Trajectory Analysis in Myndrama

Basins, funnels, and semantic whirlpools in sequential dialogue

Myndrama treats a sequenced dialogue as more than a collection of individual responses. Each turn changes what becomes available to the next participant. The result is a trajectory: a path produced by a particular sequence of prompts, personas, interpretations, and updates.

If repeated runs are represented within the same operational space, patterns may begin to appear. Some trajectories remain dispersed. Others converge. Some repeatedly return to similar territory. Particular orders may lead towards premature closure, while small changes in framing may allow the dialogue to move elsewhere.

The purpose of trajectory analysis is to study these patterns without reducing them to isolated “good” or “bad” outputs.

A misunderstanding, for example, may not be best understood as a single erroneous answer. It may arise because a sequence of locally reasonable turns gradually moves the dialogue into a region from which alternative interpretations become difficult to recover.

This is the sense in which Myndrama can be used to investigate a landscape of possible dialogue trajectories.

From trajectories to landscapes

A run can be represented geometrically by locating successive turns within a small number of measured dimensions. Possible dimensions might include clarity, openness, trust, uncertainty, closure, or other variables appropriate to the research question.

Connecting those observations gives a trajectory.

When several comparable trajectories are plotted together, recurrent structures may become visible: regions repeatedly approached, routes rarely taken, narrow passages between interpretations, or areas from which trajectories seldom escape.

These can provisionally be described using landscape metaphors such as basins, ridges, funnels, traps, and whirlpools.

The metaphors are useful only if their evidential status remains clear. A visually attractive hollow in a fitted surface is not by itself evidence that a genuine attractor has been discovered.

Basins and evidential status

Four terms are useful for distinguishing what has actually been observed from what is merely suggested.

Occupied basin
A region repeatedly entered by observed trajectories.

Candidate basin
A region suggested by clustering, trajectory behaviour, or a fitted representation, but not yet supported strongly enough to regard it as established.

Avoided basin
A candidate region for which there is evidence of accessibility under nearby conditions, but which a particular experimental condition systematically fails to enter.

Speculative basin
A possible region suggested mainly by theory, visualisation, or modelling assumptions and not yet adequately supported by observed trajectories.

This distinction is important. An avoided basin is not simply an empty part of a graph. There must be some reason to think that the region is locally reachable.

The vocabulary therefore records degrees of evidential commitment, rather than merely giving names to shapes on a plot.

Basins, traps, funnels, and whirlpools

Not every recurrent region has the same dynamics.

A basin is a region towards which trajectories tend to converge.

A trap basin is a basin that is comparatively difficult to leave once entered.

A funnel describes a different structure. Trajectories may begin with substantial freedom but are progressively channelled into a narrower range of possibilities.

A whirlpool requires more than simple convergence.

In a genuine dynamical whirlpool, trajectories do not merely move towards a low point. They repeatedly circle through related states while also being drawn inward. The corresponding idea in dialogue is therefore one of recurrent but increasingly constrained movement.

For this reason, the term semantic whirlpool should be used conservatively.

A candidate semantic whirlpool would normally show several of the following:

• repeated return to closely related semantic territory;

• repeated return to a nearby region of the measured trajectory space;

• declining novelty across successive returns;

• difficulty escaping despite further turns;

• little or no increase in discriminative resolution.

Repetition alone is not enough.

A dialogue may return several times to the same question because each return improves understanding. That is productive recursion, not a whirlpool.

The important distinction is between recurrence that develops the problem and recurrence that increasingly confines it.

Path-dependent basins

For Myndrama, perhaps the most interesting structures are path-dependent basins.

These are not simply fixed hollows waiting to receive any trajectory. Their accessibility depends upon the order in which updates occur.

A contribution from Skeptos followed by Orphea, for example, need not produce the same conversational state as the same contributions encountered in the opposite order. The first turn changes the interpretive conditions under which the second is received.

In this sense the updates may be non-commuting.

A dialogue can therefore arrive at a particular region not because any single contribution was defective, but because successive locally reasonable updates created a trajectory from which some later possibilities became harder to reach.

This is one reason Myndrama focuses on the sequence itself rather than treating the final response as the sole object of analysis.

 

Closing-persona effects

Order effects need not concern the whole sequence equally. One experimentally tractable possibility is that the persona occupying the final position exerts a distinctive effect on the terminal state of the dialogue.

An exploratory pilot suggested this possibility: changing the closing persona while retaining the same broad interaction produced different endpoint profiles. This should not yet be interpreted as evidence for persona-specific attractor basins. A single closing contribution may act simply as a terminal operator, moving an existing trajectory in a characteristic direction.

The stronger hypothesis is testable. If a persona repeatedly draws trajectories towards similar regions across different starting conditions, prompt variants, and preceding orders, then it becomes reasonable to ask whether that persona contributes to a recurrent region of attraction.

This provides a useful distinction between path effects, produced by the sequence as a whole, and terminal effects, associated with the participant occupying the closing position.

Local perturbation sampling

One way to investigate the neighbourhood around a trajectory is to make small controlled changes to the initial ask.

The aim is not to replace one scenario with another. Instead, the baseline prompt is perturbed slightly through changes in wording, salience, scope, emphasis, or framing.

The resulting runs can then be compared.

Do nearby trajectories remain close?

Does a small alteration push the dialogue across an apparent boundary?

Does a previously unoccupied region become accessible?

Does an apparent attractor remain stable when the wording changes?

This procedure can be thought of as local perturbation sampling.

It allows the surrounding topology to be investigated experimentally rather than inferred from a single trajectory.

It may also help distinguish a merely speculative basin from one that becomes occupied under mild perturbation.

Semantic signatures

Coordinates alone should not determine the interpretation of a basin.

If several prompt variations move trajectories towards the same region, the shared semantic feature of those prompts may provide a useful provisional description.

A region might therefore acquire a working label such as:

• ambiguity basin;

• mistrust basin;

• premature-closure basin;

• excessive-caution basin;

• conflict basin;

• over-accommodation basin.

These labels describe semantic signatures, not natural kinds.

Their purpose is to summarise the family of pressures associated with entry into a region, while leaving open the possibility that later evidence will require the label to be changed.

The same caution applies even more strongly to terms such as semantic whirlpool. The name should follow the observed dynamics, not precede them.

The map is not the semantic space

Any geometrical representation introduces a substantial measurement problem.

A three-dimensional plot using clarity, openness, and trust does not reveal the intrinsic geometry of dialogue. It shows a projection constructed from selected variables and a particular scoring procedure.

An apparent basin may therefore depend partly on:

• which dimensions were chosen;

• how they were operationalised;

• who or what performed the scoring;

• the scale properties of the measures;

• the interpolation or modelling procedure used to construct the surface.

This distinction is essential.

The plotted state-space should not be confused with semantic space itself.

It is an operational measurement representation designed to make particular features of a trajectory observable.

Different representations may reveal different structures, and apparently robust findings should therefore be tested across alternative measurement schemes where possible.

Visualising trajectories

Several representations can be useful, depending on the question.

A trajectory plot shows the sequential path directly and is particularly useful for examining order effects.

A two-dimensional contour map can make recurrent regions and boundaries easier to see across many runs.

A three-dimensional surface may help illustrate candidate basins, ridges, and funnels, although visually striking surfaces should not be mistaken for evidence in themselves.

A basin table can record coordinates, occupancy, experimental condition, replication status, and evidential classification.

The visualisation should always remain subordinate to the trajectory data from which it was derived.

Separating hypothesis generation from testing

AI systems themselves may be useful in proposing nearby prompt perturbations or suggesting possible interpretations of recurrent regions.

But hypothesis generation must be separated from confirmation.

A useful sequence is:

1. identify a recurrent or potentially avoided region;

2. inspect the trajectories and prompt variants associated with it;

3. generate a small set of nearby perturbations;

4. run those perturbations under the same controlled Myndrama protocol;

5. determine from the resulting trajectories whether the proposed structure persists.

Teleosynthesis may be useful at the third stage as a generator of possible probes. It should not determine whether its own proposed basin exists.

The empirical runs remain the test.

A working principle

The central methodological principle is simple:

Trajectory analysis should distinguish what the dialogue actually did from what it might plausibly have done under nearby conditions.

That is why occupied, candidate, avoided, and speculative structures must remain distinct.

The aim is not to turn every conversational pattern into a landscape metaphor. It is to develop increasingly disciplined ways of asking whether apparently recurrent features of dialogue are stable, path-dependent, experimentally perturbable, and reproducible.

Next steps

The immediate empirical task is modest.

A small canonical set of synthetic examples can first be constructed to demonstrate the differences between:

• a simple basin;

• a trap basin;

• a funnel;

• a spiral attractor;

• a path-dependent basin.

These provide reference cases against which empirical Myndrama trajectories can be compared.

The next stage is then to take selected baseline runs and probe their local neighbourhoods with controlled prompt perturbations.

If recurrent structures survive changes of wording, persona order, scoring method, and repeated generation, the language of basins and attractors begins to acquire empirical content.

At that point, Myndrama moves beyond plotting conversations towards something more ambitious: the investigation of local semantic topology in sequential human–AI and AI–AI dialogue.