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Mah¡bh£tas in JyotiÀa á¡stra

S. D. Sharma

Ancient sages had insight into the cosmogonical and cosmological aspects of the universe. Through the advanced stages of thought experimentations (Yogic pratyakÀa as you may call these) they inferred the existence of subtle stages of matter in the evolution process and correlated the same with the gross elements. They had a constant dialogue with nature and in this process they correlated the microcosm with the macrocosm. Interestingly, their inferences have many fundamental affinities with the insights of modern Astrophysicists.

In the cosmogonical evolution process from subtle stages of matter, the ancients arrived at the notion of paµcamah¡bh£tas the gross elements, considered to be the building blocks of the macroworld around us. It may be pointed out that this categorization should not be confused with the present-day periodic table classification of elements. The former is the categorisation based on indriyagr¡hyat¡ (faculty perceptibility) of materials in the world. Sir John Ballantyne in his Ny¡ya Kaumud¢  (Litho print 1885 ad) has confused the two categorisations and states:

          bh£t¡nyupaÀaÀ¶i sa´khy¡ni               

i.e., there are bh£tas  about 60 in number. He is referring to Hydrogen, Helium, Oxygen, iron and other elements as mah¡bh£tas. Note that at the time of Prof. Ballantyne, there were only sixty elements known to scientists.  Needless to say, this statement is erroneous, for mah¡bh£tas are not the same as basic elements of physics. It may be noted that paµcamah¡bh£tas of S¡Ækhya philosophy result as a consequence of paµc¢kara¸a process on paµcatanm¡tras, which are subtle stages in the evolution process and on the other hand are connected with the senses of perception. The concepts based on mah¡bh£ta classification prevail all the branches of philosophy and religion, but Ëyurveda has used these concepts for practical applications. JyotiÀa á¡stra too being a discipline of experimental verifications must have used these concepts for developing the laws of nature and in understanding the cosmic genesis. JyotiÀa á¡stra and Ëyurveda have put the philosophical concepts on experimental verification tests. Here the attempt of this paper is to study the concept of  paµcamah¡bh£tas in relation to JyotiÀa á¡stra. What ideas were developed by ancient JyotiÀ¡c¡ryas regarding cosmogonical evolution? How far did their findings tally with those of philosophers, and to what extent they had advanced further through their observational verifications? This paper seeks to address these questions and explore possible answers.

JyotiÀa á¡stra deals mainly with time and space. The former is not in the list of paµcamah¡bh£tas. But space is the ¡k¡¿a of the mah¡bh£tas. In fact in modern philosophy, time and space are so correlated that their unison is referred to as "space-time continuum". JyotiÀa á¡stra takes into account p¤thiv¢ (earth) and other elements. The P¤thiv¢ of Jyotisa á¡stra should not be confused with the p¤thiv¢ mah¡bh£ta, as the latter is the most generalised term to represent anything perceptible. Similar are the cases with other mah¡bh£tas. JyotiÀa áastra talks of mah¡bhautika entities in the cosmos and these terms should not be confused with the general terms of mah¡bh£tas philosophy. The bhautika entities as individual units are studied in JyotiÀa á¡stra. This ¿¡stra discusses the properties of the bhautika entities like earth, planets, water, tejas bodies, stars, suns, etc. and goes to the maximum extent to explore the very nature of space. Some aspects are dealt within siddh¡nta JyotiÀa and some of them are studied under the heading of Ëstrology'. Any way in this exposition we should like to explore the references to the concepts of mah¡bh£tas in JyotiÀa through the studies of bhautika entities without confusing the terminologies of the two disciplines. Here we have tried to survey the literature as far as possible in a chronological fashion, starting from Ved¡´ga JyotiÀam and up  to the Saiddh¡ntika JyotiÀa traditions. As such in Ved¡´ga JyotiÀam of Lagadha, which is exclusively a text of JyotiÀa, we do not find reference to mah¡bh£tas but earlier and later Vedic v¡´gmaya has important notions which paved the basis for cosmogony. So here we will deal first with the cosmogony and then having discussed the genesis and the evolution, will go over to the properties of mah¡bh£tas as inferred in JyotiÀa á¡stra and then see if some universal laws have been formulated in JyotiÀa tradition on the basis of philosophical grounds.

It may be remarked that in addition to cosmogony etc., JyotiÀa  á¡stra deals also with cosmography and cosmology, the sciences of form and age of the universe. Hindu, Jaina and Buddhist traditions discuss the geometrical models of the universe and the terrestrial earth, (ref. Cosmography of Hindus, Buddhists and Jainas by Nerifil). All these models are  indicative of their philosophical notions. Even modern astrophysicists talk of cosmology models which are based on highly complex mathematical exercises. Concerning the age of universe, Jainas talk of very big cycles like utsarpi¸i, apasarpi¸i, k¡la etc. The Siddh¡nta JyotiÀa texts talk of big life spans of Brahm¡,ViÀ¸u, Mahe¿a and Yuga systems which are of much importance for astronomical computations. Here we do not discuss these in detail but will elaborate the more interesting philosophical ideas of the ancients  regarding the cosmogonical process.

Cosmogony

The concepts about creation of the world, consisting of all stars, sun, planets and the animate and inanimate world, are found in the Vedic and later Sanskrit literature. The oldest strata of Vedas and allied literature have deep philosophical notions about cosmogony. In these very notions we find astronomical and astrophysical concepts of ancient sages. We discuss here few references from Vedic literature and then will come to JyotiÀa texts later.

In Îgveda we find Bh¡vita S£kta describing all void in the world and darkness engulfing all around. The cosmos came into existence through k¡ma (desire) which was the primal seed or germ of the spirit. We will not give all details of the text material of the S£kta but may point out that the notions as expounded in this S£kta are quite similar to the ones put forward in modern cosmogonical hypotheses. An Astrophysicist from U.S.A compared the Bh¡vita S£kta notions with the origin of world out of the Black Hole state of the matter. The ancients seem to have arrived at these notions through yogic pratyakÀa which is just an advanced stage of thought experimentations, while the modern astrophysicists inferred somewhat similar, through analyses of observable data.

In ÎV, 10.190.1.3 we have the following hymns:

¤tam ca satyam c¡bh¢ddh¡t tapaso'dhyaj¡yata

tato r¡tryaj¡yata tataÅ samudro ar¸avaÅ. (1)

samudr¡dar¸av¡dadhi sa´vatsaro aj¡yata

ahor¡tr¡¸i vidadh¡t vi¿vasya miÀato va¿¢.(2)

s£ry¡-candramasau dh¡t¡ yath¡ p£rvamakalpayat

divaµca p¤thiv¢µ c¡ntarikÀamatho svaÅ. (3)

Truth and truthfulness were born from intense penance. Hence was darkness born hence the watery  ocean. (1)

From the watery ocean was born the year ordaining days and nights the controller of every living moment. (2)

The creator then created in due order Sun, the Moon, the sky, the earth and the regions of the air and light. (3)

tasm¡dv¡ etasm¡d¡tmana ¡k¡¿aÅ sa=mbh£taÅ, ¡k¡¿¡dv¡yuÅ v¡yoragniÅ  agner¡paÅ, adbhyaÅ p¤thiv¢, p¤thivy¡ oÀadhayaÅ. oÀadh¢bhyo'nnaÆ, ann¡t puruÀah. (Tait. Up. Brahmavall¢). (1)

Verily from this soul, space arose; from space arose air; from air fire; from fire, the waters; from waters, the earth; from earth vegetation; from vegetation, the food; and from food, the man.

There is one more from ÎV, describing creation of the Sun, Moon, mah¡bh£tas

candram¡ manaso j¡tas'cakÀoÅ s£ryo'j¡yata.

mukh¡dindra¿ c¡gni¿ca pr¡¸¡d v¡yuraj¡yata. (13)

n¡bhy¡ ¡s¢dantarikÀam ¿irÀ¸o dyauÅsamavartata

padbhy¡=m bh£mir di¿aÅ ¿rotr¡t tath¡ lokamakalpayat. (14)

                                                            (ÎV, 10.190-13,14)

The moon was gendered from his mind and from his eyes the sun had birth; Indra and agni from his mouth were born and V¡yu from his breath. (13)

Forth from his navel came mid air, the Sky was  fashioned  from his feet and from his ear the regions. Thus they formed the worlds. (14)

Now we come to jyotiÀa texts and see what the later astronomers contemplated about cosmogony. The Bh£gol¡dhy¡ya of S£ryasiddh¡nta discusses the creation of the universe, including the earth, and the evolution of paµcamah¡bh£tas. The relevant text stanzas are the following:

v¡sudevaÅ param brahma, tanm£rtiÅ puruÀ]aÅ paraÅ.

avyakto nirgunaÅ ¿¡ntah paµcaviÆ¿¡t paro'vyayaÅ. (1)

prak¤tyantargato devo bahirantas'ca sarvagaÅ.

sa´karÀa¸o'paÅ s¤À¶y¡dau t¡su v¢ryamav¡s]¤jat. (2)

tadan·amabhavaddhaimam sarvatra tamas¡v¤tam

tatr¡niruddhaÅ prathamam vyakt¢bh£taÅ san¡tanaÅ. (3)

hira¸yagarbho bhagav¡neÀacchandasi pa¶hyate.

¡dityo hy¡dibh£tatv¡t pras£ty¡ s£rya ucyate. (4)

para=m jyotistamaÅ, p¡re s£ryo'ya=m saviteti ca.

paryeti bhuvan¡nyeÀa bh¡vayan bh£ta-bh¡vanaÅ. (5)

prak¡¿¡tm¡ tamohant¡ mah¡nityeÀa vi¿rutaÅ.

¤co'sya ma¸·alam s¡m¡nyusr¡ m£rtiryaj£´Ài ca. (6)

tray¢mayo'yaÆ bhagav¡n k¡l¡tm¡ k¡lak¤d-vibhuÅ.

sarv¡tm¡ sarvagaÅ s£kÀmaÅ sarvamasmin pratiÀ¶hitam. (7)

rathe visvamaye cakra=m k¤tv¡ sa=mvatsar¡tmaka=m.

chand¡´sya¿v¡Å saptayukt¡Å parya¶atyeÀa sarvad¡. (8)

trip¡damam¤tam guhyam p¡do'ya=m praka¶o'bhavat.

so 'hank¡ram jagats¤À¶yai brahm¡¸amas]]¤jat prabhuÅ. (9)

tasmai ved¡nvar¡ndattv¡ sarvalokapit¡mahaÆ.

pratiÀ¶h¡py¡¸·a-madhye'tha swaya=m paryeti bh¡vayan. (10)

atha s¤À¶y¡m manascakre brahm¡hank¡ra-m£rtibh¤t.

manasascandram¡ jajµe suryo'kÀ¸ostejas¡=m nidhiÅ. (11)

manasaÅkha=m tato v¡yuragnir¡po dhar¡ kram¡t.

gunaika-v¤ddhy¡ paµcaiva mah¡bh£tani jajµire. (12)

agn¢Àomau bh¡nu-candrau tatastva´g¡rak¡dayaÅ.

tejo bh£kh¡mbuv¡tebhyaÅ krama¿aÅ paµca jajµire. (13)

Parambrahma is V¡sudeva. His form is parama puruÀa  who is avyakta (unmanifested), nirgu¸a (devoid of sattva, rajas and tamas), ¿¡nta (undisturbed), avyaya (non-changing) and is beyond the twenty-five tattvas of S¡Ækhya philosophy. (1)

This internally and externally omnipresent Deva having entered the Prak¤ti in the form of Sa´karÀa¸a created  waters and saw the seed (of the universe). (2)

This became a golden egg which was surrounded by darkness all around, out of the same, first appeared san¡tana (everlasting) aniruddha. (3)

This is referred to as hira¸yagarbha in Vedas. Having appeared first, it is called ¡ditya which because of having created all the animate and inanimate world is referred to as s£rya. (4)

Being in the form of most intense light and because of having dispersed all the darkness it is referred to as savit¡. This bh£tabh¡vana, i.e., the creator, preserver and destroyer of the whole world traverses the worlds dispersing the darkness. (5)

The same in the form of light, disperser of all darkness is known as mahattattva. His ma¸·ala is Îgveda, kar¸a is S¡maveda and m£rti is Yajurveda. (6)

Thus this is tray¢maya, i.e., in the form of three Vedas and this is also in the form of 'Time' as this is the one who creates time and is omnipotent. He is the soul of all and is omnipresent. He is subtle and whole of the world rests in him. (7)

He always travels in the world-cart with the year wheel having saptac chandas as seven horses. (8)

His three cara¸as being immortal are obscure, i.e., they are beyond comprehension, only the fourth cara¸a is manifested. The same Prabhu, the omnipotent, created Brahm¡ in the form of ahaÆk¡ra, i.e., the ahaÆtattva of S¡Ækhya philosophy. (9)

Having handed over the desired Vedas to the Grand father of the world (the Brahm¡) and having made him sit in the egg aniruddha travels illuminating the whole world. (10)

Brahm¡ in the form of ahaÆtattva first created manas and from manas; the moon appeared and from the eyes appeared the ocean of tejas, the 'Sun'. (11)

From manas appeared "¡k¡¿a , from ¡k¡¿a came v¡yu (the air), from air, agni; from agni, the water; and from waters appeared p¤thiv¢. Thus five mah¡bh£tas appeared with the increase of each gu¸a (qualities, sound, r£pa (form), rasa (taste), touch and smell at each step of manifestation. (12)

After the creation of fiery Sun and Soma Moon, Mars was created from tejas, Mercury from p¤thiv¢, Jupiter, from ¡k¡¿a, Venus, from water, Saturn from air. (13)

It may be remarked that the above stanzas are the replies to the questions of May¡sura, by the S£ry¡´¿a puruÀa. This cosmogonic descritpion is an admixture of s¤À¶ikramas from S¡Ækhya Ved¡nta and ár¢madbhagavatam. The parable of Sa´karÀa¸a and Aniruddha is somewhat different from the one in Bh¡gava-tadharma. According to the latter, from V¡sudeva Parame¿vara, manifested    the J¢va Sa´karÀa¸a; from Sa´karÀa¸a, Pradyumna was born and from Pradyumna, Aniruddha (i.e., the ahaÆtattva). Some schools do not mention Pradyumna in the sequence. Note that in the above stanzas paµcatanm¡tras are not categorically mentioned but these are automatically understood in right order in the sequence because the text refers to the V¡sudeva to be beyond twenty-five tattvas of S¡Ækhya philosophy.

Now we come to other texts which exclusively deal with JyotiÀa á¡stra. In JyotiÀa Ved¡´gam of ÎÀi Lagadha we do not find as such any reference to any of the paµca- mah¡bh£tas except to the Sun and Moon which are tejas bhautika bodies. In Pur¡¸as, (like M¡rka¸·eya Pur¡¸a) we do have exclusive sections dealing with jyotiÀa, but these have mostly the same contents as the proper JyotiÀa á¡stra texts like JyotiÀa Ved¡´gam, S£rya Prajµapti, Candra Prajµapti, Jamb£dv¢pa Prajµapti and JyotiÀa-Kara¸·aka in Pr¡k¤ta (of Jaina Tradition), á¡rd£la Karn¡vadana of Buddhist tradition. So it is worthwhile to discuss here only the references to mah¡bh£tas or bhautika entities as found in proper JyotiÀa texts.

B¤hat-saÆhit¡ of Var¡hamihira (6th century ad) has many chapters exclusively on various aspects of astronomy. It talks of cosmic evolution as follows:

¡sittamah kiledaÆ tatr¡p¡m taijasebhavaddhaime.

svarbh£¿akale brahm¡ vi¿vak¤da¸·¡rka-¿a¿inayanaÅ. (6)

                                                   (Var¡ha B¤S. 1.6)

Before creation, there was nothing but darkness everywhere. Then water came into being, wherefrom sprang a golden egg consisting of two parts of the shell, i.e., the earth and the heavens. There arose the creator of the universe Brahm¡ with Sun and Moon as his eyes. (6)

Note that here Sun and Moon are said to have born simultaneously with Brahm¡ (in a lyrical simile in the language) while S£rya Siddh¡nta talks of creation of Sun and Moon after Brahm¡'s appearance in the genesis sequence.

The Concepts About Bhautika Entities in JyotiÀa Texts

Earth (one entity in the big assembly of paµcamah¡bhautika world in infinite space) is described in detail by Indian astronomers in their respective treatises. Var¡hamihira in Paµca-siddh¡ntik¡ describes the earth as a paµcamah¡bhautika body standing in space without support, like an iron ball in a cage of magnets. See diagram 8.1.

The Notions predecessor of law of gravitation on the basis of

symmetry property of space (¡k¡¿a)

panca-mah¡bh£tamayast¡r¡ga¸apaµjare mah¢golah.

khe'yask¡ntastho loha iv¡vasthito v¤ttaÅ. (1)

                                                 (Var¡ha. B¤. S. 13.1)

It may be noted that in JyotiÀa mostly Sop¡dh¢k¤ta mah¡bh£tas  are discussed.

Var¡hamihira gives the simile with the iron ball held at the centre of a magnetic cage, while some thought of the supporting power of Brahman responsible for the Earth's held up position in space.

Earlier the rotation of earth was not conceived, the revolutions of heavens during day and night were considered to be caused due to Prav¡ha V¡yu. Since very old days of the saiddh¡ntika astronomy, Lalla's SiÀyadh¢ v¤ddhida tantra discusses the seven types of air in seven shells around the earth. The atmospheric air enveloped around the earth is known as ¡vaha. Its radius is said to be 537 yojanas. But it is interesting to note that Ëryabha¶a about five hundred years earlier than Lalla, claimed the rotation of earth about its own axis, but the hypothesis was not accepted and was much criticised by Lalla.  It may be remarked that the basic unit of time is defined using the rotation of earth as standard. This definition stands even now when atomic watches are invented for use in scientific works. The other units of time are defined on the bases of motion of the sun and the moon. The time so defined is sop¡dhika while in Ny¡ya philosophy this is absolute but gets into use when defined in relation to the motion of a body in space (¡k¡¿a). This way it is rendered sop¡dhika. Time and space are one and the same in Eiensteinian frame-work of the theory of relativity. But astronomers like Newton took space and time as absolute and considered these to be different pad¡rthas. We discuss the implication of these concepts as used by our exponents of JyotiÀa.

Absoluteness of Space and Law of Gravitation

It may be noted that JyotiÀa á¡stra is a discipline, where the theories are evolved and hypotheses are supported or rejected through the mathematical arguments based on observations. JyotiÀa á¡stra texts describe the methods of determining the direction(s) in space. The directions (dik) are  nothing but sop¡dhika space. The directions are always relative to a particular point in space and thus will have no meaning in absolute sense. Thus dik is just the sop¡dhik¢kara¸a of space. Although JyotiÀ¡c¡ryas developed mathematical techniques to determine Directions/Subdirections or any relative orientation of a system, yet they were aware of the absolute nature of space. Using this concept they arrived at the concept of law of gravitation qualitatively (of course Newton treated the problem mathematically.) Before we discuss the notion about force of attraction of earth and planets in ancient or medieval Indian traditions, it is desirable to point out how the ancient seers thought of causes of planetary motions.

It is interesting to note that in ancient JyotiÀa á¡stra tradition, the notions on causes of planetary motions were based on the philosophical concepts regarding time and space. S£rya Siddh¡nta talks of the agents of planetary motion as the invisible personified Time Gods standing at the cardinal points (Apogee, perigee and the nodes) on the orbit. These Gods were indentified mathematically with manda kendra (anomaly) ¿¢ghra kendra (the elongation argument) and p¡ta (the orbital nodes). It was conjectured that these Gods stand at their specific positions and drag the planets by their left and right hands on both the sides.

The notions predecessor of law of gravitation based on the symmetry property of space (¡k¡¿a).

As ¡k¡¿a is all around symmetric or directionless, how the planets can move? There must be some force?

Diagram 8.2

Broken arrowheads show the direction of the force due to the divine agent at  ucca (Full arrowheads show the direction of velocity vector of the planet) S£ryasiddh¡nta (SS) talks of Divine agents of force (Representative of Compelling Time harmonicities) which are responsible for changes in velocity through invisible air ropes (The action at a distance).

Broken arrowheads indicate just the directions of action of force agent, located at ucca. The velocity increases on one side and decreases  on the other side of ucca.

(See the diagrams 8.2, 8.3 which show the details of this model of drag-hypothesis). On the basis of this model they explained the variations in speeds of planets (and even argued to have proper signs for their accelerations). Even comparing the velocities of Moon and Mars etc., they attributed their relative velocity magnitudes to their sizes and masses while under the force of drag by the invisible Time Gods. Motion towards the north and south of ecliptic were explained on the basis of the dragging force due to Gods at the p¡tas. Mercury and Venus are said to be under the faster attractive drag force due to the God at ¿¢ghra kendra. It may be remarked that on the basis of this model they could not explain the vakra gati (Retrograde motions)of planets. Note that they did study the different types of possible velocities but just reported these types without explaining. These are the earliest notions about force of attraction and it may be pointed out that in these notions time is considered to be the compelling force, which causes changes in velocitites and keeps planets moving along the curved space but no force of attraction responsible for keeping the planets in orbits could be assigned.  There is no doubt that the notion similar to the above one is quite natural because Time binding on the motion is likely to be taken as a compulsion on the moving body and the cardinal points are the points from where the change in velocity starts  developing. Even in the frame-work of the law of gravitation, the motion is represented by Sin(nt), (where nt = anomaly), the acceleration starts developing from the cardinal point (velocity = n radians per unit of time).

The Notions Predecessor of law of Gravitation, based on the symmetry property of space (Ëk¡¿a)

Diagram 8.3

The S.S. talks of divine agents of force also at the nodes which drag the planets towards northern or southern hemispheres.

Bh¡skar¡c¡rya studying the motion of Mars, Jupiter etc. found that in case these are behind the Sun, they get accelerated and when Sun is behind any planet the latter is retarded. In fact Bh¡skar¡c¡rya had almost arrived at the conclusion that Sun attracts the planets but he missed the point without the necessary elaborations. On the other hand, he could arrive at the most important conclusion about earth's gravity using absoluteness (leading to the all round symmetry) of space. How was the concept of the absolute or relative nature of space used in arguments by Bh¡skar¡c¡rya in arriving at the hypothesis about the law of gravitation in case of earth? This would be clear from the following paragraph.

Symmetry of Space (¡k¡¿a) is a property which could be easily inferred. In fact Newton's first law of motion, that nothing can move unless some force is applied, is a notion conceived by man since the beginning of creation. Newton just postulated the same in categoric statements and developed the laws of motion mathematically. Note that this law is just a mathematical translation of the fact that space is all around symmetric. It has no direction downward, upward or north, east, south or west. All the directions in space lack any preference for any directivity if there is no object at a point (which is negation of space at that point). If you suppose that the body will move in a particular direction defined with respect to a point in open space (without any other body) one can counter-argue, "what is space with that direction?" "Why should the body not move in another direction?" Thus on simple logical grounds even the primitive man might have had familiarity with the first law of motion  qualitatively. In addition to this, so naturally accepted inference, the spherical shape of the earth helped a lot in arriving at the notion of the force of gravitation. This fact will be clear in the following discussion.

When it was clear to man that the earth is a figure like a ball and he knew that there are habitants all over the earth, it helped to conclude about gravitation due to the earth. S£rya Siddh¡nta describes the symmetry of space in a good philosophical way as follows:

sarvatraiva mah¢gol«e svasth¡namupari sthitam.

manyante khe yato gol¡stasya kvordhvam kva v¡pyadhaÅ.

                                           (S.S. Bh£gol¡dhy¡ya, Stanza 53)

i.e., Everywhere on the spherical earth, the observer's place is above (i.e., his head points towards upward direction), because this sphere (earth) is (held) in space. So which direction is upward and which direction is downwards? The directions have no meaning in space. Bh¡skar¡c¡rya advanced further to infer about gravitation of the earth. His statement is :

¡krÀ¶a¿akti¿ca mah¢ tay¡ yat

khasthaÆ guru sv¡bhimukhaÆ sv¡sakty¡

¡k¤Àyate tat patat¢va bh¡ti

same samant¡t kva patatviyam khe?

The earth has capability to attract and due to this very property, in fact, this attracts any heavy object in space and the latter appears as if 'falling'. In the space which is symmetric all around, where it can fall?

It is clear that Bh¡skar¡c¡rya arrived at the notion about gravitational force on the very basis of the principle of the 'Falling apple' about five hundred years earlier that Newton. There is no doubt that the credit to Newton is for all mathematical developments regarding motion which led kinematical studies to dynamical treatments, but Bh¡skar¡c¡rya was the first to state categorically about existence of gravitational force of earth and argued more beautifully on the basis of symmetry of space and the spherical figure of the earth. As the earth is populated all around, for a man at a certain place (say Ë', see diagram 8.4) on the globe there is one 'B' just below on the other side of the earth, like a shadow in water. There are other people too whose positions are along directions inclined with respect to the p[osition of the first one. There are also along 900 away (i.e., along perpendicular directioon (S)), but none falls away from earth's surface. Everyone thinks of himself standing above or towards-upwards direction. In this diagram are shown stones thrown by men at A and B falling to the earth from opposite directions. Thus one concludes that there exists force of attraction which is responsible for the "fall of bodies in space". So in fact the 'falling apple' theory is explained by Bh¡skar¡c¡rya.

The Physical laws derived from the fact that Ëk¡¿a is all around symmetric

Diagram 8.4

(Falling stone Syndrome in Bh¡skar¡c¡rya's Siddh¡nta áiroma¸i)

It also talks of the directionlessness of ¡k¡¿a as inferred from the spherical shape of the earth which is all around populated by human beings (on the one side (above) and on the other side in P¡t¡la (or just below). But Bh¡skar¡c¡rya advanced further to infer that Earth attracts the heavy things (say a stone) left in space and the latter appears ¡s if falling". He argues, where can the stone fall? Ëk¡¿a is all around symmetric whichever direction is above or just below (like the  shadow of a man in water)as the earth has spherical shape. This falling stone principle of Bh¡skar¡c¡rya (1150 ad) came about five centuries earlier than Newton (1676 ad).

There is no doubt that for mathematicians space is symmetric and infinite, and they use the former property to arrive at the law of gravitation but we find in JyotiÀa texts like S£rya Siddh¡nta, Bh¡skar¡c¡rya's Siddh¡nta áiroma¸i etc., the dimensions of ¡k¡¿a kakÀ¡ (the orbit of space) which in fact is defined as the limit up to which point Sun's rays reach. Thus it is limited to ¡k¡¿a. Yet for them too, ¡k¡¿a is vibhu (all around and hence symmetric) and infinite, but unlike in qualitative philosophy they could go ahead and conclude about the laws of motion and universal gravitation functioning in nature by translating symmetry of space in mathematical language.

Conclusion

The references to JyotiÀa in Vedic v¡´gmaya and later texts give details of cosmogonic evolution leading to the creation of paµcamah¡bh£tas from t¡masa bh£t¡di ahaÆk¡ra. The stars and planets have evolved out of these mah¡bh£tas. Astronomical and astrological texts make use of the concept of mah¡bh£tas in their working principles. They used the sop¡dhika ¡k¡¿a in determining the directions/subdirections in two-dimensional and three-dimensional space, which helped in specifying the positions of terrestrial and celestial objects. They also made use of the vibhu absolute and infinite nature of space in inferring the existence of law of gravitation functioning in nature and derived the laws of conservation of momenta from its symmetry properties. The development of the laws of motion and gravitation are the most interesting developments in the hands of astronomers, which grew out of the philosophic concepts of mah¡bh£tas. They attributed the reasons for the gravitational forces to the very nature of matter, for example Bh¡skar¡c¡rya gives the simile of a natural phenomenon like the heat in fire, hardness in stones etc. for the gravity of the earth. These modern studies in space science and other disciplines of study of mah¡bhautika entities have advanced to remarkable extents, which have served the causes of human conveniences all over the world.

It may be pointed out that Hayata, an Arabic astronomical text (translated into Sanskrit) talks of bodies (Vasita, Falaki, Uns¡ri, etc.) with one, two or more mah¡bh£tas but excluding ¡k¡¿a. (The Graeco-Arabic philosophy does not include ¡k¡¿a in the list of mah¡bh£tas. There are only four mah¡bh£tas in this system of philosophy) Ny¡ya philosophy too talks of bodies made up of specific mah¡bh£tas taken each individually but áa´kar¡c¡rya's Paµc¢kara¸a (a process claiming mixtures of tanm¡tras in the gross mah¡bh£ta elements) has no provision for pure single mah¡bh£ta elements. S£rya siddh¡nta the astronomical text talks of five star planets out of five mah¡bh£tas taken individually. Thus there are differences in various schools of philosophy. But there is no doubt that the JyotiÀ¡c¡ryas went ahead to use the properties of the mah¡bh£tas to arrive at laws of motion and the gravitational law working in the universe which served the cause of scientific development.

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