We have described TPC as being involved with the transcendental awareness of the total continuum or process of thought considered purely as such, as merely a process of thought. But TPC has an important aspect: transcendental philosophical consciousness involves the transcendental awareness of those preconditions and structures upon which ordinary consciousness entirely depends and at the same time of which ordinary consciousness as a rule is oblivious of. It is almost as if ordinary consciousness only exists, can only exist, under the condition of it carrying a forgetfulness of its own transcendental preconditions and predetermining structures. Transcendental consciousness is thus also the consciousness of what non-transcendental consciousness must necessary forget. If TPC in turns does not have full knowledge of such transcendental preconditions and structures, it falls back into a false dualism, limitation and illusory reification. Two of the most important of such preconditions are selfhood and temporality. That which claims to be a being which we carry along as a huge burden - all possible transcendental questioning, untangling and analysis being forgotten - and that which we must forget in the first place in order for the very being-ness of being to arise. Only then we arise to the selfless liberated insight into the pure universal sphere and flux of pure thought processes: only thus is further progress of TPP possible. The ordinary self is the protoype of illusory unquestioned, posited, composite being. The original prototype of being in transcendental temporal oblivion. One task is to study the formative tendency which constructs this prototype employing among other things certain classes of conscious phenomena.This prototype is the the scaffold upon which world-positing and world-directedness and the mutual feedback of the identity construct takes place. Being-in-the world is not a transcendental condition or principle but a non-transcendental illusion conditioned by transcendental ignorance and forgetfulness. Following Plato a philosophical consciousness must include knowledge concerning the phenomenology of love and beauty. This is a transcendental illusion which yet in its purest form participates of the some of the modalities of TPP-liberated consciousness. It paradoxically offers a glimpse of the bliss of beinglessness falsely conditioned and limited by being, by the illusory directed network of the self-prototype and its world. When we are born we are forced to build our identity and learn the world; when 'born into the spiritual life' our duty is to unbuild this identity and learn to see through the illusion and construct of the world. It is as if the first phase were like being plunged into the water, a downwards journey into illusion and forgetfulness. The second phase is when we begin to rise again and make our way back towards the surface and the air of light and truth. TPP is not about an 'individual' detaching itself from the 'world' and still less about an 'individual' transferring its feelings, desires, volitions and tendencies to alternative 'imaginary friends' or any kind of ontological construct - rather it is about seeing through both the 'individual' and the 'world' and their dependent interplay and mutual constitution. There is no contradiction between Yogacara and Madhyamaka. Two of the main tasks of TPC-based philosophy are: i) the untangling of all concepts and categories and the showing forth that they all exhibit the mark of the alleged being of the prototype (self), ii) exhibing the absoluteness of the moral law, that the absolute can be characterized as morality (dharmakaya). The profound affinity between the consciousness and act of TPC and TPP and that of the essence of morality. In all of the above the great interest of Kant is patent. A model of the universal flux of pure consciousness (Indra's net): neural nets, cellular automata, music theory, formal grammar, tessellations, Wang tiles, knots (and our own theory related to this) - unfolding of the concept of computation (paticcasamupada) and its concurrent parallel interconnected forms. And most importantly the theory of (meta) reflection and representation. And the logical and mathematical theory of programs, specially the hierarchy of function definitions. The way forward in physics, the way to transcend and rectify quantum field theory, seems to us to involve a radical new foundation for physics based not on the formalism of functional analysis and operator algebras but rather on finitary combinatorics, theoretical computer science, graph theory and algebra. Maybe something following Birkhoff's lattice approach.
A mathematical model of transcendental pure consciousness (which can only be a limited exterior projection, a partial mirroring...) will involve a spatialization of concepts (structures) wherein their interconnection and mutual (meta) reflection takes place - in a temporal dimension. A general theory of networks which generalizes neural nets, cellular automata, tessellations, crystallography, (higher)category theory and proof theory. This will include the spatial, topological aspects of music, and the architecture of a semantic universe (semantic space) or lexicology. But we can take also an atemporal space-time approach. Has the effects of special relativity on the physical realization of Turing machines been studied? Could special relativity be the key to how physical systems could compute beyond the Turing limit? Perhaps the quantum effects on physical computational systems can be studied in a way different from the current work in 'quantum computing'. In Hegel's Logic we can discern a marked spatial, geometric way of thinking of concepts, their unfolding, mirroring and interaction.
The knot, the tangle, the projection, the multiplicity is not real, what is real is the formative energy which ties and then unties, tangles and then untangles, projects and then dissolves, multiplies and then unites. Is this not the ultimate meaning of the Hegelian Idea, the holomovement of skepsis which though necessarily dealing in formalism is not itself entirely formalizable ? Each thought (unit of consciousness) containing implicitly all other thoughts and each thought only existing through its relationship to them? That by trying to isolate a thought 'in itself' it inevitably looses the essence of what it really is.
Another approach is to view space-time as characterizing non-transcendental consciousness and being characterized by its algebraic and logical properties. Thus pure transcendental consciousness should be represented by a structure in which some of these logical or algebraic properties are different, the most famous being Heyting rather than Boolean (Brouwer), non-commutativity (Connes) or non-distributivity (Birkhoff). Birkhoff's explaining away of the uncertainty principle as simply an expression of non-distributivity. However this approach does not go beyond the previous proposal, it is still a priori and phenomenologically a spatialized or space-time based 'collection' of components, parts, connected to each other by some kind of relation or network. And the essence of representation theory is bringing this spatial substrate further into the foreground.
The philosophical elephant in the living room is that we have not explored something which should occupy a fundamental place in TCP. That of symmetry, quasi-symmetry and analogy. Like temporality and the prototype of the self, it is so pervasive as to be habitually consigned to an implicit oblivion. Symmetry and its allied modes pervade biology, psychology, linguistics, chemistry, physics, mathematics, logic, computer science, engineering, the structure of philosophical systems, poetry, music,...so deeply, in such a far-reaching manner, that like temporality or the construction of self, we simply forget and cannot fathom its central, universal transcendental a priori role (symmetries abound in the architecture of Kant's and Hegel's systems, also in the Pali suttas, and linear logic brought forth the implicit symmetries and modalities in classical logic). We end with the following preliminary (Hegelian) descriptions: symmetry is the quality of a being which allows it to change and yet remain the same. Symmetry is also that by which a being may produce itself (notice than in symmetric tiling we can transport any tile to any other tile while preserving the identity of the whole). Symmetry is the foundation for reflection-into-another and reflection-into-self. Recall how spinors capture the 'memory' (homotopy class) of a rotation in SO(3), much like the dialectic in Hegel. An object may be brought back to itself and yet have gained something permanent. Symmetry is that by which an inherently dynamic process can produce the illusion of stability and being. Symmetry allows us to fathom essentially interrelated holistic systems (illustration of 'maps of consciousness': dictionaries, grammars, thesauri, manuals of stylistics and translation, encyclopedias, biographies, novels).