IKS Chapter 5 — Exam Study Guide

1

Concept of Atom — Vaiśeṣika School High priority

Who & When

1

Maharṣi Kaṇāda proposed atomic theory around 600 BCE or earlier.

2

He called the ultimate particle aṇu — the smallest indivisible bit of matter that takes part in chemical reactions.

3

In modern context: aṇu = molecule; in discussions here aṇu = atom (ultimate constituent).

8 Key Theses

1

Aṇu is invisible and ultimate particle of matter; matter cannot be reduced further than aṇu.

2

Aṇu is an energy point of zero mass and no dimension.

3

Aṇus are spherical, indivisible, eternal, indestructible, imperceptible — must be inferred, not perceived.

4

Of the five bhūtas, except ether, only 4 are perceivable. Ether has infinite extension and single identity — no atoms.

5

Aṇus of similar properties combine → form mono-bhautik molecules; with different classes → hetero-bhautik compounds (binary, tertiary, quaternary).

6

Variety of substances results from atoms of different bhūta-classes.

7

They have chemical combinations and form dyaṇuka (diads) and tresareṇu (triads).

8

Vaiśeṣika proposed chemical changes under temperature — collocation of aṇu and group of aṇus.

Key Sūtras

VS 1.1

Molecules emerge from combinations between fundamental atoms.

VS 5.2

Initial motion of aṇu occurs when time begins; aṇu exists in two states — absolute rest and motion.

aṇudyaṇuka (diads)tresareṇu (triads)Kaṇāda

2

Sāṃkhya & Jaina Atomic Theories High priority

Sāṃkhya School

1

Genesis of matter by tanmātrā (infra-atomic particles) — NOT aṇu. Tanmātrās constitute atoms. Concept is deeper than Vaiśeṣika.

2

Atom is infinitely small, still has dimensions, divisible into tanmātrās. Tanmātrās are integrations of bhūtadi.

3

Tanmātrā series: Śabda → Sparśa → Rūpa → Rasa → Gandha Tanmātrā

4

Tanmātrās share characteristics of both mind and matter — link between continuum and discrete aspects of universe.

Jaina School

1

Matter = pudgal (eternal, always transforming). pud = combine; gal = dissociate.

2

Describes atomic bonding, mutual interactions, and formation of molecules.

3

Chemical combination due to chemical affinity — mutual attraction and repulsion amongst atoms.

tanmātrābhūtadipudgal

3

Laws of Motion High priority

5 Types of Motion (VS 1.1.7)

1

Utkṣepaṇa — Upward motion

2

Avkṣepaṇa — Downward motion

3

Prasaraṇa — Shearing / expansion motion

4

Ākunchana — Contraction (release of tensile stress)

5

Gamana — Linear, rotational and vibrational motion

3 Laws Side by Side

L1

Vaiśeṣika: "Vegaḥ: nimitta-viśeṣat karmaṇo jāyate" — Force is the specific cause of motion.
Newton: Object at rest stays at rest; in motion stays uniform unless external force acts.

L2

Vaiśeṣika: "Vegaḥ: apekṣāt karmaṇo jāyate…" — Change of state proportional to action. (VS 5.1.8)
Newton: F proportional to rate of change of momentum.

L3

Vaiśeṣika: "Kāryavirodhi karma" (VS 1.1.14) — Reaction (kārya) always in opposition to action (karma).
Newton: Action and reaction are equal and opposite.

F = ma (VS 5.1.8 → Newton's 2nd Law equivalent)

vegakarma (motion)kāryavirodhisaṃskāra

4

Electricity & Agastya's Battery Important

Source — Agastya Saṃhitā

1

Agastya Saṃhitā (~2nd millennium BCE). Contains: electric battery cell, electrolysis, electroplating.

2

Modern battery cell has similar methods — validates Agastya's descriptions.

Battery — Materials & Procedure

1

Materials: Earthen pot, copper plate, wet sawdust, zinc amalgam with mercury and copper sulphate.

2

Procedure: Copper plate in pot → add CuSO₄ → moist sawdust layer → mercury-amalgamated zinc sheet → produces mitra-varuṇa śakti.

3

Result (verified 1990): Open circuit voltage = 1.38 V; short circuit current = 23 mA.

mitra-varuṇa śaktiśikhigrīvā = CuSO₄prāṇavāyu = O₂

5

Light & Gravity Important

Velocity of Light

1

Sāyaṇa (14th c CE): "Light travels 2202 yojana per half nimeṣa" → 4404 yojana/nimeṣa.

2

= 1,86,000 miles/second. Modern (Michelson-Morley) = 1,86,282 miles/second. Remarkably close!

3

Bhāratīya knew light has finite velocity. Western world believed it was infinite until much later.

Speed of light = 4404 yojana/nimeṣa ≈ 3,00,000 km/s

Concept of Gravity

1

Ṛgveda: Earth floats freely in space; oceanic tides caused by moon.

2

Bhāskarācārya: Earth has āṛkṣṭi śakti (attractive force). ~500 years before Newton.

3

Śatapatha Brāhmaṇa: "Sun strings planets to itself on a thread" — thread = gravitational force.

gurūtva = gravityāṛkṣṭi śaktiBhāskarācārya

7

Vedic Cosmology High priority

Big Bang & Origins

1

Taittirīya Brāhmaṇa: "Earlier there was absolutely nothing..." — parallels modern Big Bang.

2

Hiraṇyagarbha = cosmic egg with golden color = primordial fireball.

3

Mahat sphoṭa = Big Bang. First kick of creation — "bang" + galloping radiation.

Expanding & Cyclic Universe

1

Brahmāṇḍa = universe. Brahman (to expand) + aṇḍa (egg) = "expanding egg".

2

Cyclic universe: Universe cannot arise from nothing — cycles of creation and destruction.

HiraṇyagarbhaMahat sphoṭaBrahmāṇḍa

8

Zero, Pi & Number System High priority

Zero (Śūnya)

1

Zero = śūnya. First recorded use: 3rd–4th century CE as dot symbol in Bakhśālī manuscript.

2

Brahmagupta (628 CE) — first to formally define Zero, give it a symbol, show n−n = 0.

3

Piṅgala (450–200 BCE) — first to use 'śūnya' for Zero in binary numbers.

Pi (π)

1

Āryabhaṭa: Diameter = 20,000 → circumference = 62,832 → π = 3.1416.

2

Mādhava-Leibniz Series (14th c CE): Calculated π to 11 digits, 300 years before Leibniz!

π/4 = 1 − 1/3 + 1/5 − 1/7 + ⋯ (Mādhava Series)

śūnyaPiṅgalaBrahmaguptaMādhava

10

Kerala School & Vedic Math High priority

Kerala School of Mathematics

1

Founded by Mādhavācārya (14th–17th century CE).

2

Yuktibhāṣā (1530) of Jyeṣṭhadeva: Taylor series with proofs. Considered world's first calculus text.

3

Nīlakaṇṭha Somāyājī formulated equation of centre for planets 100+ years before Kepler.

Vedic Mathematics

1

By Swami Bhāratī Kṛṣṇa Tīrtha. Based on 16 sūtras from Atharvaveda.

2

Ekādhikena Pūrveṇa — By one more than previous.

3

Nikhilam Navataścharamam Daśataḥ — All from 9, last from 10.

YuktibhāṣāTantrasaṅgrahaSwami Bhāratī

IKS: The Knowledge System of Bhārata