An essay on the structure of knowledge, semantic recomposition, and the emergence of intelligence
For several decades, research in artificial intelligence, cognitive science, learning, innovation, and complex systems has helped us understand many mechanisms related to the production of knowledge.
We now know that an intelligence can learn.
We know that it can memorize.
We know that it can generalize.
We know that it can reason.
We know that it can combine information from different sources.
Yet a fundamental question remains largely open:
How can an intelligence produce knowledge that is not explicitly contained anywhere in what it already knows?
This question lies at the heart of scientific discovery, technical invention, artistic creativity, economic innovation, and, more generally, every form of cognitive progress.
Every time a human being formulates a new theory, discovers a physical law, invents a technology, or establishes an unprecedented link between two domains, they seem to produce more than what was directly contained in their initial knowledge.
The question then becomes unavoidable:
Where does this apparent surplus of knowledge come from?
The usual answers generally invoke reasoning, imagination, intuition, or creativity.
These answers describe mechanisms.
They do not necessarily answer the deeper question.
For before we can understand how an intelligence discovers, we must understand what is being discovered.
Is it truly a creation?
Or is it something else?
The hypothesis proposed here is the following:
Knowledge contains more information in its relational structure than in the individual pieces of knowledge that compose it.
This statement may seem abstract.
Yet it lies at the heart of the problem.
Traditionally, we consider pieces of knowledge as the fundamental units of knowledge.
A formula.
A theory.
A concept.
A fact.
An observation.
A definition.
In this view, knowledge is made of an accumulation of elements.
Intelligence then consists in manipulating these elements.
But this representation has an important limit.
It implicitly assumes that information is contained in the objects themselves.
Yet this assumption may be incomplete.
Another possibility exists.
The most important information may not reside in the objects, but in the relations that connect them.
Imagine one hundred isolated pieces of knowledge.
Each piece of knowledge has a certain informational value.
Now imagine those same pieces of knowledge connected by thousands of relations.
Some relations express similarities.
Others express oppositions.
Others express dependencies, causalities, or compatibilities.
In the first case, we possess a collection.
In the second case, we possess a system.
The difference is considerable.
For a system possesses properties that are not contained in any of its elements taken separately.
In other words:
Structure contains information.
This observation is well known in many domains.
A cell cannot be reduced to its molecules.
A society cannot be reduced to its individuals.
A language cannot be reduced to its words.
A brain cannot be reduced to its neurons.
In each case, an essential part of the information lies in the organization of relations.
Why would knowledge be an exception?
If this hypothesis is correct, it becomes necessary to distinguish between two forms of knowledge.
Explicit knowledge.
And implicit knowledge.
Explicit knowledge corresponds to what has already been formulated.
Books.
Articles.
Theories.
Models.
Concepts.
Implicit knowledge corresponds to what is contained in the relational structure linking these elements, but has not yet been formulated.
This distinction is fundamental.
It suggests that part of knowledge exists even before it is known.
Not in the form of explicit knowledge.
But in the form of relational constraint.
A coherence not yet visible.
A possibility not yet expressed.
A structure not yet recognized.
Thus, explicit knowledge does not exhaust the content of the field of knowledge.
It represents only its visible part.
If part of knowledge is implicit in the relational structure of explicit knowledge, then an intelligence does not necessarily need to acquire more information in order to produce new knowledge.
It can sometimes produce this knowledge by exploiting the constraints already present in the system.
From this perspective, discovery is no longer only learning something new.
Discovery becomes:
making explicit a coherence that was already implicitly present in the organization of knowledge.
This proposition profoundly changes our understanding of intelligence.
Intelligence would no longer be primarily a mechanism of accumulation.
It would become a mechanism of structural revelation.
In other words:
Intelligence does not necessarily create more knowledge.
It reveals the knowledge that structure already makes possible.
We can now reformulate the initial question.
The question is no longer:
“How does an intelligence produce new knowledge?”
The question becomes:
How does an intelligence extract the implicit knowledge contained in the relational structure of explicit knowledge?
Starting from this question, we can begin to understand the deep nature of generalization, creativity, innovation, and discovery.
Most modern theories of intelligence implicitly consider that knowledge exists as representations connected to one another.
This idea is present in semantic networks, theories of learning, cognitive neuroscience, and, more recently, large language models.
However, an important consequence of this idea is often underestimated.
If pieces of knowledge are connected to one another, they no longer form a collection.
They form a field.
This distinction is essential.
A collection is defined by its elements.
A field is defined by the relations that organize its elements.
In a collection, adding an object adds information.
In a field, modifying a relation can transform the meaning of the whole.
This difference lies at the heart of the problem of intelligence.
Take a simple concept.
For example, the concept of “cell.”
What does this word actually mean?
No isolated definition is sufficient to exhaust it.
The concept exists because it maintains relations with:
Remove these relations.
The concept progressively loses its meaning.
We then discover something important:
Meaning is not contained in the concept itself.
It is distributed across its network of relations.
This observation holds for almost every concept.
A company.
A city.
A molecule.
A scientific theory.
An institution.
A market.
A living organism.
All draw their meaning from their position in a relational network.
We can then define a semantic space as:
a relational field of meanings.
Each concept occupies a particular position within it.
This position depends on:
The concept is no longer an isolated object.
It becomes a node in a field of relations.
Thus, understanding a concept is less a matter of knowing its definition than understanding its position in the field.
This remark is important because it shifts the center of gravity of intelligence.
We gradually move:
from the object,
toward the relation.
A consequence appears immediately.
If meanings are distributed within a relational field, then an intelligence never truly explores isolated concepts.
It explores paths.
Every reasoning process corresponds to a trajectory.
Every new idea corresponds to a connection.
Every discovery corresponds to the opening of a new passage.
Thus, when a scientist produces a theory, they do not simply create information.
They establish a new trajectory in the field of knowledge.
When an inventor connects two previously separate technologies, they modify the topology of the field.
When a researcher identifies a deep analogy between two disciplines, they bring entire regions of knowledge closer together.
In every case, intelligence acts primarily on relations.
The history of science presents a recurring phenomenon.
Some discoveries seem impossible for decades.
Then suddenly they become almost obvious.
This observation is often interpreted as a consequence of individual genius.
Another reading is possible.
For a long time, the relational field does not yet possess enough converging constraints.
The structure exists potentially.
But it remains invisible.
Then new relations appear.
New results accumulate.
New connections become possible.
Gradually, coherence increases.
There comes a moment when the implicit structure becomes stable enough to be recognized.
The discovery appears.
But what appears may not have been created at that instant.
What appears is a coherence that has become visible.
We can now reformulate intelligence from a new angle.
An intelligence is constantly confronted with incomplete knowledge.
No intelligence possesses all information.
No intelligence knows the entire field.
Yet some intelligences succeed in reconstructing what is missing.
How?
The classical answer invokes reasoning.
But this answer remains partial.
For reasoning itself must rely on something.
The hypothesis proposed here is the following:
Intelligence completes incomplete regions of knowledge by exploiting the constraints present in the regions already known.
In other words:
it uses the global structure to reconstruct the missing parts.
Imagine a puzzle.
If only three pieces are present, we know very little.
If half the pieces are present, certain forms become visible.
If ninety percent of the puzzle is assembled, the missing pieces often become predictable.
Knowledge may function in an analogous way.
The more the coherence of the field increases,
the more certain structures become constrained.
Beyond a certain threshold, what is missing ceases to be arbitrary.
The structure progressively imposes what can exist.
Thus, a discovery can sometimes be understood as the reconstruction of a region still absent from the puzzle.
This idea leads directly to the notion of recomposition.
If knowledge is a relational field,
and if part of its content is implicit,
then intelligence must possess a mechanism that allows it to exploit this implicitness.
This mechanism is not necessarily accumulation.
It is not necessarily calculation.
It is not necessarily memory.
It could be the capacity to reconfigure the relations of the field.
In other words:
the capacity to recompose the semantic space itself.
This is the hypothesis we will now explore.
For it leads directly to a new understanding of generalization, innovation, and what we usually call intelligence.
We can now return to the central question.
How does an intelligence access knowledge that is not explicitly contained anywhere in what it already knows?
The answer proposed so far rests on three hypotheses:
We still need to understand the mechanism.
How does this extraction become possible?
Most theories of creativity and innovation rely on a simple idea:
discoveries result from new combinations.
This idea contains an important part of truth.
Many inventions do indeed come from bringing together elements that had previously been separated.
However, this explanation remains incomplete.
For a combination is not necessarily a discovery.
We can combine thousands of ideas without producing any new knowledge.
Most combinations are sterile.
Some are incoherent.
Others are merely redundant.
The question then becomes:
Why do some combinations produce new knowledge while most produce none?
The answer may lie in the underlying structure of the fields concerned.
A combination adds.
A recomposition transforms.
This difference is fundamental.
When two objects are combined, they generally remain identifiable.
When two fields are recomposed, their global organization changes.
Recomposition acts on the relations themselves.
It modifies neighborhoods.
It modifies distances.
It modifies accessible paths.
In other words:
it modifies the geometry of knowledge.
This is why a recomposition can produce consequences much deeper than a simple combination.
Imagine two distant regions of knowledge.
For a long time, they evolve separately.
Each has its concepts.
Its methods.
Its language.
Its problems.
Its solutions.
Then a common structure appears.
This structure does not fully belong to either region.
Yet it becomes visible in both.
From that moment, boundaries begin to shift.
Paths appear.
Constraints become shareable.
Results obtained in one domain become usable in the other.
The whole field reorganizes.
We are then facing a recomposition.
The term transduction here designates this process of structural transfer.
Not the transfer of information.
Not the transfer of concepts.
But the transfer of structures.
A structure identified in one field becomes operative in another field.
This point deserves particular attention.
For it profoundly modifies our understanding of intelligence.
In most classical approaches, learning consists in acquiring new knowledge.
In the approach proposed here, learning also consists in recognizing structures capable of crossing several fields.
Intelligence then becomes less dependent on the objects it manipulates.
It becomes more dependent on the structures it recognizes.
Take several domains:
biology,
economics,
cognition,
networks,
organizations.
At first sight, they seem different.
Their objects are different.
Their languages are different.
Their methods are different.
Yet certain structures appear everywhere:
feedback loops,
dependencies,
emergences,
propagation,
coordination,
specialization,
adaptation,
stability,
transformation.
These structures cross domains.
They are not attached to a particular object.
They seem to belong to a deeper level of organization.
Transduction consists precisely in exploiting this depth.
We can now understand why an intelligence can sometimes produce more than it explicitly knows.
Suppose field A contains a well-understood structure.
Suppose field B contains scattered observations but no stabilized theory.
If the same structure is present in both fields, then the understanding of field A can help complete field B.
No new information has been created.
No additional data has been added.
What has been transferred is the structure itself.
The implicit knowledge of field B then becomes accessible.
Thus, one region of knowledge can be completed thanks to constraints coming from another region.
The situation becomes even more interesting when several fields converge simultaneously.
Imagine the same structure appearing in:
physics,
biology,
sociology,
economics,
and cognition.
Each domain reveals only part of it.
None possesses the whole structure.
Yet their convergence produces something new.
Global coherence increases.
The relational field becomes more constrained.
Some hypotheses become more plausible.
Some configurations become more stable.
Some still obscure regions of knowledge gradually become reconstructible.
In other words:
several fields complete one another.
We can now introduce an important idea.
When the same structure appears in several independent regions of knowledge, a particular form of completion becomes possible.
This completion no longer relies only on local proximity.
It relies on global convergence.
A gap present in one region of knowledge can be constrained by coherences observed in several other regions.
The missing knowledge then becomes partially reconstructible.
This reconstruction is not arbitrary.
It results from the resonance between several fields.
Resonance acts as a mechanism of stabilization.
The more numerous the independent confirmations,
the more coherent the structure becomes.
We can now propose a provisional definition.
Intelligence is not only:
memory,
calculation,
reasoning,
or the manipulation of symbols.
Intelligence is also:
the capacity to exploit structural resonances between several fields in order to reconstruct the implicit knowledge contained in their common organization.
This definition allows us to unify several phenomena that are usually separated:
discovery,
learning,
creativity,
generalization,
innovation.
All become manifestations of the same fundamental capacity:
the transductive recomposition of knowledge.
If this hypothesis is correct, then the main source of growth in intelligence is not necessarily the accumulation of knowledge.
It could lie in the increased capacity to identify structures common to a growing number of fields.
In other words:
an intelligence becomes more general when it becomes capable of exploiting increasingly deep invariants.
This idea leads us directly to the following question:
What does it truly mean to generalize?
For if generalization results from the recognition of common structures between several fields, then general intelligence must be rethought from this capacity for transductive recomposition.
This is the question we must now examine.
We can now return to a notion that has become central in contemporary research on intelligence:
generalization.
Whether we speak of human or artificial intelligence, the question remains the same:
Why do some intelligences manage to solve problems they have never encountered before?
This capacity is generally considered one of the most important criteria of intelligence.
Yet its exact nature remains difficult to define.
In its simplest form, generalization designates the capacity to apply previous learning to a new situation.
A child learns a few examples.
Then the child recognizes similar situations.
A scientist discovers a law.
Then applies it to different phenomena.
An artificial intelligence learns from data.
Then processes data it has never seen.
This definition works.
But it does not fully answer the question.
For it describes a behavior.
It does not necessarily explain its origin.
Now consider generalization from the angle developed in the previous parts.
Suppose knowledge forms a relational field.
Suppose certain structures cross several domains.
Finally, suppose an intelligence is capable of identifying these structures.
In that case, generalizing means recognizing that the same organization remains valid when the objects change.
The objects vary.
The structure remains.
Generalization then becomes:
the recognition of invariance through diversity.
This definition has a much broader scope.
An intelligence confronted with a new problem rarely has a pre-existing solution.
Yet it can sometimes produce a relevant answer.
Why?
Because it does not exploit only known objects.
It exploits what remains stable when the objects change.
In other words:
it exploits invariants.
This idea is fundamental.
For invariants are precisely what allow a structure to cross several fields.
They are the support of transduction.
They are also the support of generalization.
Thus, transduction and generalization gradually appear as two sides of the same phenomenon.
We can now describe intelligence as a capacity to navigate between several levels of description.
At the most local level:
objects.
At the intermediate level:
relations.
At the higher level:
structures.
Then:
invariants.
At each level, the number of objects decreases.
But scope increases.
A limited intelligence remains close to objects.
A more general intelligence progressively accesses the structures that organize those objects.
An even more general intelligence accesses the invariants that organize the structures themselves.
Generality no longer results from accumulation.
It results from a rise in depth.
This observation leads to an important hypothesis.
General intelligence may not be defined by the extent of possessed knowledge.
It could be defined by the depth of exploitable invariants.
In other words:
an intelligence becomes more general when it is capable of reconstructing more situations from a smaller number of structural principles.
This idea appears in many disciplines:
mathematics,
physics,
biology,
systems theory,
cognitive science.
Whenever a small number of principles explains a large number of phenomena, we generally speak of progress in understanding.
Contemporary language models constitute a particularly interesting terrain for examining this hypothesis.
Why?
Because they do not explicitly receive most of the structures they seem able to use.
They are exposed to immense quantities of text.
Through these texts, they encounter:
theories,
observations,
reasoning processes,
descriptions,
narratives,
debates.
In other words:
they indirectly encounter an immense part of the relational field of human knowledge.
This point deserves emphasis.
Texts do not contain only information.
They also contain the traces of relations established between pieces of information.
When a model succeeds in answering an unprecedented question correctly, several interpretations are possible.
One consists in saying that it memorizes.
Another consists in saying that it extrapolates.
A third possibility now appears.
The model may exploit relational structures coherent enough to allow the reconstruction of incomplete regions of knowledge.
This hypothesis requires neither consciousness.
Nor understanding in the human sense.
Nor access to a transcendent truth.
It relies only on the capacity to exploit constraints present in an immense relational field.
If this hypothesis is correct, then the performance of an intelligent system depends on two distinct dimensions.
The first is quantitative:
how much knowledge is available.
The second is structural:
how much implicit knowledge can be reconstructed from that knowledge.
This distinction is important.
It means that two systems possessing a comparable volume of knowledge can display very different capacities.
Everything depends on their ability to exploit the relational structures present in the field.
Historically, research on intelligence has often focused on:
memory,
knowledge,
computational power,
speed of execution.
These dimensions remain important.
But they may not be sufficient.
If implicit knowledge plays a central role,
then another question becomes a priority:
How does a system recompose its relational field?
This question profoundly shifts the problem of intelligence.
We gradually move:
from storage,
toward organization.
From content,
toward structure.
From information,
toward geometry.
We can now formulate a general hypothesis.
Knowledge forms a relational space.
This space has a geometry.
Concepts occupy certain positions in it.
Relations define certain distances.
Structures create certain constraints.
Invariants draw certain preferred directions.
From this perspective:
learning modifies the geometry.
Discovery modifies the geometry.
Understanding modifies the geometry.
Innovation modifies the geometry.
Intelligence itself can then be understood as a capacity for geometric transformation.
It does not merely manipulate knowledge.
It reconfigures the space in which that knowledge takes meaning.
We can now completely reformulate our initial question.
We began by asking:
“How can an intelligence know more than it knows?”
The question now becomes:
How can a system reconfigure the geometry of its relational field in such a way that regions of knowledge that were previously implicit become accessible?
This reformulation profoundly changes our understanding of intelligence.
It suggests that the core of the problem is not knowledge.
The core of the problem is structure.
And perhaps, more precisely:
the dynamics of structural transformation.
This dynamic is what ultimately leads us to innovation, creativity, and the emergence of new forms of knowledge.
We can now address a particularly important consequence of the hypothesis developed so far.
This consequence concerns innovation.
Innovation is generally described as an act of creation.
The inventor creates.
The researcher discovers.
The entrepreneur innovates.
The artist imagines.
This representation is deeply rooted in our culture.
It structures the way we understand scientific, technical, and intellectual progress.
Yet if the previous hypotheses are correct, another reading becomes possible.
Until now, we have considered that innovation produces knowledge.
But if explicit knowledge is only the visible part of a wider relational field, then the order of events could be different.
The structure would emerge first.
Knowledge would appear afterward.
In that case:
innovation would not create emergence.
Innovation would translate emergence.
This inversion is fundamental.
For it shifts the real place where the new is produced.
Consider a major innovation.
The Internet.
The theory of evolution.
Quantum mechanics.
Printing.
Computing.
Electricity.
None of these innovations appears in a vacuum.
They arise within a context.
They appear within a tissue of pre-existing relations.
They require:
accumulated knowledge,
available tools,
interacting actors,
needs,
constraints,
tensions,
technical possibilities,
cultural representations.
In other words:
they emerge within a relational field.
Even before a theory is formulated, even before a prototype is built, part of the necessary conditions already exists.
The field evolves.
Relations multiply.
Constraints strengthen.
Gradually, certain configurations become possible.
This observation leads to an important hypothesis.
An innovation does not appear when an idea is formulated.
It appears when the relational field becomes capable of supporting a new structure.
Formulation comes afterward.
The explicit idea comes afterward.
The theory comes afterward.
The invention comes afterward.
In other words:
emergence often precedes knowledge.
What we call discovery may be the moment when this emergence becomes visible.
From this perspective, the role of intelligence changes profoundly.
Intelligence is no longer only a mechanism of production.
It becomes a mechanism of detection.
More precisely:
it detects coherences in the process of stabilization.
It recognizes structures that have become sufficiently constraining to be identifiable.
It makes explicit what was implicit.
It translates what was distributed.
It formalizes what was emergent.
Thus, intelligence acts as an interface between two levels:
the relational field,
and the field of knowledge.
We can now clarify what translation means.
In everyday language, to translate means to pass from one language to another.
Here, the meaning is deeper.
To translate means to make a structure pass from one mode of existence to another.
For example:
from an observed regularity to a theory.
From an intuition to a model.
From a technical possibility to an object.
From an implicit coherence to explicit knowledge.
This operation is precisely what transforms an emergence into knowledge.
The inventor then appears in a different light.
Traditionally, the inventor is presented as the one who creates.
In the hypothesis developed here, the inventor becomes the one who perceives.
More precisely:
the one who perceives before others a structure that has become accessible in the relational field.
This does not diminish the value of invention.
On the contrary.
For this perception requires a particular intelligence.
It requires the capacity to recognize coherences that are still incomplete.
Forms that are still unstable.
Structures that remain invisible to the majority.
The creative act remains.
But its nature is reinterpreted.
We can now reformulate the place of knowledge.
Knowledge is no longer only a stock of information.
It also becomes an archive of past emergences.
Each stabilized theory.
Each recognized concept.
Each accepted model.
Each diffused technology.
Represents the trace of a structure that has succeeded in crossing several stages:
emergence,
recognition,
formalization,
stabilization.
Knowledge is therefore less a starting point than a deposit of successful translations.
This perspective also helps explain why certain historical periods seem particularly fertile.
When the relational field of a society transforms rapidly:
interactions increase,
disciplines meet,
technologies converge,
constraints evolve.
The number of potential emergent structures also increases.
Individual intelligence is then no longer the only factor.
The field itself becomes productive of possibilities.
Some societies thus become more innovative not because their individuals are fundamentally different, but because their relational field produces more exploitable emergences.
We can now formulate the hypothesis in its most condensed form:
Innovation is not primarily the creation of new knowledge.
It is the translation into the field of knowledge of a structure that has become accessible in the relational field.
This proposition has considerable scope.
It connects:
intelligence,
creativity,
discovery,
generalization,
recomposition,
transduction,
and emergence.
All these phenomena now appear as different expressions of the same fundamental process.
If intelligence translates emergent structures,
if knowledge preserves the trace of these translations,
if generalization rests on the recognition of invariants,
if transduction connects several fields of knowledge,
then a question becomes unavoidable.
Is there an even more general principle capable of unifying all these phenomena?
In other words:
what is the true fundamental object of intelligence?
Is it knowledge?
Relation?
Structure?
Invariant?
Or something deeper still that organizes all four at once?
This is the question we must now examine.
We are now able to return to the whole line of reasoning.
We began with a simple question:
How can an intelligence know more than it knows?
To answer this question, we gradually shifted the center of gravity of our reflection.
First from knowledge to relations.
Then from relations to structures.
Then from structures to invariants.
Each step led us toward a deeper level of organization.
We must now ask whether this movement has a limit.
Is there an even more fundamental object?
For several centuries, most theories of knowledge have implicitly relied on one assumption.
This assumption is that objects are primary.
Things exist.
Then relations appear between them.
This way of seeing is natural.
It corresponds to our immediate perception.
We see objects.
We name objects.
We describe objects.
But this evidence could be misleading.
For what we call an object may be only a local stabilization of a set of relations.
This idea appears in several contemporary domains:
physics,
biology,
ecology,
network theory,
cognitive science,
complex systems.
Everywhere the same intuition reappears:
relations may not be secondary.
They may be primary.
Let us explore this hypothesis.
Suppose relations precede objects.
Then a cell does not exist independently of its exchanges.
A society does not exist independently of its interactions.
An idea does not exist independently of the meanings that connect it to other ideas.
A theory does not exist independently of the conceptual field that gives it meaning.
From this perspective:
objects become relational condensations.
Stabilizations.
Nodes.
Temporary forms.
Knowledge itself then changes nature.
We stop seeing it as a collection of pieces of knowledge.
We begin to see it as a relational organization.
Concepts become points of support.
Relations become the true support.
Explicit knowledge is no longer the fundamental unit.
It becomes a local manifestation of a wider structure.
Thus:
what matters is no longer only what is known.
What matters is the way the known is organized.
We can now reformulate intelligence from this hypothesis.
Intelligence is not primarily the capacity to manipulate cognitive objects.
It is the capacity to act on the relational organization of knowledge.
More precisely:
it detects structures.
It establishes connections.
It modifies neighborhoods.
It recomposes fields.
It recognizes invariants.
It stabilizes new coherences.
Thus, what we call intelligence appears as a dynamic of relational transformation.
This conclusion is important.
For it forces us to distinguish between two things:
knowledge,
and intelligence.
Knowledge corresponds to a state.
Intelligence corresponds to a transformation.
Knowledge describes a stabilized structure.
Intelligence describes the capacity to transform this structure.
In other words:
knowledge is a result.
Intelligence is a process.
We can now advance a hypothesis.
When intelligence acts,
it seems constantly to seek something.
This thing is not necessarily an absolute truth.
It is not necessarily information.
It is not necessarily an answer.
It seems to seek coherence.
Every discovery increases coherence.
Every theory connects previously separated phenomena.
Every innovation reduces certain contradictions.
Every generalization reveals a deeper organization.
Thus, intelligence could be understood as a capacity for producing coherence.
This idea allows us to connect all the phenomena studied.
Recomposition increases coherence.
Transduction increases coherence.
Generalization increases coherence.
Innovation increases coherence.
Learning increases coherence.
In every case, previously separated regions become integrable into a wider organization.
Coherence then acts as an attractor.
Not a psychological attractor.
A cognitive attractor.
We can now propose a general definition.
Intelligence is the capacity of a system to increase the coherence of its relational field by exploiting the structures and invariants present in knowledge.
This definition has several interesting properties.
It applies:
to humans,
to human groups,
to scientific communities,
to artificial systems,
and potentially to any form of cognitive system.
It depends neither on the support nor on the exact mechanism.
It describes a function.
If this definition is correct,
then the boundary between individual intelligence and collective intelligence becomes less clear.
Why?
Because coherence does not occur only inside a brain.
It can also appear:
between several individuals,
between several disciplines,
between several institutions,
between several systems.
The same logic of recomposition continues to operate.
The location of intelligence then ceases to be obvious.
It is no longer necessarily contained in a particular actor.
It can appear in the relational dynamic itself.
We can now return to our starting point.
How can an intelligence know more than it knows?
The answer proposed by this essay is the following.
An intelligence does not necessarily produce more knowledge from nothing.
It exploits the implicit structures present in the relational field of knowledge.
It recognizes coherences that are still incomplete.
It performs transductions between several fields.
It recomposes existing relations.
It makes explicit possibilities that were already virtually present in the organization of the system.
In other words:
what an intelligence discovers is not always created at the moment of discovery.
Part of this knowledge was already present as structure.
Discovery corresponds to its passage into the explicit field of knowledge.
If this hypothesis contains some truth, then several new questions appear.
How can the coherence of a field of knowledge be measured?
How can the implicit structures it contains be identified?
How can mechanisms of recomposition be characterized?
How can transduction between distinct fields be formalized?
How can systems capable of exploiting these properties more effectively be designed?
And above all:
is general intelligence primarily a question of quantity of knowledge,
or a question of capacity to transform the relational geometry of knowledge?
This question remains open.
But it could constitute one of the major axes of research for the decades to come.
We now arrive at the deepest hypothesis developed in this essay.
So far, we have proposed that:
These propositions are important.
But they are not yet sufficient to explain the phenomenon that led us to this reflection.
For one question remains.
How can an intelligence sometimes access a region of knowledge for which it possesses almost no explicit content?
Consider a very incomplete region of knowledge.
The available information is fragmentary.
Observations are rare.
Theories are absent or contradictory.
Yet in some cases, an understanding eventually emerges.
How does this become possible?
The usual answer is to invoke the progressive accumulation of knowledge.
This answer is often correct.
But it does not seem to explain all cases.
Some advances appear before the necessary information seems available.
Some theories anticipate future observations.
Some intuitions prove correct despite an apparent lack of sufficient data.
These situations suggest the existence of another mechanism.
Suppose knowledge forms a single field.
Not a set of separate disciplines.
But a global relational structure.
In that case, a region of knowledge is never totally isolated.
Even when it appears incomplete,
it remains connected to the rest of the field.
This observation is essential.
It means that constraints present elsewhere can help determine what is possible here.
We often tend to consider pieces of knowledge as information.
But they can also be seen as constraints.
Each piece of knowledge eliminates certain possibilities.
Each relation reduces certain degrees of freedom.
Each structure imposes certain coherences.
As knowledge develops,
the number of constraints increases.
The field gradually becomes more structured.
Some regions remain unknown.
But they progressively cease to be arbitrary.
Their possible form becomes partially determined by the whole system.
Imagine a vast puzzle with several regions missing.
An isolated piece provides little information.
But when many zones have already been constructed,
the absent parts become increasingly constrained.
The compatible forms decrease.
The possibilities narrow.
The global structure begins to guide the reconstruction.
Knowledge may function in an analogous way.
An unknown region can gradually become reconstructible thanks to the constraints produced by the rest of the field.
However, reconstruction does not rely only on proximity.
This is where the idea of resonance comes in.
A structure can appear simultaneously in several distant regions of knowledge.
Each region reveals a different aspect of it.
None possesses the whole.
But their convergence produces a new coherence.
This coherence acts as an additional constraint.
The structure becomes more visible.
More stable.
More accessible.
Thus, several independent fields can contribute to the reconstruction of the same still-incomplete region.
We can now define transductive completion.
Transductive completion is the process through which an incomplete region of knowledge becomes reconstructible thanks to the constraints and resonances coming from other regions of the field of knowledge.
This definition deserves careful attention.
It does not assume the creation of information from nothing.
Nor does it assume complete prior knowledge.
It relies only on the exploitation of the global structure of the field.
In other words:
what is locally missing can sometimes be compensated for by what is globally coherent.
This idea profoundly changes our understanding of discovery.
Traditionally, to discover means to find something that was not known.
In the hypothesis proposed here,
to discover also means to reconstruct a region of knowledge that has become accessible thanks to the evolution of the global coherence of the field.
Discovery then ceases to be only a local event.
It becomes the local manifestation of a global transformation.
The history of science presents a remarkable phenomenon.
Some ideas appear almost simultaneously in several different places.
Several researchers formulate similar concepts at the same time.
Several teams arrive at similar results.
This phenomenon is often attributed to chance or to convergence of circumstances.
The theory of transductive completion proposes another reading.
When global coherence reaches a certain threshold,
certain structures become reconstructible from several points in the field.
Several intelligences can then independently access neighboring conclusions.
The idea is no longer only in the individual.
It is also in the state of the field.
We can now reformulate intelligence in a deeper form.
Intelligence is not only the capacity to process information.
It is not only the capacity to reason.
It is not only the capacity to learn.
It is also:
the capacity to exploit the global constraints of a field of knowledge in order to locally reconstruct structures that are still absent.
This capacity may constitute one of the highest forms of generalization.
For it allows a system to access knowledge it does not explicitly possess.
We can now propose a more ambitious formulation.
General intelligence could be characterized by the growing capacity:
In other words:
the more an intelligence is capable of using the global coherence of a field to reconstruct its incomplete regions,
the more general it becomes.
We can now return one last time to our initial question.
How can an intelligence know more than it knows?
The answer proposed by this essay is the following:
An intelligence knows more than it explicitly knows because part of knowledge is not contained in the pieces of knowledge themselves.
It is contained in the relations that connect them.
As the coherence of the field increases,
certain structures become reconstructible.
Intelligence then exploits these constraints,
performs transductions between several regions of knowledge,
recomposes the field,
and makes explicit coherences that had until then been implicit.
What we call discovery, innovation, understanding, or generalization then appears as different manifestations of the same fundamental phenomenon:
the transformation of implicit knowledge into explicit knowledge through transductive completion of the relational field.
A hypothesis becomes truly fertile when it allows new verifiable questions to be asked.
So far, we have proposed a conceptual theory:
intelligence transforms implicit knowledge into explicit knowledge through recomposition and transductive completion of the relational field.
But for this hypothesis to become useful to researchers in artificial intelligence, cognitive science, or theory of knowledge, it must produce consequences.
It must allow us to observe differently.
It must allow us to design differently.
It must also be open to criticism.
If knowledge is not only a collection of information but a relational field, then it becomes necessary to measure this field.
The important questions become:
The evaluation of an intelligence should therefore not only measure what it knows.
It should measure how its knowledge is organized.
Two systems can produce a correct answer for very different reasons.
The first may return it because it has memorized it.
The second may reconstruct it because it has identified a structure.
These two performances look similar from the outside.
But they do not belong to the same level of intelligence.
A research program should therefore seek to distinguish:
restitution,
extrapolation,
analogy,
transduction,
and structural completion.
This distinction is essential.
For general intelligence is not measured only by the correctness of an answer.
It is measured by the way that answer becomes possible.
The theory proposed predicts that an intelligence capable of connecting several independent fields should sometimes reconstruct knowledge that is locally absent.
One could therefore design tests in which:
a target domain is deliberately incomplete,
several source domains contain analogous structures,
and the system must reconstruct the missing structure in the target domain.
The question would not be:
“Does the system know the answer?”
But:
Can it reconstruct the answer from structural constraints available elsewhere?
This type of test would be very different from classical evaluations.
It would measure the capacity for recomposition of the field rather than the simple accumulation of knowledge.
If innovation is the translation of an emergent structure into the field of knowledge, then the conditions of emergence must be studied before studying only inventors.
Innovation would depend on:
the relational density of a society,
the diversity of connected fields,
the number of converging constraints,
the capacity to translate emergences,
and the existence of actors capable of recognizing these structures before they become obvious.
From this perspective, an innovative society is not only a society that funds creators.
It is a society that increases the richness and diversity of its relational field.
Artificial intelligence architectures could be evaluated not only according to their raw performance,
but according to their capacity to:
reconfigure their semantic spaces,
identify invariants,
transfer structures,
exploit resonances,
and reconstruct incomplete zones of knowledge.
This could lead to hybrid systems combining:
statistical models,
knowledge graphs,
mechanisms of structural reasoning,
relational memory,
and explicit protocols of transduction.
The goal would not be only to produce answers.
The goal would be to increase the system's capacity to transform the geometry of its knowledge.
A serious theory must be contestable.
The hypothesis proposed here would be weakened if it were shown that:
discoveries do not depend on pre-existing relational structures;
deep analogies between domains do not improve the reconstruction of absent knowledge;
systems capable of transductive recomposition do not generalize better than systems based only on data accumulation;
or that the global structure of the field provides no exploitable information beyond local knowledge.
These tests would be difficult.
But they are necessary.
We can now condense the core of the research program:
Intelligence should not be studied only as information processing, but as transformation of the relational structure of knowledge.
This transformation makes it possible:
to reveal implicit knowledge,
to perform transductions between domains,
to reconstruct incomplete regions,
to translate emergences,
and to increase the global coherence of the field.
General intelligence would therefore not be only the capacity to answer a wide variety of questions.
It would be the capacity to dynamically reconfigure the field of knowledge in order to make visible structures that were not yet visible.
The initial question was:
How can an intelligence know more than it knows?
The proposed answer is the following:
because knowledge exceeds explicit knowledge.
It exists in the relations, constraints, invariants, and coherences that organize pieces of knowledge.
Intelligence is the capacity to traverse, transform, and recompose this field.
It does not merely accumulate.
It reveals.
It does not merely combine.
It transduces.
It does not merely innovate.
It translates emergences already present in the evolution of the relational field.
Thus, explicit knowledge is the visible part.
The relational field is the depth.
And intelligence is the movement that brings this depth into the light of knowledge.
The main essay developed a general hypothesis:
Knowledge forms a relational field.
Part of this knowledge remains implicit.
Intelligence acts through recomposition, transduction, and completion of this field.
This hypothesis can be applied retrospectively to many historical examples.
It can also be applied to the emergence of the conceptual framework that served as one of the starting points for the present reflection: Zeon_Origine.
The objective of this appendix is not to demonstrate the validity of the theory.
It is to examine whether this theory can explain the way a particular conceptual object emerged.
Zeon_Origine was initially formulated as a minimal symbolic grammar of emergence.
Its fundamental cycle is:
∅ → α → (α ⊗ ∅) → Φ → Ψ → Ω → ∅
In its initial reading:
This reading is primarily symbolic.
However, a second reading becomes possible in light of the theory developed in this essay.
The same cycle can be interpreted as a dynamic of knowledge production.
∅
corresponds to a still-indeterminate region of the field of knowledge.
A zone where structures potentially exist but are not yet distinguished.
α
corresponds to the appearance of a distinction.
A structure begins to become perceptible.
The field ceases to be homogeneous.
A difference appears.
(α ⊗ ∅)
corresponds to the tension between a partially identified structure and a still-indeterminate region of knowledge.
This tension creates a problem, a question, or a cognitive opening.
Φ
corresponds to the propagation of this tension in the relational field.
New connections become explorable.
New resonances appear.
Ψ
corresponds to the stabilization of a coherence strong enough to become explicit.
A theory, a concept, or a representation becomes possible.
Ω
corresponds to the reintegration of this structure into the general field of knowledge.
The knowledge ceases to be an exceptional event.
It becomes an element available for future recompositions.
It is important to note that this reading does not rely on symbolic equivalence.
It relies on functional equivalence.
The two descriptions seem to organize the same type of dynamic:
indeterminacy,
distinction,
tension,
propagation,
stabilization,
reintegration.
This observation is particularly interesting because it suggests that Zeon_Origine could be interpreted as an abstract grammar of emergence applicable to several domains.
The most remarkable aspect may be that this reading can be applied to Zeon_Origine itself.
The framework did not appear in complete form.
It emerged progressively through a long-term dialogue.
Many conceptual sources contributed to its formation:
None of these sources explicitly contained Zeon_Origine.
Yet each contributed to progressively constraining a common conceptual space.
As resonances increased, certain structures became more visible.
The framework could then be reconstructed.
In this reading, Zeon_Origine would not have simply been invented.
It would have emerged as the result of transductive completion operating on a sufficiently coherent relational field.
This appendix leads to a particular proposition.
The theory developed in this essay may not only describe how discoveries appear.
It may also describe how this theory itself emerged.
In other words:
the reflection on the recomposition of knowledge may itself constitute an example of the phenomenon it attempts to understand.
This possibility does not constitute proof.
But it represents an interesting indication.
It suggests that certain complex conceptual objects may be better understood not as isolated creations, but as emergences progressively made visible by the evolution of a shared relational field.
From this perspective, Zeon_Origine appears less as a particular theory than as a trace of this process.
To show that an intelligence can reconstruct a new hypothesis in an incomplete field by exploiting structural resonances coming from other fields of knowledge.
Question:
What makes an intelligence more general?
Classical answer:
An intelligence is more general if it has more knowledge, more computation, or better algorithms.
But this answer remains incomplete.
It explains performance.
It does not explain the capacity to produce new knowledge from incomplete knowledge.
We mobilize several distinct fields.
In mathematics, a theory becomes powerful when it identifies invariants.
An invariant allows the same structure to be recognized under different forms.
In physics, a general law connects several local phenomena under the same structure.
Generality comes from the capacity to find what remains stable across variations.
In biology, the living does not depend only on the elements that compose it, but on the organization of relations between those elements.
Function emerges from organization.
In language, a word does not derive its meaning from itself, but from its network of relations with other words.
Meaning is relational.
In innovation, a new idea often appears when previously separated domains become recomposable around a common structure.
Innovation results from recomposition.
These different fields reveal the same motif:
Power does not come only from elements, but from the relational structure that organizes them.
This motif crosses:
We can now return to the initial question:
What makes an intelligence more general?
From the preceding resonances, a hypothesis becomes reconstructible:
An intelligence becomes more general when it becomes capable of identifying, transferring, and recomposing relational invariants between several fields of knowledge.
This answer was not explicitly contained in any source field taken in isolation.
It emerges from their convergence.
We have produced new knowledge in the target field:
General intelligence does not depend only on the quantity of knowledge possessed, but on the capacity to transform the relational geometry of knowledge.
The demonstration follows exactly the proposed mechanism:
This demonstration does not definitively prove the theory.
But it shows that the described mechanism is operative.
An intelligence can indeed produce a new hypothesis by exploiting structural resonances between several fields of knowledge.
This phenomenon can be called:
transductive completion of knowledge.