God as absolute is a mirror to us. This was stated in a previous answer, but of course that raises the question as to what is mirroring. Of course, the mirroring of ourselves in God, which we project, and which projects us is perfect mirroring, i.e. is the limit case of mirroring. It is even beyond infinite mirroring. But let us return to basics and look at our theory of mirroring.
Of course, our theory of mirroring shows up first in mundane mirrors. And what mirrors underline is the chiral nature of our experience. Kant remarked on chirality saying that it showed that space was itself and independent singularity. And the most significant thing for us to understand is that the fourth dimension is anti-chiral in the sense that anything that is enantiomorphic can be rotated through the fourth dimension to become its own Chiral opposite. So that mirror image that confronts us that is anti-chiral can be turned into though a four-dimensional rotation.
When we confront people, facing them there is a completely different experience to the confrontation with our own anti-chiral image of ourselves. So there is a fundamental difference between mirroring in which we see ourselves and the confrontation of the other in the flesh, i.e. experientially in daily life.
Now what special systems tells us is that this mirroring ramifies. So the most basic level is that there is one mirror in which we are looking at ourselves rather than the different other. And in that mirror we are seeing ourselves as anti-chiral which only the fourth dimension can render symmetrical. But the Dissipative Ordering Special System has as its analogy two mirrors facing each other. And most of us have experienced that in a barbershop or solon when we have mirrors before us and behind us, and we see the ramification of our image. But both of these images, front and back are still anti-chiral with regard to our bodies. But this anomalous experience is the analogy for the neg-entropic system as described by Prigogine as Dissipative Structures via the complexnions called normally complex numbers. Onar Aam pointed out this analogy long ago during our collaboration with Ben Goertzel and Tony Smith.
He noted that each hyper-complex algebra had an analogy for a configuration of facing mirrors. Thus the Autopoietic Symbiotic special system had the analogy of the for the quaternions of three mirrors facing each other, and the Reflexive social special system had the analogy of four mirrors facing each other or an inwardly mirrroring tetrahedron which is related to the octonion. After that you either had to have warped mirrors which Onar Aam called the Funhouse of circus fame or separated mirrors like those we see in light experiments in physics. Since the quaternions are the group of four dimensional space then what we see is that with the second mirroring level which is analogous to the theory of Materana and Varella concerning autopoiesis actually embodies the anti-chiral transform itself. And the reflexive social special system embodies two of these anti-chiral transforms in relation to each other which is what we experience in embodied experience facing another human being, hence it is the source of what Sartre calls the fused group and Canetti calls the fact and it is what Castoriadis calls the Imaginary institution of society which he describes in terms of magma.
In essence the Autopoietic Symbiotic special system grabs the generator of the anti-chiral transform, and the Reflexive Social special system places two such embodied generators in a mirroring relation with each other which then simulates the actual confrontation of the other whose chirality is independent of our own. The sine quo non of this is Marriage. And since Gender is not a kind of a kind as Smith has said but in fact a modification, we see in marriage a mirroring across the category theory modification divide. So that means that there are probably mirrorings across each of the categoric theory divides such as the series of elements, arrows, functors, natural transformations, modifications and fluctuations.
For instance we know that the SET category has Anti-Set which is just the set, and so it is self-dual. But there is an actual inverse dual of the SET which is MASS, that is also self-dual under a functor, so the difference between SET and MASS and their logics (syllogistic and pervasion) must be a natural transformation. To go up to the next level of mirroring across the categorical divide would be to find an equivalent of gender for SET and MASS. Such an equivalent if we consider them to appear in spacetime, i.e. as schematized might be chirality. Thus for a SET there is a difference between it and its chiral opposite, and the same with a MASS. Not sure anyone has thought this through before. It might not be chirality but some other property like that. But let us stick to our guns for the moment and consider that there can be left and right-handed sets and masses at the level of modifications. If we want to go up to the next level of fluctuations then there would be some other even more subtle characteristic that is fractal ramified throughout Sets and Masses. We know that the difference here is something like the difference between Hue and Saturation, as color has these fine distinctions worked out. If Hue is like chirality which is like gender, then saturation is like X which is like individual personal differences.
The problem is that chirality implies self-order, which sets do not have. In order to have self order we must allow for a list, in which case you can think of the beginning and end of the list and you can think about them as having start and end, and being configured in space such that we could differentiate right and left-handed lists. So if we take away internal ordering what is the equivalent of the chiral for a SET.
We know that the first step way from the set of particulars is a bag which allows repetition but no ordering.
After the Bag then we can have various orderings which are called by Klir Methodological Distinctions in his book Architecture of Systems Problem Solving. These possible orders form a lattice which goes as follows:
No order = SET or MASS
Partial order = BAG (times two called a DOMAIN) or SOLUTION
Either Partial Order with Distance TOPOLOGY or Linear order with no distance LIST
Full order with distance NUMBER THEORY or DIFFERENTIAL TOPOLOGY
[Combinatoric Order] Power Set ARITHMETIC or MATROID
Real Number line, i.e. continuity hypothesis an infinity of infinities. ALGEBRA or GEOMETRY
[This is speculative, any help from a mathematician would be appreciated]
What we do know about SETS however is that they themselves are bland but they are a collection of particulars, and those particulars have characteristics and they may have the internal organization necessary to have chirality, and on the other hand with Masses instances are all the same, but the mass level (unlike the set) has all the interesting qualities so it may have enough internal order to have chirality. The interesting thing about chirality is that it is dependent on the internal ordering of things not on external ordering, and it is fully contextual in that it only appears locally within a space.
So although the SET itself might not have enough structure to be chiral the particulars that make it up may have chirality, and similarly although the instances of a mass may not be chiral the mass as a whole with its global characteristics in a structure may have chirality.
Particulars and Masses may be chiral, and Sets and Instances are too nondescript to have chirality because they lack the requisite internal structure. But what we know is that for chirality to appear there must be at least a local spacetime in which things express some inward structure.
So for the moment we leave as an open question what might be the fluctuation of the Set and Mass differentiation in themselves without the differentiation outward that we note above, except to note that just like we think of fluctuations in people at individual differences, we can also think of many individual structural differences in particulars and masses that differentiate them from one another. So these differences hat make a difference (ala Bateson) between the particulars in a set or the masses that emerge beyond their instances may be seen as these fluctuations.
Now when we look at mirroring within facing mirrors we note that they appear to be quasi-infinite regresses. And this holds up for each level of mirroring in the special systems. So the approximation of the infinitude of the mirroring appears in the special systems. With the derivative we note the points of incidence of the beams of light on the mirrors as the images ramify, and the integral is the space volume within which the ramification occurs. And of course no mirroring would be seen without the light which can ramify bouncing off the reflective surfaces. Conway showed that there is always at least one path which is closed in such a system, so that the light path closes on itself to produce a circuit. So within all the dispersed ramified light there is also a circuit of light which does not scatter from its series of incident points. So the dispersion of the ramifications has as its opposite the closed loop of self incidence of the loop of light within the mirror configuration.
This loop is different from either the identification of the points of incidence that are the derivative of the path, or the area of dispersion that is the integral. We might call the loop a hypercycle of reflection or a circuit, or self-reinforcing of an auto-catalysis. This cycle is in acupuncture called the five Hsing with their production and control cycles. Famously this circuit is called the Jing Chi. So mirroring itself has an inner relation to infinitude and its description in terms of limits in the calculus, but also there appears the nondual between the derivative and integral which is the self-creating cycle, what is called psychologically “flow”.
So now that we know something about mirroring at the mundane level that appears in the world as anomalous special systems we can consider absolute mirroring. In mirroring we look at ourselves, and this is a special anomalous situation because normally we are facing others. Lacan famously identified the mirror stage with the childs self-development. When the child recognizes itself in the mirror then it forms a concept of itself as different from the Mother and the name of the Father (floating signifier). We hardly think that looking into mirrors is a necessary condition for developing an ego, but this is merely an analogy. Essentially you must have a self-concept in order to have any experience as Demasio tries to show. So the self is built-in to experience itself. But the mirror anomaly serves to give the illusion of self. It is the subjunctive mood that goes beyond indicative or imperative moods.
We latch onto this anomaly of mirroring as a simulacrum for the ego itself and from it Lacanian psychoanalytic theory unfolds structurally and semiotically. Zizek reads Lacan as merely another version of Hegel. And in Hegel we confront not just the idea of the transcendental from the human perspective (necessary condition for the possibility of experience) but the idea of the absolute. This is seen in religion as the Nirguna Brahman of Hinduism and the Godhead in Meister Eckhart closer to home. The Absolute is beyond all characteristics. And when we look into the absolute there is absolute mirroring rather than contingent mirroring. Every aspect of our own finitude is contrast sharply with the absolute mirroring of our finite characteristics in the characateristiclessness of God as absolute. This absolute mirroring is beyond what we can bear. We latch on to mirrors as anomalies in the world, and then recognize that the fundamental organization of consciousness, life and the social is based on a kind of self-mirroring that compounds that initial confrontation of with a mirror in our experience. By the mirror we realize the nature of the chiral, by its violation of it, and we realize that the anti-chiral can only be resolved via four-dimensional rotations, which the special systems allow us to appropriate to ourselves, and our relations with others. And within mirroring we recognize that there is an infinitude of ramification, or recursion that is possible. And we deal with that infinitude via calculus which is our means of handling infinitude. But we recognize that the circle of auto catalysis goes beyond the dualities of the derivative and the integral. But all this does not prepare us for absolute mirroring.
What it prepares us for is to understand the mirroring which is interpenetration, i.e. the mirroring of all things in each other which is the jeweled net of Indra of Huan Yen Buddhism and mentioned by Fa Tsang that set up a hall of mirrors for the Empress in order to give her some idea of the nature of interpenetration. In Interpenetration each thing is what it is by its difference from everything else. We realize our place in the golden fabric of all existence. But beyond existences are the absolutes. And the difference between the mirroring of interpenetration and the mirroring of the absolutes is radical. But we can only approach the mirroring of ourselves in the absolute by means of the mirroring in existence.
Now we know that all the special systems and the normal system ifs into the Emergent Meta-system. And we know that there are both Supervenient and Emergent Systems and Meta-systems. But absolute Mirroring goes beyond all those differences as well. Absolute mirroring cuts to the core of our finitude, but also goes beyond the infinitude of mirroring.
So here is something to my mind which is strange. We note that mirroring is an anomaly. If that is the case then absolute mirroring must be an absolute anomaly. And we have seen that mirroring occurs across all the levels of category theory unto and including fluctuations, that are individual differences. So absolute mirroring must be related to a certain subset of fluctuations that are unique. In this sense then calling it God as an abstraction cannot be right. That is why we talk about the name of the monotheistic God, like the name of a person as Yhwh/Allah/El. And in the bible we learn that Seth was the first to call on that name. He was the third brother after Cain and Able. The unique non-representable yet nameable nature of the anomalous absolute within which we find our absolute mirror is an aspect of the mirroring of God that we have not taken into account enough. This Absolute in which we find our ultimate mirroring cannot be an Abstraction, nor an essence like the essence of things. As we mount the stairs of the divided line eventually we reach the whoness of the unique absolute, and it says to us Where then are you going?