What's Your Sign?

Astrology - many people like this pseudoscience and believe in it's ability to predict the future and a person's personality. I admit that occasionally you can even see shared personality traits within a group, but then that may have something to do with those I socialize with (I'm sure all Libra's aren't bossy little know-it-alls - funnily enough I've never seen that written in an astrology book).

I was just going to say that there are many different versions of astrology, all taking the planets and constellations into account. So, I was thinking why not see how many star signs there actually are?

For the sake of simplicity, I won't go into numerology and such and stick just to those that depend on the stars.

This leaves us with 4 kinds: the Western Zodiac, the Chinese Zodiac, planetary influences outside of your Western Sign, and the Lunar cycle.

The Western/Roman Zodiac is the one most of us are familiar with and varies between the months: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.

The Chinese Zodiac depends on one's year of birth in accordance to the Lunar Calender: Rooster, Dog, Boar/Pig, Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep/Goat, and Monkey. I will mention that like the Western Zodiac begins with Aries, the Chinese actually begins with the Rat but I was listing them in order of which of the WZ signs they should be associated: e.g. Aries = Rooster. (This is the correlation I was taught but I have read many different versions.)
However, these guys have a couple of additional factors: firstly, depending on which "Year of the ANIMAL" you were born in, your element will be different from someone born in another year. The possible elements are Wood, Fire, Earth, Metal, and Water.
The second factor is "Yin" or "Yang" - this varies between what a sign is naturally, and whether you are male or female. For instance the Rooster is naturally Yang, but the Sheep is Yin - once again your gender/year will change this.

Next up we have planetary influences - these correspond to the Western Zodiac with Aries and Scorpio being ruled by Mars (the latter also getting Pluto in recent years), Taurus and Libra getting Venus, Gemini and Virgo going to Mercury, Cancer going to the Moon, Leo to the Sun, Sagittarius and Pisces getting Jupiter (the latter also Neptune), and finally Capricorn and Aquarius being ruled by Saturn (the latter being joined with Uranus).
However depending on where in the sky these planets are you will get the influence of yet another sign. Except the sun... in that case it matters what time of day you're born... which also matters to everyone else according to other books.

And that's not even getting into those who are born on the cusp of two signs.

Next the lunar cycle - it has approximately 29 days in it and, depending on who you ask, are all very important. I, however, would prefer to just say that there are 9 main parts: new moon, waxing cresent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning cresent, new moon, and somewhere in there there can be a lunar eclipse.

So, now we will have MATHS! Yay! My favourite subject! To simplify the formulas I will include what time of day you're born (separated into 12 houses), directly link Yin/Yang to gender, and also assume that for the signs with two ruling planets that they are in the same segment of the sky at the same time (slightly justified as during the Scorpio month Mars is in the same sign as Pluto... supposedly.)
For the lunar cycle calculations we will only include new moon, waxing cresent, waxing gibbous, full moon, waning gibbous, waning cresent, and the lunar eclipse for the sake of fairness. So 6.

First, just helping your vocabulary:
A combination is when you have a set of events/numbers/etc where the order does not matter. A permutation is where the order does matter.
"My fruit bowl has a combination of bananas, oranges, apples, and grapes."
"The combination to the safe is 593".
In the first instance it is a combination - we really don't care what order the fruits come in. So it only calculates "one" order.
In the second instance we do care what the order is as 395 or 935 certainly wouldn't work. We often call it a combination but it is in fact a permutation. So it calculates every possible order.

Let's go through all the combinations and permutations, shall we?
The sign of Leo shall be calculated separately as it doesn't have the "outside" factors. In order to find a combination, we must multiply put all the factors.

Here are the functions.

So, there are 1,149,120 star signs according to this.

Now, the world's population as at 2010 was 6,840,507,000. So divide that by 1,149,120 and we get 5,952.82216 people for each starsign.

What I'd really love to see is if someone actually did individual predictions for each of these signs and then published it! X) Then I'd have a better measure of it's accuracy. :P