Problems of House Division above the Arctic Circle

I recently downloaded a PDF file titled THE MATHEMATICS OF ASTROLOGY, DOES HOUSE DIVISION MAKE SENSE? by Kevin Heng Ser Guan, Department of Physics at the National University of Singapore who was working under a Supervisor, A/P Helmer Aslasken, Department of Mathematics at the same university (Semester II 2000/2001). The author was probably doing it as a requirement for a Masters degree. The focus is on the spherical trigonometry behind the processes involved in the creation of houses using the various systems available. The author gets the astronomy right and is quick to differentiate between the sidereal and tropical zodiacs. 

Before tackling the problem of house division above the Arctic Circle, the author arrives at the following observation:

Hence, the speed of the ecliptic, when it crosses the horizon, varies from place to place on Earth. It follows that the probability density of the Ascendant is uneven at a given latitude, no matter which system of house division we use. Assuming that the birth rate is fairly even, we can conclude that at that latitude there will be more people born with a certain Ascendant. Since the Ascendant is supposedly an important part of the horoscope, the question to ask is do we really believe that character traits vary with latitude? 

It's a fair point but births in hospitals are certainly not evenly distributed throughout the day. For example, the following May 8th 2015 article from Time gives us insight into the unequal diurnal distribution at least in the United States:

According to new data, American mothers-to-be aren’t having too many late night surprises. A new report shows the highest percentage of U.S. births in 2013 (the most recent data available) happened during morning and midday hours. 

The new study from the U.S. Centers for Disease Control and Prevention (CDC)’s National Center for Health Statistics looked at 2013 birth certificate data from the National Vital Statistics System (NVSS), and found that the highest percentage of births took place during the hours of 8:00 a.m. and noon. Less than 3% of babies were born during each hour from midnight to 6:59 a.m. 

Though most births happen during the day, the latest findings report that when babies are born on a Saturday or Sunday, they are more likely to happen in the late evening or overnight—11:00 p.m. through 5:59 a.m.—compared to births that happen between Monday to Friday. 

When it comes to how women gave birth, there were also some distinct patterns in timing. The researchers reported that compared to induced and non-induced vaginal deliveries, caesarean deliveries were the least likely to occur during evening and early morning. Non-induced vaginal births were more likely to happen in the early morning compared to caesarean and induced vaginal births. Births in out-of-hospital settings were most likely to happen in the early morning hours starting at 1:00 a.m. 

“As the use of medical interventions for childbirth (i.e., induction of labor and caesarean delivery) has increased during the last few decades, an increasing proportion of deliveries occur during regular daytime hours,” the study authors write. 

Of course the induction of labour and the use of Caesarian section is another interesting topic in itself. It's a topic that was explored by Michel Gauquelin as I recall but I won't go into that here but may return to this in a later post. My point here is to simply address the university student's criticism that the duration of rising signs varies depending on the latitude. In the case of births, certain signs are more likely to be rising than others during the different months of the year, although the effect would more or less balance out over the entire year.

Toward the end of his paper, he makes an interesting observation:

Inside the polar regions, a part of the zodiac never rises above the horizon. Hence, certain signs can never be Ascendant there. Examples are northern Alaska, northern Norway or Siberia. In these places, the signs of Sagittarius and Capricorn never rise above the horizon, while the opposite signs, Gemini and Cancer, always remain below the horizon. Therefore, people born there cannot have these four signs as their Ascendant. One of the questions to ask is whether a noticeable number of people walk around in these regions without the characteristics of the signs of these Ascendants. 

Furthermore, the article goes on to announce that the whole system of house division collapses above the Arctic Circle:

On the Arctic and Antarctic Circles, the ecliptic coincides with the horizon at a certain time of the day. This means that the Ascendant and the Descendant are either everywhere or nowhere. There is also no MC or IC. Since these four points form the basis of house division, it follows that houses cannot be defined. 

I quite accept what he's saying and these are certainly points that need to be addressed. Consequently, I set to investigate matters further. The issue is addressed in this article titled Astro-Geometry, Astrology article by Alova:

Meet little Andrey, a real, live new-millenium boy. He was born on January 1st, 2000, at 00:00:30 am in Murmansk, Russia, 68° 34' N, 33° 8' E. If you use the Placidus House System, you cannot construct a natal horoscope for Andrey. Nor will you be able to construct a chart for a wedding or important event for Andrey in Murmansk. Nor can you construct a natal horoscope for any of the 320,900 people born in Murmansk— nor in Nordvik, Republic of Sakha (population 55,000), Holsteinsborg, Greenland (population 5,222), or Point Hope, Alaska (population 760). The Placidus House System is undefined for latitudes above 66°33', the Arctic Circles.

The author of the article goes on to explain how the Placidus house system works and why it became so popular. He also declares:

The Alcabitus, Campanus, Horizontal, Poli-Equatorial, and Regiomontanus House Systems are similarly undefined for latitudes above the Arctic Circles. None of these House Systems can be used for nativities or events in polar latitudes. The Sunshine House System depends on sunrise and sunset, so the Ascendant and Descendant are normally not 180° apart, and houses are undefined for polar areas when there is either no sunrise or no sunset on a given day. 

Figure 1: Astrolog House Systems

I've heard of the Regiomantanus house system but not of the other systems mentioned. Figure 1 shows the house systems that can be selected using the astrological software program Astrolog. As can be seen, I've gotten into the habit of using the Koch house system. The author of the Astro-Geometry article goes on to discuss his experimentation with the Porphyry, Sripati, and Natural Gradation house systems, none of which he found yielded accurate interpretations.

He was left with "the Birthplace House System, developed by German Astrologer Dr. Walter Koch after becoming disillusioned with the Regiomontanus System, and the Topocentric House System developed by Wendel Polich and Nelson Page in Argentina in 1961. These depend on both time and space to determine intermediate house cusps". The former is still undefined for polar latitudes at certain times and so he was left with the Topocentric. Here is his description of this system:

Instead of looking at the Earth from outer space, drawing Great Circles on it and dividing them in various ways as other house systems do, the Topocentric House System looks at the heavens from the point of view of someone standing at the location itself. With the location fixed in our reference frame, the Earth rotates around an axis parallel to the North-South Pole once in 24 hours. This time period is divided into 12 equal sections, and the house cusps are defined as the degrees of the zodiac that are ascending at each 2-hour interval—at different poles, or latitudes. There is also a different pole of the Ascendant for polar latitudes (more on this important topic in a future article). This feature is a key point in the Topocentric House System. 

What is even more significant is that the astrologers who discovered this system did not do so by contemplating the celestial-terrestrial sphere and pondering how to divide it. They discovered it by experiment! For example, Mr. Polich recorded the exact time—to the second — of every single small event that happened every day for three weeks: when he awoke, when a letter arrived, when a visitor came. Without exception, every one of over 1,000 events occurred within one minute of the time of transit of the mundane Ascendent. Numerous similar tests were conducted. 

In practice, the Topocentric House System yields excellent results, in my experience even better than Placidus. Natal horoscopes, transit forecasts, and even horary charts cede their knowledge. When combined with small arcs of the zodiac, the Topocentric House System generates astounding interpretations. The astrologers who developed this System also tested it by experiment, and its success in their experience was their principle claim for adopting it. It works.

Using Astrolog, the Topocentric system does indeed allow for the construction of a horoscope at say 70° North where the Koch system fails. I need to investigate this proposed solution more closely but for the time being I'll post this rather than leave it as a draft. I'll add to it as I get more information and experience.

Lilith

On the subject of Lilith, viewed from an astrological perspective, it is easy to be confused. Consider the following description taken from https://darkstarastrology.com/three-liliths/: 

There are three Liliths in astrology that you can place in your chart. We have Black Moon Lilith, Asteroid Lilith and the lesser known Dark Moon Lilith. I used to see them together as the Triple Moon Goddess and thought it made sense to use them in that way. I then found out that Demetra George had come up with a similar concept about Lilith, so I thought we might be onto something. Comparing the three Liliths to the bible story she says:

“The Asteroid Lilith describes the first stage in the mythical journey where she is suppressed, humiliated and flees in a fiery rage to the desolate wilderness. The Dark Moon Lilith depicts the pain of her exile where she plots and executes revenge. The Black Moon Lilith shows how she transmutes her distorted image back into its natural healthy expression

Not to be outdone, this site includes a fourth, Osculating Lilith:

• Black Moon Lilith is also known as Mean Lilith. This Lilith uses the average orbit of the theoretical Black Moon. This is why she is called mean Lilith. Mean refers to the average, not her temperament. 

• Asteroid Lilith is the only Lilith that is an actual, verifiable physical body. 

• Osculating Lilith is also called True Lilith. Her orbit oscillates wildly this is why she is called true Lilith. This Lilith uses the real orbit of the Black Moon. Her orbit is the real orbit of the Black Moon rather than an average. This is another theoretical point. Some people, like Juan Antonio Revilla, believe that she is the most important Lilith and most accurately portrays Lilith’s uncontrollable nature. 

• Dark Moon Lilith is also called the Waltemath Black Moon, or Waldemath Black Moon. Some people have claimed to have seen this Moon, but those claims cannot be substantiated.

To find your Liliths, go to Astro.com, free horoscopes, extended chart selection and scroll to the bottom of the page. Copy and paste these numbers into the empty box on the bottom left side of the screen: 1181, H13, H21, H58
Press “Click here to show the chart.”

• Asteroid Lilith: 1181
• Osculating Lilith/ True Lilith: h13
• Black Moon Lilith/ Mean Lilith: h21
• Dark Moon Lilith/ Waldemath Black Moon: h58

The fixed star Algol (associated with Lilith) is at a fairly steady 26˚ Taurus. Algol is a star in the head of Medusa in the constellation Perseus.

I tried it and it works fine. However, an astrological chart is already cluttered enough. We have the luminaries (Sun and Moon) and the planets (Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune) as well as the recently demoted, dwarf planet Pluto. It's quite common to include Chiron, one of the Centaurs, and perhaps Ceres, the largest of the asteroids orbiting between Mars and Jupiter. These astronomical bodies are located within the circle of the zodiac and the circle of houses, all mutually interacting by casting various aspects to one another. To introduce one Lilith, let alone three or four, will complicate things even more, so there needs to be a good reason for doing this. Let's see if the inclusion of one, two, three or even four Liliths can really be justified.

Let's start with asteroid Lilith because it's the most straightforward to deal with. Here are some astronomical facts about the asteroid taken from Wikipedia:

1181 Lilith, provisional designation 1927 CQ, is a metallic asteroid from the middle region of the asteroid belt, approximately 23 kilometres in diameter. It was discovered on 11 February 1927, by Russian–French astronomer Benjamin Jekhowsky at Algiers Observatory in Algeria, Northern Africa, and named after French composer Lili Boulanger. The asteroid orbits the Sun in the middle main-belt at a distance of 2.1–3.2 AU once every 4 years and 4 months (1,587 days). Its orbit has an eccentricity of 0.20 and an inclination of 6° with respect to the ecliptic.

In terms of asteroid size, Lilith is rather puny. Ceres, the largest asteroid in the belt has a diameter of about 945 kilometres and can be spotted with a pair of binoculars. Other large asteroids include Pallas Athena, Juno and Vesta, all measuring in the hundreds of kilometres. It doesn't seem logical to assign too much importance to this little asteroid. I personally wouldn't include it in a chart analysis. The Dark Moon Lilith, also known as the Waltemath or Waldemath Black Moon, I would also dismiss because it's not really been proven to exist.

So that leaves us with the Black Moon Lilith (also known an Mean Lilith) and Osculating Lilith (also known as True Lilith). Let's try to differentiate between the two of these. A diagram will help:

The eccentricity of the Moon's orbit is highly exaggerated in the diagram above but it illustrates the idea behind the Black Moon. An ellipse has two foci: the Earth occupies one focus and other focus is empty. The line of sight from the centre of the Earth to this empty focus points to a position on the ecliptic and this should mark the position of the Black Moon Lilith. This empty focus is about 36,000 kilometres from Earth so it's not far away and, because of its proximity, there is a not inconsiderable difference between its geocentric and topocentric position in the zodiac.

What complicates the matter even more is that the Moon doesn't simply move around the Earth in a simple ellipse. What happens is that The Earth and the Moon both orbit around the centre of mass of the Earth and Moon. This is called the Earth-Moon Barycentre or EMB. It is about 4,671 km from the centre of the Earth or about 1,700 km below the Earth's surface. It is described further at the same site from where the diagram was taken:

The Moon travels along an elliptical path around the Earth. An ellipse has two focal points, and the other focal point, not occupied by the Earth has been called the Dark Moon, the Black Moon or Lilith. This is a slightly simplified definition, since, actually, the Moon and the Earth both move around their common centre of gravity, and the path of the Moon is not a neat ellipse, but a rather wobbly affair. One must distinguish between the mean orbit of the Moon, which is a slowly elongating ellipse, and the actual orbit, which vaccillates around the mean path, due to interference of various kinds. Just as there a "mean" and a "true" Lunar Node, so there is a "mean" and a "true" ellipse and a "mean" and a "true" Lilith. I write "true" in inverted commas, because the Moon's Node is only "true" about twice per month, when the Moon is actually on it, for the rest of the time, it is as "untrue" as the mean Node. In fact, when working with a point so close to the Earth, one should also take the great parallax into consideration, i.e. consider, from which point on the Earth one is actually looking at a point in the heavens. Astrology observes the planets geocentrically, as if from the Earth's centre, and not topocentrically, from the actual place of the observer.

This is getting complicated. Clearly the True Lilith is to be preferred over the Mean Lilith but is the inclusion of this difficult to calculate point in a chart really justified? I really don't think so. My feeling is that there's been a push to promote Lilith by one means or another because in the Hebrew tradition she is such a powerful figure (taken from Wikipedia):

Lilith is a figure in Jewish mythology, developed earliest in the Babylonian Talmud (3rd to 5th centuries). Lilith is often envisioned as a dangerous demon of the night, who is sexually wanton, and who steals babies in the darkness. The character is generally thought to derive in part from a historically far earlier class of female demons in ancient Mesopotamian religion, found in cuneiform texts of Sumer, the Akkadian Empire, Assyria, and Babylonia. 

In Jewish folklore, from the satirical book Alphabet of Sirach (c. 700–1000) onwards, Lilith appears as Adam's first wife, who was created at the same time (Rosh Hashanah) and from the same dirt as Adam – compare Genesis 1:27. (This contrasts with Eve, who was created from one of Adam's ribs: Genesis 2:22.) The legend developed extensively during the Middle Ages, in the tradition of Aggadah, the Zohar, and Jewish mysticism. For example, in the 13th-century writings of Isaac ben Jacob ha-Cohen, Lilith left Adam after she refused to become subservient to him and then would not return to the Garden of Eden after she had coupled with the archangel Samael.

With the exception of Venus, all of the planets are male: Mercury, Mars, Jupiter, Saturn and Neptune. Pluto is male as well of course. While the asteroid Ceres and the dwarf planet Eris are female, there is certainly a shortage of objects named after strong females in the traditional astrological chart. I've recently taken to including Ceres in my chart analysis but I won't personally include Lilith in any of her variants at the moment.

Topocentric versus Geocentric

I think that astrological programs like Astrolog report the celestial longitude and latitude of astronomical objects from a geocentric perspective whereas an astronomical program like Stellarium reports it from a topocentric perspective. How large are the differences between these two systems of measurement. I'll explore this by reference to my own natal chart.

For my natal Moon, Stellarium gives a topocentric longitude of 59°32'42.4" or 29°32'42.4" Taurus. Astrolog gives a geocentric figure of 29°26'22" Taurus. This is a difference of slightly more than six minutes of arc. This isn't much but it could constitute a difference of sign if applied to my natal Saturn in 0°00'47" Virgo. Fortunately, this is not the case. Stellarium reports a topocentric longitude of 0°00'41.9" for Saturn. This is a difference of only about 5 seconds of arc.

I'll list the differences comprehensively below with Astrolog listed first and Stellarium second (measurements are rounded to the nearest second):

Sun -->        12°47'13" versus 12°47'51"
Moon -->      29°26'22" versus 29°32'42"
Mercury -->  2°14'36" versus 2°15'11"
Venus -->     9°09'42" versus 9°10'17"
Mars -->       9°15'54" versus 9°16'27"
Jupiter -->   28°47'00" versus 28°47'15"
Saturn -->    0°00'47" versus 0°00'42"
Uranus -->  26°52'14" versus 26°52'29"
Neptune -->13°15'24" versus 13°15'12"
Pluto -->     14°16'26" versus 14°16'24"
Chiron -->    8°57'05" versus NOT FOUND
Ceres -->   11°34'23" versus 8°41'52"

The glaring difference in positions is apparent for Ceres. I've checked carefully and that discrepancy of almost three degrees is very real and very disconcerting. What's gone wrong? What program is in error and why? Given that Ceres is between Mars and Jupiter, the difference should be measured in seconds of arc. Let's check the differences between the two program's for Ceres today (14th February 2018): Astrolog gives 8°13'07" Leo whereas Stellarium gives 8°54'06" Leo, which is a smaller discrepancy than in my natal chart.

For the time being, leaving out Ceres, the differences between the two sets of measurements is slight but significantly greatest where the position of the Moon is concerned. For a lunar position that is greater than 29°50" or less than 0°10" of a sign, the geocentric position should be checked against the topocentric to determine whether a change of sign is involved. If so, I would say that the topocentric measurement that should be used and not the geocentric.

As for Ceres, it will be useful to check some other asteroids as well, namely Juno, Vesta and Pallas. In my natal chart, Pallas is located at 29°09'00" Gemini according to Astrolog, while Stellarium puts it as 29°38'17" (almost a half degree different and much larger than the discrepancy between the Moon's positions). Vesta is located at 23°42'21" Sagittarius using Astrolog but 21°42"00' using Stellarium (a difference of a full two degrees). Juno is located at 27°16'47" Taurus using Astrolog but at 28°23'11" using Stellarium (a difference of more than a degree). So for the asteroids at least, there are significant differences between the celestial longitudes as reported by the two programs. This is not due to a differences between topocentric and geocentric positions. These should be slight. The difference is due to a software bug.

What is happening with Ceres on a day to day basis according to Stellarium? As mentioned earlier, it is currently in 8°54'06" Leo, so I'll track its weekly progress:

21st February: Stellarium 7°32'20" Leo versus Astrolog 7°01'01" retrograde
28th February: Stellarium 6°26'41" Leo versus Astrolog 5°54'55" retrograde
7th March: Stellarium 5°40'08" Leo versus Astrolog 5°07'49" retrograde
15th March: Stellarium 5°12'42" Leo versus Astrolog 4°39'22" retrograde
19th March: Stellarium 5°08'57" Leo versus Astrolog 4°35'35" Leo stationary direct
22nd March: Stellarium 5°10'58" Leo versus Astrolog 4°37'18" direct
29th March: Stellarium 5°30'25" Leo versus Astrolog 4°56'06" direct

Stellarium and Astrolog both report Ceres turning stationary direct on the 19th March, it's only that there is a consistent difference of about half a degree between positions on any given date. I suspect that the Astrolog software is in error with the error increasing as one travels back in time. For the time, it is sufficient to add about 30 minutes to the position as reported by Astrolog. I'll try to find out more about the source of this problem.