Mathematical Structure and Vedanta Philosophy

If the universe can be reduced to a pure mathematical structure, then descriptions of enlightenment within the Vedanta tradition gain a new fresh perspective

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I’m about three-quarters of the way through MIT physicist Max Tegmark’s book called: Our Mathematical Universe. In it, he argues that the universe can be fundamentally thought of as a pure mathematical structure. He defines this as: a set of abstract entities with relations between them. He begins his argument by outlining three levels of reality — Internal, Consensus and External.

Internal Reality consists of our subjective perceptions of the world. It is plagued by our own personal biases, as well as the multitude of heuristics embedded in our cognition.

Consensus Reality is the world as we experience it collectively. This is reality independent of our subjective lens. It is governed by the laws of classical physics. This reality isn’t free from illusion — but it aims at being free from personal distortion. It is determined collaboratively, answering the question: what is a stable conception of the world that the majority of humans can agree on.

External Reality is the way reality actually is. Once we try to see beyond our subjective position and see through our heuristics, we can then wonder about the fundamental nature of the world. What is the basis of consensus reality?

Tegmark claims that the link between Internal and Consensus reality is the domain of cognitive science, whereas the link from Consensus to External is the realm of Physics. His claim is that external reality is isomorphic to a mathematical structure. Namely, the features of our consensus reality, at the deepest level, are purely mathematical quantities. As an example, subatomic particles cannot meaningfully be thought to be small balls or planet-like structures. Instead, a total description of them simply involves fixing parameters such as angular momentum, principle quantum number and so on. At the deepest level, these particles are simply a set of numbers.

Into the Vedas

Some of the most ancient religious scriptures in the world are known as the Vedas. Originating in what is now India, these texts span a vast array of philosophical systems. Yet, we can parse out two fundamental features of reality.

Prakriti: objects, matter, time, name & form, causation, manifest existence, the energy of which the world is composed, fluid and changing, maya

Purusha: pure, unconditioned witness consciousness, higher Self, eternal, all pervasive

In the Vedanta traditions, it is said that humans are confused. We are stuck within the cycle of samsara. We are deluded by the realm of prakriti in that we think our bodies, thoughts, relations, experiences are what we truly are. We identify with these fleeting phenomena and create a self-structure around them. As fluidity is the nature of prakriti, our world inevitably falls apart. Our bodies decay, our thoughts whirl around, our friends and family change, and we experience immense suffering.

Have you ever wondered who experiences a thought, feeling or sensation?

When a thought arises, to whom does the experience occur — who is watching it?

It is said that Prakriti is the movie watched by Purusha. Purusha is the pure/free/bare/witnessing awareness that stands before all of manifest existence. Yet, our conditioned experience makes us forget that we are, as Rupert Spira puts it, “the movie screen onto which the dream of the world is projected.” The movie screen is never affected by the projections on it. It is both immanent and transcendent, in that every scene of the movie is preconditioned by the existence of the movie screen, yet the screen is other than the film.

Through Yoga — it is possible to remember, and recognize your true nature as Purusha. There is an experiential state of existence, free from being confused by prakriti. You have a mind unperturbed by the world, identify fully with purusha, and are liberated. This state is called by many names: mukti, moksha and nirvana.

Return to Tegmark

Can you uncouple from the way your brain instantaneously intuits the world, and perceive the true form of external reality. When we look out into the world, before our conscious perception occurs, we have already processed enormous amounts of data. The fact that certain objects in our field of vision are more salient to us is not a feature of the external world itself, but of our brain prioritizing said object for one reason or another.

The question is: can we see through all of our intuitive processes and experience reality raw?

Whether this is possible is up for debate, but if you could, what would the experience be like? To me— it seems like it would mukti.


I’ve reproduced the model of cognition presented in Tegmark’ book below.

There is external (mathematical, ever present, infinite) reality which interacts in a limited capacity with our sense organs. We then form an internal cognitive model both of the world, and of ourselves as the agent. When we interact with the world, we are actually interacting with our mental representation of the world, not things-in-themselves. From this world model, we become aware of ourselves as a separate entity with limited agency, and create a subsequent self-model. I think that the boundary between internal and external reality is more permeable than Tegmark posits.

The Vedas say that the ultimate state, mukti, is Satchidananda. Sat is existence, chid is pure awareness, and ananda is bliss. So pure awareness of existence brings bliss — this is the experience of mukti, this is liberation.

The experience of satchidananda, which is an experience of mukti, is the experiential realization of this permeability.

When the boundary between internal reality is seen for what it is, you are ‘liberated’ from the false reality of your internal world. You immediately perceive the pure, changeless, timeless, infinite, expansive qualities of reality.

Why is it timeless, infinite and changeless?

In an infinite universe of pure mathematical structure — we are all just complex braids in a static 4D spacetime. Einstein’s conception of reality is that we exist in a 4D Minkowski space — which is a fancy way of saying we exist in our normal three dimensional world with an extra time dimension . A consequence is that the experience we have of our lives unfolding is just that, an experience.

In actuality, spacetime does not exist within time, it contains time. It doesn’t exist within space, it contains space. So everything exists completely and totally already. As Tegmark says, “[The concept of] creation is only meaningful within a spacetime.” If we could view this 4D spacetime from a higher perspective, we would appear as elongated, and complex braid like patterns. Embodying a higher perspective means that we would not be within time or space. This higher perspective is Purusha. The objects we perceive are Prakriti.

The proof of infinitude given by Tegmark is the current observation that the universe appears to be inflating at an accelerated rate. Eternal Inflation, if true, would dictate a universe in which every possible arrangement of atoms occurs — and as such — everything that can happen will and has already happened. A consequence of mathematical structure and our current predicament of being alive and aware is that consciousness appears to emerge out of this structure. Whether there is an inflection point at which sentience arises out of complexity is unknown, yet here we are.

However, if we take the view that awareness itself has ontological priority, then we find ourselves with the possibility of entities who can be aware of the entire history of the infinite cosmos. Enter Krishna, from the Bhagavad Gita.

The Gita is a section within one of the great Hindu epics called the Mahabharata. The story is magnificent and timeless: a great war is about to occur — and right after the war shells are blown, the leader of the good guys, Arjun, notices that the opposition is made up entirely of his cousins and childhood friends. He becomes totally incapacitated — realizing he’s about to kill everyone he loves and engage in a war he doesn’t believe in. The Gita is the story of his chariot driver, Krishna, talking him down from his panic. Krishna expounds many different forms of yoga, explains creation, birth, death, and ethics to his friend Arjun. He explains the past, present and future of the universe. At one point, Arjun asks his friend how he knows this — Krishna then reveals his true form as an incarnation of Vishnu — one of the three primordial aspects of the Absolute. (Brahma the Creator, Shiva the Destroyer, Vishnu the Preserver). He gives Arjun a mighty vision of his true form.

“Tell me who you are, O Lord of terrible form! I want to know who you are, you who existed before all creation”

“I am time, the destroyer of all; I have come to consume the world. Even without your participation all the warriors gathered here will die. I have already slain all these warriors; you will only be my instrument.”

The great war Arjun is so scared of participating in has already happened. All of this knowledge, if he were to shed his identification with his conditioned self, was available to him right then and there. Krishna granted him this vision.

The concept, of the entire universe being accessible to someone here and now, again falls in line with a mathematical universe. If the universe is strictly a mathematical structure — then we don’t need to go explore outwards with spaceships, but inwards with our thoughts and computers. If physical existence equal mathematical existence — then exploring the universe is akin to exploring the limits of mind and computation. Alternatively, if what we are truly is just awareness, then ‘exploring’ is a misnomer, and once we drop off our false sense of self — we become aware of the totality of the cosmos, as it is. Everything is here and now, always and forever.




Tegmark, M. (2015). Our mathematical universe: My quest for the ultimate nature of reality. London: Penguin Books.

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