Status: Open paper, presented for discussion. This is not a finished theory. The claim is narrower: there may be a useful structure here, precise enough to develop and test.
A system can preserve the sound of a sentence without preserving a statement. It can produce a correct answer without operating on the concepts expressed by that answer. It can distinguish patterns without treating them as symbols. These differences are difficult to describe with a single term such as intelligence or a single score intended to measure it.
This paper proposes a matrix for describing information-handling systems. One axis contains proposed aspects of informational organization: signal, pattern, symbol, primitive, concept, statement, thought, association, memory, knowledge, learning, teaching, and wisdom. The other contains five capacities a system may have at any aspect: receive, record, expose, transform, and reason.
Each cell asks whether, and how well, a system can perform a capacity on information organized at a particular aspect, as that aspect. Preserving the signal pattern of a sentence is not the same as recording a statement as a statement. Cells can be measured by criteria such as fidelity, reliability, range, transfer, and independence, and the resulting profile can be tracked through time.
The matrix is not offered as a completed theory of mind or intelligence. It is a candidate descriptive foundation for comparing biological, artificial, and collective information-handling systems, tracing how information moves through them, and investigating communication, cognition, learning, teaching, and wisdom without reducing them prematurely to one quantity.
Questions about minds and intelligent systems often combine several different questions:
- What kind of informational organization is available to the system?
- What can the system do with information in that organization?
- How well can it do it?
- How does that capacity change?
Ordinary terms such as understanding, knowledge, learning, and wisdom bundle these questions together. Scalar measures introduce another problem. They imply that systems can be placed on one ladder, even when their capacities differ in kind rather than only in amount.
A chess engine, a young child, a search index, a scientific community, and a language model may each exceed the others in different regions of informational work. Calling one simply “more intelligent” removes much of what needs to be explained.
The proposal begins by separating two variables:
- informational aspect: the organization in which information is available to a system;
- system capacity: what the system can do with information in that organization.
The answer is not necessarily a score. It is a profile.
The title is therefore provisional. The matrix can describe systems that no one would call minds. Whether some profiles or trajectories deserve that name is a question the proposal is intended to help investigate, not an assumption built into it.
A system may receive a pattern but fail to record it. It may record symbols but be unable to transform the primitives they encode. It may expose statements that it cannot reason with.
The informational organization and the capacity applied to it must therefore be represented separately.
A capacity is attributed at an aspect only when the system handles the information as that aspect, rather than merely manipulating a lower-aspect carrier that an observer interprets at the higher aspect.
This is the central discipline of the proposal. Without it, the same observable output can be credited to incompatible internal capacities.
The vertical axis follows a working construction hypothesis: units available at one aspect may be organized into a structure that becomes available to the system as one unit at another aspect.
A collection is not enough. The organization itself must become operable as one. The practical criterion is that the larger structure can be received, recorded, exposed, transformed, or reasoned with as a unit.
Whether the same construction principle adequately describes every transition remains open.
The present sequence is:
Signal
→ Pattern
→ Symbol
→ Primitive
→ Concept
→ Statement
→ Thought
→ Association
→ Memory
→ Knowledge
→ Learning
→ Teaching
→ Wisdom
The order is provisional. It does not imply value, consciousness, biological development, or chronological acquisition. “Higher” means only that the proposal treats the aspect as being constructed from organized units available at an earlier aspect.
| Aspect | Working description |
|---|---|
| Signal | A difference made available to a system. It is the lowest aspect selected for the present model, not an asserted absolute minimum. |
| Pattern | An organization of signals distinguishable from other possible organizations. |
| Symbol | A pattern functioning as a distinguishable state within a system of alternatives and used to represent something beyond its immediate pattern. |
| Primitive | A unit represented or encoded by one or more symbols and treated as one in the construction of concepts. |
| Concept | An organized system of primitives available as one unit. |
| Statement | An organized system of concepts available as one assertion, relation, or presented configuration. |
| Thought | An organized system of statements available as one unit. |
| Association | An organized system of thoughts whose availability or operation is linked. |
| Memory | An organized system of associations retained or reconstructible across time. |
| Knowledge | An organized system of memories available to guide further informational work. |
| Learning | An organized system of transitions in knowledge or in a system’s capacities. |
| Teaching | An organized system of learning structures directed toward, demonstrated to, or observed in another system. |
| Wisdom | A proposed higher organization of teachings, their outcomes, contexts, and consequences, available for further reasoning. |
These are technical working descriptions, not claims that the words must retain all of their ordinary meanings.
A pattern functions as a symbol only within a system of alternatives. A visible mark may appear singular, but its symbolic capacity depends on what could have occurred instead.
A switch in the “on” state can encode something only because “off” is possible. A single mark can encode a primitive only because the symbolic system contains at least the distinction between:
mark present
mark absent
The token may be singular. The symbolic system is not.
One symbol may encode a primitive, and multiple symbols may encode one primitive. In both cases, the primitive is made available through a configuration within a symbol system, not through an isolated token considered alone.
A primitive is not claimed to be absolutely simple. It is a unit whose internal organization is not being resolved in the current operation.
The same structure may be analyzed as a system in one context and used as a primitive in another. This allows a complex organization to function as one unit without requiring every operation to reopen its full construction.
Learning, teaching, and wisdom stay on the axis because removing them would decide the structure too early.
The current proposal is that knowledge transitions may form learning structures, learning structures may form teaching structures, and teaching structures considered with outcomes and consequences across contexts may form wisdom structures.
Their placement is less secure than the lower part of the sequence. Learning may also be a change in the matrix through time. Teaching may also be an interaction between systems. Wisdom may turn out to be a property of the whole profile rather than one row. The matrix allows these alternatives to be stated without deleting the terms in advance.
The sequence itself may eventually branch into a lattice. A higher aspect may be constructed from several earlier aspects at once. The current chain is a hypothesis about organization, not a finished ontology.
The second axis contains five capacities.
| Capacity | Working description |
|---|---|
| Receive | Admit, detect, or reconstruct information at the specified aspect. |
| Record | Preserve information so that it remains recoverable at the specified aspect. |
| Expose | Make information available beyond a selected boundary. Expression, display, repetition, publication, and transmission are forms of exposure. |
| Transform | Change informational organization. Analysis, composition, decomposition, encoding, decoding, translation, compression, abstraction, comparison, and selection are transformations. |
| Reason | Transform information by applying rules available to the system. |
These are functional distinctions, not mutually exclusive mechanisms. Receiving information generally changes the receiver. Recording is itself a transformation of state. Exposure often requires transformation into a form that can cross a boundary. Reasoning is a subclass of transformation.
The distinctions remain useful because the capacities can vary independently in practice.
The boundary relevant to exposure must be stated. It may separate physical systems, agents, software components, or subsystems of one larger system. Transmission is exposure across such a boundary through a carrier or shared medium.
For reasoning, it is not enough that an observer can describe the behavior with a rule. The rule must be available to the system in some operative form. Whether that availability must be explicit, selectable, inspectable, or merely effective remains an open measurement question.
Cross the informational aspects with the capacities:
| Informational aspect | Receive | Record | Expose | Transform | Reason |
|---|---|---|---|---|---|
| Signal | |||||
| Pattern | |||||
| Symbol | |||||
| Primitive | |||||
| Concept | |||||
| Statement | |||||
| Thought | |||||
| Association | |||||
| Memory | |||||
| Knowledge | |||||
| Learning | |||||
| Teaching | |||||
| Wisdom |
Each cell asks:
To what extent can this system perform this capacity on information organized at this aspect, as this aspect?
A binary answer will rarely be sufficient. A capacity may vary in fidelity, reliability, range, speed, resistance to noise, independence from external support, transfer to unfamiliar conditions, and reversibility after transformation.
For a system (X), the descriptive object can be written as:
M_X(a,c,q,t) -> s
where (a) is an informational aspect, (c) is a capacity, (q) is a measurement criterion, (t) is time, and (s) is the measured strength.
At a fixed time, the values form a profile across the matrix. This paper uses shape as an intuitive name for that profile. Across time, the profile forms a trajectory.
Two systems may have similar snapshots and different trajectories. One may be acquiring capacities while the other is losing them. A static score would miss that difference.
Consider an idealized passive voice recorder. It receives pressure variations, records them, and later exposes a similar signal pattern. The recording may carry a spoken statement for a listener. That does not establish that the recorder received or recorded the statement as a statement.
A more complex recorder may detect silence, segment speech, apply a codec, label files, or manipulate symbolic metadata. It may therefore occupy additional signal, pattern, or symbol cells. The point is not that every recorder occupies the same cells. The point is that preserving a carrier does not by itself establish capacity at the aspect carried.
The same rule applies to any system that produces a sentence, image, proof, plan, or decision. Identical exposed outputs do not imply identical informational organization.
A claim that a system occupies a cell should be tested by controlled perturbation:
- Choose a target aspect and capacity.
- Vary lower-aspect carriers while preserving the target organization.
- Vary the target organization while controlling lower-aspect similarities.
- Measure whether behavior tracks the target aspect across the relevant criteria.
Evidence for a higher-aspect capacity becomes stronger when performance survives irrelevant variation below that aspect and remains sensitive to changes at the target aspect.
No single task is likely to establish occupancy conclusively. The matrix calls for converging tests rather than interpretation from one output.
The matrix describes what a system can do at an aspect. It does not fully describe how information moves between aspects.
A second object is therefore required:
T_X(a_i,a_j,q,t) -> s
Here (a_i) is a source aspect and (a_j) is a destination aspect. The transition can be measured for fidelity, cost, directionality, reversibility, context dependence, and rule use.
Examples include:
pattern → symbol
symbol → primitive
statement → thought
thought → statement
Two systems may occupy similar cells while differing sharply in their transitions. One may record statements but fail to form stable thoughts from them. Another may reason with thoughts but expose them poorly through statements. The static matrix alone would not capture those differences.
Communication can be represented as a coupled path:
- a sending system transforms information into an aspect it can expose;
- that information becomes available across a specified boundary;
- a receiving system receives it at some aspect;
- the receiver transforms or reconstructs further organization using its own capacities.
The model does not assume that every boundary is crossed only by signals. Speech usually exposes signals. A shared database may expose symbolic structures. Tightly coupled systems may share more complex organizations. The boundary and exposed aspect must be stated rather than assumed.
A useful default hypothesis is that higher organization is reconstructed by the receiver rather than transferred ready-made. This remains a boundary-relative empirical claim, not a universal theorem.
The transition view gives communication failure a more precise anatomy. A mismatch may occur because a signal was missed, a pattern was not distinguished, a pattern occupied a different symbol system, symbols encoded a different primitive, or the resulting primitives, concepts, statements, thoughts, memories, or knowledge were organized differently.
These are different failures and need not have the same remedy.
The upper terms can now be handled without forcing them into one conventional definition.
Learning as an aspect is an organization whose content is a transition in knowledge or capacity. Learning as a dynamic is a measured change in the matrix or transition map through time.
Teaching as an aspect is an organization of learning structures. Teaching as an interaction is structured exposure by one system intended to alter the matrix or transitions of another.
Wisdom remains the most provisional aspect. It may be a higher organization of teachings, outcomes, contexts, and consequences. It may instead be a capacity that regulates transformations across many aspects, a property of the whole profile, a collective achievement, or some combination of these.
The matrix preserves these alternatives rather than settling them by ordinary-language definition.
The same applies to cognition and intelligence. The matrix can be applied before deciding which systems are cognitive. Systems may then cluster by occupied regions, transition structures, learning trajectories, or rule use.
Intelligence may eventually be described through several properties:
- reach across informational aspects;
- breadth of capacities at each aspect;
- fidelity of operation;
- mobility between aspects;
- flexibility of transformations and rules;
- transfer across carriers and contexts;
- plasticity through learning;
- capacity to influence another system through teaching;
- scope across context, time, outcomes, and consequences.
This does not prove that intelligence is the whole matrix. It provides an object from which competing definitions and measures can be derived and compared.
A scalar summary may later prove useful for a particular purpose. It should be derived from the profile and validated against that purpose rather than assumed in advance.
The matrix and transition map may provide a common language for several tasks.
Profiles can reveal partial overlap and genuine incomparability. A system with narrow but powerful reasoning may differ fundamentally from one with broad reception, learning, and teaching capacities.
The question becomes not only whether a system produced an answer, but what it received, what it recorded, which transitions it performed, which rules were available, and at what aspect it exposed the result.
Instead of saying that a receiver “did not understand,” the model asks where the path diverged. The remedy for a missed signal differs from the remedy for a symbol mismatch, a missing primitive, an unstable concept, or a conflict with prior knowledge.
Profiles can be compared across time to describe acquisition, generalization, stabilization, decline, or reorganization. Teaching can be studied as an attempt to alter particular cells and transitions rather than as generic transfer of content.
The same descriptive language may be applied to a person, a model, a team, an institution, a scientific field, or a culture, provided the system boundary is explicit. This does not make those systems equivalent. It makes their differences expressible in the same coordinate system.
The proposal is useful only if it can fail.
Capacities should dissociate across aspects. A system may receive or expose a higher-aspect carrier without recording, transforming, or reasoning at that aspect.
If controlled measurements show that all proposed cells collapse into one undifferentiated competence, the matrix is unnecessarily complex.
A genuine capacity at a target aspect should show some robustness to changes in lower-aspect carriers that preserve the target organization. It should also remain sensitive to changes at the target aspect when lower-level similarities are controlled.
Across several adjacent aspects, it should be possible to identify cases in which organized lower units become operable as one higher unit, and in which that unit can later be decomposed or transformed.
If this structure does not recur, the proposed vertical order must be revised, branched, or abandoned.
Acquisition of higher-aspect capacities should depend on identifiable capacities and transitions already available to the receiving system. Perturbing those supports should impair acquisition even when exposure remains unchanged.
Matrix and transition profiles should predict behavior, generalization, failure, acquisition, or decline better than surface output alone and, for at least some purposes, better than a single aggregate score.
If they do not, the additional structure has not earned its cost.
Whether the full profiles can be compressed into a smaller number of useful parameters is an empirical question. Compression should be accepted only if it preserves the dissociations the matrix was introduced to reveal.
The proposal intersects with information theory, semiotics, hierarchical representation, symbol grounding, educational taxonomies, psychometrics, cognitive architectures, systems theory, and research on communication and learning. It is not presented as a replacement for those fields, and no individual component is claimed as unprecedented.
The intended contribution is the assembly:
- informational aspects and system capacities are separate variables;
- capacity is attributed only when information is handled as the claimed aspect;
- a symbol functions through a system of alternatives rather than as an isolated token;
- the matrix is extended by measurement criteria, time, and transitions between aspects;
- learning, teaching, and wisdom remain inside the investigation rather than outside it as unexplained labels.
A proper literature review and comparison with existing formal models remain necessary. The paper also makes no direct claim about consciousness, subjective experience, moral status, or the ontology of information.
The main open questions are:
- Do the informational aspects form a chain, a lattice, or another structure?
- How should system boundaries be chosen?
- What experiments can establish cell occupancy and compare strengths across systems?
- Under what conditions does a symbol system encode, construct, or reveal a primitive?
- What must be true for a transformation to count as reasoning by the system?
- Are learning, teaching, and wisdom rows, dynamics, interactions, global properties, or combinations of these?
- Can useful lower-dimensional coordinates be discovered without erasing meaningful differences?
- Does the sequence continue beyond wisdom, perhaps in collective or long-lived systems?
The proposal consists of three related objects:
- a capacity matrix describing what a system can receive, record, expose, transform, and reason with at each informational aspect;
- a transition map describing how the system moves information between aspects;
- a trajectory describing how both structures change through time and interaction.
Together they replace the question “How intelligent is this system?” with a more informative set of questions:
- What informational organizations are available to it?
- What can it do with each one?
- How reliably can it do it?
- How does information move through it?
- How does the profile change?
- How does it affect, and become affected by, other systems?
This is not yet a theory of mind or intelligence. It is a candidate descriptive foundation from which such theories might be built and compared.
The immediate next step is narrow and empirical: choose a small number of cells and transitions, define tests that distinguish target aspects from their carriers, and compare several different systems over time.
That is enough structure to find out whether there is, in fact, something here.