""the Mathematics of Astrology: Does House Division Make Sense?" - Undergraduate Research Opportunities Programme in Science, National University of Singapore" - Singapore

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Undergraduate Research Opportunities
Programme in Science
THE MATHEMATICS OF
ASTROLOGY
DOES HOUSE DIVISION
MAKE SENSE?
By Kevin Heng Ser Guan
Department of Physics
National University of Singapore
Supervisor:
A/P Helmer Aslasken
Department of M athematics
National University of Singapore
Semester II 2000/2001
Undergraduate Research Opportunities
Programme in Science
THE MATHEMATICS OF
ASTROLOGY
DOES HOUSE DIVISION
MAKE SENSE?
By Kevin Heng Ser Guan
Department of Physics
National University of Singapore
Supervisor:
A/P Helmer Aslasken
Department of M athematics
National University of Singapore
Semester II 2000/2001
Table of Contents
I. A Brief Overview of Astrology
-
Introduction
2
-
Different Genres
2
-
Methodology of Astrology
2
-
Geocentric Model vs. Heliocentric Model
3
II. Formalism of Astrology
-
Basic Terminology
4
-
Great Circles on the Celestial Sphere
5
III. The Planets
7
-
Retrograde Movement of the Planets
9
IV. The Zodiac
-
Constellations
10
-
Zodiac
10
-
Astrological Meaning of the Zodiac
11
-
Problems With the Zodiac
12
V. The Houses
-
Terminology of House Division
14
-
Astrological Meaning of the Houses
15
-
Different Systems of House Division
16
1. Equal House System
2. System of Campanus
3. System of Regiomontanus
4.
System of Placidus
-
Differences in Sizes of Houses During Course of Day
20
-
Uneven Probability Density of Ascendant at Different Latitudes
21
1. Theory
2. Derivation of V, the Speed of the Ecliptic When it Crosses the Horizon
3. Derivation of the Exact Form of the General Formula
4. Analysis of the ‘+’ and ‘−’ Roots
5.
Graphs of V at Different Latitudes
-
The Polar Problem in House Division
27
1. Ill-defined Ascendant and Descendant
2. No Ascendant / Stationary Ascendant
3.
Ill-defined MC
4.
Discontinuous Ascendant
VI. References
36
1
I. A Brief Overview of Astrology
• • Introduction
Astrology is the belief that there exists a meaningful relationship between the positions of
celestial bodies and human experience, and that we can systematically determine this
relationship.
A common misconception is to confuse astronomy with astrology. Astronomy is the
scientific study of the universe. Astrology is “astromancy”, or divination by the stars.
An astronomer studies the stars using the scientific method. An astrologer casts
horoscopes to predict earthly events, like the fates of nations and individuals.
The only possible method to test the validity of astrological influences or predictions is
using statistical studies. This means gathering large samples of individuals, tabulating
their character traits, and checking if there exists a correlation between these and their
horoscopes. This is not the focus of the project. Instead, the aim is to highlight some
mathematical problems in the formalism of astrology. The focus is specifically on
geometric problems encountered in house division.
• • Different Genres
Astrology has many faces. There is popular astrology, commonly found in newspapers.
There is also serious astrology, which is the casting and interpretation of horoscopes of
individuals. Serious astrology is itself sub-categorized. Natal astrology deals with the
horoscope calculated at the moment of birth. Horary astrology determines the auspicious
moments to make personal decisions. Mundane or world astrology studies the fates of
countries or nations.
• • Methodology of Astrology
The input data an astrologer needs are the date, place and exact time of birth. These will
provide the material for the calculations needed to construct the individual’s horoscope.
A horoscope is nothing more than a map or diagram of the various planets’ positions at
any one point in time, with respect to the earth. The word “horoscope” is derived from
the Greek word “horoskopos”, meaning “hour watcher”. Basic ingredients of the
horoscope include the sun-sign, the Ascendant, information on the Houses, the Aspects,
etc. The astrologer will then proceed to interpret the horoscope, and hence offer advice.
2
• Geocentric Model vs. Heliocentric Model
The heliocentric model places the Sun at the centre of the solar system. The geocentric
model places the Earth at the centre of the solar system.
Technically, it is not wrong to adopt the geocentric model, as we would be merely
considering different frames of references. We live in a geocentric world. Astrology is
preoccupied with how the planets relate to an individual on Earth, and hence their relative
positions. Generally, the heliocentric model is good for explaining how things work in
the solar system, in accordance with the laws of physics. By contrast, the geocentric
model is suitable for descriptive purposes.
3
II. Formalism of Astrology
• Basic Terminology
Astrology deals with projective geometry, meaning distances to celestial bodies are
inconsequential. Only their relative positions on the celestial sphere are important. In
other words, only the angular differences from the Earth matter. We need to define
certain key terms to obtain a graphical idea of the celestial sphere.
North Celestial Pole
Zenith
Celestial Equator
Observer
Earth
Horizon
South Celestial Pole
A schematic view of the celestial sphere
1. Celestial Sphere
The celestial sphere is an imaginary dome around an observer on Earth. The observer is
at the centre of the dome, with all the visible celestial bodies on its surface. It is a model
of how the sky appears to us. In reality, the various celestial bodies are not the same
distance from the Earth.
2. Celestial Poles
The celestial poles are the centres of rotation of the celestial sphere. They are called the
north and south celestial poles (NCP and SCP).
3. Zenith
The zenith is the point on the celestial sphere straight overhead of an observer on the
Earth.
4
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