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Are the Zod PDs full coherent?
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Sun Jan 08, 2012 11:11 am    Post subject: Are the Zod PDs full coherent? Reply with quote

Hello to everybody.

Investigating the possibility to cast double mundane astrological charts, PDs oriented, I discovered something quite startling, forcing me to a question that surely the traditional astrologers will see with suspicion : are the current Zodiacal PDs based on the best theory?

The topic is too wide for a detailed debate, but I hope a qualitative hint will be enough. At least for interested students. Even so, the content of this post is quite demanding and requires a certain astronomical knowledge.

Let’s me simplify as possible: semiarc, Zod PDs without latitude, i.e. pure zodiacal. The key is not essential. Basically the current arcs of direction are reckoned according to the standard mathematical procedures, used for planets in mundo, applied to the ecliptic planetary projections. We’ll suppose the generic couple of promissor/significator located in the same quadrant.

***********
Probably all of us realized that sometimes, reckoning the arcs of direction (i.e. the equatorial degrees covered by the celestial sphere in its diurnal motion), the prommissors have to cover a journey towards the significators very different from the ecliptic distances they have at the birth. Too different. For example: for two planets distant 70° in zodiac, in radix, has a sense a PD arc between them 90° wide? I don’t think so, even if this happens normally (my benchmark is Morinus but as I know it is in agreement with Placidus). According to the*secondary* motion (i.e. the astronomical arc in zodiac) never the equatorial coordinates change so much, up to 90° to cover an ecliptic arc of 70°. Everything (mainly the celestial latitude) included. Note I am not referring to the secondary progressions, not involved in the matter.

***********
This is not the only doubtful detail. If we reckon arcs of directions for aspectual PDs in zodiac, their values are quite far from proportional values compatible with the related partial paths in zodiac. For example, if 70° in the signs are covered with an arc of direction 90° wide, for an arc in zodiac = 35° an arc of direction = about 45° is waited, but this does not happen (generally is quite different).
The reason is hidden in the mathematical assumption. In the generic PD:
Z - Promissor – D/C – Asp Significator
we have
Asp Significator = (Projection of Significator in Zodiac) + aspect in Zodiac
But is this assumption the best one?
What we do in this way is a *significator replacement*, with the consequence that each PD is an alone mathematical computation not integrable in a full coherent pseudo-astronomic context. One possible, partial solution to solve this second problem should be the following:
Asp Significator = [Mundane Position of (Projection of Significator in Zodiac)] + aspect in Mundo
but we would introduce a complex theoretical puzzle and the first problem should be not solved anyway.

***********
In my opinion everything finds a solution if we consider *the full ecliptic itself as a whole significator*, frozen on the celestial sphere as it was at the birth moment.

I mean:
--We have the radix planetary positions in zodiac (significators)
--We can move the celestial sphere according to its primary motion (PDs)
--During the primary motion we can project continuously the full planetary positions set (promissors) onto the frozen ecliptic
--We can evaluate the reciprocal angular distances between these full sets of promissors and significators getting the Zod PDs information all together

The results are:
--Equatorial arcs of direction (conjunctions and aspects) congruent with the native zodiacal distances
--A full coherent pseudo-astronomic context

Accordingly:
--It’s possible to create true graphical charts of Zodiacal PDs *in zodiac*. Note Morinus already has (*almost*) these charts (see Options\PDs in chart\Celestial\Full pseudo-astronomic) unless two details due to the little different viewpoint they are cast from. In any case, with the necessary instructions, to test the method they are fit for the purpose

Moreover:
--The technique is insensitive to the type of PDs (semiarc or all the UTP). Obvious: we analyze the effects of the primary motion in zodiac and the mundane positions are not important any more. Only the key remains significant
--Under this point of view, is the use of the partial latitude well founded or it is only a manner to play with the astronomical trigonometry?

***********
The necessary math is easier if compared with the math used to reckon the Zod PDs according to the accepted methods. As I tested the formulas, all is in perfect agreement with the above considerations. And as any fisher narrates of his big fishes Very Happy , I find the results in very good agreement with the real events of the life.

The above suggested method arises, in my opinion, from the requirement to satisfy the most elementary astronomical necessities. Anybody open to this *heretical* possibility?

Regards
Roberto
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Ed F



Joined: 22 Jan 2008
Posts: 301
Location: Ipswich, MA USA

Posted: Mon Jan 09, 2012 8:15 pm    Post subject: Re: Are the Zod PDs full coherent? Reply with quote

robhywolf wrote:


The above suggested method arises, in my opinion, from the requirement to satisfy the most elementary astronomical necessities. Anybody open to this *heretical* possibility?

Regards
Roberto


Hi Roberto,

What do you consider to be the elementary astronomical necessities to be met? I didn't get them from the text of your message.

Thanks and regards,

- Ed
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Tue Jan 10, 2012 6:15 pm    Post subject: Reply with quote

Quote:
What do you consider to be the elementary astronomical necessities to be met? I didn't get them from the text of your message


Hi Ed.

The Zod PDs are not a banal concept.

According to their definition, we create fictitious bodies (the planetary projections in zodiac) and then apply to them the formulas of spherical trigonometry according to the mundane PDs. In other words the equatorial, daily motion the celestial sphere has, is anyway the game rule. Doing so, to reckon the arcs of direction, the zodiacal projections are moved out from the ecliptic plane and regarded as any other celestial object in their equatorial, mundane motion. If we accept these premises, the current results are mathematically correct.

But hidden in their wishes there is something like: “Let’s move the celestial sphere according to its equatorial motion to see the arcs of direction that the promissors (in zodiac) need to reach the significators (in zodiac)”. Now *in zodiac* means on the ecliptic plane. If we regard the matter under this point of view, and if we desire a more credible framework, the equatorial arcs cannot be so far from the real, conjugated ecliptic arcs. So, even if the Zod PDs are not a true astronomical picture of the sky, a more plausible (pseudo) astronomical method should be, perhaps, desirable.

The second point is related to the aspectual Zod PDs.
For the reason I hinted in my previous post, currently any PD reckoned in zodiac, involving an aspect, is out of any (pseudo) astronomical framework that permits a continuous equatorial movement jointed to a continuous set of arcs of direction.

In other words, the most elementary astronomical “necessities” (compatible ecliptic - equatorial arcs and continuity in the equatorial motion to cover a continuous zodiacal scenery) with the current Zod PDs are not satisfied.

Regards,
Roberto.
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Ed F



Joined: 22 Jan 2008
Posts: 301
Location: Ipswich, MA USA

Posted: Tue Jan 10, 2012 9:12 pm    Post subject: Reply with quote

robhywolf wrote:


In other words, the most elementary astronomical “necessities” (compatible ecliptic - equatorial arcs and continuity in the equatorial motion to cover a continuous zodiacal scenery) with the current Zod PDs are not satisfied.

Regards,
Roberto.


Which reflects more on the essential oddity of zodiacal directions than anything else. I'll stick with mundo directions, which satisfy the spherical version of your second requirement.

- Ed
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Wed Jan 11, 2012 8:54 pm    Post subject: Reply with quote

Ed wrote:

Quote:
Which reflects more on the essential oddity of zodiacal directions than anything else. I'll stick with mundo directions, which satisfy the spherical version of your second requirement.


So, we have three possibilities:

-We use the mundane PDs only
-We accept the zodiacal PDs as well, regardless to their defectiveness (sometimes they work)
-We can try to help our ancient masters, in the soul of their teaching, using the astronomical and mathematical tools perhaps they did not master as we can do now. Conceit? A real possibility to improve what they did? Never we’ll know without an earnest, deep analysis.

In my first post a modest try in this direction.
Roberto
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Ed F



Joined: 22 Jan 2008
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Location: Ipswich, MA USA

Posted: Wed Jan 11, 2012 9:04 pm    Post subject: Reply with quote

I'm in sympathy with your aim. I have not found the additional interpretive material available through zodiacal directions to help me personally. So, I stick to mundo directions. There's still room for improvement. For instance, why not include secondary motion?

Regards,

- Ed
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Martin Gansten
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Joined: 05 Jul 2008
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Location: Malmö, Sweden

Posted: Wed Jan 11, 2012 9:43 pm    Post subject: Reply with quote

Roberto and I have had this discussion outside of Skyscript so many times that I don't want to get involved in it again (for anyone curious, my answer to the initial question is Yes: the traditional method of primary directions is indeed fully consistent). But I wonder if the thread really belongs here in the Traditional forum. After all, Roberto is proposing a new technique, not a traditional one. Wouldn't it be better to do so in the General forum?
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Tom
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Posted: Thu Jan 12, 2012 11:51 am    Post subject: Reply with quote

I don't mind if it's here, but I tend to agree with Martin. Unfortunately, I don't have the ability to move entire threads, or if I do I don't know how. As long as the discourse is civil it can stay. It's half traditional.
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Thu Jan 12, 2012 5:54 pm    Post subject: Reply with quote

Hi Tom. Thanks for the hospitality. It was not in my intention to violate the netiquette of this marvelous, unique forum. On the other hand, where to speak of PDs if not here? As I remember, somewhere I read Kolev says the PDs theory is quite far from the end. Moreover, as I know, techniques not really ancient are appreciated by the traditionalist astrologers. But, to say the truth, the core of the matter is not a new method (I do not pretend so much for my suggestion). And the subject are not the PDs in their wholeness. Martin is right: the traditional method of primary directions is indeed fully consistent. Only, under my point of view, the mundane and the zodiacal cannot be regarded in the same way. The first are fully consistent in their math applied to a full astronomical scenery, the zodiacal are consistent in their math if we limit the consistency to their mathematical definition. The question is: “Is such a mathematical definition in perfect agreement with an astronomical picture?” A sincere answer must be at least doubtful. My own answer is no, or at least this is not the best marriage. And, without astronomy or trigonometry, anybody is able to understand this, if we play with a simple, true example. Astrology and astronomy were one thing only: it’s not our duty to do our best in this direction?

Ed, excuse me if I do not reply to your post now. I’ll do that in the next one.

Regards,
Roberto
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Ed F



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Posted: Thu Jan 12, 2012 6:38 pm    Post subject: Reply with quote

No issue, Roberto. At your convenience.

- Ed
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Sat Jan 14, 2012 5:33 pm    Post subject: Reply with quote

Hi Ed.

Quote:
I have not found the additional interpretive material available through zodiacal directions to help me personally. So, I stick to mundo directions.

Sorry, but my astrological training about the ancient interpretative techniques is quite poor. So, I am not able to give you information or hints. My competence is astronomy oriented. I hope to fill my lacuna in the … third part of my life!

Quote:
There's still room for improvement. For instance, why not include secondary motion?

This is a very important conceptual detail. With a professional, technical eye let me say PDs are an “engineering” astrological technique applied the Ptolemaic model. Very powerful. For an engineer, and for an astronomer, if something is = 100.1234567… this something is 100.12 (bankers and economists have different ideas). The secondary motion is the equivalent of the figures 0.0034567… Not for the Moon, of course and, with small errors, for Sun and inner planets when the arcs of direction are wide. Really the accuracy we reach, neglecting the secondary motion, is enough. As everybody know, only the Moon needs a correction.

But with a deeper analysis I’d say the PDs as they are were a necessity. In their reckoning, all the necessary astrological data are included in the radix, attached to the native astronomical parameters. With a trigonometric procedure all the arcs are discovered at once (unless the figures 0.0034…) If you try to compute a *true* arc of direction only one method is possible: cast a new chart XX minutes after the birth (solar or sidereal? with which differences? But this is another matter) and compare the mundane position the promissor has here, with the mundane position the significator had at the birth. With the probability of 99,99% they will be different, so a further chart will be necessary. And so on, till, after N charts cast with successive approximations, you can arrive at the *true* astronomical arc, figures 0.0034… included. Tiresome, long, impracticable.

And if this procedure is performed by a PC? Why not? I am sure our old parents would be enthusiastic for this possibility. This is the best we can do: discover the true astronomical moment a promissor reaches the loved significator. This is why I consider a nonsense do not use the secondary motion everywhere, if possible (promissors only, of course). Note that the secondary motion has an orthogonal component towards the celestial equator, causing diurnal arcs not exactly overlapped to the parallels of declinations. The result are small changes in the semi-arch values during the diurnal motion. If in Regio and Campanus PDs this has not further consequences on the mundane position, in Placidian PDs the effect is an additional error (the intermediate cusps change their temporal position in the local space).

Excuse me for this wide divagation. In my later posts, if Tom permits, I’ll show with a simple example:
-why in my opinion the Zodiacal PDs, with their current premises, are not the most logical
-the most logical, always in my opinion, astronomical alternative (secondary motion included)
-an interpretative comparison between the two methods
If welcome, the mathematical foundations and the related formulas will be showed as well.

Regards,
Roberto
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Sun Jan 15, 2012 1:36 pm    Post subject: Reply with quote

Hello.
As promised I had prepared the following post, and I send it as it is.
At the bottom a ... surprise ending.

************************
To understand what is wrong is easier to understand what is right. If I find just only one black sheep, the assertion “All the sheep are white” is false. So, let me show one black sheep in the Zod PDs. Take care: *Zodiacal* PDs only.

I’ll use my birth data:
ROBERTO
Date 18 Oct 1954
Time 01: 20: 00
Lon 10° 29' E
Lat 43° 50' N
TZ +1 - CET
Place Lucca, ITALY

The first planet will be Saturn. For astronomical reasons, higher is the celestial latitude, darker is the sheep so, for technical reasons, the second planet will be Pluto that can have, for this parameter, a very high value. Moreover, in some consideration, I’ll round the values to the next degree. To find the Placidian Mundane Position (PMP) for an ecliptic projection, Morinus offers the possibility to define an user planet. Its speculum is showed, as well.

SATurn
[1] Its Long: SAT_lon = 9° 56’ 02” Sco = 219° 56' 02"
[2] Its RA: SAT_RA = 218° 13’ 19”
[3] Its mundane position (3rd place): SatPMP = 87° 10' 16"
[4] Its ecliptic projection (foot) mundane position (3rd place): SATzPMP = 86° 37' 47"

PLUto
[5] Its Long: PLU_lon = 26° 22’ 28” Leo = 146° 22' 29"
[6] Its RA: PLU_RA = 152° 14’ 34”
[7] Its mundane position (12th place): PluPMP = 358° 19' 36"
[8] Its ecliptic projection (foot) mundane position (1st place): PLUzPMP = 5° 23' 29"

[9] Their distance in zodiac: ZodDis = 220° - 146° = 74°
[10] Their zodiacal distance in mundo: MunDist = 86° - 5° = 81°

Using Morinus, in the PDs options select: Placidus(semiarc)/Zodiacal/Use latitude of: Neither.
Let’s reckon now the two following Zod PDs (analogical key and hit-dates are insignificant), with a remark.
I’ll use direct and converse directions for technical reasons only. I do not enter in the validity of the converse ones. Morinus shows:

********************************************
[11] Z - Plu - C - Sat - (69.932) = 70.0° ......... to cover roughly 74° in zodiac (and 81° in mundo)
********************************************
[12] Z - Sat - D - Plu – (94.499) = 94.5° ........ to cover roughly 74° in zodiac (and 81° in mundo)
********************************************
The first result is plausible, but the second one? A difference 20° wide? Moreover, even if values of the two reverse arcs are generally different, is the amount of the difference credible? An astronomer should say immediately whichever definition is under the above algorithm is not compatible with the astronomy. For those of us not so expert in astronomy will see below why.

First of all, let me verify if Morinus is correct computing manually the second PD (Take care: the following formula is valid only if the significator is located in the first quadrant).

[13] DA=RASat(zod)-RAIC+(90-ADSat(zod)(MDPlu(zod))/(SAPlu(zod))
[14] DA=217.524722-221.445278+(90+14.691389)72.833611/77.475000 = 94.499

So, Morinus is correct, and the value of the arc [12] is due to the premises of computation that, we remember, use the ecliptic planetary projections as bodies that apply the general PDs algorithms.

We must now discover the acceptable values for the second [12] PD. To do that, I believe we must remain faithful to the teaching of our ancient masters. The greatest of them, thanks to God, is still alive: the sky. So, let’s ask to the sky which are the rough equatorial arcs permitted for it. It’s easy. We must find two true dates: the first in which Saturn has the native Pluto longitude, the second in which Pluto has the native Saturn longitude. For such dates we must verify the planetary RAs end finally, for difference with the native RAs, understand the approximate, conceivable equatorial arcs.

First date, when Pluto reaches the native Saturn longitude
To find quickly the date, I use the Astrolog32 animations.
On 3 Nov 1997, time 16:09:32 (other data according to my radix) Pluto is located in zodiac at 9° 56’ 02” in Sco, the same Saturn had at moment of my birth.
Its Right Ascension, in such a “future” moment, is
[15] RA Plu_f= 222° 24’ 49”
So, starting from the birth, to cover the arc in zodiac we have in [9], i.e. 74°, Pluto travelled along the equator in the amount of a real, astronomical *Progression* Arc, PA,
[16] Pluto PA = RA[6] – RA[15] = 152° 14’ 34” – 222° 24’ 49” = – 70° 10’ 15” = C 70°
This value is in perfect agreement with [11] and with our qualitative considerations.

Second date, when Saturn reaches the native Pluto longitude.
On 21 Aug 1948, time 2:20:00 (other data according to my radix) Saturn is located in zodiac at 26° 22’ 28” in Leo, the same Pluto had at moment of my birth.
Its Right Ascension, in such a “past” moment, is
[17] RA Sat_f= 149° 02’ 21”
So, starting from the birth, to cover the arc in zodiac we have in [9], i.e. 74°, Saturn travelled along the equator in the amount of a real, astronomical *Progression* Arc, PA,
[18] Saturn PA = RA[2] – RA[17] = 218° 13’ 19” – 149° 02’ 21” = + 69° 10’ 58” = D 69°
This value is in perfect DISAGREEMENT with [12]. We found the BLACK SHEEP.

Well: up to here we have verified that the current assumptions the Zodiacal PDs are based on, under a (pseudo) astronomical viewpoint, are not credible. At present, the arcs of direction are sometimes clearly absurd. Therefore we can suppose even when the DAs are credible, their values are not the correct ones, even if with smaller errors. In the next post we’ll see the second, heavy inconsistency.

Of course I am open to comments and objections. We are dealing of ancient techniques, tested for centuries, and I am aware I can be wrong somewhere. So please, see this my initiative as an aloud, public reflection.

************************
Before to send this post, I verified the same PDs under Regio. The situation is the same. So, the problem is general. My alternative method is a possible solution (it works), but now I have a doubt. Perhaps another possibility exist: try to recover the bug existing in the current Zodiacal PDs. In the example, the first PD is correct, only the second is wrong. 90% the problem is hidden in the evaluation od the sign the Ascensional Difference has in some circustances. Of course the second inconsistency is inevitable. Asap I'll investigate on the matter. For the moment I suspend my posts. Probably the tradition can be ... recovered :-)

Regards,
Roberto
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Ed F



Joined: 22 Jan 2008
Posts: 301
Location: Ipswich, MA USA

Posted: Sun Jan 15, 2012 2:58 pm    Post subject: Reply with quote

The part that bothers me about your observation is that the directional arcs are based on oblique projections into the mundane sphere, while your arcs are based on right projections to the equator. The former necessarily involve geographic latitude, while it plays no role in the latter (and does not factor in the relationship between the horizontal and equatorial coordinate systems.

If the bodies involved were observable, you could see this difference in the sky.

- Ed
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robhywolf



Joined: 08 Jan 2012
Posts: 22
Location: Lucca, Italy

Posted: Sun Jan 15, 2012 4:33 pm    Post subject: Reply with quote

Ed F wrote:
The part that bothers me about your observation is that the directional arcs are based on oblique projections into the mundane sphere, while your arcs are based on right projections to the equator. The former necessarily involve geographic latitude, while it plays no role in the latter (and does not factor in the relationship between the horizontal and equatorial coordinate systems.

- Ed

You mean the method I suggest? Yes it's the truth. And better to say "right projections *from* the equator" by the ecliptic circles of longitude. Really what happens in this way is we can reckon the pseudo-zodiacal positions thanks to a simple coordinate system transformation: equatorial to pseudo-ecliptic. But do not forget the frozen ecliptic is located in the local space. The new pseudo-zodiacal positions that arise during such a motion, change their coordinates in the horizontal system (the astrological local space). On the other hand, this is a basic rule: posizions in zodiac are what they are, regardless to the geographic coordinates.

Ed F wrote:
If the bodies involved were observable, you could see this difference in the sky.

- Ed

Sorry: here I am not able to follow you. Can you tell me with different words?

Roberto


Last edited by robhywolf on Sat Aug 17, 2013 12:24 pm; edited 1 time in total
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Ed F



Joined: 22 Jan 2008
Posts: 301
Location: Ipswich, MA USA

Posted: Sun Jan 15, 2012 5:37 pm    Post subject: Reply with quote

robhywolf wrote:

Ed F wrote:
If the bodies involved were observable, you could see this difference in the sky.

- Ed

Sorry: here I am not able to follow you. Can you tell me with different words?

Roberto


Try this. Find two planets, one on the ASC and one on the MC (zodiacally). Use your method to move the one at the ASC to the MC degree. I'm pretty sure your resulting arc will (most likely) not be that of the diurnal semiarc of the ASC and MC zodiacal degrees.

- Ed
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