Indian Philosophy, Logic, and Vedic Mathematics Concepts

Posted on Feb 2, 2026 in Philosophy and ethics

Foundational Concepts in Indian Thought and Logic

I. Epistemology and Logic (Nyaya School)

1. Defining Knowledge Acquisition (Pramāṇas)

  • Pratyaksha: Direct perception through the senses.
  • Anumana: Knowledge gained through inference (e.g., smoke implies fire).
  • Upamāna: Knowledge derived from comparison or analogy.
  • Shabda: Knowledge received from reliable verbal testimony.

2. Components of Inference (Anumāna)

The five-step syllogism:

  1. Pratijña: The proposition (e.g., The hill has fire).
  2. Hetu: The reason (Because it has smoke).
  3. Udāharaṇa: The universal rule (Wherever there is smoke, there is fire).
  4. Upanaẏa: Application of the rule (The hill has smoke).
  5. Nigamana: The conclusion (Therefore, the hill has fire).

3. Types of Argumentation

  • Vadā: A debate aimed at discovering truth using valid logic.
  • Jalpa: A debate aimed only at winning, often using tricky arguments.
  • Vitanḍā: Destructive criticism where the opponent’s claim is refuted without offering a counter-claim.

II. Metaphysics and Mind (Sankhya and Yoga)

4. Sankhya Philosophy Structure

A dualistic system based on two eternal realities:

  • Purusha: Pure consciousness.
  • Prakriti: Matter/Nature, comprising the material world and mind components (Manas, Ahamkara, Buddhi).

5. Yoga Philosophy and Mind Control

The primary aim is to realize the true self by removing mental disturbances.

Chitta-vrtti-nirodhah: The cessation of the fluctuations (vrttis) of the mind-stuff (chitta).

Pillars of Knowledge in Yoga: Śraddhā (faith), Vīrya (energy), Smṛti (memory), Samādhi-prajñā (wisdom in concentration).

Chapters of Sutras: Samadhi Pada focuses on Enlightenment.

III. Ancient Computation and Linguistics

6. Vedic Mathematics Sutras

Vedic Mathematics uses concise sutras for fast calculation.

  • Ekādhikena Pūrveṇa: “By one more than the previous one.” Used for squaring numbers ending in 5. (Example: $45^2 = (4 \times 5) | 25 = 2025$).
  • Parāvartya-Yojayet: “Transpose and adjust,” used in division.

7. Meru-Prastāra and Chandas

Meru-Prastāra: A triangular arrangement of numbers showing combinations, similar to Pascal’s triangle. It shows combinations of syllables in poetry.

Chandasāstra: The study of poetic meters, developed by Pingala. It uses binary logic based on Laghu (short syllable, 0) and Guru (long syllable, 1) combinations to determine meter structure.

8. Panini’s Ashtādhyāyī

Ashtādhyāyī: Panini’s comprehensive Sanskrit grammar text, organized into eight chapters of concise statements (sutras). It employs algorithmic techniques like recursion and meta-rules for linguistic derivation.

IV. Ancient Cryptography

9. Secrecy in Arthashastra

Kautilya’s Arthashastra details methods for secret communication to avoid enemy detection.

  • Mlecchita Vikalpa: Cipher writing techniques.
  • Techniques: Word substitution, hidden messages in objects, and coded scripts.

10. Modern Parallels to Ancient Security

Ancient concepts parallel modern security:

  • Dvāra (Gate): Access Control/Login Systems.
  • Mantra-shakti: Passwords/Secret Codes.
  • Two-step rituals: Multi-factor authentication.

V. Comparative Analysis

11. Machine Learning vs. Yogic Mind

Similarities: Both involve repetition (abhyāsa/iterations) and error correction (nirodhah/loss minimization) leading to improvement.

Differences: Yoga seeks self-realization (conscious goal); ML seeks task performance (computational goal) and lacks consciousness.