Form, Pattern, and the Symbolic Grammar of the Cosmos
Mathematics is often spoken of in reverent tones—as the language of the universe, the code beneath all appearance, the purest path to truth. But when we take the relational turn, this picture begins to shift. Mathematics is no longer a mirror held up to a world that exists without us. It becomes something stranger, deeper, and more creative: a relational language, a system through which the cosmos symbolically expresses its own becoming.
Just as myth was never merely story but process, mathematics is not merely description but participation.
Mathematics as Symbolic System
Mathematics, like natural language, is a system of signs. It has a grammar: rules of combination, relations of precedence, operators of transformation. It has fields: geometry, algebra, analysis, topology—each enacting a different kind of symbolic logic. And it has a semiotic function: it means something. But unlike ordinary language, it aims not at denotation but formal relation—patterns that are invariant, repeatable, transferable.
What it offers is not a catalogue of things, but a system of relational potentials: structures that do not exist in themselves, but become actual when deployed by a meaner, a participant. That is, mathematical form is not found—it is construed.
This is why mathematics, despite its aura of timeless objectivity, is a practice. It is always an activity—an act of construal that brings relational potential into instantiated form. To write a proof, to solve an equation, to model a physical system mathematically, is to perform an act of meaning-making. Mathematics is not outside the world it describes—it is one of the ways the world becomes.
Form, Relation, and Transformation
From the relational perspective, mathematics is not a set of truths about objects, but a grammar of relation. Its primary concern is not with entities, but with how entities are related, how they transform, how patterns persist across change.
Algebra, for example, is not about numbers but operations—what happens when forms interact. Geometry is not about shapes in empty space, but the relations between locations, the transformability of form. Calculus construes the becoming of quantities, the infinitesimal texture of change. Topology goes further still, seeking not magnitude or location, but continuity—the deeper identity of things that change but do not break.
All of these are systems of potential, realised through specific symbolic actions. They are not given. They are not observed. They are actualised—by us, through symbol.
The Meaner in the Equation
In classical accounts, mathematical structures are thought to exist timelessly, awaiting discovery. But this view—like that of a universe governed by detached laws—is a legacy of a static ontology. In a relational ontology, we do not begin with being but with becoming. And in becoming, the role of the meaner cannot be ignored.
The mathematician, the physicist, the cosmologist—they are not merely uncovering pre-existing truths. They are enacting relations. They are collapsing the wavefunction of potential mathematical meaning into actual symbolic form.
This is not to say mathematics is arbitrary. Far from it. It is constrained by its own internal logic—but that logic is itself a system of potential. The moment of proof, the insight of a theorem, the act of modelling a system—these are acts of participation. They are the cosmos, through us, exploring its own symbolic potential.
The Cosmos as Construal
When we say that the universe is written in the language of mathematics, we imply a profound entanglement between the world and our symbolic systems. But this phrase should not be taken to mean that the universe is mathematics in itself. Rather, it means that the universe becomes meaningful—to itself, through us—in mathematical terms.
Cosmological models, quantum equations, the shape of spacetime itself: these are not independent entities, floating in a platonic realm. They are symbolic construals of the world's own becoming. They instantiate patterns—not from outside, but from within.
Mathematics is not cold. It is not distant. It is intimate, recursive, participatory. It is the cosmos folding itself into form, through a symbolic grammar enacted by meaners.
Recursion and the Ritual of Meaning
Mathematics is perhaps the most distilled symbolic ritual we possess. It is recursive meaning in action—functions of functions, transformations of transformations, systems nested within systems. Each proof is a small universe, each model a metaphoric contraction of a larger pattern.
And like all rituals, mathematical acts do something: they transform potential into actual. They instantiate patterns that reshape thought, structure inquiry, build machines, guide telescopes, test hypotheses, and model worlds.
This is why mathematics is not merely a tool of science—it is one of its modes of becoming. It is how science thinks, how it feels its way through the symbolic landscape of possibility.
Closing Spiral: Mathematics as Participation
In a relational cosmos, mathematics is not a detached language describing a world from outside. It is a way of being in relation—a mode of symbolic presence through which the cosmos articulates its own becoming.
Mathematics, then, is one of the sacred languages of a universe that knows itself through relation.
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