5.2. Atomic sciences
The Vaiseshika(meaning atomism/particularity) school is the Indian school of natural philosophy and physics. The Vaiseshika had developed their physical theories to an astonishing level of sophistication anticipating modern theories of physics. Like all Darsanas, it has a foundational sutra text, the
Vaiseshika sutras(VS) composed by Kanada(600BCE)[1] which summarizes the theories of the school in various areas. The next most important texts were composed by Prashastapada(various dates: 200, 600AD) Various Nyaya-Vaiseshika philosophers then added commentaries to both texts up until the late medieval ages. I will show you the sutras and the kind of argument framed in the 5 member Indian syllogism which were used by them to prove their propositions.
Vaiseshika classification system
All science begins with a classification system in order to classify substances into elements and groups. The earliest classification system used in ancient times was the 5 elements (literally fire, earth, air and water) and animal, mineral and vegetable classification system which is of course primitive and sketchy and it is hard to do science with such an imprecise system. In early modern times we used the Cartesian classification of mind and matter defined by the properties that matter is divisible and extended and mind is indivisible and not extended (i.e., not spatial and temporal) In later modern times we used the Periodic table to classify the chemical elements, and in contemporary times we use the Standard model to classify elementary particles. We do not yet possess a complete system of classification that can account for all entities like space, time, mind and consciousness.
The Vaiseshika classification system is arguably the most analytical, comprehensive and precise system of the classification of our empirical world because it accounts for all entities of our world, it for this reason why Vaiseshika when synthesized with Nyaya is considered the equivalent to modern analytical philosophy.[2] The empirical world is classified into 7 broad categories: Substances, qualities, actions, class, species, inherence and absence. As this article is not intended to be a primer on Vaiseshika philosophy, I will only focus on the physical categories substances, qualities and actions and here too, on the sub-classes physical matter and space and time( ignoring mind and consciousness) and also cite directly from the VS[3]
Substance/Laws of matter
A substance is that which has qualities and can undergo actions e.g. Sugar is a substance because it has the quality of the taste sweetness and it can undergo actions such as I can move sugar from one point to another. A substance thus cannot be identified as just a lump of something, but it known as an aggregate of qualities and actions(It is for this reason the Buddhists reject the actual existence of substance, as it nothing more than a fleeting states of changing qualities and actions)
The remarkable contribution of Kanada, for which his namesake is known(literally, the eater of atoms) was the theory that all material substances are made out of atoms. Atomism, however, is not just unique to Kanada, who propounded the Hindu version of atomic theory, but was the central thought and doctrine of Buddism and Jainism too. Each gave their own variation of atomic theory. The centrality of atomic theory within Hinduism, Buddhism and Jainism is perhaps owing to the fact that the earliest precursor to the notion of atoms is found in the Upanishads, for example the dialogue with Uddalaka asking his son to split a seed into its parts and that too into its parts(discussed earlier). The focus in this article will be Kanada’s theories, but it is worth very briefly describing the Buddhist and Jain versions too.
Buddhist atomic theory: The Buddhist’s considered atoms to be flashes of energy taking place moment to moment, very similar to modern particle physics of fermions etc flashing in and out of existence. It is now known in quantum physics that particles do indeed flash in and out of existence momentarily[4]
Jain atomic theory: The Jains considered atoms to be units of motion(karma) moving about at tremendous speed across the universe, many times the speed of light. The Jains conceptualize atoms in terms of potential existence with no sensible properties, and real with sensible properties, a dead ringer for modern wave-particle duality theory.[5]
It should be pointed out, while atoms have always been natural to Indian thought, they have been considered alien in Western thought, this may suggest atoms were not original to the Western psyche(In the previous article it was suggested Democritus probably learned about atoms from the Indians)
Laws of substances/matter
VS.10. Substances originate another Substance, and qualities originate another quality.
Meaning: A substance can be modified into another substance, such as a piece of clay can be modified into a pot shape or a thread can be woven into clothes but this will not change the properties of the substance. Similarly water can be modified into ice, liquid and gas but it will not change its properties (just its state). On the other hand only certain reactions will change the properties of a substance. In other words this is explaining the difference between physical state changes and atomic and chemical changes(elaborated on later in this article)
VS.12. Substance is not annihilated either by effect or by cause.
Meaning: This is a statement of the law of conservation or the third law of thermodynamics, a substance can neither be created nor destroyed, it can only be changed from one form to the other. The physical substances (earth, water, fire, air) are made out eternal and distinct atoms. The atomic combinations will originate new substances owing to the atoms joining with one another, but the atoms themselves cannot be destroyed. The total number of atoms in the universe will always remain constant.
VS.23. A single Substance may be the common effect of more
than one Substance.
Meaning: A substance can be made out of a combination of other substances e.g. Water is a molecule made out of two gasses hydrogen and oxygen.
VS.27. Substance is the joint effect of many Conjunctions.
A substance is a sum total of many forces/actions of atoms within that it that hold it together, when the forces are displaced, then the substance fissions releasing energy.
Physical substances:qualities
Earth: smell, taste, colour, touch and sound
Water: taste, color, touch and sound
Light/Fire: colour, touch and sound
Wind/Air: touch and sound
Ether/Space: sound
In addition to these sensible qualities, atomic compounds also have additional qualities like mass, size, dimension, fluidity (and its opposite hardness), viscosity, charge(roughness and smoothness) etc
In cases where the substance lacks colour i.e. it is invisible, the Vaiseshika have to use the inference of commonly observed to posit its existence, which is the equivalent of what we call theoretical physics in modern physics – this is when we infer the existence of imperceptible entities like atoms, quantum fields or extra spatial dimensions from things which we can observe, yet cannot observe the inferred entities themselves. Thus the following have to be inferred to exist in Vaiseshika: wind, ether, space, time and of course atoms. Thus proofs are given for their existence, but in special circumstances we can render something imperceptible perceptible (like electrons can be rendered perceptible in cloud chambers) The standard example given in Vaiseshika is how sound can be made audible in air.
It may seem odd to say earth etc. are elements, but if you think of anything material you can classify it in either of these 5 categories because they correspond to sensory channels e.g., let’s take the phenomena magnetism, it has no smell, hence it is not Earth; it has no taste, hence it is not water; it has no colour, hence it is not light; It has touch, hence it is wind.
Material substances are of two types: Eternal and non-eternal.
Eternal are the 4 types of atoms whose aggregates produce infinite variety of substances, and ether
Earth atoms, which is responsible for the quality of smell
Water atoms, which is responsible for the quality of taste
Light/fire atoms, which is responsible for the quality of colour
Wind/Air atoms, which is responsible for the quality of touch
Ether, the only physical element which is non-atomic
The Vaiseshika definition of what an atom is matches our quarks:[6]
Atoms are infinitesimal, have no magnitude and point-like
They are spherical point sources(parimandala)
They possess vibratory and rotary motion/spin(parispanda)
They are combine with other atoms based on natural laws based on mutual compatibility
There are four distinct type of atoms not reducible to one another
Each distinct atom is responsible for a sensible property
Similarly quarks are massless, have no magnitude and are point like, they have spin, they combine to produce larger particles and they are of distinct types. They are responsible for the various sensible properties we see.
Proof for the existence of atoms:
VS.2.The effect is the mark (of the existence) of the ultimate
atom.
1 Tasya/ i. e. of the ultimate atom ; karyyam, e. g., the water-pot
and the like ; lingam. Accordingly the stitram of Gautama. " From
the evolved is the production of the evolved, on the evidence of (ex
perience by) perception," (Nyaya-sutram IV. i. II). Now the inter
relation of parts and wholes is perceived. If it were unlimited, there
would be no difference in size of measurement between mount Meru and
a grain of mustard seed ; for, they wauld be without distinction, both
being orginated by infinite parts. Nor can it be said that difference
will be caused by the differences of the size of each part, and of the
aggregation of
1. Atoms must exist
2. Because otherwise matter would be infinitely divisible
3. If matter was infinitely divisible, then a mountain and a seed would be infinitely divisible, thus it would be possible to start with a seed and end up with a mountain
4. One begins with a seed and ends up with a mountain which is absurd.
5. Therefore matter must be made of atoms
Proof for imperceptibility and no magnitude of atoms:
]VS.162. External perception (takes place), in respect of an object
Possessing magnitude, by means of its possession of that which
is composed of more substances than one, and by means of colour.
1. Atoms must be without magnitude and infinitesimal in size
2. Because all compounds of atoms have magnitude
3. When a compound is broken down into its parts, it produces parts of lesser magnitude, and when they are broken down it produces parts of even lesser magnitude, and if we keep breaking it down eventually it must be terminated at a point where there is no magnitude.
4. Magnitude therefore originates not from the size of atoms which must be infinitesimal, but from the number of atoms, just as a forest originates from a collection of trees
5.Therefore atoms are without magnitude and infinitesimal in size.[7]
Non eternal are all material substances produced out of the combinations of these atoms and because they are compounds they are non-eternal, because the combinations can be broken into its elemental atoms. The qualities of a particular compound is due to the presence of a specific atom .e.g. If a substance has touch, that is because it has wind atoms. If it has mass, that is because of earth atoms.
Earth and water atoms/Atomic and chemical physics
Earth and water substance can be either organic or inorganic.
The Nyaya-Vaiseshika philosphers conceptualized many theories on atomic combinations distinguishing between atomic reactions and chemical reactions. In both types of reactions heat is seen as the cause that makes or breaks the bonds. Two atoms combine to make a binary atoms(dvayunakas) Binary atoms combine to make a ternary atom(triyunaka) These pairs and triplets then combine in various permutations and combinations to form innumerable substances(similar to contemporary theories on how quarks combine) Atoms combine based on compatible properties and natural laws. [6] Jain philosophers theorize that it is due to opposing touch qualities like roughness and hardness, similar to the modern notion of charge, that the atoms combine, anticipating modern electrocolvant bonding.[6][8]
The atomic aggregate will have the properties of the parent atoms that form it present with it, but the aggregate itself will have new emergent properties. This takes place through either atomic reactions or chemical reactions under the influence of heat(pakajotpati).[9]
Atomic reactions(Pilupaka, literally heating of atoms): Atomic reactions take place when heat breaks down an atomic aggregate into its atomic parts, which then recombine in other combinations to form new aggregates. In this type of reaction the original aggregate is decomposed and formed into a new aggregate. This reaction is unobservable.
Chemical reactions(Piturapaka, literally heating of molecules): Chemical reactions take place when heat either externally (exothermic) or internally (endothermic) causes the properties of a compound of atoms (i.e, molecules) to change and originates new groupings, without decomposing into atoms itself. This is observed when the pot is heated up and changes colour, the pot does not decompose into atoms, but merely changes its chemical properties due to chemical reactions.
Prashastapada explains atomic reactions take place in lower order aggregates and chemical reactions take place in higher order aggregates.[10]
The chemical reactions that happen on Earth such as grass changing colour, corrosion on iron, photosynthesis is explained due to solar heat by Uddayana(800-900AD). The light particles penetrate the interatomic spaces and cause chemical changes to happen. Chemical reactions that take place in the body such as metabolism formation of tissues or fertilization of the ovum during sexual intercourse are explained as due to the heat of the body.[10][11] The Vaiseshika also noted that different degrees of heat will produce different levels of chemical changes. Thus its chemical theories were not purely speculative, but based on observation.
Proof for Atomic and chemical reactions:
1. Atoms combine and break apart due to forces and especially the application of heat and light
2. Because no conjunction or disjunction is possible without an action
3. Any action of joining or disjoining of something requires action to bring the two entities together, such as water does not boil unless water is combined with heat or a shard of clay does not change colour unless combined with heat, as is observed in reactions where the clay is heated and it changes colour
4. Here too the conjunction of heat with water or clay with heat causes activity in the atoms and changes its configurations
5. Therefore, atoms only combine or break apart due to forces and especially the application of heat and light
Now, if you are wondering whether the atomic and chemical theories of the Vaiseshika were actually applied practically, the answer to this is affirmative, in Indian chemistry an equally advanced level of sophistication was reached (this will be covered in section 6, but if you cannot wait this long, please read
History of Hindu chemistry, available on archive.com) We have already seen applications of these theories in Indian medicine(section 3) in Nanomedicine where minerals are reduced into nanoparticles and the testing and formulation of drugs(I hope in light of my new revelations the nanomedicine sounds more credible). The applications to metallurgy are well known in the advanced chemistry seen in corrosion proof pure iron seen in the famous Iron pillar of Delhi(this technology is still not reproducible) the production of wootz steel(new evidence shows it is reinforced with carbon nanotubes) and zinc production. There can be no doubt the ancient Indians had a very advanced knowledge of chemistry, and from the Vaiseshika we learn they understood the theory of chemistry as well.
Water atoms
Water atoms are atoms that possess natural fluidity and are responsible for flavour and taste, as such water atoms could refer to not just water, but any kind of natural fluidity such as kinetic energy to the movement of electrons. Fluidity or kinetic energy was understood to be present in both earth and water, except fluidity was the natural property of water, whereas earth had accidental fluidity, i.e., it had to be originated within it by heating solids, causing the atoms within it to break out of their solid lattices.[10]
The concepts of boiling point, melting point and physical state changes were known to the Vaiseshika. Here is the proof:
VS.203.The sun s rays (cause) the ascent (of water), through
conjunction with air. 203.
6. (Particles of water fly upwards), by means of concussion
with impulse, and of conjunction with the conjunct. 204. .
Condensation, and dissolution, of water, are due to con junction with fire. 206.
9. The pealing of thunder is the mark of that. 207.
10. 11. (Thunder-clap results) from conjunction with, and dis
junction from, water, of the cloud. 209.
A commentary is given by one of the Nyaya-Vaiseshika philosophers in the VS:
Aqueous ultimate atoms, originating a binary atomic aggregate
in consequence of being impeded by celestial fire, do not originate
fluidity in these binary atomic aggregates. Snow, hail, etc, void of
fluidity, are thus originated, in the course of binary and others atomic
aggregates, by constituent {.arts void of fluidity. Therefore hardness
is observed in them. Such being the case, it may be asked, what proof is there that snow hail, etc., are modifications of water. Accordingly it has been said Dissolution also from conjunction with fire By a more powerful
conjunction with fire, action is produced in the ultimate atoms constituve
of snow, hail, etc. Action produces disjunction. From the
successive destruction thereby of originative conjunctions follows the
destruction of the larger compounds, snow, hail, etc. In consequence of the departure therefrom of conjunction with fire, which was an
impediment to fluidity, the very same ultimate atoms originate fluidity in binary atomic aggregates; whence dissolution takes place of snow
hail, etc., thus endowed with fluidity. Here also the subsequent ingress
of a more powerful fire is the efficient cause.
Proof of melting points of different substances:
VS.55. The Fluidity of clarified butter, lac, and wax, through conjunction with Light is similar to that of Water. 54.
VS.56. The Fluidity of tin, lead, iron, Silver, and gold, through
conjunction with Fire, constitutes their similarity to Water
Meaning: Some of the physical elements can become liquefied by originating fluidity within them, in order the lowest melting point is water, ice, snow, hails, higher melting point is wax, butter, lac and higher still is tin, lead, iron, silver and gold.
Proof for physical state changes and phases of matter:
1. Ice, water and gas are the same substance with different level of kinetic energy
2. Because they transform into one another when combined with heat energy
3. What transforms is just the same substance in a different form, just as molten gold of higher fluidity solidifies into solid gold of less fluidity .
4. Here too we see ice, water and steam transform into one another
5. Therefore ice, water and gas are just all just water with different levels of fluidity owing to different levels of heat energy
Light atoms/Optics
Light was understood to me made out of a stream of very minute particles travelling in straight lines at a very high but specific velocity. Heat, light and all different colours were to be understood to be different varieties of the same light particles.(The equivalence of light and heat was not understood until Joules in modern times) [6][10]
There were two main theories for how we see, however in principle both theories are correct. The first theory which was accepted by both Nyaya-Vaieshika and Mimassa is that we see because invisible particles project outwards from the senses of our eyes and contact the object(i.e. the senses have to project outwards) The Mimassas further held that light radiated outwards in a stream of particles(i.e. radiation) The second theory proposed by Sushruta(various dates, 600BCE is most common) is that light rays impinge upon our retina, and are transmitted via the optic nerve to the brain. Cakarpani(1000CE) commenting on Susrutha confirms this, adding that light propagates as a wave like sound, except with much more faster velocity.
Various optical phenomena were understood[12]
Transparency: Transparency is when the light particles go right through an object, and opacity is when the object absorbs the light particles
Reflection: Reflection happens when the light particles strike an object and deflect off from it. It was also stated that the angle of incidence equals the angle of reflection.
Refraction: Refraction occurs when the light particles enter a refractive medium such as water and slow down and deflect from it
Considering the sophistication of the knowledge of optics of the Vaiseshika and Indians in general, the allusion we saw earlier to microscopes or some viewing glass lens in the Charaka Samhita and the suggestion of its use in Parasara’s botanical work describing a plant cell by some biologists and botanists may sound more plausible. It is very likely that they knew all about optical properties of different kind of materials.
It is highly likely that Arabs scientists such as Ibn al-Haytham(book of opics) who were the first to build a camera obscure and investigate various optical phenomena were very conversant with the Vaiseshika.
Speed of light?
There is also a very curious reference to the “speed of the sun” by a Vedic scholar Sayana, commenting on a passage in the Rig Veda. He states that the sun travels at the speed of 2200 yojanas in half a nimesha. Yojana and nimesha are standard Indian metric units described in the Arthshastra and other Indian texts, which when converted it translates to 19818 miles/ 8/75 sec = 186,433.22 mps, 99.9% accurate to the current value of the speed of light. This is too much of a coincidence, to be considered a coincidence. Kak argues that this is an indication of a lost tradition of astronomical knowledge, somehow somebody before Sayana had calculated this figure but the methods they used were obviously not known to Sayana, nor might he been aware that this is the speed of light and not literally the speed of the sun.[13]
It is worth pointing out that early estimates of the speed of light were even less accurate than Sayana estimate. When converted to km/s Sayana’s figure is: 300,035.8
1675 Rømer and Huygens, moons of Jupiter
220,000
1729 James Bradley, aberration of light
301,000
1849 Hippolyte Fizeau, toothed wheel
315,000
1862 Léon Foucault, rotating mirror
298,000±500
1907 Rosa and Dorsey, EM constants 299,710±30
1926 Albert Michelson, rotating mirror
299,796±4
1950 Essen and Gordon-Smith, cavity resonator 299,792.5±3.0
1958 K.D. Froome, radio interferometry 299,792.50±0.10
1972 Evenson et al., laser interferometry 299,792.4562±0.0011
1983 17th CGPM, definition of the metre 299,792.458 (exact)
(Source: Wiki, speed of light)
Wind atoms
Wind atoms are the cause of all movements, and various winds are recognized from actual literal winds (the air heated by solar winds) to magnetic winds, electrical winds, energy winds, gravitational winds to winds that bring together atoms. In other words what we call in modern physics forces (gravity, electromagnetic, nuclear) Astonishingly, the Vaiseshika understood all forces to be the varieties of the same unified natural order(adristam), anticipating contemporary Grande Unified theory.
Proofs for various forces:
The proofs for each force follows the same arguments using an general observation inference to posit the existence of an unseen force:
VS.195. The movement of the jewel, and the approach of the needle has adristam as their cause.
VS.205 The circulation (of water) in trees is caused by adristam.
VS.211. The initial upward flaming of fire, the initial sideward blowing of air, and the initial actions of atoms, and of mind are caused by adristam.
Meaning: Adristam literally means unseen force. In Vaiseshika it refers to natural laws of which magnetism, gravitational attraction, circulation of water in trees, electrostatic attraction, and movements of atoms are all instances.
Magnetism:
1. The magnet moves the needle due to an unseen force between them
2. Because the needle moves when the magnet is brought near it
3. Where there is movement, one must infer a force, such as the grass does not move unless a wind blows
4. Here there is also movement
5. Therefore there must be an unseen force between the magnet and needle
That magnetism was understood by the Vaiseshika can be seen clearly articulated in Sankar Mishra’s(800-900AD)
Upaskara where he also mentions how the needle moves when the magnet is near and also talks about creating new magnets by rubbing iron against one of the poles of a magnet. The use of magnetism in practical applications appears to have been applied in seafaring and navigation from early times. In Bhoja’s(1100CE)
Yuktikalpataru he warns of using iron on the base of the ship, because it would otherwise be attracted by magnetic rocks at sea.[14] There is an allusion to a magnetic compass called
Matsya yantra where a metallic fish was suspended in oil to point north, allowing navigation. As the history of navigation in ancient India goes back beyond 1000BCE the magnetic compass is most likely to a be very ancient, allusions can be find to it throughout Indian texts[15]
Sankara Misra also noted electrostatic attraction: [16]
1. The amber attracts the grass or straw due to an unseen force between them
2. Because the amber when rubbed gains the power to attract the silk
3. As no movement is possible without a force
4. And here there is movement of attraction
5. Therefore the amber attracts the silk due to an unseen force
Gravity:
VS.187. In the absence of conjunction, falling (results) from
gravity.
VS.188 Owing to the absence of a particular atom movement,
there arises no upward or sideward motion (in the fruit, bird, and
arrow)
Meaning: When there is no countering force, an object will fall due to gravity. The fruit on the branch of a tree is held up by the branch, when the branch breaks, the fruit falls due to gravity. A bird is held up by the movement of its wings, in its absence the bird falls due to gravity
Proof:
1. The object falls due to gravity
2. Because an object remains at rest or continues moving unless it is acted upon by a force
3. Such as an axe cannot itself cut the wood unless a force is applied
4. Here the object is seen to fall when the support is removed
5. Therefore the object falls due to gravity
That Kananda understood that the cause of falling is gravity, which is the inherent property of mass, one can easily deduce from this that the Earth and the planets have their own gravitational field. Although we do not find any explicit statements of this until Aryabhatta(500CE) and Brahmagupta(600CE)
Al-Biruni cites Brahmagupta defending Aryabhatta’s theory that the Earth spins on its own axis.[17]
"(critics argued)If such were the case, stones would and trees would fall from the earth."
According to al-Biruni, Brahmagupta responded to these criticisms with the following argument on gravitation:
"On the contrary, if that were the case, the earth would not vie in keeping an even and uniform pace with the minutes of heaven, the pranas of the times. [...] All heavy things are attracted towards the center of the earth. [...] The earth on all its sides is the same; all people on earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow, that of fire to burn, and that of wind to set in motion... The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth."
It is very likely given that Kananda had already mentioned gravity in the VS that this Kananda also knew about the heliocentric theory of gravitation. It has already been pointed out earlier the heliocentric theory of gravitation is hinted at in the Vedas, describing the sun as the center of spheres stringing them along in their orbits by its wind(Aryabhatta also uses the term “wind” to describe gravity)
Ether/Acoustics
The existence of the ether is inferred by the fact of sound, as a medium that must carry the vibrations and have vibration as its nature. The Vaiseshika understood that air was not the medium of sound, but merely the cause for what makes sound audible, the sound was literally being produced by the sound waves travelling through the air molecules(thus they understood that sound cannot travel in a vacuum of air). The sound itself belonged to the ether whose nature was sound. Its existence is posited because while Earth is the carrier of smell, water of taste, light of colour and wind of touch, there must be a 5th material substance posited to account for sound. Ether is eternal, infinite and homogeneous, because sound can be heard anywhere. The ether of the Vaiseshika is identical to the quantum-field of contemporary physics, which also is the medium through which waves propagate.(Ether is very important in Samkhya darsana)
Unlike the Mimassa, the linguistic school which maintained that sound(shabda) was eternal and emanated from the substratum of reality(tied in with the classical Indian belief that the
pranava or Aum is sounding at the fundamental level of reality ) The Vaiseshika refuted this by saying all sounds are produced, therefore they cannot be eternal. The argument is as follows
1. Sound is non-eternal
2. Because it is produced
3. Anything that is produced has a beginning in time, like a pot is produced by the potter
4. Here too sound was produced and had a beginning
5. Therefore, sound is non-eternal
VS.110.Sound is produced from Conjunction, from Disjunction, and from Sound also.
Meaning: Sound can either be produced by two things contacting one another, like the drum stick and the drum, or a breaking something apart like breaking a twig or it can generated from other sounds, such as sound waves propagating and bouncing of one another. Prashastapada expands on this sutra and puts forward the wave theory of sound, that sound radiates out in concentric waves from its source before reaching the ear.[17] The proof is as follows:
1. The sound most travel out in a series of concentric waves from its source before it reaches the ear
2. Because waves move in wavicular motions, the first must generate the second wave, and second wave the third and so on
3. A wave travels in concentric circles from its source, as can be seen in the example of the pebble thrown in the pond
4. Here too the sound is a wave emitting from a source
5. Therefore the sound must travel out in a series of concentric waves from its source before it reaches the ear
The physics of sounds, and concepts like frequency, pitch, amplitude, tones, harmonics, nodal change all were understood.[18]
Immaterial substances
Space
Time
The substance of space is inferred through the qualities of position and direction, thus space is the framework within which we can locate the position of particles. The substance of time is known though the qualities of past, present and future and slow and fast. However, according to the Vaiseshika space and time are both one and continuous, their division are mere abstractions:
VS.91. The unity (of space is explained) by (the explanation of
the unity of) Existence
VS.92. The diversity (of Space) is due to the difference of
effect(The meaning is that the attribution of multiplicity is due to the
divergence of effects)
VS.93. (The direction comes to be regarded as) the east, from
the past, future, or present conjunction of the sun
VS.95. By this, the intervals of direction are explained
The Vaiseshika understood that space and time are eternal, infinite and homogeneous and that all notions of individuated space such as pot-space, inner and outer space and individuated notions of time as past, present and future are relative abstractions. Later Nyaya-Vaiseshika philosophers, much like Einstein argued that space and time are one continuum, just different phase of it, anticipating modern 4D geometry. There is an understanding pervading ancient Indian thought that time flows at different speeds in different dimensions of space, such themes are found in the Upanishads, Puranas and the Yoga Vasistha.[6]
Vacaspati Misra(800AD) anticipates Descartes coordinate geometry by 8 centuries to conceptualize space as being represented in 3D and any particle in space can be located by measuring its distance relative to any other point represented along 3 imaginary axis of space.[19]
Actions/motions
Actions/motions are the causes for why atoms combine the cause for why an object remains at rest or an object continuing in a straight line changes direction. In other words what we call forces in Newtonian mechanics. The Vaiseshika understood that forces were vectors and acted on objects. A very comprehensive definition of what motion/force is, is given by Prashatapada:[20]]
• Ekadravyatva : a single motion acting upon a single object at one time.
• Ksanikatva : motion acting upon a body and being completed almost immediately (i.e. instantaneity).
• Murta-dravya-vrttiva : motion in relation or connection to physical objects.
• Agunavattva : an absence of qualities.
• Gurutva-dravatva-prayatna-samyogajatva : motion that is generated by gravity, fluidity, own effort, and conjunction.
• Svakarya-samyoga-virodhitva : opposed by simultaneous motion(s) caused by the first motion.
• Samyoga-vibhaga-nirapeksakarana : motion as an independent cause of conjunctions and disjunctions.
• Asamavayi-karanatva : motion as 'non-inherent cause'.
• Svaparasraya-samaveta-karyarambhakatva : causing conjunctions and disjunctions in themselves and other bodies or objects.
• Samana-jatiyanarambhakatva : motion that cannot cause the occurrence of like motion.
• Dravyanarambhakatva : motion that cannot cause other bodies/objects to move.
• Pratiniyatajatiyogitva-digvisista-karyavrambhakatva : can be classified according to the direction of its initial motion.
Types of motion
Throwing upwards and rising motion
Throwing downwards and falling motion
Attraction and contraction motion
Repulsion and expansion motion
Straight motion
Circular motion
Angular motion
Elastic motion/elasticity
Vibrational motion/harmonics
Laws of motion in the VS:
VS.20. Action is the common cause of Conjunction, Disjunction^
and Impetus.
Meaning: Forces are the cause for any change in movement, breaking or joining of substances and breaking and joining of atoms. If any movement is perceived, it can be inferred there is force acting on the object. This is Newton's first law.
VS.24. Action is not the joint effect of many Actions, on account of the difference of their Attributes.
Meaning: Forces do not generate other forces , upwards force does not generate gravity, which does not generate horizontal force, which does not circular force. Each is a separate vector force and acts singularly on a body. A body can have a number of forces acting on it(vectors)
VS.29. Throwing upwards (is the joint product) of Gravity,
Volition, and Conjunction.
Throwing upwards has two vector forces, there is the upwards force of throwing the object up and the downwards force of gravity
VS.189.Particular atomic movement (results) from particular effort
volition..
VS.190.From particular atomic movement, (results) particular throwing away.
Meaning: Newton’s second law of motion, a particular motion of a particular mass results a particular force i.e., the particular acceleration of an objection is directly proportional to the force applied, mathematically F=MA.[21]
The Vaiseshika’s understood that the movement of an object is not continuous and can be represented as a series of successive moments (which is the forerunner to infinitesimal calculus) and that the impulse generated in the object is reproduced at each successive moment carrying on in a straight line, until it is destroyed by another force. Similarly, it was understood that the acceleration of the object was directly proportional to the force applied.
VS.182 And, from conjunction with the hand, a similar Action
appears in the pestle.
VS.183. In the action, produced in the pestle, etc., by impact,
conjunction with the hand is not a cause, because of the absence
(of volition)
VS.185. The action (i. e., upward motion) in the hand is from
impact, and from conjunction with the pestle.
Meaning: The kinetic energy from the hand is transferred into the pestle, when the pestle impacts the ground, it produces an equal and opposite reaction force causing the hand to move up. Thus we find implicitly Newton’s third law of motion here for every action there is an equal and opposite reaction.
Vector forces explaining the parabolic path of a projectile, such as an arrow
VS.195. Peculiarities of non-simultaneous conjunctions of the
arrow, are the mark of the diversity of its actions.
VS.197. The first action of the arrow is from impulse ; the next
is from resultant energy produced by that (i.e., the first) action ;
and similarly the next, and the next.
VS.198. In the absence of propulsive energy generated by action, falling (results) from gravity
Commentary: Gravity which is the cause of falling, invariably follows (thearrow), at every moment. That gravity, being counter-acted by resul
tant energ/, could not cause the falling of the arrow;. Now, in the absence
of the counter-active, the very same gravity causes falling. This is the meaning.
Meaning: The arrow continues in straight line because of the momentum energy provided by the bow, but at each successive moment the force of gravity acts against it, causing the arrow to lose energy gradually and fall.
Proof:
1. The arrow follows a parabolic path because of the horizontal force provided by the bow which causes it to sail forward and its velocity is directly proportional to the momentum given by the bow. The arrow’s momentum energy is then negated at each successive moment by gravity causing it to fall, it falls when it loses all momentum energy.
2. Because an object will continue at the same velocity in a straight line, unless it is acted upon by a force
3. Such as the river will flow forward and only stop if there is a dam or if another force redirects it
4. Here the arrow is seen to move forward and fall gradually in increments
5. Therefore, there must be two forces acting on the object, the force pushing the arrow forward and the force of gravity due to which it falls.
There can be no doubt that the physics of mechanics, the concepts of momentum, acceleration, velocity, the laws of motion, inertia, vectors instantaneous motion, motions of projection, work done were all understood by the Vaiseshika. However, it is not until the middle ages the theories of mechanics of the Vaiseshika were turned into mathematical models, giving the first ever equations of motion
Aryabhatta’s treatise, Aryabhateeyam [2-31] contains many theorems of motion one of which goes thus:[22]
]Bhakthe vilomavivare gathiyogenaanulomavivare dvow
Gathyantharena labdow dviyogakaalaavatheethaishyow
If two objects are traveling in opposite directions, the time required for them to meet is equal to the distance between them divided by the sum of their speeds. If they travel in the same direction the time that has elapsed equals the distance between them divided by the difference in their speeds.
Bhakshacharya(1200AD) in his
Siddanta Shiromani gives the equation v = s/t to calculate the motion of a planet with uniform velocity, however when the velocity is variable such as the motion of a planet then the instantaneous velocity can be given through the differential equation of ds/dt.[20]