In certain philosophical and religious traditions, the soul is not necessarily conceived as something forever beyond physical explanation. The deeper possibility is that what we have historically called soul may eventually admit a natural description—one that we do not yet possess because our mathematics has been better suited to analyzing parts than wholes.
This possibility motivates an idea proposed in my 2026 book Thus Spoke Arta: an approximation to the natural geometry of holistic units of analysis may be within our reach.
The prospect is not as speculative as it might initially sound.
The artificial intelligence revolution has given us an extraordinary clue. Human language, reasoning, perception, and many forms of intelligence—phenomena once treated as uniquely mysterious properties of biological minds—can be approximated through mathematical structures involving vectors, matrices, transformations, high-dimensional spaces, and geometric relationships. The remarkable lesson of AI is not merely that machines can imitate aspects of human intelligence. It is that some phenomena we experience as extraordinarily complex may possess an underlying mathematical structure that becomes visible once we discover the appropriate representation.
Perhaps the same lesson can be extended beyond the human mind.
Consider the great holistic systems of our planetary environment: the heliosphere, geosphere, hydrosphere, atmosphere, biosphere, and noosphere. We ordinarily study these as collections of interacting components. We measure particles in the heliosphere, geological processes in the geosphere, circulation in the hydrosphere, gases in the atmosphere, organisms in the biosphere, and information and cognition in the noosphere.
But what if each of these is more than the sum of its measurable components?
A forest, for example, is not simply a collection of trees. An atmosphere is not merely a statistical aggregate of molecules. A biosphere is not adequately represented by a list of organisms. And the noosphere—if we take the concept seriously—is not simply a collection of individual human minds.
Each is a whole with its own geometry of relationships, boundaries, dynamics, identity, and potential.
Our existing mathematics is extraordinarily powerful at describing interactions among components. Physics, statistics, differential equations, network theory, information theory, and computational mathematics have given us increasingly sophisticated ways to model complex systems. Yet there remains a conceptual asymmetry: we often begin with the parts and attempt to reconstruct the whole.
What if, for certain classes of phenomena, we need to reverse the direction?
Instead of asking:
How does the whole emerge from its parts?
we might also ask:
What mathematical structure belongs to the whole before we decompose it into parts?
This is where the idea of a holistic mathematics begins.
My initial intuition was that category theory might provide the necessary foundation. Category theory is, after all, exceptionally powerful for describing relationships, mappings, transformations, and structures at a high level of abstraction. It offers a language in which the relationships between mathematical objects can sometimes matter more than the internal constitution of those objects.
But I increasingly suspect that category theory alone does not answer the question.
The problem is one of direction.
Category-theoretic abstraction can be understood as an integration of structures from below: we begin with objects, morphisms, and relationships and progressively abstract away their particular contents. What I am looking for is almost the inverse operation—a fresh abstraction from the top.
The starting point would not be an inventory of elementary constituents.
The starting point would be the holistic unit itself.
We would first ask what it means mathematically for something to constitute a coherent whole: What defines its boundary? What gives it identity? What is its internal geometry? How does it transform while remaining recognizably itself? How does it exchange matter, energy, information, and agency with its environment? And perhaps most intriguingly, how does a whole contain a structured space of possible futures?
Only after establishing this top-level geometry would we descend into its components.
This would not mean abandoning reductionism. Reduction remains indispensable. Rather, it would mean adding another direction of mathematical inquiry: top-down formalization of wholes alongside bottom-up analysis of parts.
The AI revolution may offer an important precedent. We did not solve language by individually encoding every sentence humans might ever speak. We discovered mathematical representations in which vast spaces of linguistic possibilities could be organized geometrically. Intelligence emerged as a property of relationships within that representational space.
Perhaps holistic systems require something analogous.
Perhaps the heliosphere, the biosphere, the noosphere—and ultimately the Earth itself—can be represented not merely as collections of interacting variables but as geometrically structured spaces of possibility.
If so, the challenge before us is not simply to develop more powerful mathematics for analyzing increasingly complicated systems. It is to discover whether there exists a mathematical language in which a whole can be represented as a whole without immediately reducing it to its constituent parts.
That would constitute a significant conceptual shift.
We have learned to mathematize matter. We have learned to mathematize energy, information, probability, networks, and increasingly intelligence. The next frontier may be to mathematize holism itself.
And if that becomes possible, questions once relegated to philosophy—about life, consciousness, planetary agency, and perhaps even what ancient traditions called the soul—could acquire new mathematical forms.
Not because mathematics would prove those traditions correct.
But because we may finally have a language capable of asking their oldest questions in a new way.