For the record, I'm an atheist.
The Holy Trinity is, first and foremost, a concept developed by the early Church Fathers a few centuries after Christ. They formulated the idea out of inquiry as to the essential nature of God; that is, the metaphysical and not just apparent nature of their deity.
Basically, they stated that divinity is of a singular nature. It is immutable, cannot be changed, and has forever existed. In this view, divinity, or "God-ness" cannot be anything other than one single thing. Jesus, by his divine nature, is one and the same with his Holy Father. They are one, in that they are both divine. They cannot be seperated by their nature, and coexist through their essential "God-ness". This is the metaphysical nature of God: singular, immutable, sovereign of any other substance.
However, in physical terms, God-ness is indeed seperate. Though the underlying divinity remains singular, it manifests seperately on a physical level. The Son is God on earth, the Father is God in heaven, the Holy Spirit is the Father in heaven
through the Son on earth. It is the means by which God exerts his will on earth, through the person of Jesus.
To summarize, according to the Holy Trinity doctrine, God is one being. God manifests itself through 3 persons: the Father, the Son, the Holy Spirit. These 3 are not corelated. They are exactly of the same nature. The only difference is that, in phyiscal terms, they are divided. Underlying this physical seperation, on the plane of divinity, they are one.
As complicated as that may seem, it's just a synopsis. Through theology, the concept of the Holy Trinity has gone through innumerable speculation, revision, and accessment.
To actually answer the question of the thread, the Holy Spirit, once again, is the will of the Father made manifest on earth through the conduit of Jesus Christ.
And to touch on the numerical God thing: The Judeo-Christian deity neccesitates a plurality. Though this may be nothing more than the limitation of human language and communication, the word for God in Hebrew is "Elohim". This word is not in itself singular; it is an umbrella term for any type of divinity. The Hebrew bible uses it to refer to God, as in the God of Israel, just as it refers to multiple deities (as in the first commandment wherein God declares that we shall "have no other gods")
The plurality of Elohim can cause all sorts of theological debate. It could be insight into God's nature, or it could just be the particular character of the Hebrew language.
On a more philosophical level, numbers are representations of quantity. It has no "form", as it is a concept. It can however, be represented by a numeral, i.e. 1,2,3, etc. These are symbols which represent numbers, which in turn represent quantity.
Quantity, as a property of a particular thing, does have form. In the Holy Trinity doctrine, God is said to be of 1 substance. This substance, though infinite, is nonetheless
1 substance. It is all encompassing in its 1-ness, and it's 1-ness will never change. Were divinity more than 1 substance, it wouldn't be immutable, and thus, wouldn't be divine. Were it less than 1, it wouldn't exist, as it would have the quantity of 0.
Though divinity has a quantity, it cannot be divided into discrete measurements. You can't have some God over here, and a little less God over there. God's quantity exists on a continuum. As such, God is infinite. Not in the sense that God is an infinite number of things. As we've seen, God is no more and no less than 1 thing. Rather, the 1-ness of God is infinite.
The means by which God makes himself known to us on a material level, however, is different. As finite beings, and limited by our tangibility, humans cannot comprehend infinity. This does not mean that God is no longer infinite. Rather, the means by which God manifests itself to us must be finite. Thus, Jesus Christ is 1 of 3 persons of a singular entity. The Father is 1 , the son is another, the Holy Spirit the last. Each one nothing more than different beings of the same nature: divinity. In physical terms, they can be divided. Obviously, the Father is in heaven, seperate from the physical world. The Son is on earth, seperate from heaven. The Holy Spirit is in heaven and earth, but only where the Father and Son direct it to be. Though they exist discreetly and seperate in location, they each share the essential being of God-ness, which cannot be said to be either here of there. It is infinite, and thus, all-encompassing.
It's all very convoluted. In fact, everything I just typed should serve to show exactly why I am an atheist. A being who makes that little amount of sense ain't gettin' my worship.
