The spherical geometry involved confused me to no end when I first started out. I finally had to draw my own 3D model just to figure out what was going on in three-dimensional space with all these planes and angles.
On this very (or at least related) topic, this evening I unearthed a 1976 Journal of Geocosmic Research in which Rob Hand explained why it's more accurate to use geographic/astronomical latitude in chart calculation rather than geocentric latitude. It has to do with the Earth being an oblate sphere, flattened a bit on the top and bottom. For years I always made the 11' subtraction from the atlas values to make this correction. I didn't notice the option being offered in the computer programs I use now. Wonder which one they use.
Yes I must admit that I had to puzzle a bit over the spherical geometry (SG) in Gansten, as my maths is statistics based not geometrical LOL.
Whilst some knowledge of SG is necessary I have a philosophical problem with it. That is, to what extent, if any, does a given increase in our SG accuracy lead to a measurable increase in the accuracy of our Astrology. I think we need to here distinguish between Natal delineation and prediction. I don't think
any increase in SG accuracy has a discernable impact on natal delineation. Indeed I see no
a priori reason why a reading from a Whole Signs chart should not be as useful as reading from a quadrant systems based chart - notice I use the word
useful rather than accurate here. The emphasis of the reading might be different but it may still produce at least as useful insights into the native's character. The same holds true for different quadrant systems being used or indeed using the sidereal rather than tropical zodiac.
When it comes to prediction, the situation may be different. Quadrant systems were introduced to support the predictive technique of Primary Directions, which does depend on measuring (by space or time) the progres of a degree of the zodiac between two point in the sky - for example the position of a planet at birth and the point of the Ascendant. That clearly does require some use of SG. This problem is compounded if we wish to measure the progress of a planet to the degree of a natal house cusp, because it appears to require us to come up with an accurate system of identifying the intermediate house cusps - the angles themselves are more easily identified.
In principle this appears to suggest that if we can improve our SG we will automatically improve our predictions. However to what extent is this possible - can we achieve 100% accuracy or is there a point at which further increases in the accuracy of SG have no discernable effect - possibly because of random error in human behaviour - we are not entirely automatons, or alternatively because if we can't come up with a definitive house system, does an improvement elsewhere in our SG, get lost in the grey area or where house cusps lie.
Astrology is primarily divination - an attempt to read the mind of God. It might make more use of mathematics than most other types of divination but is the mind of God, amenable to total description by mathematics and is the Astrologer the passive applicant of mathematical rules that yield the required knowledge or does he or she have an interaction with the mind of God that is difficult (or impossible?) to express in a mathematical way.
We are after all studying
Astrology - the word or message of the stars, not
Astrophysics - the physical properties and dynamic processes of celestial objects. The latter might well be very helpful in establishing the context of the message but the message is more than the properties and processes.