In the comments of Alan Roebuck’s recent post on the God of the Philosophers, Josh asked us to explain how God can be a Trinity and yet also Simply One. It’s a tough question. While I can’t honestly say that I understand the notion, I do feel as though I have the beginnings of a grasp on it. I worry about it a lot; I have for about 30 years. Every now and then, I feel as though my grasp has improved appreciably. Five days ago, I awoke out of a sound sleep at 4:00 am, thinking about the Trinity, and observed for two hours as my grasp improved a bit. It wasn’t as though I did anything, other than watch a flower unfold.

What follows is a record of my thoughts that morning. It was an interesting couple of hours, spent in a state half dreamy, half-awake, yet fully aware the whole time, and every ten minutes or so turning on the bedside light to make another note. Eventually the sky turned grey, and I arose to get some coffee.

I begin with Chastek’s recent blog post, Lecture on the Trinitarian relations (in media res), which I know for sure catalyzed the deep tectonic boil that resulted in my hypnagogic trance; it is well worth reading in full, carefully, and with as much attention to imaginative detail as possible:

In the last class we introduced the ideas that allow us to organize what we know about the mystery of the Trinity: we borrowed the term “procession” from Latin and used it to name not only what the Latin texts of the creeds and the Scripture called processio, but we also applied used it as a general term containing the ideas of “to be generated” or “be born” or (in a qualified sense) “to be sent” or “to be spoken”. After examining all the relevant quotations, there seemed to be two different processions, and it follows from this that there are four relations, since there is a pair of relations between a thing that proceeds and what it proceeds from.

In this class we’ll perform a sort of theology that might be called “casting” or “molding”. We’re going to take something that we know is not like the Trinity, and which suffers serious inadequacies in representing it, but which nevertheless has a kernel of truth, and then we’ll try to knock away everything but that kernel of truth. When you cast a candle in a die, for example, you have a large iron mold that looks nothing like a candle, but which has within it some likeness to a candle. You use the die like a scaffolding that allows you to get to the point when you pull the die itself apart and are left with only the wax center that was within it. Here is what is going to serve as our die for understanding the Trinity: the action of using a paintbrush to make a line going from left to right. It’s a very simple idea (though maybe not as simple as a shamrock) but be sure the image is clear in your head. We’re talking about this… (Takes out paintbrush, makes a stroke from left to right.)

Now what am I doing when I do this? Notice that you can isolate two different things that happen:

1. You pull the brush left to right (do it).
2. Then a third thing happens as a result, namely you not only get a line that goes left to right, it also has a top and a bottom. Now all you wanted to do was have a line that went left to right, but you find in doing this that you give rise to a top and a bottom too.

Now not everything in this image can be taken as illuminating something about the Trinity, but I want to draw your attention to the nature of this process. Note first that we can isolate a left-right relation which necessarily gives rise to a top-bottom relation. These relations are different and arise in a certain order. We want to draw the left before the right, and we get a result out of this that was outside our intention to have this horizontal distance. Nevertheless, while there is an order among the relations they are nevertheless all simultaneous: you cannot isolate a “pure left” or a “pure right”, nor can you keep this left right line from being a top that has a bottom. You have one undivided reality that admits of three distinct relative oppositions.

Now in this metaphor, “Left” is the Father, “right” is the Son. So what about the Holy Spirit? Notice that we can say that in one sense he proceeds from the Father-Son together (so far as they form a “top” to which he is “the bottom”) and in another sense proceeds from the Father alone, so far as everything that follows “the left” proceeds from it. Both expressions isolate some feature of the same reality, and so depending on what questions we want to answer, it might be more useful to consider the Holy Spirit as arising from the single Father-Son source or from the Father alone. It is also useful to describe the Holy Spirit as “from” the Father and “through” the Son, but this is simply a third account of the same reality. The accounts are not distinct from one another by one being true and the others false.

So much for the kernel of truth in the metaphor – where is it inadequate? What part is the “die” that needs to get pulled off and set aside? It is an incredibly difficult removal: we must isolate the relations themselves apart from the parts of the quantity that we know them in. Talking about “left-right” is impossible for us apart from some image of a physical body, but we have to separate out the pure relation from the physical parts of which it is the relation. Though we must look at a body to see a left and right, we have to tell ourselves that we are only considering the left right and not the body. But how can we understand this, given that we certainly can’t imagine it? It helps to return to our consideration of the intelligible difference between parts (or most accidents) and relations. The quantity has parts that each exist of themselves, but the relation consists precisely the co-existence of things. Quantitative parts, to the extent it has its own existence, must destroy the existence of the whole. You can’t break off or isolate a part of a quantity and still have one and the same whole exist. But relations are different: because they co-exist, it is possible to have a multiplication of terms that is not repugnant to an absolutely unified whole. This co-existence is not contrary to procession of one thing from another – in fact, it can even be based upon such a procession.

In the next class we’ll take a close look at this notion of subsistent relation, and consider how these four relations can be said to give rise to three persons.

Beautiful, no? So here are my notes:

Instead of scribing a line from left to right, scribe an arrow from top (Father) to bottom (Son). All the geometric consequences Chastek notes will follow identically. The dimension of the Spirit is automatically generated. Make it explicit by drawing a perpendicular to your arrow. Now you’ve got a cross: a 2D Cartesian coordinate system, with the y axis the relation between Father and Son, and the x axis the dimension of the Spirit.

+++++++++

Scribing the Filial generation defines the whole plane, in which the Spiritual valence is implicit. The plane is the Receptacle of the Life of God; but the Receptacle is not prior to the Divine Act; on the contrary, it is an aspect of the Divine Act.

+++++++++

Now rotate the x axis 45 degrees about the y axis, and add a z axis perpendicular to both the x and y axes. You have just defined a three-dimensional solid, by scribing a three-dimensional Cartesian coordinate system. Now in doing this, you have not really done any more than you did in drawing the y axis with your first stroke. The only difference that adding the z axis has made is to make it explicitly apparent that your first downward stroke was taken in a volume rather than a plane. But the volume, like the plane, was implicit in and by virtue of the first stroke, even before you denoted it formally by scribing the z axis.

Note then that as the valence of the relation between Father and Son is downward, the valence of the Spirit is clockwise about the y axis. Note that the valence of the Holy Spirit is derived from the valence of the Filial procession, in accordance with the right hand rule. The whole motion of describing this glyph is orthologous (and dexterous!). Yet it is not as though the Pneumatic valence is subsequent to the Filial generation; on the contrary, the whole system comes as one gesture, one coherent, concretely indivisible act.

+++++++++

There are all sorts of fruitful analogies here, to magnetic fields generated by electrical currents, to spinning tops, and so forth; and to harmonic motion of all sorts. Thus also to music.

+++++++++

Note also that we have described the chi-rho, with the Χ bounded by a circle.

The motion from Father to Son, together with the motion of the Holy Spirit which implicitly proceeds from it, is just the Being of God, which is a pure motion. It is concrete, not merely abstract. The Filial and Pneumatic valences are activities.

+++++++++

The whole of geometry is implicit in this figure. From it, you can derive all trig, all calculus, all number, all domain and set theories; and all music, all sine waves and their harmonics. So in this figure – or rather, in what this figure represents, in the real actuality of which this figure is a projection – all math is concresced, and made active.

+++++++++

In this figure also are implicitly enfolded all the Platonic Forms or Whiteheadian Eternal Objects, and all their combinations in God’s Middle Knowledge of Borges’ Library of the Possible.

Guénon goes into this with staggering profundity, and in great detail, in The Symbolism of the Cross. Cf. also Pythagoras and the music of the spheres, G. Spencer Brown’s Laws of Form (which uses a glyph of his own invention, the obverse of a capital L (effectually, two adjacent arms of the x and y axes), to signify the primordial act of separation by which being is separated from non-being (by which being primordially *is*) and then uses this glyph to derive mathematics), Philo’s explanation of how the 3 is implicit in the 1 and requires 4 dimensions to be scribed, and Plotinus on the emanation from the One.

+++++++++

The actuality of the cross is a valence, a will, a motion, a life.

+++++++++

Necessity (as of the mathematical truths) derives from eternity, not vice versa. So an eternal free act will have the character of being necessary only by virtue of its actuality. I.e., if it exists, it exists necessarily. So, this is Anselm’s Ontological Argument, scribed geometrically.

+++++++++

The representation of the Trinity on paper is a projection onto two dimensions of its four-dimensional reality; which is in turn a projection onto four dimensions of its actuality (who knows how many dimensions that actuality has? Can it be less than an infinite quantity of dimensions?). The actual world likewise is a projection of the actuality of God onto the Creaturely Receptacle.

+++++++++

The Being of God – the fact of his act and the potentiality of that act – are the Supra-Personal Godhead of Pseudo-Dionysius: the blank paper, and the act of scribing in virtue of which there is the paper.

+++++++++

What then is the difference between the three Persons?

1. God Is all this: Father (Mind)
2. God Knows all this: Son (Word)
3. God Does all this: Spirit (Breath)

These are all one act, even though they are three distinct actions.

+++++++++

1. The First Motion is from the Father to the Son. The Father must first be if he is to know himself through the Son. But it is one motion.
2. The Second Motion is from the Father to the Spirit by the Son or through the Son. It derives from the Father, but takes its character from the Paternal character, which includes his Paternity; in which is implicit the actuality of the Son. God must Know who he is in order to Do what he does. Yet still all three motions are achieved in one integral act.

+++++++++

Note that it takes time to scribe the figure on paper that you already had complete in your mind, as a product of a single inward act of your mind. Likewise, it takes time for God to describe his creation; takes time for God to be described in his creation. But it does not take time for God himself to be. The description of God in creation, the engraving of God on creation, is an operation of projection of a completed actuality onto a matrix; but NB that the matrix is not prior to the projection, but rather exists in virtue thereof. The matrix is discernible only ex post facto.

+++++++++

• The Son is a final cause of the Paternal Act. He is the term at which it points, and in which it is completed.
• The Spirit too is a final cause of the Paternal Act. Draw the line from Father to Son, and you ipso facto describe the Spirit.

+++++++++

The north and south poles of a magnet are not the same thing. But each of them exists only as a pole of the same thing. The current flowing between the Father and the Son, and the corresponding magnetic rotation of the Spirit about its axis, are what the Greek Fathers called perichoresis. The Latin translation of that term, circumincession, refers with peculiar linguistic aptitude to the field effects of each pole of the Filial generation upon the other, of both upon that of the Spirit, and of the Spirit upon both of them.

+++++++++

• To describe a picture of the Holy Spirit proceeding from the Father through the Son – the compromise between Orthodox and Catholic doctrines of the Pneumatic procession – scribe the x axis at the terminus ad quem of the gesture from Father to Son.
• To describe a picture of the Holy Spirit proceeding from the Father – the Orthodox doctrine of the Pneumatic procession – scribe the x axis at the terminus a quo of the gesture from Father to Son.
• To describe a picture of the Holy Spirit proceeding from the Father and the Son – the Catholic filioque doctrine of the Pneumatic procession – scribe the x axis at the midpoint of the gesture from Father to Son.
• Note that no matter where on the y axis you originate the x axis, you have generated the same plane; likewise, no matter where on y you originate the z axis, you have generated the same volume, provided that x, y and z are all orthogonal.

+++++++++

What is the most appropriate sort of solid we could use to visualize what we have generated with the single gesture of scribing the glyph? Perhaps it would be a sphere, with a north (Paternal) and south (Filial) pole, rotating (Pneumatically) on the polar axis. But as Chastek notes, we must be careful once we have visualized this solid to detract from the vision all aspects of solidity, all aspects of extension either spatial or temporal, leaving behind only the relations of the three acts we have detected in the single act of Divine being.