Unit 2: Foundation Concepts for Science & Technology in IKS
1. Linguistics & Phonetics in Sanskrit (Pāṇini’s Aṣṭādhyāyī)
Concept & Computational Framework
Pāṇini’s Aṣṭādhyāyī (c. 4th century BCE) is a generative grammatical system consisting of around 4,000 algorithmic rules (Sūtras). It operates similarly to a formal programming language compiler, using auxiliary symbols, context-free production rules, and recursion.
PĀṄINI'S GRAMMATICAL COMPUTATION ENGINE
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MĀHEŚVARA SŪTRAS DHĀTUPĀṬHA & GAṄAPĀṬHA SŪTRA ENGINE
(Acoustic Phonetic Arrays) (Root Verbs & Class Lists) (4,000 Rule Algorithms)
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• Organizes phonemes by • Lexicon of root verbs • Applies transformation,
articulation points and semantic groups elision, and substitution
Key Components
- • Māheśvara Sūtras: A list of Sanskrit phonemes organized by acoustic sound attributes (e.g., stops, nasals, vowels), functioning as an optimized phonetic lookup table.
- • Pratyāhāras (Short Codes): Algorithmic abbreviations used to group range parameters of phonemes (e.g., Hal denotes all consonants).
- • Pratyaya (Affixes) & Dhātu (Roots): Word generation follows rigorous mathematical production rules:
Role of Verbs (Dhātus) & NLP Relevance
Sanskrit roots carry intrinsic semantic definitions. Because Pāṇini’s grammar is completely rule-based and unambiguous, NASA scientist Rick Briggs highlighted in 1985 that Sanskrit serves as an ideal natural language for Natural Language Processing (NLP) and Knowledge Representation in Artificial Intelligence.
2. Number Systems, Place Value, & The Decimal System
Concept of Zero (Śūnya) & Place Value
The conceptualization of zero as both a symbol (‘0’) and a functional mathematical number with arithmetic operations originated in ancient India. Brahmagupta (7th century CE) defined formal rules for zero in his Brāhmasphuṭasiddhānta:
- • a + 0 = a
- • a − 0 = a
- • a × 0 = 0
DECIMAL PLACE VALUE SYSTEM
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UNITS (Eka) TENS (Daśa) HUNDREDS (Śata) THOUSANDS (Sahasra)
10⁰ 10¹ 10² 10³
Representation of Large Numbers
Ancient Indian texts defined named powers of 10 extending far beyond modern naming conventions:
3. Unique Numerical Coding Systems
To encode mathematical data, astronomical formulas, and tables into easily memorized poetic verses, Indian scholars developed alpha-numeric coding schemes.
NUMERICAL ENCODING SCHEMES
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BHŪTA SAṄKHYĀ SYSTEM KAṬAPAYĀDI SYSTEM
(Symbolic Word Encoding) (Alpha-Numeric Mapping)
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• Represents numbers through physical • Maps consonants directly to
world items (e.g., "Netra" = 2) digits 0–9 for word encoding
A. Bhūta Saṅkhyā System
Numbers are represented by everyday objects or cosmological entities associated with that quantity:
- • Candra (Moon) / Bhūmi (Earth): Represents 1
- • Netra (Eyes) / Kara (Hands): Represents 2
- • Rāma / Guṇa: Represents 3
- • Veda: Represents 4
Reading Rule: Read numbers from right to left (Aṅkānāṁ vāmato gatiḥ).
Example: “Veda-Netra” = 4 2 ⟶ 24.
B. Kaṭapayādi System
Assigns digits 0 through 9 to specific Sanskrit consonants, allowing scholars to hide mathematical values inside memorable poetic names:
4. Piṅgala & The Binary System
Acharya Piṅgala’s Chandaḥ-śāstra
In his work on poetic metrics (Chandaḥ-śāstra, c. 3rd–2nd century BCE), Piṅgala developed a formal binary system while analyzing light (Laghu, L = 0) and heavy (Guru, G = 1) syllables.
PIṄGALA'S BINARY COMBINATORICS
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MERU PRASTĀRA PRATYAYA RULES
(Pascal's Triangle Array) (Binary Search & Conversions)
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• Generates binomial expansion • Mātravṛtta algorithms convert
coefficients for combinations binary syllables to decimals
Key Mathematical Structures
- • Binary Combinations: Mapping syllable combinations to binary values (2n metrics).
- • Meru Prastāra (Pascal’s Triangle): A triangular array constructed centuries before Blaise Pascal to calculate combinations of meter arrangements.
5. Knowledge Representation & Vaiśeṣika Physical Reality
THE KNOWLEDGE PYRAMID
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[ WISDOM ]
(Applied Understanding)
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[ KNOWLEDGE ]
(Pramāṇa-Validated)
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[ DATA ]
(Prameya / Properties)
Vaiśeṣika Framework of Physical Reality
Founded by Sage Kaṇāda, the Vaiśeṣika school outlines a scientific taxonomy of the physical universe, categorizing reality into Padārthas (categories of existence) and proposing an early atomic theory (Paramāṇuvāda).
VAIŚEṢIKA PHYSICAL REALITY
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DRAVYA (Substance) GUṄA (Quality) KARMA (Motion)
• 9 Fundamental Elements • 24 Physical Attributes • 5 Types of Movement
The 9 Fundamental Substances (Dravya)
- • Pṛthvī (Earth – Solid state)
- • Ap (Water – Liquid state)
- • Tejas (Fire – Thermal/Plasma)
- • Vāyu (Air – Gaseous state)
- • Ākāśa (Ether – Space continuum)
- • Kāla (Time)
- • Dik (Space/Direction)
- • Ātman (Consciousness)
- • Manas (Mind)
Epistemology: Pramāṇa, Prameya, & Saṁśaya
Key Learning Summary