Introduction
The model for the trinity, consisting of essentially three groups; The Klein four group, the Octal, and the cyclic group of seven elements, is an almost bizarre union of compactedness. I use that term here without the ensuing mathematical use of the term. The trinity itself has three members - So how does a seven, or even eight element group come in as merely possessing three distinct members? There is also the question of the nature of the ultrafilter. A more pressing concern I found, was the trouble involved in looking at these groups as three elements and perceive naturallly the binary operation of a simple group - (the Klein four group) as following from the elements themselves. __Operands vs. Operations__
It is very difficult to perceive an overall formula for the operation of the Klein four group with the trinity model. It is perhaps easiest to say K4 x C7 = Octal... at least within the model. How then does one obtain C7 x Octal = K4 ?? We are very familiar with addition and multiplication of real numbers in the usual sense.. but may we, from our construction of extending Anselm's argument find a "formulaic" relation of K4, C7 and the octal group in a way that defines such an operation? Simply saying 2+2 = 4 because 'it has to be' in this case - a mere definition of an operation for its own sake would be of little use to me, anyway.
__1: - Trinity In Christ__
K4 = C7 x Octal... Ok, starting with the 'easy' case. Hopefully leading up to the remarkable conclusion reached earlier, we can explore the only way to come to terms with the three elements as our three groups. And by way of our initial construction, which has for the most part been left aside until now. By the same method we must look differently also at the other two elements in the pages to follow. The problem is also one of whatever situation is natural, under the necessity of consistency.
__2: - Trinity Through The Father__
Octal = C7 x K4.. Not the easy case? In order to explain this in detail; (though at first glance a no brainer...) this case has more depth to it when viewed within the construction in the previous section, as more than that a simple loop of Klein four groups provides. It also shows that there are three, not eight, (not even seven) members in the trinity. If you can wrap your head around this you have done well. It will prepare you for the toughie - next.
__3: - Trinity By The Holy Spirit__
C7 = Octal x K4.. You will be impressed here because there is no sense of "divides by" in this construction. A little more math is required here. It also shows that the situation of these three groups bound together is not a general state of affairs for finite fields. I think these three constructions, though by no means proof, (but what is 2 x 2 ?) but very beautiful in their own right are less confusing viewed this way and further reinforce the advantages of a trinitarian God over a single deity or a huge pantheon.
__They Do It With Mirrors__
Ever stood in front of a mirrored wardrobe and folded two mirrors either side and seen your reflection on either side stretch on and on whilst the one in front merely shows you once? (And perhaps a little of the others at the edges.) Is there any way to think of a viewpoint of infinite regression in this way? How do you fit in a trinity? Or, if you have two webcams linked to your pc with output windows side by side and point each webcam at the complement's window - will you gain any understanding? What about seven webcams?
__Ultrafilters Of Trinity__
I take another look at ultrafilters here, and try to justify the trinity model used in terms of the structure of Christian faith. It will help to refer in whole to the Sons of God section in the Metaphysics section. (Edit: I have at the time of writing no sense of where this will go, so this may include some furious editing as I go along.)
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