Constructor Theory: Reframing Everything as "What Transformations Are Possible?"

Physics usually asks: given this initial state and these laws, what happens?

The question presupposes trajectory thinking. You specify where you are, you specify the rules of motion, and you compute where you go. The universe is a machine that takes states to states according to fixed dynamics.

But there's another question you could ask: what transformations are possible?

Not "what will happen?" but "what can happen?" Not "what trajectory does the system follow?" but "what changes can the system undergo—and which changes are forbidden, no matter what?"

This reframing seems like a small shift. It's actually profound. Constructor theory, developed by David Deutsch and Chiara Marletto, rebuilds physics from this alternative foundation—and in doing so, opens doors that traditional physics leaves closed.

For understanding meaning, constructor theory offers something traditional physics doesn't: a framework where information, knowledge, and possibility are primary rather than secondary. Where what matters isn't just what happens but what can and can't happen. Where the structure of transformations—not the trajectory of states—is the fundamental reality.

The Basic Reframing

Traditional physics describes how states evolve. You write down equations of motion. You solve them given initial conditions. You predict where the system will be at future times.

Constructor theory describes what transformations are possible or impossible.

A transformation is a change from one state to another. "Turn water into steam." "Convert information from this encoding to that encoding." "Move the system from configuration A to configuration B."

The central question is: which transformations are possible—achievable by some physical process—and which are impossible—forbidden by fundamental law?

A constructor is something that can perform a transformation and remain unchanged, able to perform the same transformation again. A catalyst in chemistry is a constructor: it enables a reaction without being consumed. A computer is a constructor: it performs computations while remaining a computer. A living cell is a constructor: it transforms nutrients into structure while remaining a cell.

Constructors are the machines of possibility. They're what makes transformations happen.

The laws of physics, in this framing, are not primarily about trajectories. They're about which transformations are possible (some constructor could perform them) and which are impossible (no constructor could perform them, as a matter of principle).

This might seem like just a change of vocabulary. It's not. The reframing reveals structure that trajectory-thinking obscures.

Possibility as Fundamental

In traditional physics, what's fundamental is what exists and how it moves. Possibility is derivative—defined by what the equations allow.

In constructor theory, possibility is fundamental. What exists is what can be constructed. Motion is how constructors perform transformations. The laws of nature are fundamentally about what's possible and impossible, and everything else follows.

This matters because possibility has different structure than actuality.

Actual trajectories are specific. The ball took this path, not that one. The system evolved this way, not that way. Actuality is narrow.

Possible transformations are general. The transformation "turn water into steam" can be performed in many ways—by heating, by reducing pressure, by various specific processes. The transformation is more abstract than any particular way of achieving it.

Impossibilities are universal. If a transformation is impossible, it's impossible for all constructors, by all methods, forever. The impossibility is exceptionless.

Constructor theory says: understand what's possible and impossible, and you've understood what fundamentally matters. The specific trajectories are details; the space of possibility is the architecture.

For meaning, this is crucial. Meaning isn't about the specific trajectory a life takes. It's about what transformations are possible for that life—what changes can be achieved, what states can be reached. The possibility space, not the actual path, is what defines the meaningful terrain.

Substrate Independence

Constructors can be made of different stuff.

A computation can be performed by silicon or carbon or light or quantum states. The computation is the same; the substrate differs. A transformation like "compute this function" can be achieved by many different constructors built from many different materials.

This is substrate independence: the transformation is more fundamental than any particular way of achieving it.

Substrate independence has a radical implication. Information becomes as fundamental as matter and energy.

In traditional physics, information is secondary. It's a description of states, not a thing in itself. Matter and energy are fundamental; information is how we talk about them.

In constructor theory, information is primary. A transformation that preserves information is different from one that destroys it. A constructor that copies information is doing something specific and important. The informational content is part of what defines the transformation, not an overlay on a more fundamental physical description.

For psychology, substrate independence is liberating. Mental states aren't reducible to neural states, but they're not mysteriously separate either. They're a level of description where certain transformations are possible—cognitive transformations, belief updates, meaning-changes—regardless of the specific neural substrate implementing them.

The functor from neural to psychological isn't an approximation or a convenience. It's the mathematical expression of substrate independence: the transformations that matter psychologically can be multiply realized neurally. The psychological level captures what's invariant across realizations.

Possible, Impossible, and Why It Matters

Constructor theory partitions transformations into three categories:

Possible: Some constructor exists (or could exist) that performs this transformation. Boiling water is possible. Computing a function is possible. Transmitting information is possible.

Impossible: No constructor could perform this transformation, as a matter of fundamental law. Building a perpetual motion machine is impossible. Transmitting information faster than light is impossible. Creating energy from nothing is impossible.

Currently impossible but potentially possible: We don't currently have a constructor for this transformation, but no fundamental law forbids it. Curing certain diseases was in this category before we had the technology. Interstellar travel might be in this category now.

The distinction between fundamental impossibility and mere current inability is profound. Traditional physics often muddles them—if we can't do something, it's hard to know whether that's because it's fundamentally impossible or because we haven't figured out how yet.

Constructor theory forces the question: is there a principle that forbids this transformation, or just a gap in our capabilities?

For meaning, this matters directly.

When someone says "I can't change"—is that claim about fundamental impossibility, or about current inability? The manifold of their beliefs, the geometry of their psychological state, the topology of their relational patterns—do these forbid change, or merely make it difficult?

Constructor theory says: ask what's truly impossible versus what merely lacks a constructor. Often, what seems impossible is just waiting for the right transformation method—the right therapy, the right relationship, the right intervention.

The pessimism of "I can't change" often confuses impossibility with difficulty. The optimism of "anything is possible" often confuses difficulty with possibility. Constructor thinking requires precision: what exactly is the transformation, and what would make it possible or impossible?

Information and Life

Constructor theory provides new ways of understanding information and life—both crucial for understanding meaning.

Information is defined by copyability. Something carries information if it can be copied—if there's a constructor that can take the thing and produce two things with the same informational content. This is a physical definition, not a semantic one. DNA carries information because it can be copied. Text carries information because it can be duplicated. A thought carries information if it can be communicated—copied from one mind to another.

This definition makes information concrete. It's not about meaning or reference or semantics (yet). It's about whether a transformation—copying—is possible. Information is what can be copied.

Life is defined by being a constructor that constructs copies of itself, including the knowledge of how to construct those copies. A living thing is a self-reproducing constructor—something that performs the transformation "produce more of me" while retaining the capacity to do so again.

This definition is powerful because it's substrate-independent. Life isn't defined by carbon chemistry or cellular structure. It's defined by a capacity: self-reproduction with variation, maintaining the knowledge required to continue. Silicon life, digital life, life-as-we-don't-know-it would all count as life if they have this capacity.

For meaning, the constructor-theoretic view of life is illuminating. A living thing isn't just a structure; it's an ongoing transformation. It's something that maintains itself by performing the task of self-maintenance. Life is coherence under constraint—literally: the constructor persists by continually constructing itself.

Meaning, in this light, is what life does at the cognitive level. It's the ongoing transformation by which a cognitive system maintains its coherence, reproduces its patterns, adapts to perturbation. Meaning is the task that minds perform.

Coherence as Task

Reframe coherence as a constructor-theoretic task.

The task: Maintain integrated structure across perturbation.

The inputs: A system facing environmental variation, internal dynamics, noise, challenge.

The outputs: The same system, still integrated, still functioning, still coherent.

The constructor: Whatever performs this task—whatever maintains coherence.

In biological terms, the constructor is the nervous system, the regulatory apparatus, the homeostatic machinery. It takes perturbation and maintains coherence.

In psychological terms, the constructor is the self—the organizing principle that integrates experience, updates beliefs, regulates emotion, maintains identity.

In relational terms, the constructor is the relationship—the dyadic system that repairs ruptures, synchronizes rhythms, maintains attunement.

At every scale, there's a constructor performing the coherence task. The task is the same; the constructor differs.

This reframing has implications.

Coherence isn't a state—it's a task. You're not coherent like you're tall. You're coherent like you're breathing. It's something you're doing, not something you are. The task must be continually performed, or coherence fails.

Constructors can fail. A constructor that can't perform its task anymore isn't a constructor for that task. If your self can no longer maintain coherence, the self-as-constructor has broken down. Trauma, among other things, is constructor failure.

Constructors can be repaired. A broken constructor can sometimes be fixed. Therapy, medication, intervention—these are attempts to repair the coherence constructor so it can perform its task again.

Constructors can be augmented. If your own constructor is insufficient, external constructors can help. A therapist is an external coherence constructor—someone who helps perform the coherence task that you can't perform alone. Relationships, communities, institutions can all serve as augmentation for individual coherence constructors.

Counterfactuals and Knowledge

Constructor theory has a distinctive account of knowledge.

In traditional physics, knowledge is mysterious. Physics describes what happens; knowledge is about what's true or useful. The connection isn't obvious.

In constructor theory, knowledge is defined counterfactually.

Knowledge is information that, once present in a constructor, enables transformations that would otherwise be impossible.

The knowledge of how to make fire enables the transformation "wood to heat"—a transformation impossible without that knowledge. The knowledge of penicillin enables the transformation "infection to health." The knowledge of how to love enables the transformation "stranger to intimate."

Knowledge is defined by what it makes possible. If having a piece of information enables transformations that were impossible without it, that information is knowledge.

This is a pragmatic definition—knowledge is what works—but also a physical one. Knowledge is a real pattern in the world, a real presence in constructors, that makes real differences to what transformations are possible.

For meaning, this is powerful.

Meaning-knowledge—understanding of meaning, frameworks for coherence—enables transformations.

Without a way of making sense, certain life transitions are impossible. With meaning, they become possible. The knowledge of how to interpret suffering enables the transformation from suffering to growth—a transformation impossible without that interpretive knowledge.

Therapy works by transmitting knowledge—not just information, but patterns that enable transformations. The therapist knows how to regulate; the client learns; the knowledge transfers; new transformations become possible.

Cultural wisdom is constructor knowledge at population scale. The culture knows things—how to grieve, how to celebrate, how to transition through life stages—and that knowledge enables transformations for individuals within the culture.

Constructor Theory for Psychology

What would psychology look like if it took constructor theory seriously?

States would matter less than transformations. The question isn't "what state is the person in?" but "what transformations are possible for this person?" What changes can they make? What states can they reach?

Impossibilities would be mapped. What transformations are genuinely impossible for this person, given fundamental constraints? What transformations seem impossible but aren't? What transformations are possible but difficult?

Constructors would be identified. What is performing the coherence task for this person? What maintains their identity, their regulation, their meaning? Is that constructor functional? Does it need repair?

Knowledge would be central. What does this person know how to do? What knowledge would enable transformations they can't currently make? What knowledge is missing, and how might it be acquired?

Substrate independence would be respected. The psychological level of description—beliefs, meanings, intentions—would be taken seriously as a level where transformations occur. Not reduced to neuroscience, but not floating free of it either.

This would be a shift from psychology as description of states to psychology as mapping of possibility. What can this person become? What prevents them? What would enable them?

Constructor Theory and AToM

Constructor theory provides a foundation for AToM's claims.

Coherence is a task. Not a property but a transformation that must be continually performed. Systems that perform it persist; systems that fail dissolve.

Meaning is what enables coherence. Meaning is constructor knowledge—patterns that enable the coherence transformation. To have meaning is to be equipped to maintain coherence.

The geometry describes possibility. The manifolds, curvature, topology we've discussed—these describe the possibility space. What states are reachable? What transitions are possible? The geometry is the map of transformations.

Trauma is constructor damage. Trauma breaks the thing that performs coherence. The transformation "maintain integration" becomes impossible or much harder. The constructor needs repair.

Entrainment is constructor coupling. When two constructors synchronize, they begin performing their tasks together. The coupled system can perform transformations that neither could perform alone.

Therapy is constructor repair. The therapeutic relationship is a coupled constructor system. The therapist provides intact constructors that help repair the client's damaged ones. The client's coherence task becomes possible again.

Culture is population-scale constructor. Cultural knowledge, cultural practice, cultural institution—these are constructors that perform coherence tasks at collective scale, enabling transformations impossible for individuals alone.

Constructor theory doesn't replace the geometric framework. It provides a different entry point—a different vocabulary for the same structure. The geometry describes shape; constructor theory describes function. Both are needed.

The New Question

We've been asking: what is the geometry of meaning?

Constructor theory suggests a companion question: what transformations does meaning enable?

Meaning isn't just structure. It's what the structure makes possible. The coherence geometry describes a possibility space. Having meaning is being able to navigate that space. Losing meaning is losing transformations—losing the ability to make changes, reach states, become what you might become.

The mathematics of meaning, complete, would include both: the geometry of state space and the constructor theory of what transformations that geometry allows. Shape and function. Structure and possibility.

We've focused on shape. The shape is real. But the shape exists for the function. The manifold exists so that coherence constructors can navigate it. The geometry exists so that meaning can be a task that systems perform.

Meaning is coherence under constraint. Coherence is a task. The task is performed by constructors. The constructors are possible or impossible depending on knowledge, damage, coupling.

The mathematics of meaning is the mathematics of what meaningful lives can do.