Space, Time and Anu in Vaisheshika

Space, Time and Anu in Vaisheshika
Roopa Narayan

Abstract: This article summarizes the main ideas related to space, time, and the fundamental particle (anu) in Vaisheshika, the ancient Indian tradition of physics. In particular, the conception of anu, the fundamental particle of this tradition, is examined at length. Kanada used his framework of defining observables (matter) through the effect of motion in a very consistent manner. When the universe ceases to be at the end of the cosmic cycle, matter is not annihilated. Rather, the collection of anu (atoms) reaches a quiescent state where they do not undergo any motion and thus become invisible to observation. The anu in itself is not observable, and is thus an abstraction. Kanada’s framework defies the usual categories of realist versus idealist, since for him matter in itself is a result of motion. In this framework, time and space arise out of the motion that anu obtains due to its interactions. To this extent, the observer is central to Kanada’s scheme.

1. Introduction
The characteristics of all that can be conceptualized and hence named and defined in the world through comparison and contrast, is the science of Vaisheshika [1],[2]. This includes a conceptual representation of space, and the gross visible matter, which is taken to be constructed out of the varying motions of anu, the most fundamental particle of matter.
Vaisheshika approaches basic concepts in a characteristic manner. For example, the division of time as past, present and future as understood by the observer is said to be a consequence of the fact that time is a function of movement. Vaisheshika is observer centric but it acknowledges that certain entities are necessary within the conceptual framework although there is no direct way of experimental verification of these entitites. For example, anu – the fundamental particle of matter – is said to be beyond direct perception irrespective of the kind of instrument that is used to view it. Nevertheless, its presence can be inferred indirectly.
In this paper, our emphasis is to examine Vaisheshika through the sutras of Kanada (we use the English translations by Sinha [3]), although the important commentary by the fifteenth century scholar Sankara Misra [4] will also be used for clarification, wherever necessary. Other important sources on Vaisheshika are references [16-21]. An early overview of Vaisheshika is to be found in the book by Seal [5].

2. Dravya – The building blocks
Kanada in his sutras enumerates real entities irrespective of whether they can be perceived through the sense organs or not. These are conceivable by the mind of the observer who is central to his world. These are the nine dravyas and these alone describe everything existing in the universe. These are the building blocks of Kanada’s world described through their gunas/attributes and karma/motion.
Space is one among these nine and Kanada recognizes it as an independent positive entity which is neither absence of matter nor an abstract concept. Every dravya has an identifier linga which helps identify the specific dravya besides which it has a unique set of guna/attributes associated with it.

Earth, water, Fire, Air, Akasa, time, Space, atma, mind are the only nine dravyas 1.1.5.

Commentary: All the nine mentioned dravyas in the sutra although are translated as earth, water, etc are not to be understood as the planet earth or the drinking water, etc.
These nine dravyas have specific gunas/ attributes associated to them like the dravya earth has smell associated as the primary guna/attribute to it. An understanding of dravyas can be arrived at by analyzing their attributes and their interactin with the rest of the world. The dravyas shall not be analyzed in this paper but it is important to understand the division of the dravyas.
The first four dravyas: earth, water fire and air are associated with a sense organ each as sense of smell, taste, sight and touch respectively. Although sound is mentioned as the identifier of akasa – the fifth dravya, which is not translated here as ether for specific reasons, that shall be dealt with separately.
Time, space, atma and mind are the eternal or nitya dravyas and none of them are perceivable by any of the sense organs is a basic definition in Vaisesika. Although, these four eternal entities can only be conceived by the mind, they are real existent dravyas or entities. Time, space and akasa are incapable of motion (by sutra 5.2.21) and it is only the first four dravyas and mind which are capable of motion. The mind is also not visible (because it is by nature an anu like-fundamental particle, which is not visible (by sutra 7.1.23). It is only the first four dravyas which compose the matter world. A sort of motion is applicable only to the matter section of dravyas which are the first four among the nine.
The dravyas are both perceivable and possess motion represent matter. Among nine dravyas, the first four compose the non-eternal matter, mind is the eternal but invisible dravya and the remaining four are eternal and incapable of motion.

3. Definition of Dik (Space) and Kala (Time)

That which gives rise to such (cognition and usage) as “This (is remote, etc.) from this,”– (the same is) the mark of space 2.2.10.

Space is identified through the fact that it can provide the context to describe objects as being separated spatially.
Spatial separation can only apply to matter since eternal dravyas which are incapable of motion can neither be separated nor brought together. Although mind can move, it is invisible. Therefore all that remains in Kanada’s classification of dravyas is matter.
The separation is an identifier and the identification is with reference to the observing mind. It is also significant that the displacement of matter is observed relative to another piece of matter.
The essence of this sutra may be rephrased as: mind recognizes space when matter is displaced relative to another piece of matter.
In Sankara Misra’s commentary of this sutra an argument is built about the similarity of space and time in terms of their guna/attributes and a question is raised about the requirement of a new entity called space to be recognized. Both space and time are characterized by their guna/attribute of – partva-aparatva/ being together – separated.
In Kanada’s definition, the dravyas are understood and defined through their gunas/attributes and each of these dravyas is non-repetitive and unique. Therefore time and space can be recognized as two separate entities if and only if their difference is established.
The guna/attribute of partva-aparatva/ being together – separated in time signifies two objects co-existing at the same point of time or being separated in time and the simultaneity in time is defined as a function of the movement of the sun. But that reflects a dependency of time on sun’s movement whereas a dravya has to have an independent existence by definition. It is explained that the concept of ‘simultaneity’ in time (in sutra 2.2.6 commentary) indicates the movement in sun and not vice-versa.
On the other hand the guna/attribute of partva-aparatva/ being together – separated, in space is reflected by conjunction and disjunction of matter and to be understood as samkalina – simultaneity in Time, i.e. the relative spatial separation of matter in the same time frame (same time frame =time measured for the same sun movement).

Questions: The commentary raises certain questions.
1. Spatial separation for objects being defined also with respect to same time frame – Does this imply that time is to be understood as changing with different suns and such different suns and time measures exist?
2. Simultaneity in time reflects the movement of sun – It means that for the observing mind, sun’s movement is a logical conclusion from the concept of what we call ‘at the same time’ in our day-to-day life.
If ‘simultaneity in time’ is relative to the position of observer (meaning with reference to the same sun) and spatial separation of objects is not, does it mean that space is absolute but time is relative.
Time is said to be _- .__/_/ a specific outcome of state of motion – which means time as a larger concept is a function of motion and therefore indicates the general state of motion of the entire cosmos (in the commentary of sutra 2.2.10 of Sankara Misra).
In Yoga Vasistha [6] which discusses Indian cosmological perspective correlated with many other works, a similar concept of varying time with different universes is mentioned. Space for Kanada is devoid of motion and therefore it is only the matter in motion when the cosmos is mentioned and space is still.
This fits with the idea of Indian cosmological model in which time is said to collapse in the rest period between the cosmic creation and dissolution, and that must be true if time is a function of ‘state of motion’ of the cosmos which comes to a rest in this period between creations and dissolutions [7-13].

4.1 Space as dravya

Dravyatva (being a dravya) and eternality (of Space are) explained by (the explanation of the same in) Air 2.2.11.

Commentary: Space is eternal (explained later). It is concluded to be a dravya and that encompasses hypothesis like – Space is an independent entity
It is existent
It is unique
It is a padartha
It has guna/attributes associated with it
It can give rise to another dravya.
It is incapable of motion.
It is homogenous.

4.2. Space homogeneity

The unity (of space is explained) by (the explanation of unity of) existence (sutra 2.2.12).

Commentary: Here is a discussion of unity of space which is explained in the commentary by Sankara Misra as /eka-pritaktvam. is a guna/attribute of space and in Shankara Misra’s commentary, he defines it as that which differentiates one from two, or it is that kind of a guna/attribute which gives a sense of discretion about the state of dravya discussed.
In the case of space, /eka-pritaktvam must refer to the fact that space is found in one state – what ever that is, and shall always be in the same state irrespective of which point in space is considered or even which point in time is considered. This refers
to the homogeneity of space. Such a guna/attribute fits in with Space being nitya/eternal or unchanging.

4.3. Directions in Space

The diversity (of space) is due to the difference of effects 2.2.13.

Commentary: karya visesena means an outcome the specific kind of work under consideration, and because space is by definition incapable of motion, work in question can only refer to the work done by matter in space. Due to the nature of matter’s behavior in space, it appears that space itself is diverse in nature. The diversity is explained in the following sutras.

4.4. Space Time as the fundamental matrix

‘aditya-samyogat, from the conjunction of the sun ‘bhutapurvat, past and gone bhavisyatah, future ‘bhutat, what has taken place or come in to existence; present ; cha, and prachi, east. (The direction comes to be regarded as) the east, from the past, future, or present conjunction of the sun 2.2.14.

Commentary: East is recognized as the direction from which the sun rose and therefore it is in the past. The past present and future divisions of time as a result of the movement of sun are also connected to the spatial directions which are named based on sun’s movement. The directions in space are explained as relative to the position of the observer. In this sutra space and time are connected by the ‘motion’ of sun which observation is also found in many commentaries.
In the commentary of sutra 2.1.5 Sankara Misra while defining the attributes of akasha states that not only is akasha absolutely color-less but based on the same argument even time and space are devoid of the attributes of rupa, rasa, gandha and sparsha. Time and space have the same attributes associated to them (number, magnitude, pritakathva/ separateness, conjunction and disjunction). He concludes the commentary of this sutra stating that it follows that time and space are thefundamental entities of everything.
The space and time matrix are said to be fundamental because the mind perceives the world through matter which is identified through the four senses of touch, smell, taste and visibility (the eternal dravyas can only be conceptualized by the mind and not perceived).
These four guna/attributes exist in matter which always exists in a certain space and time combination.
The absence of either space or time indicates absence of motion and as is later established in this paper, no guna/attributes can exist in absolute rest or when time collapses to zero.
Space and time has to be the fundamental matrix of the matter world, and the observing mind can never escape either Space or Time during the process of observing the universe. In the Kanadasiddhantachandrika of Gangadharasuri Sastri says [14]
This division of time is said to be caused by the E_.F/intelligence and in Space it results from conjunction and disjunction of real matter and so the intelligence of the observer plays a secondary role.
In the footnote of Udayavir Shastri ‘s book [15, page 103], it is mentioned that Chandrakant Bhattacharya is of the opinion that space, time and even akasha are the same which are seen as different entities because of the nature of the effects as observed by the mind in their interactions with matter.

4.5. Directions

By this, the intervals of directions in space are explained 2.2.16.

Commentary: In these last two sutras the four main directions east, west, north, south besides which four more directions between these four directions are accounted for as relative to the position of the observer as concepts which arise only because of the nature of motion of matter in Space. Hence Space itself is homogenous and has no division of direction inherent in it.

5, 1.Eternality
The nature of both Space and, anu – the most fundamental particle of matter (sutra 7.1.8 – explained later) in Vaisheshika are said to be explained in the chapter that discusses nitya/eternal.

The eternal is that which is existent and uncaused 4.1.1.

Commentary: In this sutra Kanada begins his definition of /nityam or the ‘eternal’ but this term is a very imprecise translation of his /nityam. The term existent has a lot of significance in the school of Vaisheshika because Kanada – a realist, has set himself the task to enumerate everything in the universe through predicable – all that which can be named, expressed through words or conceptualized by the mind. Hence all that he describes are not mere theoretical concepts, but true existing entities of the real world.
The term not having a cause – is two fold. In terms of the time one must remember that Indian cosmology constantly discusses two kinds of cosmic dissolution: the primary and the secondary. There are time periods mentioned for the creation and dissolution process besides the rest period in between. The way in which Kanada links matter, space, time and mind with ‘state of motion’, the question is raised whether anything other than the anu persists through the rest period of universe when time collapses to zero and there is absolute stillness.

Questions: The question raised is, since matter, space, time and mind are all connected to one or the other kind of ‘motion’, does /eternal refer to an existence beyond these dissolutions? Is anything transferred from one process of creation-dissolution to another which are said to be cyclic in nature? Since anu cannot be reduced any further, it must exist as is through all creations and dissolutions, but since time and space are linked to ‘motion’ are they recreated after each rest period?

5.2. Anu in Real Time

The effect is the mark (of the existence) of the ultimate anu 4.1.2.

Commentary: Kanada has stated in a later chapter (sutra 7.1.8) that both anu and mahat are explained through the nitya/eternal, which must be the reason from Prashastapada to Shankar Misra all scholars explain this sutra with an extension to mean the fundamental particle – the anu.
Although in no sutra is the term paramanu mentioned by Kanada, all the other scholars talk of paramanu as the most fundamental particle of matter. We will not focus on the term, instead try to understand what anu in Kanada’s sutras is and for the purpose of this work we shall use the term ‘anu’ for the fundamental particle of matter.
Literally the sutra translates to – The work done by it is its identifier. Here ‘it’ refers to nitya/eternal as this is a section on the same. By the sutra 7.1.8 which states that both anutva and mahatva are explained by the eternal, this sutra should also refer to the two –anutva and mahtva. These terms shall be explored in detail in a later section, for now anu – refers to the most fundamental particle of matter and mahatva refers to space (mahatva – is used in the context of Vaisheshika for more than one dravya, but space is definitely one of them)
Therefore anu and space are identified by the mind of observer through the work done by these or through their effects. This must be the only way they can be identified by the mind because by definition they are not perceivable by the human sense organs irrespective of the method employed.
Sankara Misra in the commentary of this sutra discusses that the gross matter which is visible with properties like magnitude, etc implies that it must be made of smaller parts.
The parts can be further divided to reach some final indivisible entity. The final or most fundamental entity must have the least possible measure of length, mass or volume – magnitude in total, in order to avoid the infinite regression of such fundamental particle being further divisible (anu is a particle because it is capable of conjunction, later mentioned with the sutra). In the fundamental particle of matter which Sankara Misra and other scholars call paramanu there are minima of mass, volume or any measure.
Kanada does not use the term paramanu in his sutras anywhere, yet we mean the same fundamental particle of matter as other commentators who use paramanu). Kanada explores the relation between whole and its parts.
Sankara Misra states that if an enormously large piece of matter like a mountain and a small piece of matter like grain were to be composed of infinite parts of anu, then the difference in the gross size of mountain and grain being built from the same number of anu leads to logical inconsistency. This interpretation is not only used with respect to the gross form in general but in the commentary of sutra 2.1.2 there is a specific mention that the measure of a mountain and a seed would be the same in terms of magnitude, measure and volume if the relation between the parts and the whole were unlimited.
Such an unlimited whole-parts relation is not permissible because it is only during pralaya- the cosmic dissolution, the limit of the series of parts and wholes reaches a maximum. For a given whole which is the matter state of universe the maximum number of parts is reached during the time of dissolution when all matter is reduced to anu form.
This is because the only reducible dravyas of Kanada are matter which is composed of anu and the remaining dravyas are not composed of parts. This discussion of whole and parts throws light on key things.
1. Relation between whole and parts and it raises question about can infinity fit such a loose definition as – infinity added to infinity is infinity, etc.
2. Matter cannot be reduced to anything further than anu, and so matter must be conserved in the state of anu.
3. If during cosmic dissolution all matter is reduced to anu form, then it demands that anu be at rest or with zero motion. This concurs with the definition of karma/ motion in Vaisheshika which by definition is perceivable and anu by definition is not perceivable at any time, therefore anu in order to be non-perceivable must not possess any form of motion. This is exactly what is stated by the cosmological theory.
4. It further concurs with the idea of anu having an inherent potential of acquiring guna/attribute which makes sense that the four fundamental distinguishing guna/attribute of rupa/visibility, etc are associated with four distinct basic motions of anu (discussed in a later section).
5. If the maximum number of parts in to which matter can be reduced is anu which is during dissolution, then matter must not be reducible to the anu state at any other time for then the whole can be reduced to maximum number of parts at times other than dissolution too. This makes sense because Kanada does not include anu as a dravya among the only nine that exist in his enumeration of everything that exists and is conceivable. Therefore anu does not exist in real time at all or when time is non zero.
6. Anu not existing as an individual particle in real time makes sense because different scholars like Prashastapada, etc have an elaborate argument about whether anu is bound as a dvayanuka or trayanuka, etc. i.e., is anu found in conjunction with another anu in a di-anu state or tri-anu state, etc.
Once creation of universe begins time begins to click and things are no more at rest. Then the world can be perceived by the observer and some kind of motion must begin (because by definition in Vaisheshika motion is perceivable or observable). Kanada has an interesting sutra relating to motion of anu.

5.3. Initial motion of Anu

The initial upward flaming of fire, the initial sideward blowing of air and the initial action (motion) of anu, and of mind are caused by adristam 5.2.13.

Commentary: In the commentary of this sutra the initial Adyam – is said to refer to the first motion that is produced in anu by Sankara Misra when the creation of universe begins, like wise the motions of flame of fire, wind and the mind. The reason for these motions are said to be adristam – which can literally be translated as unseen (drista = what is seen and adrista = what is unseen). There are many interpretations about what adristam might mean in Kanada’s context, but we shall not dwell on it here. It is clear from this sutra that Kanada describes an initial motion for the anu and this must essentially be when time begins for time is a function of motion. This sutra implies that anu can have two states – absolute rest and a state of motion.

6. Matter and Motion

The existence (of color, etc.) in the effect, (follows) from (their) existence in the cause 4.1.3.

Commentary: The terms in the sutra ‘ and are in the saptami samasa which is a grammatical condition that implies that the sutra should be understood to mean – because of the existence (of an effect or a specific unique character) in cause it is also exhibited in the gross form. Here Kanada is specifying that anus carry some distinguishing feature in them which gets exhibited as the effect in the gross form.
Logically any thing that is not in the root cause which is the anu cannot be exhibited in the gross form of matter as well.
This is an issue about which the entire School of Vaisheshika has had constant conflict with other schools of philosophy historically. If the anu has to acquire some thing by which four distinct forms of matter – which are recognized by the observer as those with the four primary distinct guna/attributes of rupa, rasa, gandha, sparsha – visibility, taste, smell, touch, then on what basis does an anu pick up a certain attribute and what is it inherent in the anu which makes it a specific form of matter.
The anu is said to potentially have something inherent which later becomes manifested once the process of creation of universe begins.
By the above sutra of the initial movement or motion of anu which begins with creation, it is clear that the four kinds of matter are related to four distinct kinds of motion of anu which in gross form builds up to a certain kind of matter.
Also in Sankara Misra’s commentary of sutra 1.1.6 it is stated that these four attributes of rupa, rasa, gandha, sparsha – visibility, taste, smell, touch cannot co-exist simultaneously at the same point of time in the same substrate. This makes sense because an anu cannot have four distinct kinds of motion at the same time. Space too is said to be a function of samyoga and vibhaga – which is conjunction and disjunction which is declared as a kind of motion by Kanada in sutra 1.122.
Besides conjunction and disjunction are permitted for anu (sutra 4.2.4) and in Kanada’s science only real things are stated, not probable events. In sutra 1.127 it is stated that matter is formed by conjunction Kanada defines the entire creation in terms of different kinds of motion.

7.1. Visibility of Anu

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 its color 4.1.6.

Commentary: Here the condition for visibility is that the perceived entity be that is be composed of more than one kind of dravya among the nine defined by Kanada, it will have a perceivable magnitude unlike the anu, and must be the substratum of color which does not necessarily mean that it must possess a color. In the commentary Shankara Misra explains that the term which is generally indicative of the magnitude due to or elision of the mutup pratyaya here becomes an adjective to indicate its greatness in its ability to conjunct with many dravyas at a time.

In substances not possessing color, they are not objects of visual perception 4.1.12.

Commentary: In Sankara Misra’s commentary it is explained that all the dravyas from air/vayu upwards do not posses color and so are impossible to be seen through the eyes or to be perceived no matter approached in which way. Yet a specific mention is made to clarify that this does not mean they are impossible to comprehend conceptually. When
the anu is in conjunction with more than one dravya, then they acquire attributes/guna and hence may be perceived. Once anu acquires guna/attribute, Time is in motion and space too must be in existence therefore anu is invariably in conjunction with these two dravyas.
It further can possess no motion or spin as in atoms, electrons or other fundamental particles as defined by modern science because by definition motion/karma is perceivable through the senses.
This is because from the sutra on different kinds of motion (1.1.7) rotation or spin is recognized as a kind of motion or action which can be perceived and if the anu were to be in a state of motion it would mean that it is perceivable which it is not.
Therefore in conclusion anu is not visible in principle with a minima of magnitude and not possessing any kind of motion.

7.2. Is anu spherical?
In chapter seven from the sutra number 7. 1. 5 to 7. 1. 19 an argument is built by Kanada as to what ‘large’ or ‘small’ generally means magnitude wise and finally he concludes about the anu in the following sutra:

The eternal is Parimandala 7. 1. 20.

Commentary: This sutra is often translated as the anu is spherical. In his commentary on this sutra Sankara Misra points out that the term Parimandala is specifically used in the context of Vaisheshika to describe the natural state of the anu which, even though cannot be perceived through the senses has to be the same from any direction or it must necessarily possess a symmetry. In the conventional two or three dimension visualization that we are used to, it is a circle or a spherical shape.
In Kanada’s definition, length or any measurement is a quality associated only with the matter and so the anu and space with its eternality is non-measurable or at least any kind of length-measurement is not applicable to it. Kanada has coined a term parimandala which is not an adjective for spatial dimension but a concept of logical deduction which is conceived by the mind and is therefore only an abstraction.
Anu therefore by definition and logical deductions are described by Kanada as the fundamental particle of matter which is discrete and not perceivable by senses, with minima of magnitude, yet with a real independent existence beyond the perceptions.
These are not further divisible in to components and hence are concluded to be neither destroyable nor created which makes them eternal.
These are not perceivable by an observer and hence are called / super-sensible which means ‘too acute for the senses’. As these are entities with no association of magnitude, it is meaningless to fix a position for the anu and hence they are /non localizable [11].
Space also is eternal, with no measurable magnitude association, not perceivable, indivisible, non-matter and yet a dravya.
Therefore ‘existent’ or real to Kanada would not necessarily mean anything that can be perceived through senses, but also extends to anything that can be conceptualized by the human mind. The role of the individual who shall understand the predicable is consequently very central and critical.

Conjunction of anu is not restricted 4.2.4.

Commentary: Therefore the term anu is used to refer to a particle which can go through the operations of conjunction. Anu is concluded to be a particle.

The contrary of this is anu 7.1.10.

Commentary: In this chapter which is discussing the magnitude of anutva and mahatva – where anutva is already established as the minima of magnitude, anu is defined as the contrast of mahat. Therefore in terms of magnitude mahat is the maxima of magnitude or Space is the maxima of magnitude and it is not necessarily infinite at least in Vaisheshika.

8. Conclusions
The examination of the various sections of the Vaisheshika Sutras reveals that Kanada used his framework of defining observables (matter) through the effect of motion in a very consistent manner. When the universe ceases to be at the end of the cosmic cycle, matter is not annihilated. Rather, the collection of anu (atoms) reaches a quiescent state where they do not undergo any motion and thus become invisible to observation. The anu in itself is not observable, and is thus an abstraction, which is why we have not used the term “atom” for it.
Kanada’s framework defies the usual categories of realist versus idealist, since for him matter in itself is a result of motion. In this framework, time and space arise out of the motion that anu obtains due to its interactions. To this extent, the observer is central to Kanada’s scheme. Kanada’s emphasis on analysis of categories is also found in the complementary tradition of logic [22-25] and the application of these two traditions to cosmological questions [26-27]. The idea of tanmatra in the cosmology of Samkhya, which is viewed as a kind of potential out of which materiality emerges, has features similar to that of anu in the Vaisheshika system.

1. R.H. Narayan, Nyaya-Vaisheshika: The Indian tradition of physics. arXiv:physics/0701077

2. S. Kak, Indian Physics: Outline of Early History; arXiv: physics/0310001

3. Nandalal Sinha, The Sacred Books of the Hindus, Vol.v1. The Panini Office, Bhuvaneswari Asrama, Allahabad, 1923.

4. Acarya Dhundhirajasastri, Vaisesikasutropaskara of Sri Sankara Misra. Chowkhamba Sanskrit series Office, Varanasi, 1969

5. B. Seal, The Positive Sciences of the Ancient Hindus. Motilal Banarasi Dass Publishers and Book sellers, Delhi, 1958.

6. Swami Venkatesananda, The Concise Yoga-Vasistha. State University of New York Press, Albany, 1984.

7. S. Kak, Yajnavalkya and the Origins of Puranic Cosmology. 2001; arXiv:physics/0101012

8. S. Kak, Early Theories on the Distance to the Sun; arXiv: physics/9804021

9. S. Kak, Babylonian and Indian Astronomy: Early Connections; arXiv:physics/0301078

10. R.H. Narayan, The theory of matter in Indian physics. arXiv:physics/0702012

11. S. Kak, Astronomy in the Vedic Altars and the Rgveda. Mankind Quarterly, vol.33, pp. 43-55, 1992.

12. S. Kak, The Cyclic Universe: Some Historical Notes. 2002; arXiv: physics/0207026

13. S. Kak, Concepts of Space, Time and Consciousness in Ancient India. 1999; arXiv:physics/9903010

14. T. Ganapati Sastri, Kanadasiddhantachandrika of Gangadharasuri. Published under the authority of the Government of His Highness The Maharaja of Travancore, Trivandrum, 1913.16

15. Udayavira Shastri, Vaisesikadarsanam. Virajanand Vaidik Samsthan, Ghaziabad, 1972.

16. S. Kuppuswami Sastri, A primer of Indian logic according to Annambhatt’s Tarkasamgraha. 1932.

17. Jagdish Chandra Chatterji, Hindu Realism. Swastika Publications, Delhi. 1975

18. Badri Nath Singh, Vaiseshika darsana. Asha Prakashan, Varanasi, 1971

19. S. Sankaranarayanan, Vaisesika Chatuhsutri. The Adyar Library and Research Center, Chennai, 2003.

20. Ganganatha Jha, PadarthadharmaSangraha of Prasastapada. Chaukambha Orientalia, Varanasi, 1982.

21. Anantalal Thakur, Origin and Development of the Vaisesika System. Centre for Studies in civilization, New Delhi. 2003.

22. S. Kak, Aristotle and Gautama on logic and physics. arXiv:physics/0505172

23. S. Kak, The golden mean and the physics of aesthetics. arXiv:physics/0411195

24. J.N. Mohanty, Classical Indian Philosophy. Rowman and Littlefield, 2000.

25. S. Kak, The Wishing Tree. Munshiram Manoharlal, New Delhi, 2001. 26. S. Kak, The Architecture of Knowledge. CRC, New Delhi, 2004. 27. R.H. Narayan, Indian cosmological ideas. arXiv:0705.1192.


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