The Trajectory Log

Chapter 4. The Trajectory Log

TRL as working space · Three states of records · The connective vectors b, k, w · Outcome markers as a hypothesis · Personality as TRL3

4. 1. Statement of the problem

Chapters 2 and 3 described how the transformation builds maps and which devices serve its dynamics. Let us recall the two axes. The axis of structure — convolution, splice, chain — generates the maps MPx1, MPx2, MP_x3. The axis of devices serves the dynamics on these maps: the operational network OPxx executes the program of a map, the syntactic predictor SPLx builds the current unit while the semantic predictor PRDx predicts the next unit by the connective vector, motivation MTVx sets the vector distance, and the trajectory log TRLx stores the history and the plan. The present chapter treats the last device in detail — TRL.

First of all let us fix the naming of the connective vectors, used constantly hereafter. The connective vector of each transformation is designated by a lowercase mnemonic letter, uniform in form across all three levels:

1. •

   b-vector (b — behavior): the spatial-behavioral connective of GTR1. The distance between the current and the goal configuration in physical space. Stitches objects MP11 into an operation OPRN.

2. •

   k-vector (k — knowledge entity): the logical connective of GTR2. The semantic relation between two symbols (causality, belonging, implication). Stitches symbols MP21 into an utterance KLEN.

3. •

   w-vector (w — Widerspruch): contradiction at GTR3. The distance between two concepts as the measure of their opposition. Stitches concepts MP31 into a volitional act WILL.

The letters of the splice units inherit the letter of their connective: the k-vector stitches KLEN, the w-vector stitches WILL. The German Widerspruch is chosen not by chance — it ties the connective vector of the upper level to the Hegelian notion of contradiction as the driving force of development.

The trajectory log TRL is not present on all maps. It appears only where there is dynamics — on the chain maps, which are the result of a chain of splices. One trajectory log per transformation.

Table 4.1. The placement of the trajectory log.

On the convolutional maps (MP11, MP21, MP31) and on the splice maps in themselves there is no trajectory log: they store more static structures — objects, symbols, concepts, and their pairwise connectives. The emergent level (shared behavior, shared symbols, shared narratives, shared concepts, the shared personality) has no TRL of its own: it has no carrier of its own, and is supported by the trajectory logs of individuals.

4. 2. TRL is not an archive

A common error is to understand TRL as an archive: a store of completed events to which the system turns for reference. In reality TRL is a working space — the operational memory of a level, in which past, present, and future are present simultaneously. Records exist in three states.

a) Planned

Computed chains that have not yet begun to execute. These are candidates: the semantic predictor PRD has computed several variants of continuation, and they are stored in TRL until the moment of choice. Planned records are the «future» of the level.

b) Under construction

Chains in the process of execution. Part of the elements are done, part are not yet. The operational network OP is «inside» the chain under construction, conducting it step by step. This is the «present» of the level.

c) Completed

Chains whose execution has finished. Each completed record receives an outcome marker — a numeric tag determining how this experience will be taken into account further. This is the «past» of the level — but an active past, influencing planning.

The division of labor between the devices here is fundamental and differs from the first edition. The vector distance is set by motivation MTV. The variants of continuation are computed by the semantic predictor PRD — it is this, by choosing the next unit under the vector distance, that builds the route, the narrative plan, or the path of sublation (the syntactic predictor SPL in this only closes each separate unit by the rules of the level). The chosen variant is conducted by the operational network OP — the deterministic program of execution. The trajectory log TRL stores all three states and accumulates marked experience. The computation belongs to the predictor, not to the operational network: OP executes the already chosen.

4. 3. TRL1: the trajectory log of the physical level

TRL1 contains BLOM — chains of OPRN, atomic operations in physical space (the map MP13).

Planned BLOM. A b-vector arises — the distance MTV1 between the current position and the goal. The semantic predictor PRD1 computes several routes that nullify this b-vector — variants of BLOM. They are placed in TRL1 as planned. In evaluating the variants the markers of past executions are taken into account: routes with positive markers receive priority, those with negative ones are avoided.

BLOM under construction. The best variant is chosen, the operational network OP13 has begun execution. The OPRN are performed successively: each atomic operation (step, turn, grasp) is realized through the sensory-reflexive subsystem. A BLOM under construction can be interrupted (an obstacle, new information) — then control returns to the planned variants or PRD1 computes new ones.

Completed BLOM. The route is traversed. The result — the b-vector is nullified (the goal is reached) or not nullified (failure, interruption). The completed BLOM receives an outcome marker.

Example. A cat sees a mouse. The b-vector is the distance from the cat to the mouse. PRD1 computes three BLOM: a direct leap, a detour to the left, a detour to the right; all three are planned in TRL1. The direct leap is chosen (past experience: a positive marker for direct leaps at a short distance). OP13 begins execution — the BLOM passes to «under construction». The leap succeeded, the mouse is caught — the BLOM is completed with a positive marker. At the next hunt at a similar distance PRD1 will again prefer the direct leap.

4. 4. TRL2: the trajectory log of the symbolic level

TRL2 contains KLOM — chains of KLEN, utterances in the narrative space MP23.

Planned KLOM. A k-vector arises — the semantic distance MTV2 between the current state and the goal in symbolic space. The semantic predictor PRD2 builds several narrative plans — variants of KLOM. Each plan is a sequence of utterances «symbol — k-connective — symbol». The variants are placed in TRL2 as planned.

KLOM under construction. The plan is chosen, its compilation begins: the narrative MP23 is successively deconvolved downward into behavior MP13 through the reverse deconvolution of symbols (MP21 → MP11). Each utterance KLEN is compiled into physical actions. If an utterance cannot be compiled (there is no BLOM realizing this step) — the plan is revised.

Completed KLOM. The narrative is performed. The k-vector is nullified (the task is solved) or not nullified (the plan failed). The completed KLOM receives an outcome marker.

Example. A student solves a mathematics problem. The k-vector is the semantic distance from the condition to the answer in the space of mathematical symbols. PRD2 builds three plan-KLOM: apply the formula directly, expand into a series, reduce to a known problem. The first is chosen (a positive marker in TRL2 from a past application of the formula), compilation into physical actions begins (the hand writes on paper). The plan led to the answer — the KLOM is completed with a positive marker. At the next similar problem PRD2 will prefer the same method.

4. 5. TRL3: the trajectory log of the conceptual level

TRL3 contains WLOM — chains of WILL, acts of sublating contradictions in the space of concepts MP33.

Planned WLOM. A w-vector arises — the distance MTV3 as the contradiction between two concepts. The multitude of recognized but not yet addressed contradictions are the planned records of TRL3. They correspond to what a person describes as «I know that I must do something about this, but have not yet begun».

WLOM under construction. The sublation of a concrete contradiction is begun: PRD3 computes a path of sublation, which is compiled into a narrative MP23 (KLOM), and that into physical actions (BLOM). The person acts not because he wants to, and not because the plan requires it, but because he cannot otherwise. A WLOM under construction can last days, months, years.

Sublated WLOM. The w-vector is nullified or substantially reduced. The concepts have irreversibly changed. This is precisely sublation (Aufhebung) in Hegel's sense: the resolution of a contradiction with preservation and elevation. The sublated WILL receives a marker.

Example. A person realizes that his work contradicts his concept of justice. The w-vector is the contradiction between the concept of the current situation and the concept of justice (the latter largely formed by the shared concepts of culture). This is a planned WILL in TRL3. The person decides to act — the WLOM passes to «under construction». The process lasts months: narratives (KLOM), actions (BLOM), conversations, decisions. In the end — resignation and a new job. The w-vector is nullified. A positive marker. The person has become other — the concepts have irreversibly changed.

4. 6. TRL3 as personality

TRL3 occupies a special place in the architecture. TRL1 is a history of routes. TRL2 is a history of narratives. But TRL3 is a history of the sublation of contradictions, each of which irreversibly changed the concepts. The sequence of records of TRL3 determines who the person has become: which contradictions he passed through, which he sublated, which are blocked. This content is precisely Personality — the map MP33 (WLOM), understood not as a set of views, but as a stitched schema of volitional resolutions.

TRL3 does not describe the current state of the personality — for that the current configuration of MP31 (the field of concepts) is sufficient. TRL3 describes the trajectory of becoming: the path by which the personality came to its present state. Two people with an identical field of concepts may have radically different TRL3 — and will react differently to new contradictions, because their experience of sublation is different.

The markers in TRL3 determine the strategy of the personality: a person whose past acts of sublation are marked positively enters new contradictions more boldly; a person whose TRL3 is full of negative markers avoids axiological conflicts — even when his concept of the ought requires action.

Wisdom is not knowledge (MP23) and not the concepts themselves (MP31). Wisdom is a rich TRL3 with a predominance of positive markers: the experience of repeatedly passing successfully through contradictions. The wise person does not fear the w-vector, because his TRL3 contains precedents of successful sublation.

Here too is the point of connection with the book Metaphysics. Personality as a stitched schema of sublated contradictions is the individual germ of that compact transmissible pole of the whole information circuit which in Metaphysics is called IDEA (the structural analogue of the Hegelian Absolute Idea). TRL3 is the history in which this pole is accumulated node by node; its nature as an independent convolved entity is treated separately and not anticipated here.

4. 7. Outcome markers

A marker is not a binary «good/bad», but a numeric value on a scale, tied to a completed record of TRL. The principle of marking is one at all three levels and constitutes a firm part of the architecture:

The connective vector decreased — a positive marker, the strategy is remembered for repetition. The vector increased — a negative marker, the strategy is marked as to be avoided.

The marker is tied to the unexpectedness of the result, not to the result itself: an identical outcome receives different markers depending on how far it deviated from expectation. This corresponds directly to the model of prediction error in neurobiology: the signal is the stronger the greater the discrepancy between expectation and fact. The dopaminergic system of prediction error at the behavioral level is a well-confirmed empirical fact, and it is precisely this that serves as the firm anchor of the whole construction of marking.

The further attribution of concrete neurotransmitters to concrete levels should be read as a working hypothesis, not as an established correspondence. The phenomenology below is given to illustrate the intuition behind the hypothesis, and should not be taken as a proven mapping «neurotransmitter → level».

Table 4.2. Hypothetical mapping of neurochemistry onto levels (status — hypothesis, except the dopaminergic row of GTR1).

The strong side of the table is the unified principle of the marker's sign, tied to the change of the vector; it rests on the dopaminergic anchor and does not depend on the details. The weak, hypothetical side is the concrete neurochemistry of the upper rows: the attribution of serotonin to the symbolic level and of opioids to the conceptual is plausible (phenomenologically the «calm» reward of understanding and the «quiet» peace of a sublated contradiction differ from the «bright» dopaminergic pleasure), but not proven. What is substantively important is only that different levels are marked by different systems; by which exactly is a subject of further research.

4. 8. The multidimensionality of the trajectory log

The trajectory log is not one-dimensional. The number of axes along which its records are ordered grows with each level.

TRL1 — one axis. The physical causal sequence: event A before event B. BLOM are ordered along a single axis — the change of states of MP13. This is not the perception of time, but physical causality. A dog does not know that «it is now 2 p.m.»; it knows that after the bowl came the yard, after the yard the armchair. Time at this level is the product of the chain MP13, not a separate axis.

TRL2 — several axes. With the appearance of the symbolic level the log acquires a multidimensional structure. KLOM are ordered simultaneously along several axes: the causal one (inherited from below through the convolution of GTR2); the semantic one (grouping by content, not by chronology: all narratives about mathematics are adjacent, independently of time; the distance along this axis is set by the k-vector); and the axis of symbolized time — fundamentally new, not existing at GTR1. A person attaches narratives to symbolic time markers borrowed from the shared symbols: «yesterday», «in childhood», «in a week», «2 p.m.». A child who has not yet mastered the clock (no corresponding symbols MP21) has the causal and semantic axes, but does not have the axis of symbolized time.

Hence the phenomena of the perception of time. «Time flies» — few narratives are recorded over a physical interval, the semantic axis is poor. «Time drags» — many unfinished narratives, the background activity is high. A child remembers summer as endless — each day generates a multitude of new narratives, the semantic axis is dense.

TRL3 — maximal dimensionality. To the axes of TRL2 are added semantic axes that have passed an additional convolution of GTR3: what in TRL2 was a group of «narratives about justice», in TRL3 becomes the concept of justice with an axis of its own. Beyond that — the native axes of concepts: each individual forms a unique field of concepts MP31, and it generates axes of TRL3 that no one else has. A person who has passed through the experience of betrayal has a developed concept of fidelity — and this concept creates an axis along which the related WLOM are grouped; a person without such experience does not have this axis, and his TRL3 is organized otherwise.

Table 4.3. The dimensionality of the trajectory log by levels.

Two people with the same chronological experience have different TRL3 — not only in the content of the records, but in the dimensionality of the space. One who has passed through axiological crises has a multidimensional TRL3 with many native axes; one who has lived without such crises may have an almost one-dimensional TRL3 — only the chronological axis, inherited from below. Therefore wisdom is not only a rich TRL3 with positive markers, but also its high dimensionality: the ability to see a situation simultaneously along many axiological axes, evaluating an act not by one concept, but by many.

4. 9. Unfinished records: the Zeigarnik effect

A special place in TRL is occupied by unfinished records — chains under construction that have been interrupted or blocked. An unfinished record contains a connective vector that is not nullified; it remains active and generates background activity. This is the architectural explanation of the Zeigarnik effect: unfinished tasks are remembered better than finished ones, because the open vector requires nullification and keeps the record active.

TRL1: an unfinished BLOM. A dog returns to an inaccessible bowl. The b-vector is not nullified → background activation of the operational network of GTR1.

TRL2: an unfinished KLOM. Obsessive thoughts, planning at rest. The k-vector is not nullified → background activation of the operational network of GTR2.

TRL3: an unclosed WILL. An existential impasse, a blockage of development. The w-vector is not nullified → background activation of the operational network of GTR3. The deepest case: the person cannot move further along TRL3 until this contradiction is sublated.

The last case gives an architectural description of «dejection amid outward well-being»: TRL1 and TRL2 may be in order (routes and narratives closed), but TRL3 contains an unclosed WILL, maintaining a constant background activity. The person is physically healthy and solves tasks — but within cannot move. Here a caveat about status is apt: this is a structural description of a phenomenon, not a clinical diagnosis; depression as a medical condition has many causes, and the architectural picture indicates only one possible mechanism of stagnation.

4. 10. Markers and the retraining of convolutions

The markers of TRL are connected with the cycle of retraining the convolutions. What is retrained is not the operational network — it is a deterministic program and does not change. What is retrained is the trainable kernel of the convolution tied to a map. The marked units of TRL serve as training data for this retraining in the period of rest.

The convolution of GTR1 is retrained with priority on the objects MP11 that entered BLOM with positive markers. Objects connected with successful routes receive greater weight. This explains why the replay of the hippocampus in sleep reproduces predominantly routes connected with reward: retraining proceeds on successful experience.

The convolution of GTR2 is retrained with priority on the symbols MP21 that entered KLOM with positive markers. A person remembers understood material (the narrative is closed with a positive marker) better than crammed material (the narrative is not closed, there is no marker).

The convolution of GTR3 is retrained with priority on the concepts MP31 that entered WLOM with positive markers. The concepts through which contradictions were successfully sublated deepen and are refined. The maturity of the personality is connected with the richness and precision of the concepts — each successful sublation refines the convolution.

Negative markers also participate in retraining, but with a different function: they strengthen the convolution's ability to recognize patterns leading to failure, generating «defensive» objects in the map — representations that, when activated, launch avoidance, not approach.

The retraining of all convolutions is performed in the period of inactivity (sleep, the default mode). A unified cycle: the accumulation of marked units of TRL over an active period → the retraining of the convolutions at rest → more exact recognition in the next active period. «The morning is wiser than the evening» — overnight the convolutions have been retrained on the marked data; the operational networks do not change in this, only the content of their trainable kernels changes.

4. 11. Conclusions

1. •

   TRL is not an archive, but the working space of a level: planned, under-construction, and completed chains (past, present, future simultaneously).

2. •

   TRL exists only on the chain maps, where there is dynamics: TRL1 (MP13/BLOM), TRL2 (MP23/KLOM), TRL3 (MP33/WLOM). One log per transformation. On the convolutional and splice maps, and at the emergent level, there is no TRL.

3. •

   The connective vectors are named uniformly by a lowercase letter: b (behavior), k (knowledge entity), w (Widerspruch). The letters of the splice units inherit the letter of the connective (k↔KLEN, w↔WILL).

4. •

   The division of labor: MTV sets the vector distance; the semantic predictor PRD computes the variants, choosing the next unit (route PRD1, narrative plan PRD2, path of sublation PRD3), and the syntactic SPL closes each unit; OP executes the chosen; TRL stores the states and the marked experience. The computation is the predictor's, not the operational network's.

5. •

   Completed chains receive a numeric outcome marker: the sign is determined by the change of the connective vector (nullified — plus, grew — minus). This principle is a firm part of the architecture, resting on the dopaminergic prediction error.

6. •

   The concrete neurochemistry of the upper levels (serotonin — symbolic, opioids — conceptual) is lowered to a hypothesis; the phenomenology is given illustratively. Architecturally important is only that different levels are marked by different systems.

7. •

   TRL3 is Personality — the map MP33 (WLOM), the history of sublated contradictions and the individual germ of the IDEA pole (treated in Metaphysics). Wisdom is a rich and multidimensional TRL3 with a predominance of positive markers.

8. •

   The dimensionality of the log grows with the level: TRL1 — one axis (causality), TRL2 — three (causal, semantic, symbolized time), TRL3 — N (plus native axes of concepts, unique to the individual).

9. •

   Unfinished records generate background activity (the Zeigarnik effect). An unclosed WILL in TRL3 is the deepest case, blocking development; a structural, not a clinical, description.

10. •

    The marked records of TRL are the training data for the retraining of the convolutions in the period of rest (replay in sleep). The operational networks are not trained; only the trainable kernels of the convolutions change.