Science & Technology
Guṇāḥ (गुणाः): Properties of Fundamental Physical Quantities
Introduction
The first four dravya (द्रव्य) viz., solid, liquid, energy and gas are noneternal quantities, while plasma, time, and space (length vector) are eternal quantities. Thus, the first four quantities mentioned above are finite, while the others are in a sense, continuous quantities. This is the reason the properties of dravya can be stated to be one of the three types: finite, continuous, and having both characteristics. 24 types of Gunas have already been specified earlier in this segment.
The description of these properties is given in several texts devoted to Vaiśeṣika (वैशेषिक).
The properties are further divided into two classes viz., general (sāmānya, सामान्य) and specific (viśeṣa, विशेष). ‘General’ properties include number, unit, conjunction, disconjunction, smallness, largeness, gravity, temporal fluidity (cohesion), and mechanical and elastic forces. ‘Specific’ properties are enumerated as colour, smell, taste, temperature, adhesion, cohesion, and the wave aspect.
We will explore in brief some of these guṇas and the related concepts.
Gravity (Gurutva -गुरुत्व) and Gravitation (Gurutvākarṣaṇa -गुरुत्वाकर्षण):
Gravity or gravitation (as per quantum mechanics) is the universal force of attraction acting between all matter, i.e. the material substance that constitutes the observable universe. It is the weakest known force in nature. However, by its universal action, it controls the trajectories of celestial bodies in the solar system and the universe as also the structures and evolution of stars, galaxies, and the whole cosmos. The concept of gravitation is described in ancient texts like Maharṣi Kaṇāda’s (महर्षि कणाद) Vaiśeṣikaśāstra (वैशेषिकशास्त्र) ~600 BCE, Sūryasiddhānta (सूर्यसिद्धान्त) ~ 400 CE, Praśastapādabhāṣya (प्रशस्तपादभाष्य) ~ 530 CE and Bhāskarācārya’s Golādhyāya (भास्कराचार्य गोलाध्याय) – 1114 -1185 CE. According to Vaiśeṣika, gravitation is the reason for falling (patana, पतन) down of solid and liquid entities (jala-bhūmyoḥ, जल-भूम्योः).
गुरुत्वं जल – भूम्योः पतन – कर्म – कारणम् |
अप्रत्यक्षं पतनकर्मानुमेयं संयोगप्रयत्न – संस्कारविरोधि अस्य
चाबादिपरमाणुरूपादिवन्नित्यानित्यत्वनिष्पत्तयः|
– Praśastapādabhāṣya
It is invisible but can be inferred by the falling motion which is counteractive to material conjunction, effort, and action of any other force. Like the other properties of the matter the perceptibility of gravity also depends upon the finer constituent parts of the falling entity.
The same argument has also been effectively substantiated in the famous commentary on Vaiśeṣikasūtra (वैशेषिकसूत्र), the Nyāyakandalī (न्यायकन्दली).
अथ अवयवानां गुरुत्वादेव तस्य पतनं तदवयवानामपि स्वावयवगुरुत्वात् पतनमपि सर्वत्र कार्ये
तदुच्छेदः| अतः व्यधिकरणेभ्यः स्वावयवगुरुत्वेभ्योsवयवानां पतनासम्भवात् तेषु गुरुत्वं कल्प्यते
तदा अवयविन्यपि कल्पनीयं न्यायस्य समानत्वात् |
When we assume that a body is falling under gravity, it is very logical to assume that the constituent or the elemental parts of the body are also falling under gravity. Then we can justify the logical harmony between the body and its elemental parts. In light of the above statement, one can easily arrive at a conclusion that gravity is the property of the elemental parts and, hence, of the body. Therefore, a bigger body will also behave in the same way as a small body as far as the falling of the body under gravity is concerned.
In the western world, Aristotle surmised that objects on Earth moved towards their ‘natural place’ which was the centre of the Earth and that the bodies fall at the rate which is proportional to their weight. This doctrine remained undisputed till the time of Galileo (1590 CE), who asserted that all bodies fall at the same rate regardless of their weight, unless impeded by the air resistance.
It is significant here for us to know the rationale behind the idea of vector-based motion (upward and downward motion) which was known to ancient Indians. To them, the vertical fall of the bodies signified a fall towards the centre of the earth.
सर्वत्रैव महीगोले स्वस्थानम् उपरि स्थितम् |
मन्यन्ते खे यतो गोलस्तस्य क्वोर्ध्वं क्व वाप्यधः|| ५३ ||
– Sūryasiddhānta Bhūgolādhyāya (सूर्यसिद्धान्त भूगोलाध्याय)
From the above śloka (श्लोक) it is clear that everybody lying on the top or outer round surface of the earth considers oneself to be higher than the other person on the earth or in the space around the earth. Therefore, for every ‘body’ downward direction is towards the centre of the earth. Thus, for every place on earth, the falling of the body is always taking place towards the centre of earth.
The cause of the falling body has been described by Bhāskarācārya. According to him- “As the earth possesses the power of attraction just similar to a heavy body (guru, गुरु) situated in space, the attraction occurs proportional to their heaviness. These attractions exhibit as their falling and both (fallings) being equal, which of them falling into space cannot be claimed”.
आकृष्टिशक्तिश्च मही तथा यत् खस्थं गुरुं स्वाभिमुखं स्वशक्त्या|
आकृष्यते तत्पततीव भाति समे समत्वात् क्व पतत्वियं खे ||
– Golādhyāya (गोलाध्याय)
It means that it is not only the earth that attracts a body situated in the space towards it, but the different heavy bodies of universe situated in space also attract each other due to saṁhati (संहति) of each other or due to their property of attraction. They are constantly pulling each other in their own direction. (svābhimukhaṃ ākṛṣyate, स्वाभिमुखं आकृष्यते). These findings compare very well with the Newton’s law of Universal Gravitation (1665 CE) which states that: “Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them”.
Sūryasiddhānta and Keplar’s Laws of Planetary Motion:
According to Sūryasiddhānta (~ 400 CE) all planets move in a circular orbit, considering the Earth at origin, their centre being slightly away from the origin. All planets move with equal velocities. The difference of the time period is due to the difference of the radius of orbits.
Size of the planets affects the oscillation of the orbits in N-S direction.
According to Keplar’s laws of planetary motion (1571 -1630 CE)
- All planets, including the earth, move around the Sun in elliptical orbits.
- A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time, that is, the area divided by time, called the areal velocity, is constant.
- The square of the period of revolution round the Sun is proportional to the cube of the semi major axis of the ellipse. Therefore, the time period is more for planets which have a greater orbital radius.
For the details of planetary motions, one should refer to Indian ancient texts on astronomy including Sūryasiddhānta and Golādhyāya.
The Elastic Force (Sthitisthāpakatāsaṁskāraḥ, स्थितिस्थापकतासंस्कार:)
In Nyāyakandalī, a 10 th century CE commentary on Praśastapādabhāṣya by Śrīdhara (श्रीधर), elasticity has been described as follows:
ये घना निबिडा अवयवसन्निवेशाः तैर्विशिष्टेषु स्पर्शवत्सु द्रव्येषु वर्तमानः, स्थितिस्थापकः
स्वाश्रयमन्यथाकृतमवनामितं यथावत्स्थापयति पूर्ववदृजुकरोति ||
The physical bodies are constituted by densely populated elemental parts. Elasticity or sthitisthāpakatā or pratyāsthatā (प्रत्यास्थता) is the property by virtue of which, the bodies deformed (displaced or sheared) due to external deforming force (or twist) regain their original shape and form after the deforming force is removed. Scientist C.J.L. Wagstaff, in his book ‘Properties of matter’ (1934) defines Elasticity in the following words: “Elasticity is a general name given to that property of a body in virtue of which it resists and recovers from change of shape or volume. All substances resist changes in volume, and so have, what is termed as bulk elasticity, but it is only solids that have elasticity of shape; no fluid, liquid or gas can offer a permanent resistance to change of shape.” According to physics, elasticity produces vibrations in the object which travel through the body of the object in the form of waves. Due to this property, rods, strings, membranes, plates, etc., vibrate and produce sound. A similar phenomenon has been mentioned in Bhāṣāpariccheda (भाषापरिच्छेद), also known as Kārikāvalī (कारिकावली) by Viśvanātha Nyāyapañcānana (विश्वनाथ न्यायपञ्चानन) -1634 CE, in the following śloka:
स्थिति स्थापक संस्कारः क्षितः केचिच्चतुर्ष्वपि |
अतीन्द्रियो स विज्ञेयः क्वचित् स्पन्देSपि करणम् ||५९||
Elastic force is developed in solids (kṣitaḥ, क्षितः) or even in other four states of matter (caturṣvapi, चतुर्ष्वपि) which is invisible (atīndriya अतीन्द्रिय) and is cause for vibration (spanda, स्पन्द).
Sparśa (स्पर्श)
While discussing the properties of physical quantities, Vaiśeṣika has given a very lucid description of property sparśa. Generally, the sparśa is translated as ‘touch’. However, the term sparśa of Vaiśeṣika has been considered as temperature, as temperature is the physical quantity which gives the sense of hotness and coldness. According to Vaiśeṣika, when hardness or softness are to beexpressed the term sparśa must be tagged with ‘viśeṣa’ i.e., ‘viśeṣa sparśa’. For this discussion, the property of sparśa has been considered as the measure of hotness.
शीतोष्णानुष्णाशीतभेदेन स्पर्शस्त्रिविधः
Sparśa is of three types: cold (śīta, शीत), hot (Uṣṇa, उष्ण) and lukewarm or medium (Anuṣṇāśīta, अनुष्णाशीत)
Conjunction of heat energy (tejas) with a substance/matter (bhūta, भूत) gives an experience of hotness (uṣṇatva, उष्णत्व) in the body. Energy and hotness, being a fundamental physical quantity (dravya) and its property (guṇa) respectively, these two have a concomitance relation (Samavāya, समवाय).
If water is taken in a container and heated gradually, a consequent gradual rise in the volume of water is observed. In the same manner, mercury (Hg) is also seen to expand on heating and contract on cooling. The hotness or coldness of mercury is due to property of concomitance of the heat and the energy. Physics has utilized the property of expansion and contraction of mercury to device a simple thermometer. The temperature of matter (under testing) and its grade may be determined by the rise of the mercury level in the capillary which is due to the conjunction of heat. The value of the mark at which it reaches gives the temperature, which is given by a number (saṅkhyā) along with the unit (parimāṇa – degree centigrade).
Ancient Scale of Temperature: Liṅka (लिङ्क):
Baroda State Library has a manuscript of the section Vaimānika Prakaraṇa (वैमानिक प्रकरण) of ‘Yantra Sarvasva’ (यन्त्र सर्वस्व) of Maharṣi Bharadvāja (महर्षि भरद्वाज). ‘Vaimānika Prakaraṇa’, i.e. the aeronautic section also has a commentary written by Bodhānanda (बोधानन्द). In that section, several techniques related to this topic have been described, out of which one is ‘Karṣaṇa Rahasyam’ (कर्षण रहस्यम्); i.e. Gundown Technique. The original text reads as follows:
“वैश्वानरनालान्तर्गत विमानाभिमुखस्थ ज्वालिनीप्रज्वालनं कृत्वा सप्ताशीतिलिङ्कप्रमाणोष्णं यथा भवेत्
तथा चक्रद्वयकिलीचालनात् वर्तुलाकारेण तत्च्छक्तिप्रसारणद्वारा शत्रुविमानोपरि
शत्रुविमाननाशनक्रियारहस्यम्”
Vaiśvānaranālāntargata vimānābhimukhastha jvālinīprajvālanam kṛtvā saptāśītiliṅkapramāṇoṣṇam yathā bhavet tathā cakradvayakilīcālanāt vartulākāreṇa tatcchaktiprasāraṇadvārā śatruvimānopari Śatruvimānanāśanakriyārahasyam.
The text may be literally translated as follows:
वैश्वानरनालान्तर्गत = Cannon ball placed inside the combustion chamber, विमानाभिमुखस्थ = situated at the head of the aeroplane, ज्वालिनीप्रज्वालनं कृत्वा सप्ताशीतिलिङ्कप्रमाणोष्णं यथा भवेत् = should be heated up to eighty seven ‘liṅka’ magnitude of hotness by burning fuel, तथा चक्रद्वयकिलीचालनात् = then allowing the motion of a lever connected to a pair of wheels, वर्तुलाकारेण तत्च्छक्तिप्रसारणद्वारा = imparting spin to the ball aimed, शत्रुविमानोपरि = at the enemy’s aeroplane, शत्रुविमाननाशनक्रियारहस्यम् = this is the technique to ‘gun down’ the enemy’s aeroplane.
It will be interesting here to note that in ancient India, there is a likelihood that a temperature scale named liṅka, was used. However, being a technical term, liṅka was proably not used frequently and that may explain why this word does not appear in other available Sanskrit literature. However, the meaning of the word liṅka can easily be derived with the help of Sanskrit grammar and Vaiśeṣikasūtra. In Sanskrit ‘laḥ’ (लः) means 50, which tells us that the Roman numeral ‘L’ also represents 50. In this way a common origin of the words ‘‘laḥ’ and ‘L’ can be established. Thus, the word liṅka derived from laḥ can well mean a scale of temperature having 50 parts. In modern scientific world, centigrade unit of temperature bears similar meaning, as a scale of 100 parts.
According to Vaiśeṣika, śītasparśa (coldness) and uṣṇasparśa (hotness) dwell in liquid (ap, अप्) and tejas (energy, तेजस्) respectively. The representative materials of these are water and gold. As dravatva (द्रवत्व) or fluidity is also a common property of both ap and tejas, one can easily arrive at the conclusion, that the freezing point of water and melting point of gold may have been considered as the lower and higher standard temperatures, respectively. Thus, ‘liṅka scale’ should have 50 divisions between the freezing point of water and the melting point of gold. Further, as liṅka scale is a moderately high unit, a unit may be assumed as 24th part of liṅka (author’s view), and let us name it as Praliṅka (प्रलिङ्क), which will be nearly equivalent to 0.885°C. On this scale, the boiling point of water and the melting point of the gold will become 113°PL and 1200°PL, respectively, zero point being at the freezing point of water.
Śabda (शब्द): Wave Aspect:
According to Vaiśeṣika , the specific property of plasma (ākāśa), the fourth state of matter, is the wave aspect. This property is permanent to this state. It is important to note that while dealing with microscopic particles in physics, one is forced to consider the wave aspect of these particles.
Vaiśeṣika, which sets its ultimate goal as the study of ātman and manas (soul and mind), turns to explain ‘kṣaṇika śabda (क्षणिक शब्द)’ as ‘sound’ (acoustical wave) which is sensed by the ear. Vaiśeṣika considers air as a medium (vāhaka, वाहक) for sound. It is obvious that for sound to propagate through air, the air molecules must oscillate at their mean position (spanda, स्पन्द), i.e., periodic conjunctions and disjunctions. It is natural to assume that the vibrations within the intermolecular spaces occur because of the existence of plasmatic states within the molecules.
Moreover, sound is of two kinds (i) musical sound (dhvani, ध्वनि) and (ii) speech consonant (varṇa, वर्ण). Their definitions are in accordance with modern physics.
The propagation of sound in space can be explained with the analogy of the waves on the surface of water. Every point on the wave front becomes the cause for the next wave front and is exactly parallel to Huygens’s construction for the new wave front. Two types of wave propagation are considered in accordance with (i) Kadaṁbagolanyāya (कदंबगोलन्याय) – the longitudinal mode, and (ii) Vīcītarangaṅyāya (वीचीतरङ्गन्याय) – the transverse model. For further details of musical instruments, etc., other ancient literatures on Sāma (साम) and Saṅgīta (सङ्गीत) may be referred to.
According to the ancient literature, śabda is of two kinds. One is āhata nāda (आहत नाद) –
wave in a material medium, and the other is anāhata nāda (अनाहत नाद) – probably wave aspect of the matter.
If the study of śabda is done on the basis of both Vaiśeṣika and physics, it will lead to more informed discussions.
Further details regarding the guṇas, concepts of gurutva, sthitisthāpakatā, sparśa, mathematical expressions for conversion to centigrade, and the comparison of liṅka and centigrade system refer to the book ‘Physics in Ancient India’ by Dr. N.G. Dongre and Dr. S.G. Nene, NBT, Delhi, 1916