Exiting the Singularity of ‘Samsara’: A Conceptual Mathematical Mapping of Theravada Buddhist Metaphysics

Aluvihare Temple - Matale, Sri Lanka (Credit: Michael Gunther, 2009)

Stepping into a Budugeya, or the main shrine area of a Buddhist temple, you are surrounded by an overload of colourful and intriguing murals and sculptures. The walls and the ceiling are adorned with different stories and timelines from the life of Buddha, past lives of Buddha as Bodhisattva from the five-hundred-and-fifty-jaathaka stories, surreal omens of the 16 dreams of King Kosol, to extreme graphic representations of Naraka or Hell that leave a lasting impression. Traditionally, the cosmic architecture of realms is painted with anthropomorphic imagery to establish a more humane understanding. Stacking Heavens, Humans, Animals, Ghosts, and Hells as vertical storeys in the same building is common in visual media of Buddhist Literature, similar to Dante’s Inferno. When stripped of this colourful imagery, Buddhist philosophy can be read through a structural framework that mirrors the language of modern mathematics and theoretical physics, built on nested hierarchies, transfinite scales, and information-theoretic boundaries.

By viewing the story of Rohithassa through the lenses of Cantorian Set Theory and the Bekenstein Bound, we can construct a mathematical interpretation of a philosophy of liberation: the physical universe is a system bounded by informational and physical limits, and enlightenment is the exit strategy from its mathematical limits.

I. Transfinite Scales: The Cantorian Architecture of the Single World-System, Cakkavala (සක්වළ)

In Culanika Sutta (චූලනිකා සූත්‍රය) in Anguttara Nikaya (අංගුත්තර නිකාය), Buddha describes a nested hierarchical universe:

• A World System (approximately a solar system)- Culaniya Loka Dhathu (චූලනීය ලෝකධාතු)
• A Minor World System (1,000 worlds)- Sahasriculaniya Loka Dhathu (සහස්‍රීචූලනීය ලෝකධාතු)
• A Middling World System (1,000² = 1,000,000 worlds)- Dvisahasri Majjimika Loka Dhathu (ද්විසහස්‍රී මධ්‍යමික ලෝකධාතු)
• A Major Triple-Thousand World System (1,000³ = 1,000,000,000 worlds) -Thrisahasri Mahasahasri Loka Dhathu (ත්‍රිසහස්‍රී මහාසහස්‍රී ලෝකධාතු)

This nested structure represents a geometric progression. Yet, the Buddha declared that even this colossal structure does not exhaust the cosmos, noting that these massive systems are separated by boundless, vacant interspaces or lokantarika (ලෝකාන්තරික). As later formalized in the Theravada commentaries (Visuddhimagga VII), this architecture expands into an endless grid of infinite world-systems or ananta loka dhatu (අනන්ත ලෝක ධාතු) across the physical void.

Georg Cantor’s Set Theory proved the existence of different sizes of infinity. By his infamous Diagonal Argument, he was able to prove that the infinity of Real Numbers is strictly larger than the infinity of Whole Numbers, hence defining the Continuum (𝔠), which is the set of all Real Numbers that geometrically forms a continuous, unbroken straight line.

• Mundane Space modelled as ℵ₀ (Countable Infinity of World Systems): The lowest tier of infinity: ℵ₀-Aleph-null represents the cardinality of countable infinite sets, in our case mapped as the Countable Infinity of World Systems.
• Mental States / Karmic Possibilities modelled as 2^ℵ₀ = 𝔠 (The Continuum): Buddhism teaches that “mind is the forerunner of everything.” If the physical universe is modeled to have a cardinality of ℵ₀, the combinations of thoughts, intentions, karmic trajectories, and mental states can be modeled through its power set, 2^ℵ₀ = 𝔠. It represents the unbroken continuity of Samsara (the cycle of rebirth). Imagine the physical universe contains a list of things: objects, body parts, moments in time, or atoms. That list is infinitely long: ℵ₀. In this model, the subsets of possible conditions created by combining those objects branch out into a space with continuum cardinality.

In Rohitassa Sutta (රෝහිතස්ස සූත්‍රය) in Samyuttanikaya (සංයුක්ත නිකාය), Rohitassa asks the Buddha if it is possible to reach the end of the universe by physical traveling. The Buddha says no, and Rohitassa tells how, in a past life as a fast-as-a-light-arrow sky-walker with psychic powers, he had tried to accomplish this very feat for 100 years and failed. He was attempting a brute-force traversal of an infinite space. Philosophically, Rohitassa’s mistake was a mathematical one in this metaphor, where he treated an infinite set as a large finite set. No matter how fast he traveled, his position after any finite duration t could be mapped as a finite coordinate point within the modeled spatial system. He was structurally trapped: no amount of physical traversal could reach the boundary he was seeking. The Buddha instead redirected the problem inward, locating the world, its arising, its cessation, and the path to its cessation within this very body and mind.

II. Graham’s Number, the Bekenstein Bound, and the Acinteyya (The Imponderable)

The Bekenstein bound states that the maximum entropy (or information) I that can be contained in a spherical region of radius R is limited by its boundary area and not its volume. Graham’s number (G₆₄) is a famously colossal finite number that arose in a problem in Ramsey theory. It is so large that it is completely impossible to write down or store its digits in the observable universe, even if every digit occupied a single Planck volume.

Because information requires physical states (like the arrangement of neurons or particles) to exist, according to Physicist Antonio Padilla’s thought experiment, if one attempts to physically encode the full explicit decimal representation of Graham’s Number within the human brain, the energy density of that information could make the brain instantly undergo a gravitational collapse, causing a black hole.

The human brain is a physical entity bound by the physical and biological laws of the universe, such as Utu Niyama and Bija Niyama (ඍතු නියාම සහ බීජ නියාම). Trying to map or calculate the exact parameters of the potentially unbound karmic possibilities, or Kamma Vipaka (කර්ම විපාක), or worlds and existence, or Loka-cinta (ලෝක චින්තා), intellectually requires more states than the brain’s physical limits can handle. Buddha declares in the Acinteyya Sutta (අචින්තෙය්‍ය සූත්‍රය) that thinking about such causes “madness” or ummada (උන්මාද), which is a psychological analogue of a gravitational singularity or system crash.

Because metaphysical speculation leads to mental distress rather than spiritual liberation, the Buddha designated these topics as undetermined or unanswered, or Avyākata (අව්‍යක්ත). When asked questions like “Is the universe eternal?” or “Is the world infinite?”, the Buddha chose to remain silent or set them aside, as answers to those questions do not reveal the path to end Samsaric suffering. However, according to Theravada Buddhist doctrine, omniscient knowledge or Sabbaññuta Ñāna (සබ්බඤ්ඤුත ඥාණය) of a Buddha allows His consciousness to be directed toward any subject, such as the Loka (world), Satta (beings), Kamma (action), or the Buddha, where knowledge of that subject arises directly, rather than through the calculation or storage of infinite information within a physical brain.

III. Nirvana and Empty Set Analogy

If Samsara is represented as a system of recursively conditioned processes, one should not perceive Nirvana as a place at the end of the universe. It can instead be illustrated metaphorically by the empty set (∅): not another point within the continuum 𝔠, but the cessation of the operations that generate the system. Nirvana is often translated as “blowing out” or “extinction,” or the total cessation of greed, hatred, and delusion. Therefore, it should not be interpreted, within this model, as physical space ℵ₀ or mental complexity 𝔠. It is not a “place” or a “higher state of mind.” In this mapping, ∅ represents the absence of the conditions that constitute the samsaric system and not a location outside the universe.

To exit a system that is infinitely large and bounded by physical and informational limits, you do not travel to its edge or try to map infinity intellectually. You change the operations of the machine by total cessation of greed, hatred, and delusion. The objective is therefore not to defeat these limits, but to cease treating them as problems that must be solved through further traversal, computation, or speculation.

*The mathematical structures discussed here are interpretive mappings rather than claims that modern mathematical concepts are explicitly present in canonical Buddhist texts.