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Regiomontanus and Placidus
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Ed F



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

Posted: Sun Feb 10, 2008 4:02 pm    Post subject: Reply with quote

Mike,

Thanks for checking. Read the second article in your series last week. Really good. Looking forward to the rest.

- Ed
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aquirata



Joined: 31 Mar 2006
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Posted: Tue Feb 12, 2008 11:37 am    Post subject: Reply with quote

Mike,

Thank you for the detailed reply. I have since read the second part of your polar horoscope article. Glad that you have decided to republish the series here.

With respect to the issue of domification, the problems only arise due to our attempt to project houses onto the ecliptic. Houses do exist quite independently of this circle as you also note.

Overall, I think there can be two possible answers to the question, 'which is the correct method of domification':

1. All (or most or many) methods have some merit, and they all provide information from a different perspective. This is the view represented by, for example, Emma Belle Donath.

2. Only one method is correct, all others are "figments of the imagination". My understanding is that this is the view of most practicing astrologers, now or ever.

I'm quite open to #1 on the basis of symbolism, and Donath does a good job of expounding this view in her short book. From a purely mathematical standpoint, however, I would vote for Regiomontanus if #2 turned out to be true. The reason is that Regio is the only 'rational' way to divide mundane space into houses (and I may be at odds here with your view of Placido as the 'natural' division).

I agree that examining how various domification methods work in the polar regions is a good way of discovering their properties. This examination will not, however, provide the final answer. It is always good to look at the behaviour of our models at the extremes because this will lead to new insights. This is what Einstein did when he came up with the theory of relativity (i.e. a model for the extremely large), and what Heisenberg et al did for quantum mechanics (i.e. a model for the extremely small). Despite these robust theories, which both contradict classical physics (Newtonian mechanics) at the extremes, the latter has a wide-ranging validity in our everyday lives. And the unification of these three theories hasn't happened despite concerted efforts for many decades now of practically the entire physics community, which is an immensely larger collective force than what astrologers represent in terms of research. What I'm saying is that, just because a domification method fails at the polar region, this doesn't necessarily mean that it doesn't have merit under regular circumstances. But the study of the polar region is useful at the same time for it will lead us to a better understanding of domification.

I'd like to come back to one specific section in the second part of your article, namely, the second objection you raise about Regiomontanus towards the end. You say:

Quote:
As we move away from the Equator, Regiomontanus divides the celestial sphere into increasingly unequal areas, with the 3rd, 4th, 9th, and 10th houses growing in size as the other eight steadily diminish... [This] must be of serious concern as the issue raised is not confined to the Polar Regions. If the equal division of celestial space (or at least the fair chance of a planet tenanting any house) is considered important, then it must be understood that the modus rationalis favoured by Regiomontanus yields neither.

What I'm wondering about is where the requirements of "equal division of celestial space" or "the fair chance of a planet tenanting any house" are coming from. If we go back to first principles, I don't see any such requirement arising. I would appreciate if you could take the time to expand on these ideas a little more.

Many thanks again for being available to us for clarifications. I look forward to your reply.
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Ed F



Joined: 22 Jan 2008
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Location: Ipswich, MA USA

Posted: Tue Feb 12, 2008 4:11 pm    Post subject: Reply with quote

Hi Peter,

You claim that Regio is the only rational method of domification, but you didn't support the claim with your reasoning. Could you?

Thanks,

- Ed
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aquirata



Joined: 31 Mar 2006
Posts: 157
Location: Canada

Posted: Tue Feb 12, 2008 5:08 pm    Post subject: Reply with quote

Hi Ed,

The system known as Regiomontanus (popularized by Johann Muller of Konigsberg but probably originating from the 11th century or before) divides the sky along the equator. Since houses are a direct result of the Earth's rotation, dividing the equator equally is the only 'rational' way to proceed. It is really confounding why the majority of modern astrologers cling to the Placidian division (again, only popularized by Placidus and not invented by him) when this is equivalent to using planetary hours, a classical technique.

For a discussion of the various domification methods, Deb's material is an excellent reference:

http://www.skyscript.co.uk/temples/Chapter8.pdf
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Peter
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GR



Joined: 14 May 2005
Posts: 451
Location: USA

Posted: Tue Feb 12, 2008 6:19 pm    Post subject: Reply with quote

Hello Peter,

I have some questions and wild assertions Smile

Quote:
The system known as Regiomontanus (popularized by Johann Muller of Konigsberg but probably originating from the 11th century or before)


That's the first I've heard of the 11th century origination! What's the source on that?

Quote:
Since houses are a direct result of the Earth's rotation, dividing the equator equally is the only 'rational' way to proceed.


This is an assertion. It doesn't explain why Hellenistic era astrologers just simply used whole sign houses (along with some use of Porphry that I don't quite understand), and why Arabic and medieval era astrologers used both Alchabitius (the semiarc or the declination method, there seems to be an issue as to which and why) and whole signs.

In my opinion, I'd have to class the Regiomontanus system with the rest of the 'reformations' of astrology that occured in the Renaissance period: attempts to purify and clean up what they saw as a flawed system, when in fact it was their understanding and source materials that were flawed. Regio is, though, an impressive exposition of that period's mathematics, coming from one of its great scientists.


Quote:
It is really confounding why the majority of modern astrologers cling to the Placidian division


This is because Placidius was the only one available by the 19th century forefathers of modern astrology. It wasn't challenged until moderns realized there were more house systems.

Quote:
For a discussion of the various domification methods, Deb's material is an excellent reference:

http://www.skyscript.co.uk/temples/Chapter8.pdf


Yes, Deb is great. We can all agree on that. Very Happy
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Gabe
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aquirata



Joined: 31 Mar 2006
Posts: 157
Location: Canada

Posted: Tue Feb 12, 2008 7:00 pm    Post subject: Reply with quote

Hi Gabe,

Quote:
That's the first I've heard of the 11th century origination! What's the source on that?

Actually, Deb's chapter I just cited above. Smile Mike also alludes to this in his first article on polar houses.

Quote:
This is an assertion. It doesn't explain why Hellenistic era astrologers just simply used whole sign houses (along with some use of Porphry that I don't quite understand), and why Arabic and medieval era astrologers used both Alchabitius (the semiarc or the declination method, there seems to be an issue as to which and why) and whole signs.

Correct. And I had no intention of explaining these. They have no relation to why I think Regiomontanus is the only rational system.

Quote:
This is because Placidius was the only one available by the 19th century forefathers of modern astrology. It wasn't challenged until moderns realized there were more house systems.

Right but how long ago was that? I think the real answer is that most astrologers don't examine this question, and just simply accept that that's the way things are. They start working with Placidus and it seems to work for them. Which doesn't say anything quantifiable about the efficacy of Placidus or any other system of domification. What is needed is a series of objective, quantifiable studies on how well the various systems do on real data.

Quote:
Yes, Deb is great. We can all agree on that. Very Happy

No arguments there! Very Happy

Another great article on the technical bases of house division is this by Christopher Weidner:

http://www.astro.com/astrology/cw_astro_houses_e.htm

The one to read if you ever wanted to get your head around to understanding the various circles and motions. And when you're there, you may want to look around because Astrodienst is another wonderful resource.
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Peter
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Ed F



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

Posted: Tue Feb 12, 2008 7:45 pm    Post subject: Reply with quote

Hi Peter,

Thanks for the response.

aquirata wrote:
...The system known as Regiomontanus (popularized by Johann Muller of Konigsberg but probably originating from the 11th century or before) divides the sky along the equator. Since houses are a direct result of the Earth's rotation, dividing the equator equally is the only 'rational' way to proceed. It is really confounding why the majority of modern astrologers cling to the Placidian division (again, only popularized by Placidus and not invented by him) when this is equivalent to using planetary hours, a classical technique.


Placidus, since it equally divides all declination circles that rise or set, also by definition equally divides the equator. Same for Topocentric and other Placidus derivatives (within the operable ranges of their formulae). So, if by "rational" you mean proportional at the equator, then it is not the single qualifying system.

Quote:

For a discussion of the various domification methods, Deb's material is an excellent reference:

http://www.skyscript.co.uk/temples/Chapter8.pdf


Yes, I'm familiar with it, and recommend the book to many people.

- Ed
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Ed F



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

Posted: Tue Feb 12, 2008 7:53 pm    Post subject: Reply with quote

GR wrote:
...
This is an assertion. It doesn't explain why Hellenistic era astrologers just simply used whole sign houses (along with some use of Porphry that I don't quite understand), and why Arabic and medieval era astrologers used both Alchabitius (the semiarc or the declination method, there seems to be an issue as to which and why) and whole signs.

In my opinion, I'd have to class the Regiomontanus system with the rest of the 'reformations' of astrology that occured in the Renaissance period: attempts to purify and clean up what they saw as a flawed system, when in fact it was their understanding and source materials that were flawed. Regio is, though, an impressive exposition of that period's mathematics, coming from one of its great scientists....


Well, there does seem to be somewhat of a trend towards using whole sign for topical interpretation, and a quadrant system for event timing and determination of strength. After all, wasn't one of the driving forces for development of the classical quadrant systems the attempt to fully develop Ptolemy's system of primary directions? So, it looks like we have a conflation of two completely distinct beasts under the term "houses": a) topical interpretation (eg whole signs) and b) domification (quadrant systems) for timing and strength.

I certainly consider Campanus, Regio, Placidus et al to be improvements over Porphyry for "b". They all characterize diurnal motion more accurately than Porphyry. And although the chestnut about Placidus tables being what was available is still bandied about, Placidus characterizes the apparent diurnal motions most accurately of the bunch.
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aquirata



Joined: 31 Mar 2006
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Posted: Tue Feb 12, 2008 8:12 pm    Post subject: Reply with quote

Ed,

Quote:
Placidus, since it equally divides all declination circles that rise or set, also by definition equally divides the equator. Same for Topocentric and other Placidus derivatives (within the operable ranges of their formulae). So, if by "rational" you mean proportional at the equator, then it is not the single qualifying system.

Yes, this is correct. I didn't want to get into a technical discussion here, however. The difference between Regiomontanus and the other systems based on the division of the equator is that the former uses the great circles going through the North and South points and so achieves a perfectly even and balanced division in time-space. Placidus divides only by time, i.e. each point takes 1/6th of the daytime to go through the day houses and 1/6th of the night through the night houses. Topocentric has no basis in reality.

To visualize Regiomontanus, imagine that the great circle going through the North and South points are being turned as the Earth turns. The intersections with the ecliptic at successive 1/12th of the full turn mark the house cusps. There is nothing simpler than that, which is why I think this is the only 'rational' method of division. Which is not to say the only valid one.
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Peter
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GR



Joined: 14 May 2005
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Posted: Tue Feb 12, 2008 10:07 pm    Post subject: Reply with quote

Hello Peter,

Quote:
Actually, Deb's chapter I just cited above. Smile Mike also alludes to this in his first article on polar houses.


Ah, well there it is then. Smile I wonder how hard it would be to hunt down that J.D. North book ...

Quote:
Quote:
This is an assertion. It doesn't explain why Hellenistic era astrologers just simply used whole sign houses (along with some use of Porphry that I don't quite understand), and why Arabic and medieval era astrologers used both Alchabitius (the semiarc or the declination method, there seems to be an issue as to which and why) and whole signs.

Correct. And I had no intention of explaining these. They have no relation to why I think Regiomontanus is the only rational system.


Part of my argument here would be "Does it need to be rational?" While there is much that is rational in astrology (for example, rules guiding delineation), many of the ancient practictioners of astrology didn't seem to bother themselves too much on this question. I have to wonder if people are jumping down a rabbit hole when investigating this question of house systems.

Quote:
Quote:
This is because Placidius was the only one available by the 19th century forefathers of modern astrology. It wasn't challenged until moderns realized there were more house systems.

Right but how long ago was that? I think the real answer is that most astrologers don't examine this question, and just simply accept that that's the way things are. They start working with Placidus and it seems to work for them. Which doesn't say anything quantifiable about the efficacy of Placidus or any other system of domification. What is needed is a series of objective, quantifiable studies on how well the various systems do on real data.


True, most people calling themselves astrologers aren't thinking about this question, when they're too busy musing over some asteroid or some hypothetical planet. Sick

I also think we are running into trouble when we think of astrology as a science, like chemistry or physics is a science. It is certainly not a modern science, since there is no plausible material causation. There are, of course, other levels of causation, but they are not in the purview of modern science. I'm not sure we can get the same kind of statistically verifiable data as in these sciences because of this.

Quote:
Another great article on the technical bases of house division is this by Christopher Weidner:

http://www.astro.com/astrology/cw_astro_houses_e.htm

The one to read if you ever wanted to get your head around to understanding the various circles and motions. And when you're there, you may want to look around because Astrodienst is another wonderful resource.


It's certainly prettier then Munaskey's book on primary directions, which I think is now available online as well. Oh, primary directions, that's a whole argument in and of itself, but married to this one as well.
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GR



Joined: 14 May 2005
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Posted: Tue Feb 12, 2008 10:23 pm    Post subject: Reply with quote

Hello Ed,

Quote:
Well, there does seem to be somewhat of a trend towards using whole sign for topical interpretation, and a quadrant system for event timing and determination of strength. After all, wasn't one of the driving forces for development of the classical quadrant systems the attempt to fully develop Ptolemy's system of primary directions? So, it looks like we have a conflation of two completely distinct beasts under the term "houses": a) topical interpretation (eg whole signs) and b) domification (quadrant systems) for timing and strength.


Yes, I'd agree with you, Ptolemy and primary directions are a big culprit in all this, probably the biggest one. And then the issues of topical and domification house assignment begin to merge together.

Quote:
I certainly consider Campanus, Regio, Placidus et al to be improvements over Porphyry for "b". They all characterize diurnal motion more accurately than Porphyry. And although the chestnut about Placidus tables being what was available is still bandied about, Placidus characterizes the apparent diurnal motions most accurately of the bunch.


Yeah, Porphyry is not the way to go for the diurnal motion; but then again, the Greeks that were using it were probably just using oblique ascensions for their primary-like directions and just dodged the issue altogether.
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aquirata



Joined: 31 Mar 2006
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Posted: Wed Feb 13, 2008 1:31 pm    Post subject: Reply with quote

Gabe,

Quote:
I wonder how hard it would be to hunt down that J.D. North book

The book is listed but not available at Amazon, and, according to FetchBook, AbeBooks used to have a couple of copies available a few weeks ago. BookFinder couldn't locate any copies. May also be available from the Warburg Institute or the author.

Quote:
Part of my argument here would be "Does it need to be rational?"

No, it doesn't in general. For me, it does.

Quote:
I also think we are running into trouble when we think of astrology as a science, like chemistry or physics is a science. It is certainly not a modern science, since there is no plausible material causation. There are, of course, other levels of causation, but they are not in the purview of modern science. I'm not sure we can get the same kind of statistically verifiable data as in these sciences because of this.

Well, this is a big subject, but I do disagree with you here. I am personally conducting the kind of statistical research you speak of, and the evidence is unquestionably there. The first phase of research in a program of about 2,400 phases is complete, and I am writing the article for publication. The abstract and intro are done, working on the rest at present. This particular work is not about the houses by the way.
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Ed F



Joined: 22 Jan 2008
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Posted: Wed Feb 13, 2008 2:49 pm    Post subject: Reply with quote

Thanks for the responses. I may come back to this in a while, but work is keeping me too busy to think that hard right now.

- Ed
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MWackford



Joined: 25 Jan 2008
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Posted: Wed Feb 13, 2008 5:07 pm    Post subject: Reply with quote

Ed,

Again, thanks for your support and thanks very much indeed for answering some of the technical details brought up by other commentators, meaning that I won’t now have to do it.


Peter,

Quote:
our attempt to project houses onto the ecliptic


I have never understood this expression, which was first demanded of me by Chester Kemp.

Quote:
1. All (or most or many) methods have some merit, and they all provide information from a different perspective. This is the view represented by, for example, Emma Belle Donath.


Divine, if you must, but that is not what we’re about with this exercise. Again, the question of Regiomontanus will be dealt with in full as the series progresses. Deb has another, somewhat more light-hearted essay of mine that I’d rather she published right now - because it addresses the root of the problem. With Regiomontanus, you are the dividing the wrong sphere.

Please recall that the series is not aimed at mathematically-minded astrologers and that we must therefore take one step at a time.

And you have not thought through the implications of having houses of unequal size. As I said in the paper, Regio’s inequality culminates with 4 houses in place of 12. I have yet to see a better argument for equality. I will of course get around to Whole-sign houses.

Now, I said:

Quote:
"IF the equal division of celestial space is considered important"


And that is an “if,” though I would have thought this a natural pre-requisite, unless you adhere to the siderial zodiac. But that’s another matter entirely.

Your citation of Albert Einstein as an example is at best unfortunate. The man was a plagiarist and a fraud and if you doubt me, ask Poincaré, Lorenz or Mrs Einstein, to whom he donated his Nobel prize money. Do not consult Sir Arthur Eddington as he didn’t have a clue, either.

I would appreciate if you could take the time to expand on these ideas a little more

You invite me to spike the series, which for reasons of space and tedium, I decline to do. As I said to you before, let me know if I miss anything.

Christopher Weidner’s article is well diagrammed.

Quote:
Topocentric has no basis in reality


You have it on the nail there but you’re way off in your assessment of Regiomontanus. Could it perhaps be the appeal of the sine-curve that attracts you? If so, that has no basis in the real world either.


Gabe,

Quote:
It wasn't challenged until moderns realized there were more house systems.


Yes - “More” is indeed the pity. Ever heard of quality over quantity? And Yes, I will get to that bit as well.

I do not hold with your faith in evolution, which presumes that our forefathers were somehow less aware than ourselves.

PS - the methods of Campanus, Regiomontanus and Placidus all appear, together, on a 12th or 13th Century astrolabe - with each pre-dating their alleged inventors. Source: Horoscopes and History by J. D. North (Warburg).
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Deb
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Posted: Wed Feb 13, 2008 5:42 pm    Post subject: Reply with quote

I’m only just catching up with the start of this thread, so I’d like to pick up on a point that Astrojin wrote in his first post:

Quote:
The Greeks (e.g. Valens) did use a simple dynamic house system (called Prophyry) which simply trisect (by ecliptic) the places between angles but this house system is only used to check for strength of planets (esp. in the calculation of apheta or hyleg) and not for topical analysis.


I know that this is one of Robert Schmidt’s theories, but I believe he admits that it is only a theory. I have seen the comment repeated so often that lately it seems to have been taken up as fact. Even Rob Hand, who is a great advocate of whole sign, is careful to admit that it is only a suggestion – for which there is no evidence. The only reason it has been suggested seems to be to increase the supposed importance for the whole sign approach.

The fact is that Porphyry was known about, used and discussed as a system of house division in ancient astrology. And let us not forget that Valens, who usually seems to take a whole sign approach in practice, does warn the astrologer to be needful, and calculate to the degree to get the ‘pivot points’ and ‘post-ascensions’ right. (See for example, Anthology II. I. 37)

On another matter, the Warburg are committed to republishing J. D. North's book although it does keep getting delayed.

Also, towards the end of last year, I was involved in discussions with Margaret Cayhill of Wessex Astrologer, stressing the need for a good printed collection of Regio tables. She said she would be happy to publish if someone would put them together. The last I heard David McCann was looking at the work involved with a view to undertaking the project. If you are interested in Regio tables, send a quick email to Wessex –it might help to speed this project along.
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