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.