Transformation GTR2: Symbols and Narratives
Chapter 2. GTR1 Transformation: From Cells to Behavior
Dual Ontology · L-components · Multi-maps · Operational Networks · Engineering Implications
2. 1. What Is New at the GTR1 Level
The GTR0 transformation examined in the previous chapter operates at the level of pure matter. MOVE unfolds into cells and then into a multicellular organism according to strict logic. There is no learning. The description fully determines the result.
At the GTR1 level, something fundamentally new appears: information spaces whose content is not encoded in MOVE. MOVE only determines structure — the scaffold, grid, connections, substrate. What will occupy that structure is determined by the organism through its interaction with the environment over the course of its life.
Three information spaces emerge — DOM3, DOM4, DOM5 — connected by two steps of the GTR1 transformation: convolution and splice. Like GTR0, this transformation is bidirectional.
The emergence of GTR1 coincides evolutionarily with the appearance of neural tissue and locomotion. Animals capable of movement scan space, build maps of it, and recognize objects within those maps — this is precisely the process through which DOM3 and DOM4 emerge.
2. 2. GTR1 Diagram
GTR0 from the previous chapter is visible at the bottom of the diagram. The three cubes on the yellow plane correspond to DOM3, DOM4, and DOM5 — three new information spaces.
Key feature: each information space has a cellular realization. DOM3, DOM4, DOM5 are not abstract structures existing independently — they are physically realized within DOM2 (the multicellular organism) through specialized neural tissue.
2. 3. Dual Ontology: Matter and Information
The core property of GTR1 is the dual ontological nature of any of its spaces. Each of DOM3, DOM4, DOM5 exists simultaneously in two ontologies.
a) The material level
At the material level, GTR1's information spaces are specialized substructures of the multicellular organism. For DOM3 — the hippocampus and related structures (entorhinal cortex, subiculum). For DOM4 — visual cortex regions and temporal lobe areas involved in object recognition. For DOM5 — the motor cortex, basal ganglia, cerebellum, and related structures.
From the GTR0 perspective, these are simply different types of cells within the multicellular organism. They obey all the laws of cellular life: metabolism, division (at appropriate stages), death from damage, communication with neighboring cells. They are just specialized cells.
b) The information level
But functionally, those same cells realize something qualitatively new — processing information about the external world. A hippocampal neuron is not just a cell; it is a place cell that fires when the organism reaches a particular point in space. A temporal lobe neuron is not just a cell; it is a face recognizer that fires when a familiar face is seen.
This functional role is not a property of a single cell but of entire ensembles and their connections. It is emergent: arising from cells working together but irreducible to the properties of any individual cell.
c) This is one reality
Matter and information are not two parallel entities but two ontological projections of the same structure. The hippocampus is simultaneously cells (material level) and a spatial map (information level). Both descriptions are true and complement rather than contradict each other.
This resolves the question of the nature of consciousness without dualism or reductionism. There are not two worlds. There is one reality, manifesting in two ways — depending on what language is used to describe it. This is the central theme running through the subsequent chapters.
2. 4. DOM3: The Spatial Level
The first information space of GTR1. Contains a representation of the external 3D space in which the organism moves.
a) L-component as the basic unit
The basic unit of DOM3 is the L-component (from Location). An L-component represents one elementary point in space. L-components have several subtypes, distinguished by function:
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Ls (surface) — surface-type L-components. Represent points in space that serve as solid support: floor, wall, branch, water surface for aquatic animals.
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Lb (border) — border-type L-components. Represent points that are edges, boundaries, or barriers: table edge, room corner, branch end. Biologically corresponding to border cells in the entorhinal cortex.
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Lg (gateway) — gateway-type L-components. Represent points through which one elementary map connects to another. Physically exist in two maps simultaneously.
Other subtypes of L-components exist and will be examined in a dedicated chapter. The common property of all L-components is their binding to a point in space and their realization through cellular tissue.
b) MAP3: The Multi-map
The totality of an organism's L-components constitutes MAP3 — the spatial map. An important property: MAP3 is not a single global map. It is a multi-map: a collection of many small elementary maps connected to one another through Lg-type L-components.
Each elementary map is a three-dimensional grid of approximately 20×10×10 L-components. This size reflects the biological constraints of the hippocampus and is commensurate with the locomotor organs: one pixel of the elementary map corresponds to one step of a paw, one sweep of a whisker, one touch of a tongue — a linear unit measurable by the organism's body.
The total number of elementary maps in a developed animal reaches tens of thousands. Their connections through Lg-type L-components form a large connected structure that is functionally equivalent to one large map, but organizationally remains a collection of local maps.
Coordinates within an elementary map are not expressed as numbers. They are encoded through adjacency relationships. Each L-component is connected to six neighbors — like the six faces of a cube. This hexagonal connectivity is consistent with the biological observation of hexagonal organization of grid cells in the entorhinal cortex.
c) OPN3: Map filling
MAP3, constructed during embryogenesis, contains structure without content. L-components exist, their connections are defined, but the status of each L-component is not yet established: a pixel may be solid, empty, or a gateway — but which one becomes known only through the course of life.
Map filling is performed by the operational network OPN3. Its working cycle:
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The organism makes a movement (crawling, walking, turning its head).
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Sensory organs record the result: a paw meets support, a whisker hits an obstacle, a nose touches empty space.
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OPN3 interprets the sensory signal as information about the status of the corresponding L-component and writes that information into MAP3.
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As information accumulates, MAP3 fills: each L-component acquires its status.
Without active movement, OPN3 cannot function. This makes locomotion a necessary condition for forming MAP3. Biologically, this is confirmed by hippocampal development research: place cells, border cells, and grid cells in the hippocampus and entorhinal cortex gradually form during the first weeks after birth, coinciding with the emergence of active exploratory locomotion. True spatial navigation appears in rat pups by the end of the third postnatal week — precisely when they begin actively exploring their surroundings.
Notably, pre-visual sensory channels — tactile, vestibular, olfactory — are sufficient for MAP3 formation. Congenitally blind rats form normally functioning place cells (Save et al., 1998): what is critical for the map is movement itself, not any specific sensory channel. This confirms OPN3 as a mechanism bound to locomotion rather than vision.
Evolutionarily, this means: a nervous system with a spatial map only arises in organisms capable of movement. Without movement, a map has no purpose and its construction cannot compensate the energy cost.
d) Phenomenology of the information domain
As the diagram shows — the cellular substrate is identical to the DOM2 level (the lower part of the space in Diagram 1), but information about the habitat does not arise during morphogenesis but during learning — the cognitive exploration of the environment. Signals generated by sensor activity are recorded and begin to carry their own meaning and function. The physical source of such signals can be considered the sensors, which, however, merely convert external signals into neural spikes. Consequently, the real source of signals is the external environment — for DOM3 specifically, this is the physical properties of the environment represented as a 3D+time space. That is, 3D+time is not a property of external space but a model of its representation, or a technical implementation at this level of life.
The phenomenon of the information space is shown in Diagram 1 as a different plane, distinct from the material cellular space.
The isomorphic basis of the Gativus transformation presupposes both convolution and deconvolution. However, at the GTR1 level, it is technically only possible to perform convolution of the external world into DOM3/4/5 maps. Deconvolution can only be partial — from levels 4/5 down to level 3. Meanwhile, more advanced levels of the organism can already influence and modify the environment — that is, deconvolve information constructs into the environment.
2. 5. DOM4: The Object Level
The second information space of GTR1. Arises from DOM3 through convolution — the first isomorphic part of GTR1.
a) Convolution as a space transformation
Convolution is a mathematical transformation from one space to another. The CNN takes a vector from the DOM3 space as input and produces a vector in the DOM4 space as output. Each L-component (or group of adjacent L-components) of MAP3 forms an input vector, which CNN transforms into a vector in the output space.
The meaning of the transformation is an ontological change. In DOM3, vector coordinates describe a point in space (position status, connections to neighbors, geometric relationships). In DOM4, they describe an object (its properties, features, identity). These are different ontologies, and the transition between them is convolution.
b) Recognition through vector comparison
When CNN produces a vector in DOM4, that vector either corresponds to some already existing node in the DOM4 space or it does not. The check is performed through vector comparison: if DOM4 contains a node storing a vector matching the CNN output (within acceptable precision) — the object is recognized.
If no corresponding node exists — recognition has not occurred. This is either a new, unfamiliar object or a recognition error. In both cases, OPN4 can create a new node in DOM4, storing that vector, thereby learning.
c) Biological analogy
This mechanism corresponds to the known structure of the nervous system: CNN has an axon extending to the dendrites of objects in DOM4 space. The signal arriving via the axon is compared with what is stored in each receiving object. When there is a match, the object is activated — recognition occurs.
This also explains why recognition occurs so rapidly. All objects "listen" to the axon in parallel. Recognition time does not grow with the number of objects in DOM4 — it is determined by the signal conduction time along the axon, not by sequential checking time.
d) R-component — object node
The result of recognition (or creation) is an R-component (from Recognize). An R-component is a subnetwork node containing:
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A vector — the key for recognition through comparison.
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A name — the object's identifier, allowing it to be referenced from other structures.
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Optional parameters — additional properties, connections, metadata that can be attached to the object.
R-components are called "objects" in a dual sense: both as objects in the computational sense (subnetwork nodes with identity and state), and as objects in the sense of the external entities they represent (stone, tree, food, conspecific).
e) MAP4 — a map in the conditional sense
The totality of R-components constitutes MAP4. Here the term "map" is used conditionally, for consistency with MAP3 and MAP5. Unlike MAP3 — which is a genuine geographic map of space — MAP4 is more like a network of recognized objects with no spatial organization in the direct sense. MAP4 objects are connected through participation relationships, similarity, and hierarchy, not geometric adjacency.
Nevertheless, calling MAP4 a "map" is convenient: it is structured, its elements have connections, and it can be traversed and analyzed like a space. This is sufficient for unified MAP3/MAP4/MAP5 terminology.
f) R-component relationships
Each R-component is connected to the rest of the structure through several types of relationships. The primary one at this level:
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The l-relation connects an R-component to the L-components of MAP3 — the spatial points where that object was recognized. One R-component can be connected to multiple L-components in different elementary maps if the object is encountered in different locations.
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Other relationships (b-relations to actions, symbolic connections) arise at subsequent levels and are examined in corresponding chapters.
g) Ontological leap
DOM4 is a new ontology produced by convolution. R-components are not the same as L-components. An L-component represents a point in space; an R-component represents an object. An object can occupy multiple L-components, and a single L-component can be part of different objects at different times. These are two different ways of organizing reality.
Importantly: DOM3 is not converted into DOM4. DOM3 continues to exist in parallel as the material substrate of object reality. Both spaces coexist within the same organism, fulfilling different functions.
h) OPN4 requires learning
Unlike OPN3, which simply records sensor readings, OPN4 must learn to recognize objects. Learning consists of accumulating vectors in MAP4 nodes and adjusting CNN weights so that the same real object produces similar output vectors under different observation conditions.
A newborn organism does not distinguish objects — it only sees surfaces and borders (MAP3 without MAP4). Recognition develops through repeated encounters with the same patterns. Each such contact refines the vector in the corresponding R-component.
The classic experiment of Blakemore and Cooper (1970) directly demonstrated the plasticity of this level. Kittens from two weeks to five months of age were raised in a cylinder with walls covered exclusively by vertical or horizontal black-and-white stripes. After release, kittens raised with vertical stripes could not see horizontal contours — they bumped into horizontal rods and could not see table edges. And vice versa. Their visual cortex contained only the orientation-selective neurons corresponding to the experienced environment. This is direct evidence that the CNN at the DOM4 level does indeed undergo learning, and its structure depends on early experience.
This is why the CNN at GTR1 and above fundamentally differs from the "CNN" in GTR0 (where convolution is hard-coded in MOVE). At the GTR1 level, convolution is a learnable process, part of OPN4's functionality.
2. 6. DOM5: The Behavioral Level
The third information space of GTR1. Arises from DOM4 through splice — the second step of GTR1.
a) Splicing into OPRNs
MAP4 contains R-components — recognized objects. But the world of objects is static in itself. For the organism to be able to act, objects must be connected with actions.
Splice is realized through a b-vector (from behavior). The basic unit of the splice result is an OPRN (operation): a triplet R—b—R, where the first R-component is the subject, the b-vector is the action, and the second R-component is the object. This is the minimal structure of meaningful action: "who — does what — to what."
The operational network OPN5 performs the splice — connecting R-components through b-vectors into OPRNs.
b) MAP5 and BLOM
Many OPRNs constitute MAP5 — the behavioral map. But individual OPRNs do not yet constitute complete behavior. Behavior consists of sequences and structures of OPRNs connected by shared meaning and temporal organization.
Chains of OPRNs form BLOM (Behavioral LOM). BLOM are composite structures made of OPRNs organized into meaningful sequences: "approached the bowl — saw food — picked up food — ate." This is the level where recognizable action patterns emerge: hunting, nest building, courtship rituals.
Recurring BLOMs constitute the organism's behavioral repertoire. They can be used as ready-made patterns — not reassembled each time but retrieved from memory as whole blocks. This is the basis of habit formation, instinctive behavior, and motor skills.
c) TRL5 — Trajectory log
DOM5 is the first space in the GTR1 architecture where temporal dynamics appear. In DOM3 and DOM4, everything is static: L-components are fixed, R-components are bound to locations. In DOM5, actions appear — and actions unfold in time.
TRL5 — the trajectory log — records this temporal history. TRL5 logs which OPRNs were executed and when, which BLOMs formed, and what happened in the organism's life.
TRL5 is the memory of the past. Through it, the organism not only reacts to the current world but remembers what happened. Learning through repetition, habit formation, and recognition of familiar situations are all based on this.
d) Time as an axis of existence
A fundamentally important observation: time as an additional axis of reality only appears at DOM5. Before this level, the system has no time. Cells in DOM1 live in time but have no representation of it. DOM3 and DOM4 are static maps of space and objects.
With TRL5, the organism for the first time gains the ability not only to live in time but to have temporal experience — remembering the past and anticipating the future. This is a qualitative leap comparable to the emergence of information at DOM3. The organism's reality gains a fourth dimension.
2. 7. OPNT: Operational Networks
At all three levels of GTR1, operational networks — OPN3, OPN4, OPN5 — are at work. They are concrete realizations of the general concept OPNT (Operational Network in the general sense).
OPNT is a network of processes that handles information within its DOM. At different levels, OPNT performs different tasks:
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OPN3 records sensory data and places it in the L-components of MAP3. Simple status recording.
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OPN4 manages convolution: feeds a vector from MAP3 to the CNN, receives the result in DOM4, compares it with existing R-components, and creates new ones as needed.
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OPN5 manages splice: connects R-components through b-vectors into OPRNs, assembles OPRNs into BLOMs, and maintains TRL5.
a) OPNT — a deterministic program
It is important not to confuse OPNT and CNN. OPNT itself is a deterministic program. It is formed by the D-component and, from a computational standpoint, is simply platform executable code (at the level of an x86 program, microcode, or other firmware). OPNT cannot be "trained" — it can only be executed. Its logic is strictly defined.
What is trained is not OPNT but the CNN that OPNT calls. CNN is a learnable neural network with plastic weights. OPNT is the invariant program managing CNN's operation: when to call it, what data to feed, where to write the result, when to initiate learning on new examples.
This corresponds to the known division of labor in neural tissue. On one hand — plastic synapses that change with experience: their weights are adjusted through CNN learning. On the other — deterministic cellular mechanisms: neuron cytology, basic signal transduction protocols, membrane structure. These operate the same way throughout life. OPNT corresponds to this deterministic part.
b) BLOM as a heuristic for OPNT
Although OPNT does not learn, it can use recurring BLOMs as a kind of working parameter. When TRL5 reveals a stably repeating OPRN sequence, OPN5 can memorize it as a ready-made template. The next time a similar situation arises, OPN5 can retrieve the ready BLOM instead of reassembling OPRNs from scratch.
This is not learning by OPNT itself — its code does not change. It is more like caching of results, optimization through pattern reuse. The analogy: a dictionary of frequently used words that can be inserted into speech without "assembling" them from letters each time.
c) Difference from GTR0
GTR0 has neither OPNT nor CNN. There is only the deterministic deconvolution of MOVE: the entire structure of the multicellular organism is given by the description. Learning is entirely absent, even in the form of CNN.
The appearance of OPNT+CNN at GTR1 is a qualitative evolutionary leap. The organism gains the capacity for learning (through CNN) while retaining a deterministic control structure (through OPNT). The deterministic part ensures reliability and repeatability; the plastic part ensures adaptation to the environment. Both properties are needed: a fully plastic organism would be unstable; a fully rigid one would be unable to survive in a changing environment.
2. 8. Engineering Implications for Gativus
For the Gativus project, the GTR1 architecture sets concrete engineering requirements. To reproduce subjective reality in a technical system, one must construct an analogue of neural tissue — the material basis for GTR1 information spaces.
a) Substrate — GATE nodes
The physical substrate for DOM3/4/5 in Gativus will be nodes of the GNET network, realized on the GATE hardware platform. At this level, each NDDI node plays the role of a cell — the material carrier of one functional unit of the information space.
From the GTR0 perspective, such a node is an ordinary NDDI with V/A/D/M/G sections, deconvolved from a MOVE vector via RTR0. From the GTR1 perspective, the same node serves as the carrier of an L-component, R-component, or OPRN — which are treated as distinct entities.
b) Node requirements
For a node to carry GTR1 functions, it must have the following properties:
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Functional specialization. A single node realizes either an L-component, an R-component, or an OPRN. The realization resides in the D-components.
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Learning capability. Nodes realizing OPN4 and OPN5 functions must be able to update their parameters based on experience. This is ensured by dedicated D-components implementing learning procedures.
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Gateway functionality. Nodes realizing Lg-connectors must physically exist in two elementary maps — have the corresponding connections and respond to requests from both maps.
c) Architectural recursion
Note an important property: a Gativus node realizing an L-component is itself an object of DOM1/DOM2. This means the information spaces of GTR1 in Gativus are built from the same entities as biological cellular tissue. The difference is only in functional specialization.
This is Gativus's core engineering insight. No separate mechanisms need to be invented for each level. It is sufficient to build the correct cellular foundation (GATE + NDDI + GNET) and specify the correct MOVE for specialized node classes — everything else will arise automatically as the emergent functionality of organized cellular tissue.
2. 9. Summary: GTR1 Structure
In summary, the structure of the GTR1 transformation is as follows:
Space |
Basic unit |
Organs |
Operation to next level |
L-component (Ls/Lb/Lg) |
Convolution |
||
R-component |
Splice |
||
OPRN (R—b—R) |
(GTR1 output) |
All three spaces exist in dual-ontological form: informationally (as spaces of DOM3/4/5 structures) and materially (as specialized neural tissue within DOM2). The physical substrate is cellular; the functional role is informational.
2. 10. Conclusions
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GTR1 introduces information spaces DOM3/4/5 whose content is not encoded in MOVE but is formed during the organism's life.
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Each space of GTR1 has dual ontology: it exists informationally as structure, and materially as specialized cellular tissue of the multicellular organism.
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DOM3 — a spatial multi-map based on L-components (Ls, Lb, Lg). Built from elementary grids of approximately 20×10×10, connected through gateway L-components. The total number of elementary maps reaches tens of thousands.
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DOM4 — an object map based on R-components. An R-component is a subnetwork node with a vector, name, and parameters. Produced through CNN convolution: a DOM3 vector is transformed into a DOM4 vector, then compared with existing R-components via an axon-dendrite mechanism.
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DOM5 — a behavioral map based on OPRNs (R—b—R triplets). Produced through splice of MAP4. Contains BLOMs (OPRN chains) and TRL5 (the temporal trajectory log).
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Operational networks OPN3/OPN4/OPN5 are concrete realizations of the general OPNT concept. OPNT is a deterministic program formed by the D-component. It does not learn; only the CNN that OPNT uses learns. BLOMs can serve as heuristics for OPNT, but this is caching, not learning.
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Time as an axis of existence appears at DOM5. Before this level, reality is static. TRL5 is the first realization of memory of the past.
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Engineering implication for Gativus: GTR1 information spaces are realized through specialized NDDI nodes on GATE. Different functional roles are specified by different classes of MOVE.
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Architectural recursion: the same mechanisms of cellular life (GTR0) serve as the material substrate for information reality (GTR1). The new level emerges through specialization, not new entities.
2. 11. Phenomenology of the Information Domain (Supplement)
GTR0 has neither OPNT nor CNN. There is only the deterministic deconvolution of MOVE: the entire structure of the multicellular organism is given by the description. The appearance of OPNT+CNN at GTR1 is a qualitative evolutionary leap. The organism gains the capacity for learning (through CNN) while retaining a deterministic control structure (through OPNT).
The cellular substrate is identical to the DOM2 level, but information about the habitat does not arise during morphogenesis but during learning — the cognitive exploration of the environment. The physical source of signals can be considered the sensors, which convert external signals into neural spikes. The real source of signals is the external environment.
The isomorphic basis of the Gativus transformation presupposes convolution and deconvolution. At the GTR1 level, it is technically only possible to convolve the external world into DOM3/4/5 maps. Deconvolution can only be partial — from levels 4/5 down to level 3.
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