Transformation GTR3: Concepts(Begriff), Contradictions, Will

Chapter 3. GTR2 Transformation: Symbols and Narratives

Symbolic Reality · Imagination · Bidirectionality · LLMs as Theory Validation

3. 1. What Is New at the GTR2 Level

The GTR1 transformation builds information reality from perception of the external world: spatial map (DOM3), objects (DOM4), behavior (DOM5). This reality is bound to the here-and-now: current space, current objects, current actions.

At the GTR2 level, a fundamental leap occurs: information detaches from specific locations and times. Symbols emerge — compressed markers not bound to any specific point in space. And narratives emerge — structures built from symbols that describe what does not exist now, or what could exist, or what has never existed.

The fundamental novelty of GTR2 is bidirectionality, which is absent in GTR1. A reverse direction appears at GTR2: symbols and narratives can be unfolded back into object and spatial reality. This is imagination. Hegel described this descending movement as the return of spirit from the abstract to the concrete.

3. 2. GTR2 Diagram

3. 3. DOM6: The Symbol Map

The first space of GTR2. Arises from DOM5 through convolution. The GTR2-level CNN receives a vector from DOM5 (a BLOM or TRL5 fragment) and transforms it into a DOM6 vector — a compact symbolic representation.

a) Symbol as the basic unit of DOM6

A symbol is a subnetwork node structurally similar to an R-component, but with a fundamentally new property. Unlike R-components, which are connected via Lg-connectors to specific locations in MAP3, a symbol is not bound to space.

The structural content of a symbol:

1. •

   A vector — the recognition key (similar to an R-component).

2. •

   A name — the symbol's identifier. For humans, this is typically a word in natural language.

3. •

   Parameters — additional properties, connections to other symbols.

MAP6 — the symbol map. Like MAP4, a map in the conditional sense. Here there is no longer a space in the same sense as with R-components, but the map has its organization and structure as a network of connections.

b) OPN6 and the symbol kernel

OPN6 — the operational network managing symbol processing. Like OPN4, it is a deterministic program.

The symbol kernel — a learnable CNN that produces a symbol vector from a behavioral vector (a BLOM or TRL5 fragment). Learning is performed on symbols already present in MAP6 — just as OPN4's CNN trains on R-components in MAP4.

Biologically, this corresponds to the functioning of Broca's area and Wernicke's area, the anterior temporal cortex, and related regions — they convert perceptual and behavioral experience into symbolic representations.

c) The transition to a unified map

A fundamentally important transition: MAP6 is a unified map, not a multi-map. At the GTR1 level, there are multi-maps — many local maps connected through Lg-connectors. At the GTR2 level, the structure changes: a symbol is not bound to a location and therefore does not require spatial discretization.

This is a qualitative leap in information organization. Multi-maps are well-suited for navigation — local detail, precision, connection to specific movement. Unified maps are well-suited for global planning — abstraction, location independence, the ability to operate on symbols for distant things simultaneously.

3. 4. DOM7: Narratives

The second space of GTR2. Arises from DOM6 through splice — the second isomorphic part of GTR2.

a) Splicing symbols into narratives

Individual symbols do not constitute meaningful reasoning. Just as individual OPRNs cannot describe complete behavior, individual symbols cannot describe situations, events, or plans of action.

Splice at GTR2 connects symbols through a P-vector into KLEN (knowledge entity) triplets — meaningful units of knowledge. The structure of a KLEN triplet: symbol 1 — P-vector — symbol 2.

Structurally, KLEN is analogous to OPRN: three components with a connecting vector in the middle. But the nature of the connection is already different: not "who does what to whom" (behavior) but "what relates to what and how" (knowledge relationship).

b) Knowledge triplets

Many KLENs constitute MAP7 — the knowledge map. Individual P-constructs do not yet constitute complete reasoning. A complete narrative is a KLEN chain — a coherent sequence of symbols connected by P-vectors.

Narratives can have different scales: a simple statement ("birds fly south"), a scene description ("birds fly south in autumn because it grows cold"), a complex inference ("if all birds fly south, and this is a bird, then it too flies south").

c) TRL7 — History of narrative thinking

At DOM7, TRL7 appears — analogous to TRL5 at the previous level. TRL7 records which narratives were activated and when, which KLEN chains formed, and how the course of thinking unfolded.

TRL7 is narrative memory, the history of thought. For humans, this corresponds to autobiographical memory — memory of what was thought in the past, not just what was done (TRL5).

d) OPN7 — Narrative management

OPN7 manages narrative assembly: connects symbols through P-vectors into KLENs, composes KLENs into narratives, and maintains TRL7.

Like other OPNTs, OPN7 is a deterministic program. It uses a learnable CNN to produce P-vectors — analogous to how OPN5 uses CNN to produce b-vectors.

3. 5. Bidirectionality of GTR2: Imagination

The central feature of GTR2, absent in GTR1.

a) Why GTR1 is unidirectionally asymmetric

In GTR1, convolution works fully: external world→DOM3→DOM4→DOM5. Deconvolution is limited: one can partially go from DOM5 back to DOM4 and DOM3, but the external world cannot be fully reconstructed. The organism can plan actions (deconvolving from DOM5 back to DOM3), but cannot conjure new perceptual objects from nothing.

b) What changes at GTR2

At GTR2, deconvolution becomes equal in standing. A symbol can be deconvolved back into concrete R-components: uttering the word "bird," a person can imagine a specific bird — its wings, beak, call. A narrative can unfold a spatial scene. This is imagination — the descending movement of GTR2: from symbol back to object, from narrative back to scene.

c) The Hegelian perspective

Hegel described this movement of spirit as the return from the abstract to the concrete. Spirit, alienating itself in abstraction, returns to concrete life enriched by symbolic understanding.

In the Gativus architecture, this means GTR2 is a bidirectional channel between the symbolic level and the perceptual level. The descending movement is not regression but the complete cycle of spirit — from experience to abstraction, and from abstraction to new action.

d) The cycle of imagination

The circular arrow between DOM6 and DOM7 in the diagram shows that this cycle is not a single occurrence but a continuous process:

1. •

   From behavior to symbols (convolution into DOM6).

2. •

   From symbols to narratives (splice into DOM7).

3. •

   From narratives back to symbols (reverse splice).

4. •

   From symbols back to objects and space (reverse convolution).

5. •

   Result — new behavior, new actions.

This cycle is the structure of thought. Each iteration enriches all levels: new symbols accumulate, new narratives form, behavior becomes more complex and purposeful.

3. 6. LLMs as Experimental Validation of the Theory

a) The central hypothesis

If the Gativus theory is correct, then large language models (LLMs) are functional realizations of GTR2 — detached from the lower levels (GTR0/GTR1) and the upper level (GTR3). LLMs operate only at the level of symbols and narratives, with no spatial maps, no physical actions, and no value judgments.

This claim is the primary experimental test of the entire GNSS architecture. If correct, the limitations of LLMs can be derived precisely from the theory rather than discovered empirically.

b) What LLMs do well

Observed capabilities of LLMs:

1. •

   Operate on symbols and narratives at a level comparable to human performance.

2. •

   Produce KLENs and complex narratives.

3. •

   Exhibit contextual interpretation (narrative within narrative).

4. •

   Perform reverse deconvolution: create vivid descriptions, scenes, hypothetical situations.

5. •

   Make logical inferences through symbol manipulation.

This constitutes strong empirical support for the claim that GTR2 as a process can be modeled independently of lower levels.

c) What LLMs cannot do (limitations)

At the same time, LLMs have systematic limitations consistent with the theory:

1. •

   LLMs have no DOM3, DOM4, DOM5. They operate only at the symbolic level. There is no genuine spatial orientation, no physical object recognition, no real action history.

2. •

   LLMs have no TRL5. They have no memory of their own physical actions in the world — no real behavioral experience, only symbolic descriptions of behavior.

3. •

   LLMs have no axiological level (GTR3, examined in the next chapter). They can produce narratives about morality but cannot genuinely perform moral evaluation — there are no contradictions and no will in the Gativus sense.

These limitations are consistent with the theory: if LLMs are GTR2 without lower and upper levels, then precisely these limitations should exist.

d) What makes this theory falsifiable

The core implication: it is possible to extend LLMs toward a complete architecture. Adding a spatial and behavioral layer (GTR1) to the symbolic layer, and then an axiological layer (GTR3), should yield a system with genuine autonomy, real bodily perception, and moral agency.

This is the engineering task of Gativus. If the theory is correct, the task is solvable. If, having implemented the complete architecture, the expected results do not appear, the theory requires revision.

3. 7. Relationship to GTR1 and GTR3

a) Looking downward: how GTR2 uses GTR1

GTR2 does not operate in a vacuum. Symbols initially arise from the convolution of behavior: behavioral experience accumulates, the CNN learns to recognize patterns within it, and those patterns become symbols. Without rich GTR1 experience, there can be no rich symbolic vocabulary.

b) Looking upward: how GTR2 prepares for GTR3

At the narrative level, contradictions gradually accumulate: one narrative asserts one thing, another asserts the opposite. These contradictions cannot be resolved at the GTR2 level — symbolic tools are insufficient. They rise to GTR3, where they become genuine conceptual contradictions resolved through will.

3. 8. Conclusions

1. •

   GTR2 is the second information transformation in the Gativus architecture. It operates on the same information plane (yellow plane) as GTR1, but at a higher level of abstraction.

2. •

   GTR2 has two spaces: DOM6 (symbols) and DOM7 (narratives). Convolution DOM5→DOM6 and splice DOM6→DOM7 — the two isomorphic parts of GTR2.

3. •

   The fundamental novelty of GTR2 is bidirectionality. The ascending direction — convolution (behavior→symbols) and splice (symbols→narratives). The descending direction — deconvolution (narratives→symbols→objects→action). This is imagination.

4. •

   MAP6 and MAP7 — unified maps, not multi-maps. This enables global planning and abstract thinking.

5. •

   TRL7 — narrative memory, logging the history of thought.

6. •

   LLMs functionally realize GTR2 in isolation from lower and upper levels. This is strong empirical confirmation of Gativus as a theory.

7. •

   Proof of Gativus as a theory: extending LLMs to the complete architecture should yield genuine autonomy, bodily perception, and moral agency.

3. 9. The Fundamental Distinction Between CNN Learning and Operation

For each of the three convolutional neural networks, two modes of operation must be strictly distinguished.

Learning (training): adjustment of the neural network's weights. The CNN trains on objects already present in the target space — not on input data, but on objects already in the target map. CNN1 trains on R-components already in MAP4; CNN2 trains on symbols in MAP6; CNN3 trains on concepts in MAP8.

Operation (inference): transformation of input data. The CNN receives data from the lower space and produces a vector in the target space.