The habitability of constraints
Toward a relational persistence of the real
If physical laws can be thought of as a memory of the real, one question remains: where is that memory inscribed?
The usual image answers spontaneously: in space-time. Events would take place within a prior framework, like objects set down on a stage. The laws would then describe the way these objects evolve within that container.
But this image becomes insufficient as soon as one tries to think a more fundamental level. If space-time itself is emergent, it cannot be the primary support of the memory of the real. The perspective must then be reversed: space-time is no longer the originary container of relations; it becomes one of the stabilised effects of those relations.
What comes first would therefore not be a theatre, but a structure of dependencies. Not things located somewhere, but events linked by correlations, constraints and compatibilities.
In this perspective, law is no longer merely a rule applied to an already constituted world. It becomes the stabilised form of the relations that allow a world to hold together.
From object to relation
A physical object can be thought of as a local stability within a network of relations. It is not first of all a thing placed in a setting. It is a pattern that persists because certain correlations are maintained.
This shift is important. It makes it possible to move from a physics of trajectory to a physics of coherence.
In a physics of trajectory, one asks: where is the system, and how does it evolve in time?
In a relational physics, one asks instead: what correlations can exist between events, and what structures can persist without destructive contradiction?
Certain frameworks of quantum causality already make it possible to formulate this kind of question. Process matrices, for example, do not necessarily describe an evolution within an already fixed global temporal order. They describe the admissible relations between local operations.
Such a structure may be denoted W.
W must not be understood here as a psychological memory, nor as a hidden substance. It designates the formal inscription of the correlations permitted between events. It does not contain objects in a space. It contains conditions of compatibility.
If a law is a stabilised memory, W can be understood as one possible figure of that relational memory.
The guiding equation: K_rel(W) = 0
One may then introduce a conceptual equation:
K_rel(W) = 0
K_rel denotes an operator of global relational constraint. This equation does not claim to replace the equations of present-day physics. It is not yet a complete theory. It functions as a schema of formalisation.
Its role is to displace the question.
Instead of asking only how a state evolves in time, it asks which structures of correlation are admissible without presupposing a global time.
K_rel(W) = 0 therefore means: a relational structure W can be physically admissible if it satisfies a condition of coherent closure.
This closure must not be understood as a perfect immobility. A structure can contain local tensions, fluctuations and discrepancies without collapsing. What counts is not the absence of all perturbation, but the capacity to maintain a global coherence despite variations.
Coherence then becomes a relational viability.
A viable structure is not merely a non-contradictory structure. It is a structure capable of holding, of absorbing perturbations, of transmitting certain correlations and of serving as a support for other structures.
Physical law can be reread in this light: it is not only what forbids certain configurations. It is what makes possible the persistence of a relational regime.
Admissibility and relational cost
But K_rel does not suffice.
To say that a structure is admissible does not yet say why certain structures stabilise rather than others. Among the structures capable of holding, some are more robust, simpler, more transmissible or more fertile.
Two levels must therefore be distinguished.
K_rel defines what can hold.
C_rel indicates what tends to stabilise preferentially.
One may write, conceptually:
W* ∈ argmin C_rel(W), sous la contrainte K_rel(W) = 0
This formula means that the structures actually stabilised would not merely be those that are admissible. They would be those that minimise a certain relational cost.
This cost can be conceived in several ways.
A structure that is too complex, too arbitrary or too fragile will struggle to become a support. A structure that is too rigid will not allow new forms to emerge. A viable structure must therefore lie between two excesses: stable enough to transmit, open enough to transform.
A simple form may be proposed:
C_rel(W) = α · Compl(W) + β · [1 − Rob(W)] + γ · [1 − Féc(W)]
Compl(W) denotes the descriptive complexity of the structure.
Rob(W) denotes its robustness in the face of perturbations.
Féc(W) denotes its fecundity, that is, its capacity to serve as a support for other structures.
This formula remains programmatic. It does not yet claim to provide a definitive physical measure. It indicates only a direction: among admissible structures, the most fertile are those that manage to combine economy, robustness and openness.
The real would therefore not simply retain what does not contradict itself. It would preferentially stabilise what can become a durable support for other relations.
Deep constraints and historical constraints
This distinction makes it possible to pose the question of origin more precisely.
If laws are stabilised constraints, why these constraints rather than others?
Perhaps two types of constraint must be distinguished.
Some constraints seem unavoidable. They belong to the minimal conditions of any viable relational structure. Without them, no coherent closure would be possible.
Other constraints are historical. They could have been otherwise, but they became stabilised along a particular trajectory of the real. Once incorporated, they nevertheless become necessary for the subsequent strata.
A constraint can therefore be contingent in its origin and necessary in its effects.
It might not have been that one. But once stabilised, it becomes the ground on which other forms must build.
Origin is then no longer a single point. It becomes a stratification.
Some constraints belong to any possibility of a coherent world. Others result from a history of stabilisation. But all of them, once sedimented, take part in the present form of the real.
The world we inhabit would therefore be the result of a double condition: necessity of coherence and contingency of trajectory.
The emergence of time
If the fundamental network is not ordered by a global time, then the temporal arrow cannot be given in advance.
It must emerge.
Macroscopic time could appear when certain correlations become sufficiently asymmetric to function as traces. A trace is not merely a difference. It is an oriented difference: it carries the mark of a before that can no longer be entirely erased without modifying the present structure.
The arrow of time would then be an informational crystallisation.
As certain correlations stabilise, they become supports of memory. As these memories accumulate, they produce a macroscopic orientation.
Time does not necessarily precede the network. It appears when the network becomes capable of preserving asymmetric traces.
A selection parameter τ may be introduced here. This parameter does not necessarily represent a fundamental physical time. It may denote an order of stabilisation, of growth or of reconfiguration.
A stochastic expression could then take the form:
P(W) ∝ exp[−C_rel(W)] · Π[K_rel(W)]
or, in a dynamic version:
dP(W)/dτ ∝ exp[−C_rel(W)] · Π[K_rel(W)]
Π[K_rel(W)] here plays the role of a conceptual projector onto the admissible structures. Among them, the structures of lowest relational cost become more liable to stabilise.
This idea resonates with certain discrete approaches to quantum gravity or to multiway systems, in which a global structure can emerge from local rules without presupposing a classical space-time background.
In this framework, macroscopic time does not precede selection. It appears when certain stabilisations become asymmetric enough to form traces.
The habitability of constraints
It is here that the notion of habitability becomes central.
A habitable world is not merely a coherent world. It is a world situated within a critical window: ordered enough to preserve traces, unstable enough to allow new forms, robust enough to transmit constraints, open enough not to freeze all evolution.
If this window is extremely narrow, the appearance of life and cognition seems to demand an additional explanation: fine-tuning, cosmological selection, multiverse or self-consistent bootstrap.
But if the minimisation of C_rel naturally leads certain regimes toward critical zones, where robustness and innovability reinforce one another, then life and mind become less improbable.
They would not be miracles suspended above the real. They would be possible attractors of certain relational architectures: regions where stability does not block novelty, and where instability does not destroy memory.
Habitability therefore concerns not only the conditions necessary for biological life. It designates more broadly the capacity of a regime of constraints to bear forms which, in their turn, can bear other forms.
Several degrees of habitability may be distinguished.
A physical habitability, when constraints allow the emergence of stable structures.
A chemical habitability, when these structures allow persistent bonds, cycles and reactions.
A biological habitability, when certain organisations become capable of maintaining themselves, of reproducing and of transmitting a memory.
A cognitive habitability, when memory becomes capable of representing itself.
A symbolic habitability, finally, when living systems produce language, technique, science and institutions capable of collectively stabilising traces.
Life does not escape constraints. It inhabits them.
It uses physical stability as a support, then transforms that stability into biological memory, adaptation and transmission.
General scheme
This architecture may be summarised as follows:
Fundamental relational network
↓
Possible process structures W
↓
Filtering by admissibility: K_rel(W) = 0
↓
Preferential selection: minimisation of C_rel(W)
↓
Robust relational attractors
↓
Strata of habitability: physical, chemical, biological, cognitive, symbolic
↓
The observer as active memory
This scheme makes it possible to distinguish two operations clearly.
K_rel does not yet choose a particular world. It defines the space of structures capable of holding.
C_rel then intervenes as a principle of preferential stabilisation. Among the admissible structures, some become more robust, more compressible, more fertile and therefore better able to bear subsequent strata.
Conclusion
To formulate relational persistence is to displace the fundamental question.
The real is no longer thought of first as a set of objects within a given space-time. It becomes a stratification of relational constraints, in which certain structures persist because they satisfy a condition of coherence, and then stabilise because they realise a favourable relational economy.
K_rel defines the admissible.
C_rel indicates the preferential.
Habitability designates the regions where these two dimensions meet: regimes stable enough to bear memory, open enough to allow transformation.
The world does not hold together because everything is possible in it. It holds because certain impossibilities structure it.
It becomes habitable when these constraints do not close the real upon itself, but open zones where forms can emerge, endure, be transmitted and reflect upon themselves.
Life, cognition and observation are then not anomalies in an indifferent universe. They are local deepenings of this relational persistence: ways for certain constraints to become memory, and then for certain memories to become capable of reading the constraints from which they proceed.