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Regiomontanus and Placidus
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aquirata



Joined: 31 Mar 2006
Posts: 157
Location: Canada

Posted: Fri Jan 18, 2008 3:02 pm    Post subject: Reply with quote

Matt,

http://www.astrology.co.uk/Books/Subjects/bs.ReferenceBooks.html
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Peter
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Mike W



Joined: 15 Jan 2008
Posts: 4

Posted: Fri Jan 18, 2008 5:01 pm    Post subject: Reply with quote

Matt

The AFA may still do Regio tables. Try the Midheaven bookshop

email John - midheaven@compuserve.com


To Astraea

You’re welcome, though I detect little detail in my response.

I notice also that my intervention has absolutely nothing to do with your original question! In that regard, I can do no more than speculate as to why astrologers do what they do …. so I won’t.


To Papretis

Quote:
shouldn't everything work normally then (except that the houses can be very unevenly sized)?



Hi,
Yes, it does (work normally) but the inequality you perceive is not what you think. Not with Regiomontanus, anyway.

The 2nd part of the series addresses all the issues you raise, especially wth regard to Regio., and I’ve already sent it to Deb. If you still have any questions after that, I’ll be more than happy to try to answer them. Note: Part 5 returns to Regiomontanus and deals with a few imore issues.

For now I would confirm that the real ‘problems’ do, as you suggest, surface at the Polar Circles… But that’s not to say they weren’t already there. With Regiomontanus, the rot starts the moment it leaves the Equator, as will be argued. This doesn’t apply to the Topocentric system, by the way. Had you been using that one, you might well have experienced difficulties by now: Anyone born about 4 degrees to your north could find their “2nd cusp in their 12th house,” for example, which is why Topo’s tables of houses omit the few latitudes immediately below 66˝N. The Koch system also has ‘problems’ in those latitudes.
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Julie K



Joined: 03 Sep 2007
Posts: 378
Location: Australia

Posted: Sat Jan 19, 2008 12:45 am    Post subject: House Systems Reply with quote

Hello,

These posts are interesting to some on like myself as I have not worked with Horoscopes at such high Lagtitudes, even though I have certainly seen them. I live in the Southern Hemisphere and if one cares to look at a World map then you can see there is little land mass in the Southern Hemisphere where one could be born, in comparison to the Northern Hemisphere. Not many NH Astrologers consider this or think about it.

I use Placidus House System mostly for Natal work, and find it curious I have lived my life according to the particular system. I find, however, Alcabitius does appear to be more appropriate for me as the Interceptions disappear and my Leo Sun rules the 5th House.

Regiomontanus was the system to use for Horary according to my teachers so I have stuck swith this. Bernadette Brady suggests Campanus would be best for lost items as it is space based rather than time based.

I dont know how hard and fast one should be here but if a House System 'works' for you and you are comfortable with it, then it appears to make good sense to me to use it.

Julie K
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Astraea



Joined: 04 Oct 2004
Posts: 359
Location: Colorado, USA

Posted: Sat Jan 19, 2008 3:15 am    Post subject: Reply with quote

Hi Julie. Indeed, many astrologers were trained to use Placidus for natal work and Regiomontanus for horary; I've never understood the reason for this switch, but as Tom said earlier, it's probably down to training, pure and simple.
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aquirata



Joined: 31 Mar 2006
Posts: 157
Location: Canada

Posted: Sun Jan 20, 2008 11:40 am    Post subject: Reply with quote

Hello Mike,

Thanks for your detailed reply.

Quote:
On the contrary, I have not redefined the Ascendant, the signs, nor the houses, as has been suggested. Some qualification will be forthcoming in respect of the “MC” and the 10th house (because culmination can occur below a circumpolar horizon) but otherwise classical definitions of all terms are adhered to throughout.

I wasn't trying to suggest that you had redefined the Asc, MC, signs or houses. What I read in your article (and were conveying in my post) was that you were interpreting the first principles differently than others. You were arriving at a different chart than others. Meaning that your definition of parameters in the chart must be different. Not right or wrong or deviating from first principles, just different. So not a redefinition, just a different interpretation of first principles.

Quote:
The 2nd part of the series addresses all the issues you raise, especially wth regard to Regio., and I’ve already sent it to Deb... With Regiomontanus, the rot starts the moment it leaves the Equator, as will be argued.

I'm very curious to read this second part. My simple view of the Placidus system is that of dividing the day into 6 equal parts and the same for the night. Regiomontanus on the other hand produces a mathematically pleasing sine curve when I examine how much time the planets spend in the various houses (excepting their zodiacal motion within the day). So I would be very much surprised if you could show that Placidus worked beyond the polar circle and Regiomontanus didn't. I haven't really dove in detail into this topic, so I'm at a disadvantage to discuss it, but deep down, in principle, I just don't see why there should be such a drastic difference between the two.

So I really look forward to reading your entire series. What was the reaction to your articles, by the way, when they were first published? Did anyone get down into the details, or is this kind of material not of interest to (or over the head of) most astrologers?
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Martin Lewicki



Joined: 23 Mar 2007
Posts: 46

Posted: Sun Jan 20, 2008 1:04 pm    Post subject: Reply with quote

The problem of houses in the polar regions are perplexing....

http://en.wikipedia.org/wiki/Ascendant#Ascendant_in_Polar_Regions

Martin
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Mike W



Joined: 15 Jan 2008
Posts: 4

Posted: Mon Jan 21, 2008 4:27 pm    Post subject: Reply with quote

Peter,

Good to hear from you.

If I do “interpret first principles differently” it is because I will not read the mundane sphere (the houses) via the Zodiac. Nor should anyone else, though most do. For example, a planet conjoining the Asc is often presumed “on the 1st” though such is rarely the case. It is on the first house cusp as it transits the eastern horizon, which, due to planetary latitude, is rarely the same thing. (Likewise, a planet culminates when it arrives at the N/S meridian, not when the ephemeris says it is “conj. MC.”) The Asc is thus determined by the horizon, not vice versa, but the latter is what astrologers do when they reinterpret the mundane sphere via Ecliptic longitude.

I can think of no other way in which I might be interpreting ‘differently.’

Regiomontanus’ “mathematically pleasing sine curve” does not apply in the areas of celestial space that do not rise or set. Moreover, this “law of signs,” which I do not fully understand because I am no mathematician, presumes that the sky is always (what Ptolemy called) a “right sphere.” It is almost never is.

With regard to the last point of your penultimate paragraph, Regio and Placidus are indeed very alike.

The topics above won’t appear in part 2 but will be dealt with in part 5 - and in non-mathematical language. If I miss anything, please let me know. I would ask one other thing of you: read me slowly. And - NB - the meat is in the footnotes.

As for reaction to the series, I’m not sure. For starters I have limited access to the internet and,.as an AA non-member, couldn’t access the Correlation site. The first paper was in response to Robert Hand acolytes, who had piled into another internet forum with much ill-informed circumpolar advice. I’d found the site by accident at the end of 2000 and these guys were just plain wrong in what they said. I felt the need to do something about it - and “paper” turned into a series - but the nature of the material dictated that it went to the research mag rather than to the AA Journal, even though Correlation is not really a place that espouses horoscopy of this nature.

The series was interrupted, due to demands upon the editor, and thus appeared in dribs and drabs over too many years. I received but two direct communications in response. One of these was from AFA author Robert Powell, who had promptly photocopied the entire thing and was dishing it out to anyone who’d listen (and probably to several who couldn’t). His enthusiasm encouraged me to re-run it on Skyscript, where traditional values are embraced, and I can at least be on hand to respond to and clarify any issues. (That’s a point. We’re now way off the purpose of this thread. Is a new one in order?)

I don’t know if Robert understood every argument raised but Dieter Koch (author/programmer of the Swiss ephemeris and no relation to Walter) most certainly did. Dieter and I do not apply my conclusions in the same way but we most certainly share them.

I have also now appended material that came to light because of the series. I apologise in advance for the length and scope, each incurred by a determination to write in a manner fit for non-mathematicians. It addresses the mind’s-eye, not the left brain.

PS - the page linked above by Martin Lewicki is a crock …. even though parts of it do bear an uncanny resemblance to things I’ve written in the past. It starts out okay but the circumpolar section falls into the same old trap of reading everything via the Ecliptic.

MikeW
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Andrew



Joined: 31 Dec 2004
Posts: 360

Posted: Mon Jan 21, 2008 6:42 pm    Post subject: Reply with quote

Quote:
Dieter and I do not apply my conclusions in the same way but we most certainly share them.


Given that you have limited access to the internet, I'm wondering if you've had the opportunity to read either of these articles:

http://www.astrotexte.ch/sources/others/houses.pdf

http://www.auxmaillesgodefroy.com/qvviki.cgi?p=RudigerPlantiko

The second article (text reproduced below) summarizes the findings of the first:

Quote:
Notes from "On Dividing the Sky" (2004) about the history of house divisions and historical details of how they have been calculated. It was written by mathematician Rudiger Plantiko. These are notes and brief excerpts that provide an overview of his conclusions. The paper is mainly a comparison of the mathematical concepts and calculations behind the house systems.

Definitions

motus primi mobilis
The daily motion of the sky.
dominfication
Dividing the sky or at least the Ecliptic into twelve parts, taking into account in some way or another the daily motion of the sky.
theory of directions
A part of the Horoscope is taken to the house position of another part by the daily motion of the sphere. The angle of rotation, the so-called directional arc, to make this coincidence happen, is translated into lifetime using a proportionality factor which traditionally was the equation of one degree of arc with one year of the native's life.
mundane position
A quantification of the position of a celestial body in relation to its daily motion.

House Systems

Earliest house division, counted houses, was positioning the zodiac as it was seen in the sky. This was used by the Greeks and others about 2000 years ago, since it requires no math. The lots (like lot of fortune) were calculated from the sign cusp, not the ascendent.

The equal house system (all houses = zodiac sign) was more precise.

To let the first house start 5 degrees before the Ascendant, is a specialty of the Ptolemeic variant of the equal house system. Ptolemy was not consistent in his use of houses, so there have been confusing explanations for this over time.

He goes into a very detailed explanation of how house systems are calculated and what each measures. If you like the math, you should read this.

Plantiko Summarizes

* While the first methods worked on the Ecliptic alone, the introduction of the mathematical MC and the increased geometrical skills made it clear that the reference system for the houses, as a partition based on the daily rotation of the sphere, could not be the Ecliptic.

* Beginning with Rhetorios, astrologers switched to the Equator as reference plane. Since the degrees of the Equator all ascend with the same velocity, the Equator can be regarded as a big celestial clock. For a division of the sky according to its daily rotation it is therefore natural to base it on the Equator.

* The more stress was laid on the connection of house division and directional techniques, the more it became apparent that the house division should be extensible to the celestial sphere. The search for spherical house systems began.

* The Campanus/Al Biruni method was geometrically most satisfying, as the houses could be derived from a global division of the sphere by position circles into twelve perfectly equal diangles.

* Haly Abenragel and Regiomontanus corrected this tendency to the other direction and put the Equator back in his rights for this problem.

* Maginus and Placidus come back to the house division as division of times (more precisely: as division of the daily arcs described by the stars).

Primary Directions
"The system of mundane position that had been outlined by Ptolemy in his famous chapter III.10, has been used for primary directions by many astrologers. It is a strange fact that his concept has been used for domification not before the 17th century. How can this delayed evolution be explained? Why did we have to wait almost 15 centuries, until the house system has been worked out by Placidus and Maginus which belongs organically to the Ptolemeic concept of mundane positions?"

Why?

1. Lack of mathematical understanding.
2. Misunderstanding Ptolemy. (Ptolemy was not always clear and people were trying different interpretations to figure it out, dependent also on their skills in math.)
3. Belief in an ideal that astronomy should work with circles only.
4. Baroque emphasis on harmonic proportions.
5. Turn from cosmos to individual. In contrast to other house systems, the Placidus system lays a special emphasis on the subjective perception.
6. The dawn of the physical age (Placidus calls astrology physiomathematics and tries to found the complete astrological building on light and motion).
7. Increasing individualism. Each point of the sky is considered with its proper mundane coordinate system. The new individualism that started with the Renaissance times can be seen as a factor which favoured the development of this house system.
8. Increasing routine in solving iterative equations (the mathematical abilities improved).

Conclusion

"In the course of this paper, we have seen that the historical manifestation of an idea is neither a unique event nor a linear, straight process. There are many sideways, there are necessary stages to reach first, there are phases of stagnation and even fallbacks. But the example shows that in due time the idea will be fully established."


A bit more complicated than house = sign ... ?

Andrew
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Papretis



Joined: 27 Feb 2005
Posts: 346
Location: Finland

Posted: Tue Jan 22, 2008 2:13 pm    Post subject: Reply with quote

Hi Mike,

and thank you for your detailed answer. I'll read the remaining parts of your article series slowly and carefully.
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Ed F



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

Posted: Tue Jan 22, 2008 8:05 pm    Post subject: polar houses Reply with quote

Mike,

Just wanted to say that I found your article one of the clearest expositions of the issues. The Plantiko presentation is pretty good as well, but it's been a while since I looked at it, and I think I did disagree on a few points.

Your insistence on keeping the "mundo" perspective at the center of any consideration of quadrant systems is to me a key point. The ecliptic intersects of the mundo divisions are secondary - just sensitive points on the ecliptic, and not the basis for assigning points to houses. Unfortunately the ecliptic-centrism of modern astrology leads to a lot of noise when considering domification that sheds little light.

I use the method described at http://www.levante.org which is given as an alternate mathematical description of the fundamental model underlying Placidus and Topocentric. (And yes, I'm quite aware of the fudging the latter system does when crossing the +/- arctic circles). Like all formulations, there are compromises at the limits of the mathematical functions used for the description. I find the limits chosen in this case to be acceptable. I have no major problem with the 6-fold division you (and Dieter) espouse either.

I'd be curious as to your thoughts on the content of that link (after bypassing the revisionist history in the first chapter).

- Ed


Last edited by Ed F on Thu Jan 24, 2008 9:44 pm; edited 1 time in total
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Mike W



Joined: 15 Jan 2008
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Posted: Thu Jan 24, 2008 5:05 pm    Post subject: Reply with quote

Ed,

Thank you very much for your support.

Your link to LevantE was dead and although I found the site, I wasn’t able to figure out the article to which you refer. Can you specify, please?

Meanwhile, I do question a site that poses as a serious contender but then itself takes seriously and posts the original SPICA piece on Topocentrism: -

‘Hey - we drew these house lines - honest - and they weren’t great circles, either - now have the topo pole - it gives you precisely those great circles.’ (Excuse me!!?) That was Tony Page’s initial position, followed up by his ‘upon the cone’ versus ‘upon the sphere’ obfuscations, yet there it is, still on display at LevantE.

Quote:
I have no major problem with the 6-fold division you (and Dieter) espouse either.


I don’t know what you mean by this.

Mike
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Ed F



Joined: 22 Jan 2008
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Location: Ipswich, MA USA

Posted: Thu Jan 24, 2008 9:43 pm    Post subject: Reply with quote

Mike W wrote:
Ed,

Thank you very much for your support.

Your link to LevantE was dead and although I found the site, I wasn’t able to figure out the article to which you refer. Can you specify, please?


Sorry about that. Try this more specific link: http://www.levante.org/svarogich/en/principia_en/content.html

Quote:

Meanwhile, I do question a site that poses as a serious contender but then itself takes seriously and posts the original SPICA piece on Topocentrism


The author is critical of the Topocentric system as well. He put the material up there because it's difficult to find.

Quote:

‘Hey - we drew these house lines - honest - and they weren’t great circles, either - now have the topo pole - it gives you precisely those great circles.’ (Excuse me!!?) That was Tony Page’s initial position, followed up by his ‘upon the cone’ versus ‘upon the sphere’ obfuscations, yet there it is, still on display at LevantE.


I think it was rather a testament to the whole Placidus approach that they managed to come up with their somewhat wacko linear geometry model, supposedly based on empirical findings. No real astrologer would have gone to that kind of geometry to describe a house system. But of course their tone was fanatical, as were many of their claims, and some of the math really smells bad. Still, they were trying to describe and formulate the same underlying model of ascension that we share.

Quote:
Quote:
I have no major problem with the 6-fold division you (and Dieter) espouse either.


I don’t know what you mean by this.

Mike


Sorry again for the lack of clarity: I meant the use of only the "upper" 6 houses for planets that do not set, and vice-versa. That is, sticking with a strictly semi-arc based definition of the domification. S's formulation is based on great circles with moving orientation relative to each other, but that's just a specialization of his larger scoped model of astrological frames of reference. That latter part is what I find it particularly interesting: the derivation of the house system is just one example of his overall model.

- Ed
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MWackford



Joined: 25 Jan 2008
Posts: 14
Location: South Coast - UK

Posted: Sat Jan 26, 2008 7:52 pm    Post subject: Reply with quote

Ed,

Thanks for that. I downloaded the lot but given its wordiness, please forgive me if I leave it ‘til the series is out of the way.

Yeh - I jumped to the conclusion that Svarogich had taken Polich seriously because the page is there with no health warning or other obvious flag. Wikipedia also links to that SPICA page, as though it was a definitive explanation.

With regard to Topo’s maths: As it happens I know exactly how and why Topo houses came into existence. In a plot-line more accident prone than, but worthy of, the Naked Gun series, they were a direct descendant of a makeshift version of Placidus. Polich, through wilful self-delusion, was unaware of this.

Quote:
I think it was rather a testament to the whole Placidus approach that they managed to come up with their somewhat wacko linear geometry model, supposedly based on empirical findings. No real astrologer would have gone to that kind of geometry to describe a house system.


IF you’re referring to the spurious empirical graphic shown in SPICA, actually it wasn’t so whacko. Unaware that it had been done before, I came up with exactly the same type of 2D maps. And that’s how I explained house divisions to myself.

If, on the other hand, you’re referring to Page’s technical bluster after the event, in the words of my old friend Neil, who corresponded with him: “The trouble was, they had the topocentric pole but got their balls caught ‘round it..” and thus span out of control.

As for Topo, it runs its houselines through the Equator at exactly the same angle as its Placidian counterparts and at exactly the same equatorial points. Topo’s then run off in a straight line while the Placidians curve slightly away. Polich thought that Placidus really did use poles and, unaware of the authentic version, was in fact failing to re-invent it. All that talk about a topocentre was just wishful thinking.

Quote:
I have no major problem with the 6-fold division you (and Dieter) espouse either.

With regard to Dieter, this is news to me. The last time we spoke, he ‘hated’ the 6-house ‘lid’ as an ugly add-on (whereas I consider it an elegantly obvious extrapolation of first principles). He programmed the thing but didn’t like it. Maybe I should get back in touch with him.
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Ed F



Joined: 22 Jan 2008
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Location: Ipswich, MA USA

Posted: Mon Jan 28, 2008 3:00 pm    Post subject: Reply with quote

Thanks for the "behind the scenes" on the Topocentric stuff.

As far as Dieter goes, I do not pretend to speak for him. I probably inferred incorrectly that he espoused the 6 house polar approach because I saw its description in the sweph manual, or something.
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MWackford



Joined: 25 Jan 2008
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Posted: Sun Feb 10, 2008 3:52 pm    Post subject: Reply with quote

Ed

I've now been in touch with Dieter and confirmed his opinion remains, for now, as discussed. This may however be subject to change.

m
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