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Equal verses unequal house systems
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Ruud66



Joined: 05 Apr 2009
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Posted: Mon Jun 29, 2015 10:09 am    Post subject: Reply with quote

Hello,
This topic is close to my heart and I'd like to contribute to this thread, although I find it difficult to react specificaly to everything that already has been said. Therefore I will write in a general way.

About the discussion of the Midheaven and the Nonagesimal. These points are the result of two different approaches of finding the "highest point" on the ecliptic. One approach I call static: you simply find the point on the ecliptic that has the highest altitude above the horizon. Perhaps paradoxicaly this point is constantly moving around in all directions due to the changing angle of the ecliptic in relation to the horizon.
The other approach I call dynamic, because it focuses on the effects of the rotation of the earth on its axis. The midheaven, as well as any other point on the upper meridian, is on its highest altitude above the horizon on its own apparent path that it traces on the local celestial sphere due to the rotation of the earth. This point also moves around, but only up and down along the meridian.
If you define the midheaven in a static way by saying it is the intersection of the ecliptic and the upper meridian, then you loose the notion of "highest point". Fact is that the nonagesimal cannot be defined in a dynamic way. It's position is only indirectly the result of the rotation of the earth.

In other words: the midheaven only makes sense if you define it in a dynamic way, which brings us immediately to the Placidus house system, because Placidus is the only system that can be defined in a dynamic way.

This is the big lesson that I learned from Wackford. The only way to construct the merdian circle is observing the ascension and descension of the stars and planets. Where each point reaches its highest altitude above the horizon on its own path through the sky is the upper meridian. There is no other way to find "North" and "South", because there are no built-in markers in the sky or on the horizon to guide the eye.
Placidus houses is the only system that is built 100% on this notion of ascension and descension. In all other quadrant systems you first need to find the meridian in some way and from there on continue dividing the quadrants.

Please correct me if I'm wrong.
Ruud
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Ruud66



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Posted: Mon Jun 29, 2015 10:44 am    Post subject: Reply with quote

The other thing I learned from Wackford is that each house system reveals its weaknesses most clearly in the arctic and the antarctic latitudes.
For example the Topocentric house system produces a kind of lettuce of house circles in the high latitudes and at times it becomes impossible to determine in which house a planet is located.
Koch house system gets into big problems in the high latitudes, because its cusps are defined on horizon circles as a kind of virtual ascendants and in the arctic the ascendant has a habit of jumping 180 and turning retrograde. Obviously this messes up the Koch house system completely.
In both the Campanus and Regiomontanus systems (as well as some others) the house circles are fixed on the north and south point of the horizon. Therefore in these systems the midheaven also will jump 180 twice a day in the high latitudes, turning everything upside down.

The question is: if a system doesn't make sense in the high latitudes, then why should it be any good in the temperate and tropical regions?

The systems that are working in the high latitudes are the ones that don't use the ascendant as the cusp of 1 (e.g. Morinus, Meridian), then there are the equal house systems (e.g. WSH, Equal, Vehlow etc.) and Alcabitius and Porphyry are not bad either if you can live with the idea that the houses 7-12 can be below the horizon and the houses 1-6 can be above it.

There is one more house system that remains completely intact and operational in the high latitudes according to its own definition and that also is equally accurate and precise in its representation of the dynamics of the local celestial sphere, in the high latitudes as well as in the temperate zones of the earth.
This system is Placidus houses.
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Ruud66



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Posted: Mon Jun 29, 2015 11:21 am    Post subject: Reply with quote

Since I read Wackford I did a lot of research on Placidus in the high latitudes.
These are my conclusions:
Placidus only makes sense if you view it in three dimensions. The only things you need for constructing this system is the local horizon and the rotation of the earth on its axis. No other elements are necessary.
This means that in the Placidus system the ecliptic is irrelevant. It is only because we, the astrologers, are insisting on ecliptic positions, that the ecliptic solutions of this three-dimensional system come into play.
This is not so strange as it may seem, because the ecliptic is the plane of revolution of the earth in its yearly motion around the sun and therefore has nothing to do with the local sky or the rotation of the earth on its axis.

In the placidus system the behavior of each and every point on the local celestial sphere is observed as it moves in relation to the local horizon due to the rotation of the earth on its axis.
Such a point will become visible as it rises above the horizon in the east, such a point reaches its highest elevation on its own path through the sky on the upper meridian, such a point will disappear from view as it sets over the western horizon and such a point will reach its deepest point below the horizon on its own path through the sky on the lower meridian.
The horizon divides the parallel circle into a diurnal and nocturnal arc. The meridian divides it into an ascending and a descending arc. All four events divide each parallel circle of declination into four semi-arcs and these semi-arcs are then trisected. Still the ecliptic is not introduced into the system yet.

If you connect all trisected points of all semiarcs, the 3-d placidus house curves can be drawn unto the celestial sphere. They are curves, not circles (except on the geographic equator) and they DO NOT MOVE. They remain completely stationary in the course of 24 hours of sidereal time, just like the circles of the horizon and the meridian. This whole system is completely stationary and unchanging in relation to the place of observation and all 3-d house areas are always of completely equal size.
If you move on to higher or lower latitudes this stationary system of 3-d house curves will be compressed or expanded, because of the changing size of the circumpolar sky. Its relative shape is not altered, however.

Only when we finally run the ecliptic through this system, are we confronted with all the unequal houses and distortions because of the changing angle of the ecliptic in relation to the horizon.
If you calculate intermediate placidus house cusps for arctic charts (yes! it is possible) it is quite common that the ecliptic completely misses one or more of the 3-d house curves.
This means that there are times that not all placidus house cusps have an ecliptic solution, and at other times a house cusp has more than one ecliptic solution (up to 3 ecliptic cusps of the same name are possible).


Last edited by Ruud66 on Mon Jun 29, 2015 12:03 pm; edited 8 times in total
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Ruud66



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Posted: Mon Jun 29, 2015 11:29 am    Post subject: Reply with quote

Wrapping up my posts:
If you take the house systems seriously in the arctic and the antarctic, then a lot of systems fail the test. They become either undefined or ambiguous.

The systems that don't use the Ascendant as the cusp of 1 work nicely in the arctic, but are usually not sensitive to geographic latitude.

Placidus houses work admiraby in the arctic, but are of very limited use to the astrologer: how do you find a house lord when you don't have the house cusp?
What are you going to do with the circumpolar sky?

From these considerations I have come to the following practise:

-I use both placidus houses and whole signs together (like Paul does), even in arctic charts with unimaginable distortions.

-I use whole signs (or equal houses) if I want to determine the house lords. This eliminates the problems with interceptions.

This way of working could mean that a planet can be both in the 6th house (by sign) as well as in the 12th (by semi-arc).
It takes some getting used to, but is in line with what I've seen from high-latitude charts so far (which is not enough to say something definite).

Ruud
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Paul
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Posted: Mon Jun 29, 2015 2:43 pm    Post subject: Reply with quote

Hi Ruud

I appreciate your points. Regarding dynamic and fixed in regards the nonagesimal and midheaven, really both are fixed and static depending on your viewpoint. We can imagine the MC as fixed in that it is directly south - we don't lose our sense of 'highest' here as we can simply say that it's the highest point on the ecliptic due south. Due south doesn't move in the same manner as the nonagesimal does, and so we can say, from that perspective that the nonagesimal, which, as you say, moves around more is the more dynamic.

It depends then on what we mean by dynamic and static.

The reason I highlight this is that I disagree with this premise:
Quote:
the midheaven only makes sense if you define it in a dynamic way, which brings us immediately to the Placidus house system, because Placidus is the only system that can be defined in a dynamic way.
...
If you define the midheaven in a static way by saying it is the intersection of the ecliptic and the upper meridian, then you loose the notion of "highest point". Fact is that the nonagesimal cannot be defined in a dynamic way. It's position is only indirectly the result of the rotation of the earth.


I disagree that you can only sensibly define the midheaven as dynamic in a manner that denies the nonagesimal the same sense of dynamism. I am trying to follow the relevance of the nonagesimal to that conclusion and I am taking it to mean that unlike the nonagesimal the MC (alone) is the dynamic of the two and from this you conclude about Placidus.

You say something odd about the nonagesimal being only indirectly the result of the rotation the earth, but surely, just like the MC, the rotation of the earth is not a necessity to understand or calculate it. The nonagesimal is the highest point on the ecliptic visible at any particular moment in the time. The MC is the highest point at which any individual point of the ecliptic will reach. But neither require the earth to rotate to observe or calculate it, it is just that both require the earth to rotate in order for the ecliptic to appear to pass through these points. But they both require it in equal measure.

I'm not posting to disagree with Placidus being a highly dynamic system, nor your comments on the calculation of placidus cusps in the poles, just that I don't follow some of the reasoning that went into forming that conclusion insofar as the MC and Nonagesimal are concerned. I realise it was just preamable, but wondered if it was something I'm missing or just a desire to bring the topic toward the idea of dynamism in astrology and its concerns with the placidus cusps.
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Ruud66



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Posted: Wed Jul 01, 2015 2:03 am    Post subject: Reply with quote

Paul wrote:
It depends then on what we mean by dynamic and static.

Hello Paul, you made me reconsider everything with your remarks. I appreciate that because I realise that I was using the wrong words to say what I wanted to say. Dynamic and static is too confusing.

Paul wrote:
The nonagesimal is the highest point on the ecliptic visible at any particular moment in the time. The MC is the highest point at which any individual point of the ecliptic will reach. But neither require the earth to rotate to observe or calculate it, it is just that both require the earth to rotate in order for the ecliptic to appear to pass through these points. But they both require it in equal measure.


I was trying to find a way to define the MC if you start with the premise "there are no lines in the sky". If you take a look outside at night, it is not easy to find due south if you don't know any landmarks. The only thing you could do is find the polestar and draw a line trough the zenith, then you can find the meridian. If you don't have the polestar either, you must wait to see part of the rotation of the sky and see where things culminate. That was my original idea. I realise now that this is equally true for the nonagesimal, although you need even more time to figure out where the ecliptic is.
You say: "neither require the earth to rotate to observe or calculate it". Could you explain what you mean by that? Because I don't see a way to observe where south is, for example, if you don't take notice of the rotation of the sky.

What I really had in mind was the idea that the MC is part of the meridian circle. It is where all parallel circles of declination culminate. This is therefore part of the system of right ascensions and declinations, a frame of reference specifically designed to follow the rotation of the earth. The fact that the MC is on the ecliptic is of lesser importance than that it is on the meridian, because the MC is the ecliptic solution of this mundane function of culminating.
On the other hand, the nonagesimal has no connection to this system of right ascensions and declinations as it is the direct connection of the ecliptic and the zenith. You don't need right ascension and the idea of the parallel circles of declination to describe the nonagesimal. You only need the ecliptic and the horizon and zenith.
In short: the MC is more connected to the primary motion and the nonagesimal is more connected to the secondary motion. Both are connected to the local space.
I hope this makes more sense.

My question back to you:
In the arctic, the culminating degree of the ecliptic can be below the horizon. Most articles I have read suggest that you should keep it that way and not jump the MC 180 to force it to be above the horizon.
The time the MC is below the horizon, the ascendant moves retrograde through the fast rising signs, jumping 180 each time it conjoins the MC.
However, the nonagesimal does not make that jump. At least not if you define it as the point of the ecliptic with the highest altitude.
This could mean several things in the equal house system:
- is the nonagesimal the cusp of 4 in such a chart?
- could the nonagesimal just be the point 90 before the ascendant, even if it is below the horizon?
- do you need to turn equal houses upside down to make the nonagesimal the cusp of 10 again?
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Paul
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Posted: Wed Jul 01, 2015 8:26 am    Post subject: Reply with quote

Ruud66 wrote:
If you take a look outside at night, it is not easy to find due south if you don't know any landmarks. The only thing you could do is find the polestar and draw a line trough the zenith, then you can find the meridian.


I guess it depends on what we're trying to achieve. If we're trying to discover a way of describing or defining the MC, then we do not need any rotation whatsoever, we can simply assert that the MC is the most southerly point on the ecliptic, or the intersection of the meridian with the ecliptic. That will be true regardless of whether the earth rotates or not.
If however you are trying to demonstrate a way to, observationally, discover the point of the MC then we're in more trouble. It becomes a much more difficult task. If it's night time, we are, at least, in luck. But really my reply wasn't addressing the challenges of observational astrology, but rather trying to put a question mark under the notion that the MC is dynamic in a way the nonagesimal isn't. In fact, one could argue that it's preferable to see the MC as a static point, through which the celestial sphere passes during its rotation. In this sense the MC is a cardinal direction and is unmoving. In that perspective it is the nonagesimal who is the more dynamic as its position will shift through a 24 hour period, whereas the point of the MC will not. The only thing which shifts with the MC is where it projects onto the ecliptic. But then that's true for the nonagesimal too.

If instead you're trying to achieve a sense of observational astrology, then really there are many more problems created - particularly if you have no tools, which you seem to be implying. You mention finding the polestars. Of course I could just take out a compass, a planisphere and voila, I can determine pretty much my MC. If I can see the entirety of the ecliptic, then great, I can pretty much work out roughly where my MC is provided I know south. Your reply seems to assume some hidden rule in which you cannot determine south. But really then the problem is in determining south, not in determining what the MC is or what it's doing. You could of course do it by observing over a period of time the rotation of the earth and tracking where the stars/planets culminate but in practice it becomes tedious as the whole ecliptic rises and falls in terms of altitude through the day. It just becomes an awkward exercise. And that's all assuming it's a clear sky at night. If you do the same exercise by day, you run into many more problems, chiefly because it's more or less impossible to observe the position of the ecliptic by day, you need to pretty much calculate it (assuming it's not a solar eclipse or an extreme polar region where the sun doesn't rise by day etc etc).

Quote:
I realise now that this is equally true for the nonagesimal, although you need even more time to figure out where the ecliptic is.


Not if you can observe it, and if you can't, we have issues for the MC too. After all if you cannot observe the stars/planets, you cannot observe when things culminate with any surety. The ecliptic will drift north and south through the day/night, so you just need to keep track of hte ascendant and descendant points and then choose the ecliptic midway through it, which has the advantage of being the highest point of the ecliptic at that moment in the sky. It's not less difficult than tracking culminating points, and in fact it's argue to say it's easier. You don't need any time to pass. You could be dropped into any location, and provided you can see the sky and you know your stars, you can determine reasonably accurately the nonagesimal. You cannot say the same for the MC.

Quote:
You say: "neither require the earth to rotate to observe or calculate it". Could you explain what you mean by that? Because I don't see a way to observe where south is, for example, if you don't take notice of the rotation of the sky.


What I meant was you do not need observation to determine where south is. You can use tools. But your premise seems to imply some sense of not having any tools. If that's the case you're really better off determining the polestar and working from there, than waiting around for the whole sky to shift sufficiently enough to determine a rough culminating point which will be awkward to do due to the obliquity of the ecliptic and the fact that it sort of 'wobbles' in the sky over any period of several hours.

Quote:
What I really had in mind was the idea that the MC is part of the meridian circle.


Right, but really this is what I had in mind too, because when you consider it as a point on the meridian circle, it becomes relatively obvious that the whole thing is static. The meridian circle doesn't move, it's the celestial sphere which is moving and passing through the meridian circle. It is not the meridian circle that moves.

Quote:
It is where all parallel circles of declination culminate. This is therefore part of the system of right ascensions and declinations, a frame of reference specifically designed to follow the rotation of the earth.


A couple of things here. I would disagree that if a tools is created to understand X, that therefore X is a byproduct of that tool. I see that as essentially the assumption you're making here. The parallel circles of declination within this reference system are agnostic to the meridian circle. It just happens that for a given observer, the parallel circles will indeed culminate at their merdiian circle, but that is an artefact of a system in which we can see that circle as merely a particular hour circle or 'circle of right ascension' in the first place. But all hour circles in this manner are fixed. So whether we envision it as the celestial sphere rotating or the earth rotating, the meridian is a line fixed in position and pointing to a static direction, but for which this direction may be a 'goal' or a point toward which other thigns move. But it is the other things which are moving.

Quote:
On the other hand, the nonagesimal has no connection to this system of right ascensions and declinations as it is the direct connection of the ecliptic and the zenith. You don't need right ascension and the idea of the parallel circles of declination to describe the nonagesimal. You only need the ecliptic and the horizon and zenith.


I would argue you just need the eclitpic and horizon, but yes, you do not need declination, but then, what of it? Circles of declination are not the only manner in which we can envision movement, or dynamism. After all, due to the rotation of the earth, the intersection of the ascendant/descendant with the horizon shifts north-south, and the altitude of the eclitpic increases and decreases, because of course the ecliptic is at an angle to the vector of the rotation of the earth (ie, angled to the equator). And so sure, we don't have declination, but we don't need it if we have the ecliptic, apparently, moving. The nonagesimal is just the point 90 from the shifting point of the ascendant on the horizon, or, is the highest point of the ecliptic in the sky in terms of altitude, which is in turn shifting.

So the nonagesimal only shifts because of primary motion. Alternatively, the meridian, which you say is more important for the mc to be on than the ecliptic, does not change by primary motion, only it's projection onto the ecliptic changes because the ecliptic itself is shifting through this hour circle.

So I disagree with your conclusion that:

Quote:
In short: the MC is more connected to the primary motion and the nonagesimal is more connected to the secondary motion. Both are connected to the local space.


In fact both are equally connected to primary motion, but where as one is true irrespective of latitude (ie all points on the same longitude will have the same meridian circle), the other is more specific in its determination (as it is from the horizon circle). But importantly both only shift due to primary motion, and both are defined, in some manner, from simply the intersection of one given great circle with the ecliptic. With the MC the great circle is the meridian, and the calculation is the direct intersection, with the nonagesimal the great circle is the horizon, and the calculation is the point perpendicular to it.

This post is long enough, so I'll address the rest of your post in another reply.
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Paul
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Posted: Wed Jul 01, 2015 8:45 am    Post subject: Reply with quote

Ruud66 wrote:

However, the nonagesimal does not make that jump. At least not if you define it as the point of the ecliptic with the highest altitude.
This could mean several things in the equal house system:
- is the nonagesimal the cusp of 4 in such a chart?
- could the nonagesimal just be the point 90 before the ascendant, even if it is below the horizon?
- do you need to turn equal houses upside down to make the nonagesimal the cusp of 10 again?


It's a great question and one I have no clear answers for nor had even actually considered before. The problem is in if we assume that the chief importance of, say, the 10th house cusp, is defined by the sense of height or culmination. In most latitudes planets are either objectively higher in altitude than any other, as in the case of the nonagesimal, or else achieve their own subjective highest altitude at the MC. And clearly something of the nature of this height is relevant to the symbolism of the MC.

But it may not be the only one, obviously angular relationships may be of importance here too.

What are your own thoughts on this? It seems clear to me that really we have a problem with house systems in the extreme polar regions irrespective of whether we use a quadrant based house system or not. Whilst there are clearly solutions to those problems, all those solutions make some underlying assumptions about what is important for these house systems.
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Ruud66



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Posted: Fri Jul 10, 2015 10:14 am    Post subject: Reply with quote

Paul wrote:
I guess it depends on what we're trying to achieve. If we're trying to discover a way of describing or defining the MC, then we do not need any rotation whatsoever, we can simply assert that the MC is the most southerly point on the ecliptic, or the intersection of the meridian with the ecliptic. That will be true regardless of whether the earth rotates or not.

Paul, these are exactly the kind of definitions Im trying to avoid. Let me explain what Im trying to do here in these posts and in my astrological thinking in general. My ideal is to formulate a definition of an astronomical factor (like ascendant, midheaven, nonagesimal, etc.), or system (like a house system) that is as concise as possible, that avoids all ambiguities, and that contributes to the understanding of what such a factor or system means in astrological interpretation.
I do this because I believe that it is impossible to effectively use a system or factor in astrology if you dont know exactly what it is astronomically. For example in this discussion on quadrant and equal house systems, I think it is impossible to say anything rational about that unless you have such fundamental definitions.

Your definitions of the MC are riddled with ambiguities. If you say the MC is the south point of the ecliptic (assuming you're observing it from the northern hemisphere), then you run into problems in the tropics, where the MC can be both to the north and to the south of the zenith as seen from one location. If you say the MC is the intersection of the meridian with the ecliptic, you haven't differentiated the MC from the IC, therefore this isn't a definition at all.
Maybe you could say you mean the intersection that is above the horizon. But if you say that, you run into problems in the arctic, where the MC can be below the horizon aswell. Some astrologers say the MC jumps 180, so that it is again the intersection of the meridian and the ecliptic above the horizon, but this has many other questionable implications. This has been explored in depth by Wackford.

A third definition of the MC could be that it is the intersection of the ecliptic with the meridian in the direction of the mid-equator. The intersection of the celestial equator with the meridian in the south (from the northern hemisphere) will always be above the horizon. According to this definition, the MC is the ecliptic longitude of that point.
This third definition could be a good definition if you don't want to include the idea of the Earth's rotation. You now derive the MC from the celestial equator, which happens to be the plane of rotation of the Earth on its axis... can't get rid of it after all, can you?

However, if you formulate the definition like this: "The MC is the culminating point of the ecliptic", then you have satisfied all my three criteria convincingly: it is the most concise definition, because you use the fewest elements for its construction, it is unambiguous, because it doesn't give rise to inconsistencies and it gives a clear image that contributes to the understanding of this point in astrological interpretation. Do you understand now why I can't see the MC disconnected from the Earth's rotation?

Quote:
But really my reply wasn't addressing the challenges of observational astrology, but rather trying to put a question mark under the notion that the MC is dynamic in a way the nonagesimal isn't.

Again my apologies that I used such confusing terminology.

Quote:
What I meant was you do not need observation to determine where south is. You can use tools. But your premise seems to imply some sense of not having any tools.

I agree with all the points you're making about observational astrology/astronomy. I tried to use that as a metaphor to arrive at the most fundamental definition of what something is. Maybe that was a mistake.

Continued...


Last edited by Ruud66 on Mon Jul 13, 2015 10:48 am; edited 6 times in total
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Ruud66



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Posted: Fri Jul 10, 2015 10:19 am    Post subject: Reply with quote

Paul wrote:
Ruud66 wrote:
It is where all parallel circles of declination culminate. This is therefore part of the system of right ascensions and declinations, a frame of reference specifically designed to follow the rotation of the earth.
A couple of things here. I would disagree that if a tools is created to understand X, that therefore X is a byproduct of that tool. I see that as essentially the assumption you're making here. The parallel circles of declination within this reference system are agnostic to the meridian circle. It just happens that for a given observer, the parallel circles will indeed culminate at their merdiian circle, but that is an artefact of a system in which we can see that circle as merely a particular hour circle or 'circle of right ascension' in the first place. But all hour circles in this manner are fixed. So whether we envision it as the celestial sphere rotating or the earth rotating, the meridian is a line fixed in position and pointing to a static direction, but for which this direction may be a 'goal' or a point toward which other thigns move. But it is the other things which are moving.

I'm sorry, but I have some difficulty following you here. I'm not saying that "if a tool is created to understand X, that therefore X is a byproduct of that tool", but I am saying that the way you understand astronomical factors is dependend on your point of view and therefore on your definitions. Therefore I don't see tools, I see points of view and definitions.
The parallel circles of declination are not "agnostic" to the meridian circle as soon as you start talking about "culmination".
Culmination is a phenomenon that can only exist in relation to a local horizon, otherwise it is devoid of meaning. Therefore dropping the word "culmination" in this context implies the idea of semi-arcs and all the rest of it.
Culmination in this context is then one of the bending points in the function of ascension and descension along the parallel circles of declination. Ascension and descension is always in relation to the local horizon.
I agree that all hour circles are fixed and that the meridian is fixed in relation to the horizon, that is one of the most attractive aspects of the placidean system to me. I disagree that this is an artefact of the system.
Just as the term "culmination" is devoid of meaning if it is not in relation to the local horizon, so is the term "parallel circle of declination" devoid of meaning if it is not in relation to the rotation of the Earth.
Therefore some are fixed in one point of view and not in an other and vice versa, same for dynamic. And for the third time: I regret having used these terms, because they are not at the heart of what I'm trying to find out.
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Ruud66



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Posted: Fri Jul 10, 2015 10:36 am    Post subject: Reply with quote

Paul wrote:
What are your own thoughts on this? It seems clear to me that really we have a problem with house systems in the extreme polar regions irrespective of whether we use a quadrant based house system or not. Whilst there are clearly solutions to those problems, all those solutions make some underlying assumptions about what is important for these house systems.

I'm using the arctic as a kind of Occam's razor. If a system or astronomical point cannot be defined consistently and unambiguously all over the globe, something is wrong.
That something could be our way of viewing things, sloppy definitions that need sharpening, and sometimes it means that things just don't make sense.
If something doesn't make sense in the arctic, then why should it be any good on the rest of the Earth?

I think the nonagesimal is such an example. I don't see a way of describing the idea of the nonagesimal in such a way that it makes sense.
If you say that it should contain the idea of highest point and also that it plays a role in the equal house system, then you run into the problems I outlined in my earlier post. It is not going to work that way.

My opinion is that the nonagesimal as an idea of the highest point doesn't exist. And my opinion is that we're confusing it with the 10th house cusp in the equal house system.
Therefore what has been called the nonagesimal is what I see as the predominant square to the ascendant, denoting the 10th house cusp in the equal house system.
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Michael Sternbach



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Posted: Mon Jun 04, 2018 2:26 am    Post subject: Reply with quote

As most of us are aware, the term Midheaven or Medium Coeli (MC) refers to the point where the meridian crosses the zodiac, or the cusp of the 10th house in virtually all unequal house systems. Whereas the Nonagesimal is defined as the point that is 90 degrees away clockwise from the ASC.

In my view, the issue is that with most house systems, the delineation of the axes 1-7 and 4-10 hinges on two sets of points that are derived from two different frames of reference. And then we deduce the remaining cusps based on yet another frame of reference!

For the MC and IC respectively are deduced from the meridian (or the circle that precisely connects North and South) in its intersection with the zodiac, but the ASC and DSC are not deduced from the prime vertical (or the circle that precisely connects East and West) in the intersection of the latter with the zodiac, but as the intersection of the horizon with the zodiac. Apples and oranges, in other words, at least from a geometrical or spatial perspective.

The equal house systems alone are avoiding this problem, usually by using the Nonagesimal in lieu of the MC as the cusp of the 10th. Of course, we could use the MC as our point of departure, and consider whatever degrees lie 90 degrees away from it as our 1st and 7th house cusps - there has indeed an equal system been devised that does just that, but I am not aware of any astrologers actually using it.

Now I can see consistency also in the more widely used ASC - MC - DSC - IC approach, if we look at things in purely temporal terms, i.e., if we choose the rising, culmination, setting, and counter-culmination (is there any better word for it?) of a celestial body as our frame of reference. That approach however seems to make more sense in connection with a house system that is time-based in toto, such as Placidus.

Whereas the rationale of combining the four major points in a celestial body's diurnal revolution with a spatial intersection of the equator (Regiomontanus) or the prime vertical (Campanus) etc. defies my understanding.

But if anybody wishes to share another philosophical view regarding those (or, for that matter, any of the other) systems of house division, hey - be my guest. Smile

Michael
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petosiris



Joined: 08 Oct 2017
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Posted: Tue Jun 05, 2018 5:19 am    Post subject: Reply with quote

When the sky is clear and the stars are visible, I have a hard time establishing the house cusps and quadrant MC using backyard astronomy. Perhaps it was hard for those whole sign astrologers in antiquity as well. Or perhaps they were led?/misled? by the law of parsimony.

If the zodiac is divided ideally, and whole sign aspects work with those ideal divisions, and lots were alloted to signs, then perhaps the angles too are ideal.
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james_m



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Posted: Tue Jun 05, 2018 4:42 pm    Post subject: Reply with quote

i got a kick out of john Frawley in his book - the real astrology applied... he says something to the effect they were called places, not houses - for a reason... our modern mindset in unable to understand it.. it is the difference between being a nomad and being a prisoner.. he doesn't use the last word, but i can't find the passage in the book where he talks about this... he says some stupid things too,but makes up for it with entertainment value, lol...
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Paul
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Posted: Tue Jun 05, 2018 11:44 pm    Post subject: Reply with quote

Michael Sternbach wrote:

In my view, the issue is that with most house systems, the delineation of the axes 1-7 and 4-10 hinges on two sets of points that are derived from two different frames of reference. And then we deduce the remaining cusps based on yet another frame of reference!

For the MC and IC respectively are deduced from the meridian (or the circle that precisely connects North and South) in its intersection with the zodiac, but the ASC and DSC are not deduced from the prime vertical (or the circle that precisely connects East and West) in the intersection of the latter with the zodiac, but as the intersection of the horizon with the zodiac. Apples and oranges, in other words, at least from a geometrical or spatial perspective.


Right, but that's not the perspective the house systems derive from.

Allow me to play devil's advocate with your idea here. You argue that there is an axis or frame of reference for the ascendant and descendant but the frame of reference you choose is a plane/circle - the horizon. And then the MC is the meridian - another plane or circle.

But I think it can be argued that these are focused on calculation and as a result it can appear like the frames of reference are mangled.

But what if instead there is only frame of reference - the ecliptic - and the context for examining it is visibility. Would we consider visibility the frame of reference instead? Perhaps we should. But notice how this takes us away from HOW we calculate it, to WHAT we're calculating.

If I said the only thing I'm interested in is when stars/planets become visible, become their most visible and then become invisible etc. then actually it's not some weird picking and choosing of multiple frames of reference, the necessity to pick the horizon and the MC is borne from the same context or frame of reference - the visibility of that part of the ecliptic.

I think all the house related stuff ultimately derives from that one frame of reference.
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