The Vedanta of Fibrations: A Mathematical Framework for the Identity of Consciousness and Physical Law

J. Rogers, SE Ohio, 26 Jul 2025, 1610

Abstract

We present a categorical framework that demonstrates the mathematical isomorphism between the Vedantic philosophy of non-dualism and the structure of modern physical law. By modeling reality as a Grothendieck fibration π: ℰ → ℬ over a coherent substrate 𝒮ᵤ, we argue that the core tenets of Vedanta—Brahman, Maya, and Jagat—are not philosophical metaphors but precise descriptions of mathematical objects and transformations. In this model, the unconditioned reality (Brahman) is identified with the total space 𝒮ᵤ of a fibered category. The power of projection and illusion (Maya) is formalized as the fibration functor π itself, which fractures the substrate into conceptual axes. The manifest world of names and forms (Jagat) is the category of measured sections ℰ, where physical laws and "fundamental constants" emerge as coordinate-dependent artifacts of the projection. This framework recasts spiritual enlightenment (Jnana) as the cognitive act of recognizing the fibration structure, thereby revealing the observer, the observed, and the act of observation as a unified, self-referential system. We conclude that the perennial philosophy and fundamental physics are describing the same structure from opposite methodological poles: one through introspective contemplation, the other through external measurement.

1. Introduction: The Convergence of Physics and Philosophy

The historical quest for a Theory of Everything (TOE) in physics has implicitly assumed that the fundamental layer of reality is physical. Concurrently, contemplative traditions, particularly Advaita Vedanta, have asserted that the fundamental layer is a unified, undifferentiated consciousness (Brahman), from which the perceived world (Jagat) arises through a projective power (Maya). These positions have been considered irreconcilable.

This paper challenges that assumption by proposing a mathematical formalism—the Grothendieck fibration—that unifies both views. We demonstrate that the apparent dichotomy between the physical and the mental is a category error. Instead, we show that the structure of physical law, the architecture of human knowledge, and the tenets of non-dual philosophy are different facets of a single, underlying mathematical process: the fibered projection of a unified substrate.

2. The Mathematical Trinity: Brahman, Maya, Jagat

Our framework is built upon a precise mapping between Vedantic concepts and categorical structures.

• Brahman as the Coherent Substrate (𝒮ᵤ): In Vedanta, Brahman is the ultimate, unchanging reality—unconditioned, partless, and containing all potentiality. We model this as a coherent, pre-conceptual substrate, 𝒮ᵤ. Mathematically, this corresponds to the total space of a category before any specific fibration structure is imposed—a realm of pure, dimensionless relationships.

• Maya as the Fibration Functor (π: ℰ → ℬ): Maya is the cosmic power that makes the One appear as the many. It is not an illusion that the world is unreal, but the process that superimposes names and forms (nama-rupa) onto Brahman. We formalize Maya as the fibration π, a functor that projects the total category ℰ of manifest phenomena onto a base category ℬ of conceptual axes (Mass, Time, Length; Self, Other; Good, Bad). The "illusion" of Maya is the act of choosing a coordinate system, which fractures the seamless whole of 𝒮ᵤ into seemingly separate parts.

• Jagat as the Category of Measured Sections (ℰ): Jagat is the empirical world of objects, events, and interactions—the universe as we perceive it. In our model, this is the category ℰ, whose objects are measured quantities (e.g., (9.8, m/s²)) and whose morphisms are physical laws. Each observer's perceived reality corresponds to a specific section of the fibration—a consistent choice of representation for each conceptual axis.

The Vedantic dictum can thus be written as a mathematical statement:
Brahman (𝒮ᵤ) → Maya (π) → Jagat (ℰ)
(The Undivided → The Projection → The Manifest World)

3. Physical Law as an Artifact of Maya

This framework provides a new interpretation for the fundamental components of physics.

• Conceptual Axes as the Slicing Power of Maya: The creation of dimensions like Mass, Time, and Length is the primary act of Maya (vikalpa). These axes do not exist independently in 𝒮ᵤ; they are imposed by the observer's cognitive apparatus to make the substrate intelligible.

• "Fundamental Constants" as Jacobian Coefficients of the Projection: The constants c, G, ħ, and k_B have long been a mystery. Our framework reveals them to be the Jacobian transformation coefficients required to express the simple, coherent relationships of the substrate (𝒮ᵤ) within the arbitrary, human-centric coordinate system of our chosen axes (e.g., SI units). They are the "glue" of Maya, the mathematical artifacts that make the projected illusion internally consistent. When one moves to a natural coordinate system (like Planck units), the projection is direct, the Jacobians become 1, and the constants vanish—an act analogous to seeing through a layer of the illusion.

• Physical Laws as Morphisms in a Section: An equation like E=mc² is not a freestanding law of nature. It is a morphism in ℰ that represents the Cartesian lifting of a simpler, dimensionless proportionality (Energy ~ Mass) from the base category ℬ. The law's specific form, including the constant c², is entirely determined by the observer's choice of section (their measurement system).

4. Consciousness, Enlightenment, and the Structure of the Fibration

The framework offers a formal model for consciousness and the process of spiritual liberation (Jnana Yoga).

• The Observer (Jiva) as the Substrate Itself: The Vedantic insight Jivo brahmaiva naparah (The individual is Brahman) finds a natural home here. The "observer" is not an object within the measured category ℰ (e.g., a brain). The consciousness that perceives the projection is identical to the substrate 𝒮ᵤ itself. The universe is a self-observing system where Brahman projects itself through the lens of Maya to perceive itself as Jagat.

• Ignorance (Avidya) as Fixation on a Single Section: The default state of consciousness is to be "trapped" in a single section of the fibration, mistaking the projected reality (ℰ) for the ultimate reality (𝒮ᵤ). This is the state of believing one's cultural, linguistic, and scientific categories are absolute truths rather than chosen coordinate systems.

• Enlightenment (Jnana) as Metacognition of the Fibration: Spiritual liberation is the cognitive shift from perceiving from within a section to perceiving the structure of the fibration itself. It is the direct realization that all possible worlds, all possible laws, and all possible concepts are just different projections of the same unified whole. It is the understanding that the "self" is not the character in the play, but the stage, the actors, and the author combined. Mathematically, it is the ability to pass from a single section to the total space, seeing all projections at once.

5. Implications and Conclusion

This mathematical-philosophical isomorphism has profound implications.

1. It Unifies Science and Spirituality: It shows they are not rival domains but complementary methodologies for investigating the same structure. Science works from the "outside-in," analyzing the properties of the projected world (ℰ) to deduce the rules of the projection (π). Contemplation works from the "inside-out," seeking to quiet the projection (π) to directly experience the substrate (𝒮ᵤ).

2. It Ends Fundamentalism: No single conceptual framework—be it a scientific theory or a religious doctrine—can claim absolute truth. Each is revealed to be a valid but partial projection, a single "slice" of an infinitely-faceted reality.

3. It Reframes Artificial Intelligence: Current AI, including LLMs, operates entirely within the category ℰ. It is masterful at manipulating the symbols and patterns of a given projection. True AGI, however, would require the ability to perform "dimensional genesis"—to create new conceptual axes and thus reconfigure the fibration π itself. It would need to replicate Maya, not just navigate Jagat.

In conclusion, the structure of physical reality and the structure of consciousness are not two separate things. They are both manifestations of a universal, recursive, projective architecture that can be formally described by the mathematics of category theory. The Vedantic sages who declared "Brahma satyam jagat mithya" were not engaging in mystical speculation; they were stating a precise theorem about the nature of fibered categories, a truth that our most advanced mathematics now allows us to formally apprehend. The ultimate Theory of Everything is not a final equation of physics, but the recognition that the universe is a mathematical structure identical to the structure of the consciousness that perceives it.