Why some "angles" and not others?

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Jim Eshelman
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Why some "angles" and not others?

Post by Jim Eshelman » Sat May 16, 2020 1:27 pm

(This post is a substantial rewrite of an earlier one written June 24, 2017, 1:40 PM PDT. It supersedes that prior thread, which has been deleted. - JAE)

This may be going over only material that we've gone over before, but I've been thinking through this subject for the last few days and clarifying its relative simplicity (though, initially, seeming confusion). When I write things out, I tend to get a bit more clarity for myself; so here goes...

Précis
Angles are of two types: (1) The horizon, meridian, and prime vertical circles themselves (not their intersections with anything; but the circles themselves); and (2) the longitude or right ascension of the intersections of any two of these three great circles.

Major Angles
Our working mundane (local, non-celestial) framework is based on three mutually perpendicular great circles: the horizon, the meridian, and the prime vertical. These provide the most-cited, most-referenced, and most-used angles, which, for convenience, we call major angles.

(Please get the mutually perpendicular relationships of these three circles firmly in your mind. You will be rewarded richly, throughout your study and practice of astrology, by your ability to visualize them and their interlocking relationships.)
  • The eastern and western halves of the horizon are, respectively, Ascendant (Asc) and Descendant (Dsc).
  • The northern and southern halves of the meridian are Midheaven (MC) and Lower Heaven (IC).
    (Which angle is the northern and which the southern half depends on geographic latitude.)
  • The western and eastern halves of the prime vertical are, respectively, Vertex (Vx) and Antivertex (Av).
These angles are independent of the ecliptic. Although the ecliptic intersects each of these circles, defining a pair of opposite celestial longitudes that we write onto our horoscope wheels, these longitudes are not the angles. The great circles themselves are the angles. Any planet, star, etc. conjunct the plane of the horizon, meridian, or prime vertical is conjunct the angle. We measure a planet's proximity to an angle mundanely which (for the purposes of this sentence) means we measure it within a non-celestial coordinate system anchored by one of these three great circles.

At present, we measure proximity to the horizon and meridian along the prime vertical. Experiments suggest that proximity to the prime vertical is best measured in azimuth. Other theories are possible, e.g., measuring distance from each along a perpendicular to the plane drawn through its poles (altitude for the horizon, prime vertical amplitude for the PV, and an analog of these with respect to the meridian that I have termed meridian ebb). However, the measurement in prime vertical longitude and azimuth just stated are, in the worst case, serviceable, seeming to show relative angularity accurately. (In the best case, they are exactly right.)

Despite these technical complications, the underlying concept is simple: Proximity to Ascendant and Descendant is measured by proximity to the horizon; that to MC and IC by proximity to the meridian; and that to Vertex and Antivertex by proximity to the prime vertical.

An Aside on Aspects
In practice, it appears that there is no such thing as an aspect to any angle. However, this may be a matter of how aspects are measured and defined. The wondrous interlocking of the horizon, meridian, and prime vertical provides three mutually perpendicular great circles that are permanently locked into an invariable relationship with each other. In addition to the conjunctions with each plane, though, we have oppositions (e.g., Ascendant opposite Descendant) because these three circles exist on opposite sides of the celestial sphere. We also have squares because each of the circles, at every point, is always square the other two. All points on the horizon are 90° from all points on the meridian measured along the prime vertical and 90° from all points of the prime vertical measured along the meridian. (The same is true for all combinations of these three circles.) Therefore, innate to this framework is the existence of mundane conjunctions, oppositions, and squares to each angle. If other aspects to the angles exist, we would expect that they be measured similarly for each circle in relation to the other two; e.g. (speaking theoretically), the Campanus house cusps are trines and sextiles to the meridian and horizon measured along the prime vertical. - In any case, as the angles are mundane rather than ecliptical structures, they do not have ecliptical aspects.

Minor Angles (Longitude)
The major angles (horizon, meridian, and prime vertical circles) intersect in six locations (three pairs of opposing locations) which, for convenience, we call Minor angles.
  • The intersections of the horizon and prime vertical are the Eastpoint and Westpoint of the horizon (which are poles of the meridian circle).
  • The intersections of the meridian and prime vertical are the Zenith and Nadir (which are poles of the horizon circle).
  • The intersections of the horizon and meridian are the Northpoint and Southpoint of the horizon (which are poles of the prime vertical circle).
Four of these intersection points fall on the horizon and exist in azimuth; four on the prime vertical that exist in PV longitude; and four along the meridian that exist in meridian longitude.

(Possibly the best way to think of these is as aspects - conjunctions and squares - between the great circles themselves. However, possibly that introduces unnecessary complication and is better thought a metaphor than an actuality.)

Minor angles are geometrically distinctive from major angles. Major angles are circles; minor angles are points. Practical differences observed between the two groups (e.g., different orb tolerances) likely arise from this seemingly significant distinction.

Each of these minor angle points is already "on an angle" - in fact, on more than one angle - because it is a point shared by two of the major angle circles. For example, Zenith and Nadir are formed by the intersections of the meridian and the prime vertical, so they are conjunct ("on") both of these. Simultaneously, Zenith and Nadir always exactly square the horizon measured along both the meridian and prime vertical.

Perhaps the most important distinction from major angles, though, is that minor angles - being points - can be measured in ecliptical longitude! (Ecliptical or celestial longitude is measured by a great circle passing through a point perpendicular to the ecliptic. As the major angles are all circles, by this definition they have all possible longitudes - the entire zodiac.)

Furthermore, the ecliptical longitude of the intersections of any two major angle great circles is always 90° (square) from the longitude where the third major angle intersects the ecliptic. Specifically,
  • The ecliptic longitudes of Eastpoint & Westpoint (horizon crosses prime vertical) are ecliptic squares to MC/IC.
  • The ecliptic longitudes of Zenith & Nadir (meridian crosses prime vertical) are ecliptic squares to Asc/Dsc.
  • The ecliptic longitudes of Northpoint & Southpoint (horizon crosses meridian) are ecliptic squares to Vertex/Antivertex.
Minor Angles (Right Ascension)
Separately, we can measure the minor angles in right ascension (RA) along the celestial equator. Of six minor angles, only two have positions unique from what we have seen above. Zenith, Nadir, Northpoint, and Southpoint all have the same longitude as the meridian - of either the MC or IC - therefore, no new angles are introduced by measuring them in RA.

However, the RA of Eastpoint and Westpoint are not shared by any other angles. Their conjunctions are measured in RA. (For convenience, we place in our charts the point of the ecliptic that is exactly square MC in RA to alert us when a planet may be conjunct. We use it not as an ecliptical point but, rather as an inference - a hint - of where a planet would be when it squares MC in RA. One must always go back and check the contact in RA.)

In a simpler world, I'd like to ignore this axis, but it's too compelling and inescapable a point. Our work in Sidereal Mundane Astrology alone has confirmed it hundreds of times over. We really can't get along without it, so it's good to observe its highly distinctive astronomical importance.

Summary
Our working mundane (local, non-celestial) framework is based on three mutually perpendicular great circles: the horizon, meridian, and prime vertical.

Angles are of two types: (1) Major angles (the circles of the horizon, meridian, and prime vertical); and (2) minor angles (the longitude or right ascension of the six intersection points of any two of these three great circles).

The three circles constitute the major angles:
  • The eastern and western halves of the horizon are, respectively, Ascendant (Asc) and Descendant (Dsc).
  • The northern and southern halves of the meridian are Midheaven (MC) and Lower Heaven (IC).
  • The western and eastern halves of the prime vertical are, respectively, Vertex (Vx) and Antivertex (Av).
These angles are independent of the ecliptic: The great circles themselves are the angles. We measure proximity to them mundanely, within a non-celestial coordinate system anchored by one of these three great circles. (At present, we measure proximity to the horizon and meridian along the prime vertical and proximity to the prime vertical in azimuth.)

These major angles intersect in three pairs of opposing points that we conveniently call Minor angles.
  • The intersections of the horizon and prime vertical are the Eastpoint and Westpoint of the horizon (the poles of the meridian circle).
  • The intersections of the meridian and prime vertical are the Zenith and Nadir (the poles of the horizon circle).
  • The intersections of the horizon and meridian are the Northpoint and Southpoint of the horizon (the poles of the prime vertical circle).
Major angles are circles; minor angles are points. Practical differences observed between the two groups (e.g., different orb tolerances) likely arise from this seemingly significant distinction.

Minor angles (being points) can be measured in ecliptical longitude or right ascension. The ecliptical longitude of the intersections of any two major angle great circles is always 90° (square) from the longitude where the third major angle intersects the ecliptic. Specifically,
  • The ecliptic longitudes of Eastpoint & Westpoint (horizon crosses prime vertical) are ecliptic squares to MC/IC.
  • The ecliptic longitudes of Zenith & Nadir (meridian crosses prime vertical) are ecliptic squares to Asc/Dsc.
  • The ecliptic longitudes of Northpoint & Southpoint (horizon crosses meridian) are ecliptic squares to Vertex/Antivertex.
Right ascension of four minor angles (Zenith, Nadir, Northpoint, Southpoint) is the same as RA of the meridian (MC or IC). However, the RA of Eastpoint and Westpoint are distinctive from the other angles. Their conjunctions are measured in RA. (We conveniently place in charts the point of the ecliptic exactly square MC in RA to flag when a planet may be conjunct, but one must always check the contact in RA.)
Jim Eshelman
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Re: Why some "angles" and not others?

Post by Jim Eshelman » Sat May 16, 2020 1:32 pm

In the original thread, the original (more complicated) summary suggested that the Midequator axis might be important and need to be included. The Midequator is the celestial longitude of the point where the celestial equator intersects the meridian (the 10th cusp of the Morinus house system). On 6/25/17, I wrote:
Jim Eshelman wrote:
Sun Jun 25, 2017 8:18 am
I should add, for clarification, that I haven't seen any evidence in actual charts of the Midequator being important. That's why I suggested we need to pay attention and watch it (and I think SMA is a promising way to do that, since we have no issue of accurate birth times or event times). I've known about the ME for decades from all the Lyndoe articles I devoured, but never put much stock in it or saw an example so compelling it made me stop and swoon. It's quite hard to filter it out from broader MC effects, but they often are far enough apart that precision techniques like the CapQ often have them distinguished.

I just flipped through a couple of chart collections I have and, first, there are so few ME contacts that I had little to examine and, when I found one, nothing jumped out. Planets don't seem to be magnetized toward that spot in contrast to the MC, for example. But these flip-throughs aren't what we really need so, for my part, as I'm recalculating and reexamining every chart of every event in SMA against the methods outlined in "Stretching the System," I'm going to watch for precision ME contacts as well.
On 6/28/17, I added:
Jim Eshelman wrote:
Wed Jun 28, 2017 7:58 am
Though I made a theoretical case for the Midequator above, it's only theoretical, and evidence has yet to impress me. As I'm working on a separate SMA project right now that has me recalculating and reexamining every solar and lunar ingress connected to the current event catalogue (something over 2,000 charts altogether), I'm looking at the Midequator in passing. (I started in the fires, where I'm presently working.) So far, there are very few contacts to ME at all, and the few I've seen are as likely to be wrong symbolism as right symbolism. I consider the jury still out, and suggest we all monitor and report on these contacts, but wanted to say that what I wrote above is not an endorsement. It may be that the thesis above simplifies by dropping out the celestial equator as one of the great circles in the mix. (NOTE 5/10/2020: It does. I no longer thing the celestial equator should be one of the great circles included in the mix.)
On 7/2/17, I wrote:
Jim Eshelman wrote:
Sun Jul 02, 2017 8:02 pm
To update you on my thinking... I think the Midequator isn't work pursuing. I do encourage everyone to at least casually observe it, to add to our collective expertise... but I now don't think we'll find anything worth pursuing.

I've now made it through most of the catalogue fires, recalculating every solar and lunar ingress and, among other things, checking ME contacts. I'm not impressed. There aren't a lot (strangely) and, when they exist, they are as likely to be wrong as to be right. (I'm not keeping exact numbers... just casually observing and ticking off in my head... but there hasn't been a single, "Oh, how could I have missed that before?!" moment.)
Steve added one striking example of the ME on 7/16/17 (though one example does not make the case):
SteveS wrote:
Sun Jul 16, 2017 7:26 am
Paris, France 1789 Capsolar, preceding the ‘Storming of the Bastille’ by the people of France—kick- starting the French Revolution:
Par-excellent symbolism of partile Moon-Mars 180 falling partile on ME axis.
http://imgur.com/a/C9pgx
But, where is Uranus for the ‘Revolution’? We find Uranus hidden in the Z-Analogue Altitude Chart below for this Capsolar:
Jupiter-Uranus partile IC in altitude, and Sun-Mars partile MC in altitude. This is an outlier example—but still interesting for this event, imo.
http://imgur.com/a/nB7wk
Jim Eshelman
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Re: Why some "angles" and not others?

Post by Jim Eshelman » Sat May 16, 2020 1:45 pm

I strongly encourage everyone to take the time to understand this post. It's a much tighter theory and presentation than the original from years ago and gives a single, coherent theory and simple definition of what angles are that ties the multi-dimensional, multi-framework layers of practical astrology together into a single presentation.
Jim Eshelman
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