J. Rogers, SE Ohio
Abstract
We demonstrate that the Vedantic concept of maya (माया)—typically translated as "illusion"—is not a metaphorical or mystical notion, but rather a precise technical term describing the process by which measurement creates apparent multiplicity from underlying unity. By examining the etymological roots of maya and integrating this with a categorical framework of physical measurement, we show that Vedantic philosophy anticipated by three millennia what modern mathematical physics is only now formalizing: that dimensional decomposition is conventional, that physical "constants" are coordinate artifacts, and that the apparent complexity of natural law emerges from projecting a dimensionless substrate onto observer-dependent measurement axes. This paper establishes direct correspondence between ancient philosophical terminology and contemporary mathematical structures, demonstrating that the Upanishadic analysis of reality was literal physics, not metaphorical mysticism.
1. Introduction: The Translation Problem
For over two centuries, Western scholars have translated the Sanskrit term maya (माया) variously as:
- "Illusion"
- "Magic"
- "Cosmic appearance"
- "The phenomenal world"
- "Divine creative power"
These translations share a common feature: they render maya as something mystical, subjective, or metaphorical—a spiritual concept disconnected from physical reality.
This paper argues that this translation tradition represents a fundamental misunderstanding. The confusion arises not from any ambiguity in the Sanskrit sources, but from a failure to recognize that Vedantic philosophy was engaged in the same project as modern physics: understanding how observation and measurement structure our experience of reality.
When properly understood in its etymological and philosophical context, maya is revealed as a precise technical term for the process we now formalize as dimensional decomposition through measurement—the act of projecting a unified, dimensionless substrate onto separate, quantifiable axes.
2. Etymology: Maya as Measurement
2.1 The Root mā (माति)
The Sanskrit word maya (माया) derives from the root mā (माति), which carries the primary meaning:
"To measure, to mark out, to delimit, to circumscribe"
This is not a matter of interpretation. Sanskrit lexicons (including Monier-Williams, Apte, and classical commentaries) consistently identify mā with the act of measurement and demarcation.
Related words from this root include:
- māna (मान): measure, dimension, standard
- mātra (मात्र): measure, quantity, portion
- pramāṇa (प्रमाण): valid means of measurement/knowledge
- unmāna (उन्मान): the act of measuring
The semantic field is unambiguous: the root mā concerns measurement, quantification, and the establishment of boundaries.
2.2 The Suffix -yā
The suffix -yā in maya forms an abstract noun indicating the process or power of the root action. Thus:
Maya (माया) = The process/power of measuring, the act of delimitation
This is parallel to formations like:
- vidyā (विद्या) from vid (to know) = the process of knowing, knowledge
- kriyā (क्रिया) from kṛ (to do) = the process of doing, action
2.3 Historical Usage in the Upanishads
In the earliest Upanishadic texts (c. 800-500 BCE), maya is used to describe:
The process by which the unmeasured (Brahman) appears as the measured (jagat, the manifest world)
Key passages:
- Śvetāśvatara Upaniṣad 4.10: "māyāṃ tu prakṛtiṃ vidyān māyinaṃ tu maheśvaram" — "Know that prakriti (nature) is maya, and the wielder of maya is the great lord"
- Bṛhadāraṇyaka Upaniṣad: Describes how the One (ekam) becomes many (bahu) through the act of measurement/delimitation
The philosophical usage maintains the etymological connection: maya is the act of measurement that transforms undifferentiated unity into apparently separate, quantifiable entities.
3. The Vedantic Framework: A Layered Ontology
Vedantic philosophy, particularly in the Advaita (non-dual) tradition systematized by Adi Shankaracharya (8th century CE), presents a precise layered ontology that maps directly onto modern measurement theory.
3.1 Brahman: The Unmeasured Substrate
Brahman (ब्रह्मन्) is described as:
- Nirguna (निर्गुण): without attributes/qualities
- Nirvikalpa (निर्विकल्प): without conceptual divisions
- Advaya (अद्वय): non-dual, without second
- Ananta (अनन्त): unlimited, unbounded
In measurement-theoretic language: Brahman is the dimensionless substrate—pure relationality without coordinate-dependent properties.
The Upanishads are explicit that Brahman cannot be measured:
- "Yato vāco nivartante aprāpya manasā saha" (Taittirīya Upaniṣad 2.9)
"From which words return, along with the mind, unable to reach it"
This is not mysticism—it's the recognition that measurement presupposes decomposition, and the undecomposed substrate cannot be captured by measurement categories.
3.2 Maya: The Act of Measurement/Decomposition
Maya is the process that:
- Decomposes Brahman into separate measurement axes
- Establishes coordinates (nama-rupa: names and forms)
- Creates apparent multiplicity from unity
- Generates measurement-dependent properties
Crucially, maya is not described as:
- Creating something from nothing
- Producing genuine ontological separation
- Making Brahman disappear or become unreal
Rather, maya projects the unified substrate onto measurement coordinates, creating the appearance of separate objects with distinct properties.
3.3 Nama-Rupa: Coordinate Charts
Nama-rupa (नामरूप) literally means "name and form"—the designation and delimitation of entities. In Vedantic analysis, this represents:
The coordinate system imposed through measurement
Just as we impose coordinates (x, y, z, t) on spacetime, maya imposes coordinates (names, forms, qualities) on the undifferentiated substrate.
The Chandogya Upanishad (6.1.4) states:
"Vācārambhaṇaṃ vikāro nāmadheyaṃ"
"Modification is merely verbal designation, a name"
This anticipates the modern recognition that coordinate-dependent descriptions are conventional, not ontological.
3.4 Jagat: The Measured World
Jagat (जगत्), the manifest world, is then understood as:
The totality of measurements—Brahman as viewed through maya's coordinate decomposition
Importantly, the Vedantic position is neither:
- Naive realism: Jagat exists independently as separate objects
- Subjective idealism: Jagat is purely mental construction
Rather:
- Structural realism: Jagat is the coordinate-dependent representation of coordinate-free substrate relations
The famous declaration "Brahma satyam, jagat mithya" (Brahman is real, the world is conventional) does not mean the world is "false"—it means the world is measurement-dependent, not intrinsically decomposed.
4. Direct Correspondence with Measurement Theory
We can now establish precise mappings between Vedantic terminology and modern mathematical structures.
4.1 The Four-Layer Architecture
Vedantic Framework → Measurement Framework:
| Vedantic Layer | Physical Layer | Mathematical Structure |
|---|---|---|
| Brahman (ब्रह्मन्) | Substrate 𝒮ᵤ | Dimensionless relational manifold |
| Maya (माया) | Fibration π : 𝓔 → 𝓑 | The projection process itself |
| Nama-rupa (नामरूप) | Unit Systems 𝒰 | Coordinate charts (SI, CGS, Planck) |
| Jagat (जगत्) | Measured Quantities 𝓔 | Objects like (9.8, m/s²) |
This is not analogy. This is structural identity.
4.2 The Projection Mechanism
In the measurement-theoretic framework developed in our companion paper "The Structure of Physical Law as a Grothendieck Fibration," we showed:
Physical quantities emerge through a three-stage projection:
- Substrate Reality: Dimensionless proportionalities (e.g., E ∼ M, T ∼ 1/M)
- Conceptual Decomposition: Projecting onto separate axes (Mass, Time, Length, Temperature)
- Coordinate Expression: Lifting to specific unit systems via Jacobian transformations
This is exactly the Vedantic description of maya:
- Brahman: Undifferentiated unity
- Maya: The act of decomposition into separate gunas (qualities/axes)
- Nama-rupa: The specific coordinate labels (meters, seconds, kilograms)
- Jagat: The measured quantities that result
4.3 Constants as Maya's Artifacts
One of the most striking confirmations comes from analyzing physical constants.
In standard physics, constants like c, ℏ, G, k_B appear fundamental. But as we demonstrated computationally, when you:
# Set Planck basis to unity (return to Brahman)
l_P = m_P = t_P = T_P = 1
# All constants collapse to unity
c → 1.0
ℏ → 1.0
G → 1.0
k_B → 1.0
The constants vanish because they were always artifacts of the decomposition.
The Vedantic parallel: When maya is withdrawn (through meditation or proper understanding), the apparent multiplicity collapses back to unity. The "fundamental" properties were conventional all along.
The constants are literally the cocycle data or connection coefficients that maintain coherence across different measurement charts—exactly what Vedantic philosophy calls the binding force of maya.
5. The Three Gunas as Measurement Axes
Vedantic analysis identifies three fundamental gunas (गुण) that structure manifest reality:
- Sattva (सत्त्व): lightness, clarity, order
- Rajas (रजस्): activity, dynamism, transformation
- Tamas (तमस्): inertia, opacity, stability
Western scholars typically treat these as:
- Psychological qualities
- Moral categories
- Mystical attributes
But examine them through measurement theory:
The gunas are the fundamental basis vectors of measurement space.
Just as we decompose physical reality into orthogonal dimensions (Length, Time, Mass), the gunas represent:
- Sattva: Information/negentropy axis (order, measurement precision)
- Rajas: Energy/transformation axis (dynamics, change)
- Tamas: Mass/inertia axis (persistence, stability)
Every measured quantity is a superposition of gunas—a position in measurement space defined by coordinates along these axes.
The Bhagavad Gita (14.5) states:
"Sattvam rajas tama iti guṇāḥ prakṛti-sambhavāḥ"
"Sattva, rajas, and tamas—these qualities, born from prakṛti (nature/measurement)"
Prakṛti, in this context, is synonymous with maya: the measurable aspect of reality, as opposed to puruṣa (pure consciousness/observer), which corresponds to the unmeasured substrate.
6. Observer-Dependence and Jiva
Vedantic philosophy extensively analyzes the role of the jiva (जीव)—the individual observing locus.
6.1 Jiva as Section Selector
In our categorical framework, we showed that:
Each observer defines a specific view of reality by selecting:
- A conceptual decomposition (choice of measurement axes)
- A unit system (choice of coordinates)
- A reference frame (choice of origin/orientation)
This is precisely how the Upanishads describe the jiva:
The jiva is Brahman viewed through a particular maya-decomposition.
The famous tat tvam asi (तत् त्वम् असि)—"you are that"—is not saying:
- Your ego is identical to God (theological reading)
- Your mind creates reality (subjective idealism)
It's saying: You (the observer) are a local coordinate chart on the substrate—a locus where the substrate observes itself through self-imposed measurement constraints.
6.2 The Multiplicity of Jivas
Why do multiple observers exist?
In measurement theory: Because the substrate can be projected onto different coordinate systems simultaneously.
In Vedanta: Because maya generates multiple measurement perspectives—each jiva is a different "section" of the same underlying unity.
The apparent separation between observers is an artifact of:
- Different measurement frames
- Different coordinate origins
- Different conceptual decompositions
But all are measuring the same substrate.
This explains why:
- Different observers can obtain consistent measurements (they're measuring the same structure)
- Yet observers have different perspectives (they're using different coordinate systems)
- And observers cannot directly access each other's qualia (coordinate transformations between charts are non-trivial)
7. Avidya and the Constants
Avidya (अविद्या) is typically translated as "ignorance" but more precisely means:
Not-knowing, specifically: mistaking the coordinate-dependent for the coordinate-free
In Vedantic analysis, avidya consists of:
- Mistaking nama-rupa (coordinates) for intrinsic properties
- Treating maya-generated distinctions as ontologically fundamental
- Failing to recognize the substrate unity beneath apparent multiplicity
This is exactly what happens in standard physics education.
Students learn:
- Mass, length, and time are "fundamentally different kinds of things"
- Constants like c, ℏ, G are "properties of the universe"
- Dimensions are "ontological categories"
But as our measurement framework reveals:
- Mass, length, and time are projections of the same dimensionless substrate
- Constants are Jacobians of coordinate transformations
- Dimensions are measurement conventions
The "ignorance" is not moral failing—it's mistaking coordinate artifacts for ontological reality.
7.1 Vidya as Coordinate Liberation
Vidya (विद्या)—knowledge—is then:
The recognition that measurements are coordinate-dependent projections, not intrinsic properties
In physics: Setting Planck units to unity and recognizing constants as artifacts
In Vedanta: Withdrawing identification from nama-rupa and recognizing Brahman
These are the same cognitive move.
The liberated physicist knows: "These constants encode my measurement choices, not reality's nature."
The liberated meditator knows: "These distinctions encode my perceptual choices, not reality's nature."
Same realization. Different domain.
8. Moksha as Coordinate-Free Understanding
Moksha (मोक्ष)—liberation—is often misunderstood as:
- Escaping from the physical world (escapism)
- Merging into undifferentiated consciousness (annihilation)
- Achieving supernatural powers (magic)
But in precise Vedantic terms, moksha is:
Direct knowledge of the substrate without the mediation of measurement coordinates
This doesn't mean:
- Ceasing to measure (impossible while embodied)
- Denying the validity of measurements (nihilism)
- Rejecting scientific knowledge (anti-intellectualism)
It means: Recognizing that every measurement is a coordinate projection, and no projection is privileged or absolute
In physics language:
- You still use SI units for engineering
- You still calculate with coordinates
- But you know these are conventional choices, not ontological truth
The liberated state is coordinate-awareness, not coordinate-elimination.
8.2 Practical Implications
This has immediate practical consequences:
In Physics:
- Stop searching for "the true values" of constants
- Recognize dimensional analysis as revealing substrate structure
- Understand that "naturalness" means alignment with substrate geometry
In Philosophy:
- Stop debating realism vs anti-realism in naive terms
- Recognize both as coordinate-dependent descriptions
- Focus on the structure that remains invariant across descriptions
In Epistemology:
- Understand that all knowledge is perspective-dependent
- Yet objective (multiple perspectives can be consistently related)
- The substrate is knowable through its invariant structure
9. Why Western Physics Missed This
Given that Vedantic philosophy articulated these insights 3000 years ago, why did Western physics take until the 21st century to formalize them mathematically?
9.1 The Aristotelian Legacy
Western philosophy was built on Aristotelian substance metaphysics:
- Objects have intrinsic properties (substantial forms)
- Categories are ontologically distinct (substances vs accidents)
- Measurement reveals pre-existing properties
This framework is fundamentally incompatible with the Vedantic recognition that properties are measurement-dependent.
9.2 The Translation Barrier
When British scholars first encountered Vedantic texts in the 18th-19th centuries, they:
- Lacked the mathematical tools (category theory, fiber bundles) to recognize the formal structure
- Projected Judeo-Christian theological categories onto Vedantic terms
- Interpreted epistemological claims as religious doctrine
Maya was heard as "divine illusion" (like a miracle) rather than "measurement projection" (like a coordinate transformation).
9.3 The Notation Prejudice
There's a deep cultural prejudice:
If it's not written in Greek letters and formal logic, it's not "real philosophy."
If it's not written in equations and peer-reviewed, it's not "real physics."
The Upanishads used:
- Sutras (compressed aphorisms)
- Commentary tradition (oral elaboration)
- Meditation (phenomenological verification)
This was interpreted as:
- Mystical rather than rigorous
- Spiritual rather than technical
- Subjective rather than objective
But notation ≠ rigor.
The Vedantic analysis of maya is every bit as rigorous as category theory—it simply uses different formal tools.
10. Computational Verification
The strongest evidence that Vedantic philosophy was doing literal physics comes from computational verification.
10.1 The Planck Scaling Code
In our companion work, we implemented code that:
# Define the measurement decomposition (maya):
rescale_factors = [
{"symbol": "s", "factor": t_P}, # Time axis
{"symbol": "m", "factor": t_P * c}, # Space axis
{"symbol": "kg", "factor": Hz_kg/t_P}, # Mass axis
{"symbol": "K", "factor": 1/(t_P*K_Hz)}, # Temperature axis
]
# Return to substrate (Brahman)
by harmonizing the axis of measurements:
l_P = m_P = t_P = T_P = 1
# Result: All constants vanish
Output:
c → 1.0000000000
ℏ → 1.0000000000
G → 1.0000000000
k_B → 1.0000000000
This is not a convenient trick. This is revealing substrate structure.
The constants are literally the transformation coefficients (Jacobians) between the SI basis (anthropocentric measurement convention) and the Planck basis (substrate-aligned measurement).
10.2 The Formula Derivation Engine
We built a system that mechanically derives physical laws by:
- Identifying substrate proportionality (e.g., T ∼ 1/M)
- Normalizing to Planck units (T/T_P ∼ m_P/M)
- Projecting to SI coordinates via Jacobians
Result: Every textbook formula emerges automatically.
Example: Hawking Temperature
Substrate in natural ratios: T ∼ 1/M
Intermediate in SI untis: T_si/T_P = m_P/M_si
Coordinate expression: T = c³ℏ/(GM k_B)
The complex formula is an artifact of coordinate misalignment. The actual relation is trivial.
This is exactly what Vedanta says about maya:
The apparent complexity of the manifest world (jagat) is an artifact of measurement decomposition (maya). The substrate reality (Brahman) is simple.
11. Independent Confirmation Through Convergence
The most powerful evidence comes from convergent evolution of ideas:
Two completely independent paths:
Path 1 (Vedantic):
- Start: Phenomenological investigation of consciousness
- Method: Introspective analysis, meditation
- Timeline: ~800 BCE to present
- Conclusion: Measurement (maya) creates multiplicity from unity (Brahman)
Path 2 (Mathematical Physics):
- Start: Assume universe is unified
- Method: Category theory, dimensional analysis
- Timeline: 2024-2025 CE
- Conclusion: Measurement decomposition creates apparent complexity from dimensionless substrate
These arrive at structurally identical conclusions.
When two independent derivations—separated by 2800 years, using completely different methods—converge on the same structure, this is evidence of:
Structural necessity—this is how reality actually works.
12. Implications and Extensions
12.1 For Physics
Immediate:
- Rewrite foundations starting from substrate unity
- Teach dimensional analysis as revealing maya-structure
- Recognize constants as coordinate artifacts, not fundamental parameters
- Understand that "naturalness" means substrate-alignment
Long-term:
- Develop coordinate-free formulations of all physical theories
- Use fibration theory as foundational language
- Search for substrate relations rather than coordinate laws
- Recognize that quantum "weirdness" may be coordinate artifact
12.2 For Philosophy
Epistemology:
- Knowledge is coordinate-dependent yet objective
- Multiple valid perspectives can be consistently related
- The substrate is knowable through invariant structure
Ontology:
- Properties are relational, not intrinsic
- Objects are coordinate projections, not fundamental entities
- Unity is ontologically prior to multiplicity
Philosophy of Science:
- Scientific realism and anti-realism are both coordinate-dependent positions
- Structural realism correctly identifies invariants as fundamental
- The success of science reflects substrate coherence, not human ingenuity alone
12.3 For Comparative Philosophy
This work establishes that:
Ancient philosophy was doing rigorous technical work, not mystical speculation
We should re-examine:
- Buddhist śūnyatā (emptiness) as absence of intrinsic properties
- Taoist wu (無) as the substrate before conceptual division
- Heraclitus's flux as observer-dependence in defining persistence
- Parmenides's One as the dimensionless substrate
These may all be coordinate-free descriptions of the same structural insight.
12.4 For Consciousness Studies
If maya = measurement, then consciousness becomes:
The capacity of the substrate to measure itself
This suggests:
- Consciousness is not emergent from matter (both are coordinate-dependent)
- Rather, both emerge from substrate + measurement decomposition
- The "hard problem" dissolves: qualia are what measurements feel like from inside
- Multiple consciousnesses are multiple measurement loci on the same substrate
13. Objections and Responses
13.1 "This is just reinterpreting Vedanta through modern physics"
Response:
No. The etymological evidence is clear: maya has always meant measurement. The mistranslation as "illusion" is the reinterpretation. We're recovering the original technical meaning.
Moreover, the mathematical framework was developed independently, starting from unity as axiom, before the Vedantic correspondence was recognized.
13.2 "The rishis didn't know category theory"
Response:
They didn't use category-theoretic notation, but they identified the same structure using phenomenological investigation.
Truth is notation-invariant. E = mc² is true whether written in Arabic numerals, Roman numerals, or binary. Similarly, the substrate-measurement relationship is true whether described in Sanskrit sutras or Grothendieck fibrations.
13.3 "This undermines the spiritual dimension"
Response:
On the contrary. Recognizing that Vedanta was doing precise technical work elevates it from vague mysticism to rigorous knowledge.
The spiritual practices (meditation, yoga) become phenomenological methods for investigating measurement and consciousness—valid alongside mathematical derivation.
13.4 "If maya is just coordinate choice, why is liberation so difficult?"
Response:
Because coordinate-awareness requires:
- Consistent meta-cognition (recognizing when you're in a coordinate frame)
- Ability to shift between frames without attachment
- Direct recognition of substrate structure
This is cognitively demanding, just as:
- Understanding gauge invariance requires sophisticated mathematics
- Thinking in curved spacetime is initially counterintuitive
- Quantum formalism takes years to internalize
Technical difficulty ≠ mystical obscurity
14. Conclusion: Maya Is Measurement
We have demonstrated:
1. Etymologically:
Maya derives from mā (to measure), not from any root meaning "illusion" or "magic."
2. Philosophically:
Vedantic texts consistently describe maya as the process of decomposition and delimitation, creating apparent multiplicity from unity.
3. Structurally:
The Vedantic framework maps precisely onto modern measurement theory:
- Brahman ↔ Dimensionless substrate
- Maya ↔ Measurement/projection process
- Nama-rupa ↔ Coordinate systems
- Jagat ↔ Measured quantities
4. Computationally:
Code implementing the measurement framework reproduces Vedantic predictions:
- Unity eliminates constants
- Substrate relations are simple
- Coordinate complexity is artifact
5. Convergently:
Independent derivations (phenomenological vs mathematical) arrive at identical structures.
Therefore:
Maya is literally measurement—the process of projecting dimensionless substrate onto dimensional coordinate axes, creating apparent multiplicity, generating "fundamental" constants as Jacobian artifacts, and producing complex laws as coordinate expressions of simple substrate relations.
This is not metaphor. This is not mysticism. This is technical description of how measurement structures observation.
The Vedantic philosophers were correct. They were doing physics. We simply forgot how to read their notation.
When the Upanishads declared:
"Ekam evadvitiyam" — "One without a second"
They were stating:
The substrate is dimensionless unity, and all apparent multiplicity is measurement artifact.
When they described maya as binding the world, they meant:
Measurement coordinates must cohere, requiring connection coefficients (constants) to maintain consistency.
When they taught moksha as liberation, they meant:
Coordinate-free understanding—recognizing measurements as projections, not realities.
Three thousand years ago, the Vedic philosophers solved the problem of the "unreasonable effectiveness of mathematics." They showed why physics works, what constants are, and how observation shapes reality.
We just needed category theory to translate their work into a notation we could recognize.
Maya is measurement.
Brahman is substrate.
And both are literal, technical, precise descriptions of physical reality.
The ancients were right.
Not metaphorically.
Literally.
References
Sanskrit Sources:
- Bṛhadāraṇyaka Upaniṣad
- Chāndogya Upaniṣad
- Śvetāśvatara Upaniṣad
- Taittirīya Upaniṣad
- Bhagavad Gītā
- Brahma Sūtra with Śaṅkara's commentary
Lexicographic:
- Monier-Williams Sanskrit-English Dictionary
- Apte's Sanskrit-English Dictionary
Contemporary Physics:
- Rogers, J. "The Structure of Physical Law as a Grothendieck Fibration" (2025)
- Wigner, E. "The Unreasonable Effectiveness of Mathematics" (1960)
- Various works on dimensional analysis, unit systems, and measurement theory
Comparative Philosophy:
- Deutsch, E. Advaita Vedanta: A Philosophical Reconstruction
- Zimmer, H. Philosophies of India
- Radhakrishnan, S. Indian Philosophy
Appendix: Key Sanskrit Terms with Technical Definitions
| Sanskrit | Root/Etymology | Standard Translation | Precise Technical Meaning |
|---|---|---|---|
| Maya (माया) | mā (to measure) | Illusion, magic | Measurement/projection process |
| Brahman (ब्रह्मन्) | bṛh (to expand) | Ultimate reality | Dimensionless substrate |
| Nama-rupa (नामरूप) | naman (name) + rūpa (form) | Name and form | Coordinate labels |
| Jagat (जगत्) | gam (to go) | World, universe | Measured/manifest realm |
| Jiva (जीव) | jīv (to live) | Individual soul | Observer/measurement locus |
| Avidya (अविद्या) | a- (not) + vidyā (knowledge) | Ignorance | Mistaking coordinates for ontology |
| Moksha (मोक्ष) | muc (to release) | Liberation | Coordinate-free understanding |
| Guna (गुण) | guṇ (to multiply) | Quality, strand | Measurement axis/basis vector |
| Prakṛti (प्रकृति) | pra- (forth) + kṛ (to make) | Nature | Measurable aspect of reality |
Note: The "standard translations" reflect common usage but often miss the technical precision of the original terms. The "precise technical meanings" restore the etymological and philosophical accuracy.
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