Life as transformation GTR0

Chapter 1. Life as GTR0 Transformation

Three Spaces · Convolution and Splice · Single-cell and Multicellular · Isomorphism Across Life Levels

1. 1. Why Traditional Definitions of Life Fail

Traditional definitions of life enumerate its observable properties: sensitivity, metabolism, response to stimuli, goal-directed behavior, reproductive capacity, consciousness. All such definitions are vulnerable to edge cases: viruses, prions, self-replicating crystals, mycelia, comatose patients, replicator programs, three-day-old embryos. In each case, some properties are present and some are not, making the verdict of "alive or not" essentially arbitrary.

GNSS proposes a definition based on structure rather than properties: Life is a system of bidirectional transformations connecting spaces of different ontological natures. Biological life at the cellular level is the first Gativus transformation (GTR0), connecting the organism's description (DOM0) with the working cell (DOM1) and the multicellular organism (DOM2).

1. 2. Terms and Definitions

1. •

   GTR — Gativus Transformation, consisting of forward (DTR) and reverse (RTR) flows. The first stage of GTR is a convolutional neural network (CNN) that transforms the source space into a new one. The second stage creates a change vector for objects in the space and splices objects around that vector. Several isomorphic transformations have been identified and described in Gativus, numbered sequentially: GTR0, GTR1…

2. •

   DOM — DOMain. Each transformation produces information constructs specific to it. Since each transformation stage uses different constructs, the domain scope must be defined for their description. Each GTR may contain multiple domains with unique properties, numbered DOM0, DOM1…

1. 3. GTR0 Diagram

The diagram shows three cubes placed within the overall space of "Transformation 0." Each cube is a separate mathematical space with its own object ontology. The arrows between cubes show bidirectional transformations.

The rest of this chapter examines the diagram's elements in order.

1. 4. Three Spaces: DOM0, DOM1, DOM2

The three cubes correspond to three mathematical spaces.

a) DOM0 — Description Space

The left cube. Contains descriptions of biological constructs. Each object in DOM0 is a vector defining the structure of a single cell and its position within the organism.

Biological example: DNA sequence. Technical example: a MOVE vector in MOLD description language coordinates.

The DOM0 space is static. Vectors do not change on their own. They are compact: kilobytes of description determine millions of working units upon deconvolution. They are parametric: scale details are drawn from the resources of the deconvolution environment, not from the description itself.

b) DOM1 — Working Cell Space

The middle cube. Contains living cells as active processes. Each object in DOM1 is a single working cell.

Biological example: bacteria, amoeba, yeast cell. Technical example: an NDDI node executing object code and exchanging data with other nodes.

The DOM1 space is dynamic. Cell states change continuously. Each cell has a membrane, internal metabolism, and the ability to send and receive signals. The nature of objects in DOM1 is fundamentally different from DOM0: DOM0 has no processes or time; DOM1 has no static descriptions.

c) DOM2 — Multicellular Structure Space

The right cube. Contains collections of cells connected by spatial relationships and interactions. Each object in DOM2 is a multicellular structure: tissue, organ, organism.

Biological example: embryo, plant, animal. Technical example: a subnet of interconnected NDDI nodes forming a functional whole — microcolumn, column, module.

Unlike the DOM0→DOM1 transition, the DOM2 space introduces no new ontology. Its objects are the same cells as in DOM1. DOM2 extends DOM1 by one or two additional dimensions: the spatial coordinates of cells relative to one another, and intercellular connections (contacts, synapses, signaling channels).

1. 5. Two Steps: Convolution and Splice

The transitions between spaces are not uniform. This is emphasized visually in the diagram through the displacement of cubes.

a) Full-face displacement — Convolution

DOM1 is depicted as a cube displaced by a full face relative to DOM0. This displacement denotes a complete change of ontology. The DOM0 ↔ DOM1 transition is convolution.

Convolution transforms a description into a working cell in the forward direction, and a working cell into a description in the reverse direction. In both directions, the nature of the objects themselves changes. A description in DOM0 becomes a process in DOM1, and vice versa. Mathematically, this is a transformation in the same sense as the Fourier transform: connecting two ontologically distinct spaces.

Biologically, convolution is realized through two symmetric mechanisms:

1. •

   Forward convolution (DOM0→DOM1): gene expression, constructing a cell from DNA. Result — a working cell.

2. •

   Reverse convolution (DOM1→DOM0): formation of reproductive material. Result — a description vector for transmission to offspring.

b) Half-face displacement — Splice

DOM2 is depicted as a cube displaced by only half a face relative to DOM1. This is not a new space but an extension of DOM1 along additional axes. The DOM1 ↔ DOM2 transition is splice.

Splice connects objects of the same nature (cells) around a generative structure. The ontology does not change — the same cells, now with spatial coordinates and mutual connections.

Biologically, splice is realized through the following mechanisms:

1. •

   Forward splice (DOM1→DOM2): embryogenesis. The zygote divides, cells occupy positions, establish connections, and form tissues and organs.

2. •

   Reverse splice (DOM2→DOM1): meiosis, separating a reproductive cell from the multicellular organism. A cell detaches from the organism, ready for further convolution.

c) The Complete GTR0 Transformation

Convolution and splice together form a single GTR0 transformation. The forward direction (RTR0) runs left to right: DOM0→DOM1→DOM2. The description convolves into a cell; the cell splices into a multicellular organism.

The reverse direction (DTR0) runs right to left: DOM2→DOM1→DOM0. The multicellular organism releases a reproductive cell; the cell convolves into a description for transmission to offspring.

The cycle closes: the new description unfolds into a new organism. This is the reproduction of life.

1. 6. Single-cell and Multicellular: Completeness of GTR0

Not all organisms traverse the full path through all three spaces. GTR0 can operate in two modes.

a) Single-cell organisms — GTR0 without splice

Bacteria, amoebas, and paramecia live in DOM1 and never enter DOM2. Their GTR0 is limited to one step — convolution between DOM0 and DOM1:

1. •

   Forward convolution: DNA → living cell.

2. •

   Reverse convolution: the cell forms new DNA and passes it to offspring during division.

Single-cell organisms have no spatial structure beyond the level of a single cell, no cell specialization, no intercellular connections. Their life unfolds entirely within the single cube of DOM1.

This is not a simpler or more primitive form of life in any pejorative sense. Single-cell organisms are a complete realization of GTR0 at their level. They simply do not require splice.

b) Multicellular organisms — Complete GTR0

Plants, animals, and fungi execute both steps of GTR0: first convolution (constructing the zygote), then splice (embryogenesis and growth into a multicellular structure). Their life is distributed across all three spaces: DOM0, DOM1, and DOM2.

The completeness of GTR0 means that a multicellular organism has two qualitatively distinct aspects of existence: it is simultaneously a population of cells (DOM1) and a unified whole with spatial structure (DOM2). Both aspects are equally real.

c) Intermediate forms

Bacterial biofilms, single-cell colonies, slime molds, volvox — these are examples of intermediate forms where splice only partially exists. They have some spatial relationships and simple intercellular connections, but lack complete cell specialization and differentiation. Their DOM2 is reduced: just one or two extension axes of DOM1, not the full spectrum.

Evolutionarily, these forms represent the path through which multicellularity emerged.

1. 7. GTR0 as the First of Four Transformations

GTR0 is not only fundamentally significant in itself but is especially important as the only fully material-level transformation in the architecture. All subsequent transformations — GTR1, GTR2, GTR3 — operate with information. Only GTR0 creates matter.

Nevertheless, all four transformations share a common structure: a convolution space, a result space, and a bidirectional transition. The differences are substantial but concern the ontology of objects, not the overall schema:

The most important corollary: the GTR1–GTR3 information levels cannot exist independently of matter. They are all realized through specialized subsystems of the multicellular organism — neural tissue. From the GTR0 perspective, these subsystems are ordinary cells, products of morphogenesis. From the GTR1 perspective and above, they carry information functions invisible at the level of individual cells.

This resolves the classical mind-body problem. Consciousness is not a separate entity opposed to matter (Cartesian dualism). Consciousness cannot be reduced to matter through reductionism (materialist reductionism). Consciousness is another ontological projection of the same reality: the specialized organization of cells considered not as cells but as information. This is the same reality viewed differently.

This duality is the central theme of the subsequent chapters. Chapter 2 examines GTR1 — the first information level and its cellular realization. Chapters 3 and 4 examine GTR2 and GTR3. The complete picture of four transformations constitutes the theory of fourfold transformation presented in this book.

1. 8. The Significance of Reversibility

The diagram shows bidirectional arrows between all spaces. This is not a decorative detail but an essential property of life. Neither of GTR0's two steps works in only one direction.

Having only forward convolution (unfolding a description into a cell) without reverse convolution would be pointless: constructed cells could only live once, unable to transmit heredity. Having only reverse convolution (producing a description without being able to unfold it) is also a dead end: descriptions would accumulate with no way to be realized. Life requires both directions.

The same applies to splice. Forward splice (forming an organism from a zygote) without reverse splice (isolating reproductive cells) would leave the organism incapable of reproduction. Reverse without forward would mean multicellular organisms produce seeds but cannot form themselves from those seeds.

Life is not one direction of GTR0, but the very fact of both directions existing simultaneously. The essence of life lies in the reversibility of structural transformation between ontologically distinct spaces.

1. 9. Conclusions

1. •

   Life is a system of bidirectional transformations between spaces of different ontological natures. GTR0 is the first of these — the fully material-level transformation of biological life.

2. •

   GTR0 has three spaces: DOM0 (descriptions), DOM1 (cells), DOM2 (multicellular structures).

3. •

   GTR0 consists of two steps. The first — convolution, the ontological shift between DOM0 and DOM1. The second — splice, extending DOM1 to DOM2 by adding spatial connections.

4. •

   This distinction is shown in the diagram through cube displacement: full-face displacement — convolution; half-face displacement — splice.

5. •

   Single-cell organisms perform only convolution, without splice. Their GTR0 is limited to DOM0 ↔ DOM1. Multicellular organisms perform both steps — complete GTR0.

6. •

   Both steps of GTR0 are reversible. Deconvolution (RTR0): DOM0→DOM1→DOM2. Convolution (DTR0): DOM2→DOM1→DOM0. The cycle of life's reproduction closes through both directions. Together they form the closed cycle of life's reproduction.

7. •

   GTR0 is the first of four transformations constituting complete life. GTR1, GTR2, GTR3 — information transformations resting on the cellular substrate of GTR0. They are examined in subsequent chapters.

8. •

   All information levels are physically realized in specialized neural tissue, which remains part of DOM2 (the multicellular organism). This resolves the mind-matter relationship problem through dual ontology: the same reality manifests as both matter and information.

9. •

   The technical description of GTR0 — deconvolution and convolution procedures, NDDI node architecture, the role of GATE and ANOD — is given in the book MOGE (Gativus Morphogenesis).