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THE MATHEMATICS OF ASTROLOGY DOES HOUSE DIVISION MAKE SENSE

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. 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. Basically, there will be five important sections: 1. A Brief Overview of Astrology 2. Formalism of Astrology 3. The Planets 4. The Zodiac 5. The Houses The first four sections are an introduction to the subject of astrology. A proper mathematical structure is constructed for the most common methods used in astrology. To attain a complete understanding and appreciation of certain aspects, historical references are added. The fifth section analyses the main topic of the project. PROBLEMS WITH HOUSE DIVISION House division is an attempt by astrologers to introduce a local element to the horoscope. However, there are a few fundamental problems encountered. Uneven Probability Density of Ascendant at Different Latitudes The problem of house division, at different latitudes, reduces to investigating the speed of the ecliptic when it crosses the horizon. We shall let this be V. Let the speed at which the celestial equator crosses the horizon be V0. This is the uniform speed of rotation of the Earth on its own axis. Let ε be the angle between the ecliptic and celestial equator, which is always 23.5°. Let φ be the angle between the ecliptic and horizon. Let L 90° plus latitude. Let c be the distance along the ecliptic. First, we shall derive a formula for V when the angle is φ. Since speed is defined locally, we can use Euclidean geometry. V = V0 sin L / sin φ (1) We will then use spherical trigonometry to determine how φ changes as the ecliptic moves along the horizon. sin [ cos ( cos φ ) ] V = V0 sin L = cos φ − cos ε cos L ± sin ε cos c [ sinL − sinε sinc ) ] ( 1 − sinε sinc ) (2)