This article is the 3^{rd} part of a 4 Parts series on construct of astrological rules. Please read the Part 1 and 2, before getting into this one.

This article is dedicated to ‘**Vaathiyaar**’ **Thiru. Subbiah Veerappan**, who has been writing about astrology in Tamil for a long time. Those interested to **learn astrology in Tamil** are suggested to make use of his blog (http://classroom2007.blogspot.com/).

Disclaimer: This article is originally written for an average audience, who might not have any background in statistics. I would call this article more of an approximation in terms of statistical accurateness. My objective here is to make it easy to understand than being completely accurate. Those well versed with statistics are requested to bear with me for some minor inconsistencies that might have crept in.

**The reader is requested to connect the concept through the diagrams provided.** This is a lengthy article. The reader is requested to pause in between, understand and digest the concept and then proceed further.

In Part 1 of this article, I have highlighted that for something to become a rule, it should fit the following conditions:

*A rule should fit to majority of samples and need not necessarily fit to every case.**Rules should be minimum in number and their exceptions should be even fewer.**The rules should be independently consistent and collectively converging.**Individual rules should fit to a larger system of basic constructs and not challenging the larger system.**The rules should withstand test of time, and easy to understand and explain.**The rules must be open for testing and amenable for changes to suit different times.*

Also, in Part 2 of this article I have discussed that any astrological system would focus on one of the three following dimension as its primary perspective. To quote

*“Three types of fundamental perspectives are followed in Indian astrological systems. Bhavam (Bhava or house), Bhava Athipathya (role of house lord) and Graha Athipathya (Planetary role). In all astrological systems that are popular today, one can witness that one of these three dimensions is primarily used as the main perspective (Ref: Sivadasan Ravi).”*

If we think deeper, we can understand that astrological dimensions can be more than three. In fact, **they can approach infinity**! If someone is interested to approach astrology from other dimensions, its always possible. However, the challenge lies in the fact that the new dimension needs to be unique, with its own system rules and do not imitate existing dimensions.

Now, let us understand about the dimensions in scope of Indian astrological systems.

Let us assume that we have a transparent sphere (for e.g. a big glass ball or big glass marble) in our hand, that contain some differently coloured spots/mottles inside, distributed around its core. If you are asked to provide the location coordinates for any of those spots, you would have more than one way to provide it. For the purpose of consistency and repeatability, you would need to define certain fixed base points and number of dimensions. The minimum number of dimensions required to accurately pinpoint a location in the core area is 3. However, if you increase the number of dimensions to infinity, you would be able to locate pretty much any dot inside the sphere.

Figure E007-1 shows this transition. It starts with the numerous dimensions, then reduces to few and then finally to 3. Please note that when numerous dimensions are involved, you would be able to get a closer resemblance of sphere and locate most points inside a sphere. However, as the number of dimensions gets reduced, the overall area being explained keeps getting reduced. Finally, when the number of dimension is 3, the area that is actually getting explained gets reduced to a cube (i.e. the core area).

Under normal circumstances the core of a sphere is supposed to be a dense area with most of the data points being clustered around the core. We call this as dimension optimization technique in data science. You would be able to appreciate how this core concept of data science is eloquently applied in our astrological systems and number of perspectives are limited to 3 only.

**Interestingly, Naadi based systems further reduces the number of dimensions required to address a point to just two. Vedic astrology tries to address it with 3.** Just remember through this reduction in dimension what is being explained is the area in core. Data points outside this core may not be explained well with just 3 dimensions.

**How to form rules – Explained with an example:**

Let us get little deeper and deduce how a rule might have been derived in astrology. Consider that we have few hundred individual horoscopes and want to understand the relationship of planetary positions in horoscope of people who get married at a right age (21-25 for a man and 18-23 for woman, considering current laws). Assume that we are trying to derive some generic patterns from this data that will be used to create business/astrological rules to predict new cases, who are likely to get married at right time.

If we look these horoscopes from the 3 dimensions, we would be able to draw derived variables for different dimensions involved. Assume that we are plotting the relationships between derived variables in a 3D perspective. In the picture below, this 3D view is portrayed from Bhava (Dimension 1) vs Bhava Athipathya (Dimension 3) perspective. Assume that each dot in the picture denotes relationship found in a single horoscope and collectively they form the colourful pattern depicted in the picture.

Following definitions are drawn for ease of understanding. Please take time to understand each of the item in this picture.

1.1 Highlights that infinite/numerous dimensions are involved.

1.2 Denotes reduction of dimensions to just 3 (manageable numbers).

1.3 Provide distribution of individual data points (derived and transformed) on the 3 dimensions involved. Within this picture individual components are described below.

**Boundary for Rules:**Provide the boundaries of dense core area suitable for deriving common rules. We can call this as the**solution space**. This area should pack most of the individual data points in a dense space. i.e. within a minimum area. We should be able fit most of the data points in a minimum area, for the rules to be more accurate.- A-E Rules (5 different colours): Denote subset of samples that formed specific pattern and can be further divided to create specific rules. Dotted lines have been drawn to further classify this area into 5 subsets.

- Exceptions (purple colour dots): Points that do not fit within the core, however, have their own unique pattern outside core solution area.
- Outliers (Blue and red colour dots): Points that are randomly placed and do not fit into a specific pattern in the current set of dimensions. If we extend the solution space to accommodate these outliers, the rules will get diluted. However, these outliers could still be part of a rule that can be formed when looked at from a completely different perspective.

Now let us understand Rules A-E based on the example we have selected. Boundaries between these points are drawn from Bhava Athipathya perspective. Now, let us quickly understand the placements astrologically.

- At a broader level, first Bhava is denoted by Ascendent.
- First Bhava denotes self, 4
^{th}family life, 5^{th}for kids, 7^{th}for partner, 9^{th}for Punya (good karma) and 11^{th}for Profit (also second spouse!). - The planet that is the owner of these houses is called Bhava Athipathi. For example, if someone has Cancer as Lagna, the 5
^{th}house would be Scorpio and its lord is Mars. For a native with Pisces as Lagna, the 7^{th}house would be Gemini and its Bhava Athipathi would be Mercury. - In a horoscope, if the planets associated with the above houses are ‘connected’ in ‘some’ way, we can assume that are likely to produce some positive impact leading to timely marriage.
- Let us understand the ‘some’ ways in detail. A ‘connection’ could mean these planets aspecting each other, one of them aspecting other, a position in trine, conjunction of planets etc based on the system under consideration.

Let us understand our rules A-E in this context based on their ‘connection’. Please remember that **this is a hypothetical case only** and should ** not** be applied in your horoscopes arbitrarily. These rules are not a recommendation as well.

- Rule A (Collection of red colour dots): 5
^{th}Lord and 7^{th}Lord - Rule B (Yellow dots): 4
^{th}Lord and 7^{th}Lord - Rule C (Green dots): denotes 7
^{th}and 9^{th}Lords - Rule D (Sky Blue dots): First and 7
^{th}Lord - Rule E (Deep blue dots): 5
^{th}and 9^{th}Lords - Exception 1: 7
^{th}Lord and 11^{th}Lord and - Exception 2: 5
^{th}Lord and 11^{th}Lord 😉

Now, we have got 5 rules and 2 exceptions to predict cases that are likely to get married in time. Out of these 7 rules, we have to understand which rules are more stronger and significant predictors. This can be achieved by understanding distribution pattern of individual cases against their group mean. This can be achieved through plotting the data points over a bell curve with Mean 0 and a standard deviation of 1. Readers who wants to know more about Normal Distribution and its properties are directed to read it here –> https://en.wikipedia.org/wiki/Normal_distribution

Component 1.4 depicts this transformation of data points of different rules into bell curves.

*In a bell curve, points that comply with the mean will be positioned in the middle, with points away from it assuming distance positions from peak.**A stronger rule will have a steep peak around mean and relatively flat tails.**When the min-max range is high and variation is high, that bell curve will tend to have a relative flat peak and a broader hump shape.**If all the data points are scattered across a near linear line, that particular combination can’t be considered a rule at all.*

If we analyze our 7 rules based on the above criteria, we can come to a conclusion that Rule A & D in our example are very strong rules to predict the outcome followed by Rule C. Compared to A, C and D, Rule B and E are relatively weaker rules to predict the outcome.

I can’t think of an example to depict a bell curve for Exceptions. You can assume that the green colour bell curve marked as F for exceptions. Though this curve is not following a common mean point, it still holds good in terms of strength of the distribution.

Now let us see the following picture to see how the data points could appear differently based on the different viewing perspectives, that helped us to stick to a particular dimension to draw these rules. Figure 2.1, 2.2 and 2.3 below depict the order of data points from different perspectives. Among these three, Perspective 2.1 offers clear segregation of data points, offering us the scope to draw rules.

**Synopsis: **

In this essay, we discussed the following:

- How to reduce the number of dimensions involved from infinity to few.
- How to draw a solution space within the limited dimensions and further draw subset for rules.
- How to validate the strength of particular rules and classify the rules and assign priority among rules

**Food for your thought:**

If you analyze this whole example based on the initial definitions we drew for a ‘rule’, you would be able to appreciate that construct of astrological rules in fact have a strong data science concept behind their construction. What we see externally is just the tip of the ice berg. A deeper understanding of these constructs could offer more insights into the wisdom of our forefathers and following their path could help us solve more mysteries. Are you going to be contend collecting pebbles on the sea shore or are you going to venture in the deep sea in front of you to fetch the pearls of wisdom? Which is your type?

To be continued…