
>
> Victor's data presumably pertain to 'astronomical'
> full moons; and we infer that the astronomical winter
> of 1961-2 contains only 2 full ones, in January and
> February.
>
> Frankly, I had considered that case, but decided it
> was not possible, since it would require lunations
> with extreme duration values that exceeded Meeus's
> 16-hour slop figure. But that may not be the case,
> assuming these data are correct.
>
> Clearly, Victor is on the right track in solving this
> little conundrum. Running out date/times for solstices
> and equinoxes for both schemes, then comparing them to
> full moon date times for the period of September 1961
> to March 1962 would answer that question completely.
>
> As it is, we are left to infer that the RAMS method
> would produce values for the equinox and solstice that
> would suffice to shift the seasonal definitions just
> enough to produce the effect Victor mentions. That
> certainly looks plausible, even very probable, but to
> nail it down, we'll need those RAMS figures.
>
> Regarding the nomenclature, if this explanation pans
> out, then the moon could be called Spoils moon.
> Actually, it seems odd to have a name for something
> that does not exist, but then we're fussing over Santa
> Claus at the moment.
>
> -Lance
>
>
> Lance Latham
> [hidden email]
> Phone:    (518) 274-0570
> Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
>  
>
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam?  Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com 
>
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Re: obliquity.com table discrepancy

Sepp Rothwangl
In reply to this post by Victor Engel

Am 08.12.2005 um 16:51 schrieb Victor Engel:

> * Santa Claus really could travel around the world visiting every
> household in just one night.
>

Of course "Santa" can!

The Milky Way is spinning around once every night.
See:
http://www.calendersign.com/en/am_santa.php

Servus

Sepp Rothwangl

www.calendersign.com
Y -669; CEP - 244445
=======================
Anno-Domini-hoax 2005

Since we should state not only the truth,
but also the cause of error...
Aristotle, Nicomachean Ethics VII 14
*********************************
Why organize the world's timekeeping with religious superstition?

IWWWWI============ the web is the best device to catch the ICHTHYS
IW<><WI
IWWWWI

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Re: obliquity.com table discrepancy

Charles Moyer
But doesn't get ahead of the cookies?

> From: Sepp Rothwangl <[hidden email]>
> Reply-To: East Carolina University Calendar discussion List
> <[hidden email]>
> Date: Mon, 12 Dec 2005 11:27:55 +0100
> To: [hidden email]
> Subject: Re: obliquity.com table discrepancy
>
>
> Am 08.12.2005 um 16:51 schrieb Victor Engel:
>
>> * Santa Claus really could travel around the world visiting every
>> household in just one night.
>>
>
> Of course "Santa" can!
>
> The Milky Way is spinning around once every night.
> See:
> http://www.calendersign.com/en/am_santa.php
>
> Servus
>
> Sepp Rothwangl
>
> www.calendersign.com
> Y -669; CEP - 244445
> =======================
> Anno-Domini-hoax 2005
>
> Since we should state not only the truth,
> but also the cause of error...
> Aristotle, Nicomachean Ethics VII 14
> *********************************
> Why organize the world's timekeeping with religious superstition?
>
> IWWWWI============ the web is the best device to catch the ICHTHYS
> IW<><WI
> IWWWWI
>
>
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Santa Claus RE: obliquity.com table discrepancy

Palmen, KEV (Karl)
In reply to this post by Lance Latham
Dear Charles, Sepp and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Charles Moyer
Sent: 12 December 2005 11:22
To: [hidden email]
Subject: Re: obliquity.com table discrepancy


But doesn't get ahead of the cookies?

KARL SAYS: I expect Santa gets many cookies on his PC.   Karl

> From: Sepp Rothwangl <[hidden email]>
> Reply-To: East Carolina University Calendar discussion List
> <[hidden email]>
> Date: Mon, 12 Dec 2005 11:27:55 +0100
> To: [hidden email]
> Subject: Re: obliquity.com table discrepancy
>
>
> Am 08.12.2005 um 16:51 schrieb Victor Engel:
>
>> * Santa Claus really could travel around the world visiting every
>> household in just one night.
>>
>
> Of course "Santa" can!
>
> The Milky Way is spinning around once every night.
> See:
> http://www.calendersign.com/en/am_santa.php
>
> Servus
>
> Sepp Rothwangl
>
> www.calendersign.com
> Y -669; CEP - 244445
> =======================
> Anno-Domini-hoax 2005
>
> Since we should state not only the truth,
> but also the cause of error...
> Aristotle, Nicomachean Ethics VII 14
> *********************************
> Why organize the world's timekeeping with religious superstition?
>
> IWWWWI============ the web is the best device to catch the ICHTHYS
> IW<><WI
> IWWWWI
>
>
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Re: Santa Claus RE: obliquity.com table discrepancy

Charles Moyer
Karl,
    I've heard that because Santa is so involved with graphics that he uses
an Apple iMac.

> From: "Palmen, KEV (Karl)" <[hidden email]>
> Reply-To: East Carolina University Calendar discussion List
> <[hidden email]>
> Date: Mon, 12 Dec 2005 11:29:00 -0000
> To: [hidden email]
> Subject: Santa Claus RE: obliquity.com table discrepancy
>
> Dear Charles, Sepp and Calendar People
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Charles Moyer
> Sent: 12 December 2005 11:22
> To: [hidden email]
> Subject: Re: obliquity.com table discrepancy
>
>
> But doesn't get ahead of the cookies?
>
> KARL SAYS: I expect Santa gets many cookies on his PC.   Karl
>
>> From: Sepp Rothwangl <[hidden email]>
>> Reply-To: East Carolina University Calendar discussion List
>> <[hidden email]>
>> Date: Mon, 12 Dec 2005 11:27:55 +0100
>> To: [hidden email]
>> Subject: Re: obliquity.com table discrepancy
>>
>>
>> Am 08.12.2005 um 16:51 schrieb Victor Engel:
>>
>>> * Santa Claus really could travel around the world visiting every
>>> household in just one night.
>>>
>>
>> Of course "Santa" can!
>>
>> The Milky Way is spinning around once every night.
>> See:
>> http://www.calendersign.com/en/am_santa.php
>>
>> Servus
>>
>> Sepp Rothwangl
>>
>> www.calendersign.com
>> Y -669; CEP - 244445
>> =======================
>> Anno-Domini-hoax 2005
>>
>> Since we should state not only the truth,
>> but also the cause of error...
>> Aristotle, Nicomachean Ethics VII 14
>> *********************************
>> Why organize the world's timekeeping with religious superstition?
>>
>> IWWWWI============ the web is the best device to catch the ICHTHYS
>> IW<><WI
>> IWWWWI
>>
>>