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Fixed Stars: Ptolemy vs Ulugh Beg/Regiomontanus?
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Mark
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Posted: Fri Feb 26, 2010 8:00 pm    Post subject: Fixed Stars: Ptolemy vs Ulugh Beg/Regiomontanus? Reply with quote

I have been re-reading Bernadette Brady’s Book of Fixed Stars recently and I came across an interesting historical point she refers to in regards projecting the position of fixed stars on to the tropical zodiac. Although most of her book is concerned with her interpretation of local space ‘star parans’ she does make a very interesting observation in regards the common traditional technique of projecting the position of stars on to standardised degrees within the tropical zodiac. In particular Brady suggests the traditional technique of projecting the position of stars used by Claudius Ptolemy ( 2nd century AD) was abandoned by the 15th century astronomers Ulugh Beg and Regiomontanus and that astrology followed them in this reform.

Here is Brady herself on this issue:

Quote:
The projected ecliptical degrees (called PED in this text) of Ptolemy were based on the poles of the ecliptic. His list of 1022 stars and their PED were then precessed through the ages, with each generation of astrologers adding the current rate of precession to find the ecliptical position of any star in their time. Ptolemy’s star catalogue was used in this manner for well over a thousand years until the time of Ulugh Beg (1394-1449) a Mongolian –Turkish ruler and astronomer who developed the Fakir sextant , and that of Regiomontanus (1436-1475), these two astronomers re-plotted all of Ptolemy’s star catalogue, which laid the foundation for Albrecht Durer (1471-1528) to produce star maps based on the poles of the equator rather than the manner of Ptolemy who based his measurements on the poles of the ecliptic . Using this new method of projection, each of the 1022 stars of ptolemy’s list was given a new ecliptical position. The astrologers in the time of ulugh beg and Regiomontanus seemed to accept this change in the position of fixed stars without question. Since that day , astrologers and astronomers alike have used the poles of the equator rather than the ecliptic for all such projections. Brady's Book of Fixed Stars, Bernadette Brady, p11


I am aware astronomy shifted away from the ecliptical method of locating star positions based on longitude and latitude to the equatorial approach based on declination and right ascension. However, if I am reading Brady correctly her point is that astrology also changed its technique in the 15th century of projecting the position of stars on to the tropical zodiac. The result being that the zodiacal position of a star can vary by many degrees in some instances. For example see the differences for Regulus and Arcturus below. Considering many astrologers only use a 1 degree orb for fixed stars this can be very significant in terms delineation.

I have extracted data from Brady’s tables for stars at the end of her book to give some illustrative examples of the differences using the two techniques. All star positions are for 2000AD.

Star/ Ptolemy/ Beg-Regiomontanus

Antares/ 8’30 Scorpio/ 9’45 Scorpio
Aldebaran/ 8’40 Gemini/ 9’47 Gemini
Altair/ 29’40 Capricorn/ 1’47 Aquarius
Canopus/ 13’00 Cancer/ 14’58 cancer
Regulus / 26’20 Leo/ 29’42 Leo
Arcturus/ 00’00 Libra/ 24’13 Libra
Algol/ 25’30 Taurus/ 26’10 Taurus


I must admit I had always assumed the standardised position of fixed stars in the tropical zodiac was being derived from projected ecliptical degrees through the poles of the ecliptic. Do these differing techniques require traditional astrologers to question the position of fixed stars in the tropical zodiac?

I would really welcome other members opinion on this topic. Confused

Thanks

Mark
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Last edited by Mark on Sun Feb 28, 2010 2:11 am; edited 1 time in total
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dr. farr



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Posted: Sat Feb 27, 2010 3:37 am    Post subject: Reply with quote

I believe that the shift from Ptolemy's basis represents a more precise determination of star positions, and therefore yields more correct indications of stellar influence. The Chinese astrologers also (correct me if I am mistaken) utilize the equator rather than the ecliptic in their fundamental approach to conceptualizing the heavens.
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Mark
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Posted: Sat Feb 27, 2010 3:26 pm    Post subject: Reply with quote

I should perhaps clarify that in the first star locations cited above Brady is deriving the projected ecliptical degrees through the poles of the ecliptic using Ptolemy's star catalogue. She suggests that where these produce large differences in the two techniques ( see Regulus or Arcturus) these are probably due to scribal error in recording Ptolemy's catalogue or errors of calculation made by Ptolemy himself.

Mark
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Mark
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Posted: Sat Feb 27, 2010 3:40 pm    Post subject: Reply with quote

Quote:
I believe that the shift from Ptolemy's basis represents a more precise determination of star positions, and therefore yields more correct indications of stellar influence. The Chinese astrologers also (correct me if I am mistaken) utilize the equator rather than the ecliptic in their fundamental approach to conceptualizing the heavens.


Thanks Dr farr,

While there were inevitable limitations on Ptolemy's recording ability in that historical period does that undermine the basic technique he proposed? In short why is his method inferior? This would seem a bitter pill for some traditionalists to swallow. Wink

Its correct Chinese astrology uses a largely equatorial approach. However, this is rather like comparing apples and pears. As you know the Mesopotamian-Hellenistic/Indian astrological traditions were founded on the ecliptic. Why therefore should be abandon the ecliptic for an equatorial co-ordinate system in this instance? There is no denying that the equatorial co-ordinates of declination and right ascension are extremely helpful for calculating things such as the rising times of stars or whether they are circumpolar or invisible from a certain location.

Perhaps there is a perfectly sound mathematical explanation for this. Unfortunately, I dont know what it is. If there is a clear improvement delivered in the Ulugh Beg/Regiomontanus approach to projecting fixed stars on to the tropical zodiac I would really like to hear what it is.

Regarding Bernadette Brady it needs to be said that she has little time for either method she cites. Its largely a Trojan Horse argument before making the case for the superiority of star parans in all instances.
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johannes susato



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Posted: Sat Feb 27, 2010 6:55 pm    Post subject: Reply with quote

To ascertain the position of a star you can refer to the celestial poles and the equatorial level. The position is given by right ascension and nothern or southern declination.
But you can also refer to the ecliptic and its poles. The position is then given by ecliptical longitude and northern or southern ecliptical latitude.
This has Mark already explained too.
Once a star's position is determined it can be converted in ecliptical or equatorial measurement or contrariwise. But the position itself, projected on the Ecliptic and measured in ecliptical longitude and latitude remains always the same even then when calculated first to right ascension and then to ecliptical longitude - or vice versa.

The differences mentioned by Brady and quoted by Mark do not have their origin in these differing reference systems because there is no difference as to the ascertained point: Both systems lead you to the same star! The differences are by wrong - becaue at his time dated - position data which Ptolemy claimed to have gathered by own observation but which in reality he only cited they being gathered some time earlier (100-150 years?) by his antecessors. It was not before Ulugh Beg and Regiomontanus - and probably some other astrologers/astronomers, but very little, earlier than they - that the differences between tables backing to Ptolemy and the real positions were discovered by observation. The differences may be of the same amount as the precession for the time gone after the observations of Ptolemy's antecessors and his own period.


Last edited by johannes susato on Sat Feb 27, 2010 11:00 pm; edited 1 time in total
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Mark
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Posted: Sat Feb 27, 2010 10:43 pm    Post subject: Reply with quote

Quote:
Once a star's position is determined it can be converted in ecliptical or equatorial measurement or contrariwise. But the position itself, projected on the Ecliptic and measured in ecliptical longitude and latitude remains always the same even then when calculated first to right ascension and then to ecliptical longitude - or vice versa.


Hello Johannes,

Thanks. If as you state both methods of projecting stars on to the ecliptic produce identical results, if done correctly, then there really is no substantive issue at stake here. Instead the issue just seems to revolve around astronomical or later scribal errors in Ptolemy's star catalogue. From a practical astrological point of view that is quite reassuring. Very Happy

I suspect Brady's reason for highlighting this point is largely polemical as anyone who has read her work or heard her speak knows she is a severe critic of Ptolemy's approach to fixed stars.

Mark
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Last edited by Mark on Sun Feb 28, 2010 2:08 am; edited 2 times in total
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johannes susato



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Posted: Sun Feb 28, 2010 1:32 am    Post subject: Reply with quote

Hi Mark,

sorry for this confusion. It is you to whom my article is addressed to and correction as to your name is made already.

Johannes
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Mark
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Posted: Sun Feb 28, 2010 2:05 am    Post subject: Reply with quote

Hello Johannes,

Ok I will delete my question then!

Thanks.

Mark
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dr. farr



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Posted: Sun Feb 28, 2010 4:24 am    Post subject: Reply with quote

As a near-fanatic regarding the use of stars in macrocosmic analysis ("fixed star Farr"!) I obtained the Brady book immediately when it was published. A lot of interesting material in it, but I personally was not motivated to follow Brady in substituting paran considerations for our more commonly applied star-delineation techniques (longitudinal conjunction, parallel/contra-parallel of declination, etc) But I was stimulated to compare the Ptolemy-observed star positions with the positions determined by the techniques used in astrology over the past 500 years. I took a look at about 12 (maybe 13) charts in my possession, each of which contained substantial stellar indications. When I applied the Ptolemy-observation based star positions (via Brady) to these charts, I noticed a SUBSTANTIAL REDUCTION in the number of meaningful stellar testimonies (and the orbs of influence I use-relative to longitude- are not all that tight: fully 3 degrees for 1st mag, 2 degrees for 2nd + 3rd mag, only going to 1 degree in the case of 4th mag stars) This little finding of mine led me to speculate that perhaps Ptolemy's star-position inaccuracies might have led to disappointments in attempts to accurately determine stellar testimonies in astrological practice during the centuries subsequent to Ptolemy, as later "Greeks", Persians and "Arabs" developed the fundamentals of the Western astrological model. It had always struck me as odd why (compared to ancient Egypt, Mesopotamia, and of course to the Chinese systems) the stars have been considered essentially as secondary factors (at best) in our Western tradition. Perhaps disappointment from attempts to obtain meaningful stellar testimony using Ptolemy's inaccuracies is the historical cause? However, this is only my own personal (tentative) speculation.
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margherita



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Posted: Sun Feb 28, 2010 9:48 am    Post subject: Reply with quote

dr. farr wrote:
A the stars have been considered essentially as secondary factors (at best) in our Western tradition. Perhaps disappointment from attempts to obtain meaningful stellar testimony using Ptolemy's inaccuracies is the historical cause? However, this is only my own personal (tentative) speculation.


Sorry if I disagree, but we are sure that stars are been neglected in Western tradition? Moreover because of Ptolemy's mistakes Smile

What about the stellar catalogue of Anonymous 379 repeated in Rethorius, Mashallah (see Dr.Dykes Persian nativities), Albumasar (translated by Prof. Burnett) and printed and re-printed as Liber de stellis beibenie.
And what about all the list of stars meaning in all Renaissance authors (myself I translated Stade and Cardano one)?

And the other thread coming from Teucer' sphera barbarica from which derives Albumasar facies and Astrolabium Planum and their visual representation in Italian Renaissance art like Schifanoia frescos or Agostino Chigi birth chart painted in the ceiling of his villa?

I would say that we have so many reference to stars in astrological literature.

margherita
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Tom
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Posted: Sun Feb 28, 2010 12:53 pm    Post subject: Reply with quote

I'm curious about Regulus. Since Regulus is on the ecliptic, why is there a three degree difference in the commonly used position of 29 Leo and the other one? It would seem that it would remain where we've always used it.

Tom
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Eddy



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Posted: Sun Feb 28, 2010 12:56 pm    Post subject: Reply with quote

I had a look in the Almagest here in the library.

Aldebaran 12°40' Taurus
Canopus 17°10' Gemini
Regulus 2°30' Leo
Spica 26°40' Virgo
Arcturus 27°00' Virgo
Antares 12°40' Scorpius
Altair 3°50' Capricornus

To get the 2000 values ca. 27° has to be added because of precession. There seem to be no serious mistakes (larger than a degree or so) in Ptolemy. If in Brady's table Spica and Arcturus would be strongly different, then there's reallysomething wrong. Can someone have a look please? They are namely in conjunction. Aldebaran and Antares are in opposition. These positions change but slightly, some arcminutes per century and aren't much different from Ptolemy's times. I read once in an ephemeris this quote:
Quote:
An error in the calculation of an ephemeris is as sinful as the murder of a Brahmin. (Varaha Mihiras Brihat Jataka, ca. 540 A.D

Perhaps the mistakes aren't that sinful but very inconveniant.

Quote:
Regarding Bernadette Brady it needs to be said that she has little time for either method she cites. Its largely a Trojan Horse argument before making the case for the superiority of star parans in all instances.
Quote:
I suspect Brady's reason for highlighting this point is largely polemical as anyone who has read her work or heard her speak knows she is a severe critic of Ptolemy's approach to fixed stars.
Especially someone who criticizes someone's elses work should clearly explain and understand what technique was used and mention sources. Her list is not the Almagest's and the positions are plain wrong, I wonder what her source for these star positions was.

Here's the difference between ecliptical and equatorial coordinates.
Aha, that's what these [Img] things are for.. Smile

Johannes is right
Quote:
Both systems lead you to the same star!


I hope this link works, the image funtion didn't work on this. The situation here is close to the picture above but then seen from inside out, how we would see. Hamal in Aries could be close to that position. Now if we look in the fourmilab picture. The coordinates show in equatorial and ecliptica positions. Here are these positions in numbers, click Hamal for the details.

There is also a conversion formula for equatorial to ecliptical which can be performed with a calculator. http://en.wikipedia.org/wiki/Ecliptic_coordinate_system

As for the change to equatorial coordinates, I think the astronomers did this for conveniance. The measuring instruments (armillary spheres) for star positions would be easier to build and don't need the ring for the ecliptic. Hence the instrument could be made bigger and thus more exact. The astronomers had disposal over (co)sine tables etc to convert to ecliptical positions for astrology. I don't know if astrologers outside China used the equatorial coordinates as Brady seems to say. Perhaps the Chinese might have inspired the western astrologers to use equatorial coordinates/instruments (see. Christopher Walker's 'Astronomy Before the Telescope', p.261).

It seems that Brady simply prefers mundane/paran star positions over ecliptical. For which method is the better one, that's a different discussion.

Tom wrote:
I'm curious about Regulus. Since Regulus is on the ecliptic, why is there a three degree difference in the commonly used position of 29 Leo and the other one? It would seem that it would remain where we've always used it.

Tom
I don't know what is exactly wrong with the table but because of precession Regulus won't remain for always in tropical Leo. In just a few years the 'Heart of the Lion' will be in .... Virgo Surprised.
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margherita



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Posted: Sun Feb 28, 2010 1:12 pm    Post subject: Reply with quote

Tom wrote:
I'm curious about Regulus. Since Regulus is on the ecliptic, why is there a three degree difference in the commonly used position of 29 Leo and the other one? It would seem that it would remain where we've always used it.


I have the same curiosity, but obviously Mark is just reporting Brady, we should ask her.

Eddy wrote:
It seems that Brady simply prefers mundane/paran star positions over ecliptical. For which method is the better one, that's a different discussion.


Paranatellonta is a traditional method.
This is Albumasar from "Albumasar is Sadan" (I've the whole text, not the abstract given by Thorndyke, I think he jumped this)

Fixed stars have a great influence in nativities; especially the ones near the equinoctial circle have great strength at the Ascendant.
But the ones who are far from the equinoctial circle have weak effects


If Brady says that we should take stars when they arises with the Ascendant or culminating with MC, she is traditional.
Or does she say something else?

For me- following CieloeTerra method- when a star has the same oblique ascension than the Ascendant is rising, when it has the same right ascension than the MC is culminating, for the rest I take their position "in mundo" and compare with the position "in mundo" of planets.

p.s. Just I want add I liked very much Joseph Crane chapter about fixed stars in "Astrological roots." Very like I was taught.

margherita
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johannes susato



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Posted: Mon Mar 01, 2010 12:50 am    Post subject: Reply with quote

Gjiada wrote:
dr. farr wrote:
A the stars have been considered essentially as secondary factors (at best) in our Western tradition. Perhaps disappointment from attempts to obtain meaningful stellar testimony using Ptolemy's inaccuracies is the historical cause? However, this is only my own personal (tentative) speculation.


Sorry if I disagree, but we are sure that stars are been neglected in Western tradition? Moreover because of Ptolemy's mistakes Smile

What about the stellar catalogue of Anonymous 379 repeated in Rethorius, Mashallah (see Dr.Dykes Persian nativities), Albumasar (translated by Prof. Burnett) and printed and re-printed as Liber de stellis beibenie.
And what about all the list of stars meaning in all Renaissance authors (myself I translated Stade and Cardano one)?

And the other thread coming from Teucer' sphera barbarica from which derives Albumasar facies and Astrolabium Planum and their visual representation in Italian Renaissance art like Schifanoia frescos or Agostino Chigi birth chart painted in the ceiling of his villa?

I would say that we have so many reference to stars in astrological literature.

margherita



Margherita,

of course you are right with the catalogues. But my understanding of dr. farr's opinion is that he only points out that
Quote:
the stars have been considered essentially as secondary factors (at best) in our Western tradition.

This argument is not disproved by the catalogues. Antiscia are also mentioned by nearly every author but surely not used as primary factors (with the exception of Firmicus Matrernus possibly). The same as to fixed stars, I think: They have surely been used but they have not been primary factors in western tradition really, haven't they?

And when dr. farr continues:
Quote:
Perhaps disappointment from attempts to obtain meaningful stellar testimony using Ptolemy's inaccuracies is the historical cause?

is it not a fact meanwhile that the declaration of the fixed star positions by Ptolemy was erroneous?
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Mark
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Posted: Mon Mar 01, 2010 1:38 am    Post subject: Reply with quote

Eddy wrote:
Quote:
It seems that Brady simply prefers mundane/paran star positions over ecliptical. For which method is the better one, that's a different discussion
.

Margherita wrote
Quote:
Paranatellonta is a traditional method.


In my opinion you are both correct. However, I do think there is a serious question mark over how closely Brady's 'Star paran' technique resembles the Paranatellonta mentioned in the tradition. In fairness though, that is an issue outside the strict scope of this particular thread. Nevertheless, its something I do hope to specifically focus on in a new thread in the near future.
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