# Topocentric House System

Popularity of house systems among astrologers[1]

The topocentric house system (a.k.a. Polich-Page system) was invented in Argentina by the Hungarian-German astrologer Wendel Polich and the British Anthony Nelson Page and presented to the public for the first time in the journal Spica in 1964.[2]
It is especially popular in the Spanish-speaking world.

## Technique

The authors state that they have discovered the house system empirically by observing Primary Directions and argue that it is therefore scientifically the most well-founded of all house systems. Since this assertion is supposedly not based on statistical evidence, it should be treated with caution.[3] Topocentric house cusps generally deviate less than one degree from Placidus house cusps in the lower and middle latitudes. The differences become more apparent only towards the arctic circle and beyond.

### Calculation

Mathematically, the calculation is very simple, albeit not very comprehensible: the tangents of the polar elevations of the intermediate houses correspond to one-third or two-thirds of the tangent of the polar elevation of the Ascendant, i.e. the geographic latitude of the birth place. The individual house cusps lie on Great Circles that intersect the Celestial Equator at intervals of 30°. The great circles of the houses do not meet exactly at the north and south point, however.

### Problems

Since the great circles that define the houses do not intersect exactly in the north and south points, the house position of celestial bodies in the vicinity of these points is often unclear. Sometimes problems also arise in the calculation of house cusps beyond the arctic circle. In the example below, the order of the house cusps is as follows: 10-1-11-12-2-3. This problem perhaps can be solved in the following way: looking at the chart drawing, the ecliptic does not seem to run through the houses 11 and 12 at all, but runs from the 10th house directly into the first house. Furthermore, the drawing shows that the house cusps 11 and 12 are located in the sector of house 1. It is therefore advisable to ignore the 11th and 12th house cusps. The ecliptic then only runs through the houses 10, 1, 2, 3, 4, 7, 8, 9.
Similar problems exist in the Placidus house system.

## Assessment

Although it is well known how to calculate the "topocentric houses", and many computer programs will do so, the point of this calculation method is incomprehensible. The geometrical explanations provided by Polich and Page are inadequate and flawed.

Chart of a person born near the North Pole (Northern Norway)
• Bob Makransky comes to the conclusion, after a thorough examination of the house system, that it is not clear what concept of mundane positions the authors wanted to model.[4].
• Michael Wackford, who has studied the history of the Placidus House System in detail, explains the origin of the "topocentric" house system in the following way: Polich would have misunderstood the Placidus system and believed it was constructed with great circles. At the same time the true idea of the Placidus system somehow hovered in his mind as well. In his attempt to realise this idea mathematically, he took a wrong line and created the "topocentric" house system.[5].
• Ptolmei Svarogich also questions the mathematical competence of Polich and Page. Nevertheless, he makes a case for this house system, because "it combines, in a harmonic way, the mathematical and geometrical elegance of Regiomontanus with the practical accuracy of Placidus."[6]

The question remains, why this system should be more "topocentric", i.e. centered on the birth place, than other systems. It is sometimes said that it is a "further development" or a "perfection" of the Placidus system,

1. Because the calculation of the house cusps seems to be much easier and more elegant.
2. Because this house system, unlike Placidus, would not cause problems beyond the arctic circle.
3. Because it was discovered empirically, and not derived from theoretical considerations like all other systems.

This can be refuted as follows:

1. More relevant than the complexity of the calculation is the question whether a particular subdivision of the sky makes any sense at all. The philosophy of Placidus - the uniform subdivision of diurnal arcs - is easy to follow. The philosophy of the "topocentric" system, however, does not appear to be justified, not even according to recognised experts of house calculation. Besides, the house division of Porphyry would even be simpler and more "elegant", as it can do completely without mysterious spherical trigonometry ("tangents", etc.).
2. The Placidus system can – contrary to common prejudice – by all means be used in polar regions. On the other hand, in many cases the topocentric house system will also run into problems beyond the arctic circle. At times, house cusps will appear that are meaningless or difficult to interpret (see chart above.)
3. Other astrologers likewise "empirically" swear by their own house systems.[7]