The chronological frame sketched is somewhat different from the dogma of the generation past. Then we were told that India was invaded around 1500 BC by Aryans from Central Asia or, perhaps, even South Europe. This dogma was at the basis of the construction of an elaborate scenario related to strife between the speakers of the Aryan and Dravidian languages.

As the science of language, historical linguistics in the early 19th century saw itself as providing a framework for studying the history and relationships of languages in the same manner as biology describes the animal world. But whereas biology has been revolutionized by the discovery of the genetic code, no similar breakthrough has brought new illumination to linguistics. Over the protestations of its many critics, mainstream historical linguistics has remained within the parameters of 19th century thinking. In the meanwhile, archaeological discoveries have altered our understanding of ancient Eurasia.

The Indo-Europeans are seen to be present in Europe a few thousand years earlier than was supposed before. The Indian evidence, based on archaeology as well as the discovery of an astronomy in the Vedas, indicates that Vedic Sanskrit is to be assigned to the 4th and the 3rd millennia BC, if not earlier. The Indian cultural area is seen as an integral whole.

The Vedic texts are being interpreted as a record of the complex transformations taking place in the pre-2000 BC Indian society. We understand how the 19th century construction of the Orient by the West satisfied its needs of self-definition in relation to the Other. To justify its ascendancy, the Other was defined to be racially mixed and inferior, irrational and primitive, despotic and feudal. This definition was facilitated by a selective use of the texts and rejecting traditional interpretations, an approach that is now called Orientalism. The terms in the construction were not properly defined. Now we know that to speak of a “pure” race is meaningless since all external characteristics of humans are defined in a continuum.

In the 19th century atmosphere of European triumphalism, what was obtained in Europe was taken to be normative. With hindsight it is hard to believe that these ideas were not contested more vigorously. Although this was the age that marked the true beginnings of modern science, old myths continued to exercise great power. When it was found that the languages of India and Europe were related in structure and vocabulary, the West responded with what J.-P. Vernant calls “a tissue of scholarly myths. These myths were steeped in erudition, informed by profound knowledge of Hebrew and Sanskrit, fortified by comparative study of linguistic data, mythology, and religion, and shaped by the effort to relate linguistic structures, forms of thought, and features of civilization. Yet they were also myths, fantasies of the social imagination, at every level.

The comparative philology of the most ancient languages was a quest for origins, an attempt to return to a privileged moment in time when God, man, and natural forces still lived in mutual transparency. The plunge into the distant past in search of ‘roots’ went hand in hand with a never forgotten faith in a meaningful history, whose course, guided by the Providence of the one God, could be understood only in the light of Christian revelation.

As scholars established the disciplines of Semitic and Indo-European studies, they also invented the mythical figures of the Hebrew and the Aryan, a providential pair which, by revealing to the people of the Christianized West the secret of their identity, also bestowed upon them the patent of nobility that justified their spiritual, religious, and political domination of the world.” Although the term Aryan never had a racial connotation in the Indian texts, the scholars insisted that this was the sense in which the term ought to be understood. It was further assumed that Aryan meant European by race. By doing so Europe claimed for itself all of the “Aryan” texts as a part of its own forgotten past. The West considered itself the inheritor of the imagination and the mythic past of the Aryan and the idea of the monotheism of the Hebrew.

This dual inheritance was the mark of the imperial destiny of the West. Vernant reminds us that despite his monotheism, the poor Jew, since he lacked Aryan blood, should have seen “the dark silhouette of the death camps and the rising smoke of the ovens.”

On the other hand, the Asiatic mixed-blood Aryan had no future but that of the serf. He could somewhat redeem himself if he rejected all but the earliest core of his inheritance, that existed when the Aryans in India were a pure race. For scholars such as Max Müller  this became ultimately a religious issue. Echoing Augustine, Müller saw in his own religious faith a way for progress of the Asiatic. We would smile at it now but he said,

“Christianity was simply the name ‘of the Language Wars , true religion,’ a religion that was already known to the ancients and indeed had been around ‘since the beginning of the human race.’

But ideas—bad and good—never die. Müller’s idea has recently been resurrected in the guise that Christianity is the fulfillment of Vedic revelation!

A linguistic “Garden of Eden’’ called the proto-Indo-European (PIE) language was postulated. Europe was taken to be the homeland of this language for which several wonderful qualities were assumed. This was a theory of race linking the Europeans to the inhabitants of the original homeland and declaring them to the original speakers of the PIE. By appropriating the origins, the Europeans also appropriated the oldest literature of the Indians and of other IE speakers. Without a past how could the nations of the empire ever aspire to equality with the West? Indian literature was seen to belong to two distinct layers.
At the deepest level were the Vedas that represented the outpourings of the nature-worshiping pure Aryans. At the next level, weakened by an admixture with the indigenous tribes, the literature became a narrative on irrational ritual.

Science and Pseudoscience

In scientific or rational discourse the empirical data can, in principle, falsify a theory.This is why creationism, which explains the fossil record as well as evolution by assuming that it was placed there along with everything else by God when he created the universe in 4004 BC, is not a scientific theory: creationism is unfalsifiable. Building a scientific theory one must also use the Occam’s razor, according to which the most economical hypothesis that explains the data is to be accepted.

Bad intent should not turn anyone away from good science. Why isn’t PIE good science? It looks reasonable enough: If there are biological origins then there should be linguistic origins as well. And why don’t we believe that the nature of language tells us something about culture? If Europeans have been dominant in recent history, then why don’t we accept it as a characteristic of the European? Thus the origin of the PIE must be in the European sphere from where the energy of its early speakers carried them to the far corners of Asia and allowed them to impose their language on the native speakers. There are several problems with the idea of PIE. It is based on the hypothesis that languages are defined as fixed entities and they evolve in a biological sense. In reality, a language area is a complex, graded system of several languages and dialects of a family.

The degree of homogeneity in a language area is a reflection of the linkages, or interaction within the area. For a language distributed widely in the ancient world, one would expect several dialects. There would be no standard proto-language. It is clear that language families belong to overlapping groups, because such a view allows us to represent better the complex history of the interactions amongst their ancestor languages.

Such an overlap need not imply that the speakers of either group intruded into the overlapping region. We note further the warning by N.S. Trubetskoy (1939) that the presence of the same word in a number of languages need not suggest that these languages descended from a common parent:

‘ There is, then, no powerful ground for the assumption of a unitary Indogerman protolanguage, from which the individual Indogerman language groups would derive. It is just as plausible that the ancestors of the Indogerman language groups were originally quite dissimilar, and that through continuing contact, mutual influence and word borrowing became significantly closer to each other, without however going so far as to become identical.’

The evolution of a language with time is a process governed by context-sensitive rules that express the complex history of interactions with different groups over centuries. The changes in each region will reflect the interaction of the speakers with the speakers of other languages (most of which are now extinct) and various patterns of bilingualism. There is no evidence that can prove or disprove an original language such as PIE.

We cannot infer it with certainty since the historically attested relationship between different languages could have emerged from one of many competing models. If one considers the situation that prevailed in the New World when Europeans arrived as typical, the ancient Old World had a multitude of languages. It is from this great language diversity that a process akin to biological extinction led to the currently much smaller family of languages.Scholars now say that the metaphor of a perfect or pure language leading to large diversity must be replaced by the metaphor of a web. This becomes clear when we consider biological inheritance. We inherit our genes from more than one ancestor. The postulation of PIE together with a specific homeland in Europe or Turkey does violence to facts.

There is no evidence that the natives of India for the past 8,000 years or so have looked any different from what they look now. The internal evidence of this literature points to events that are as early as 7000 years ago and its geography is squarely in the Indian region. If there was no single PIE, there was no single homeland either. The postulation of an “original home”, without anchoring it to a definite time-period is to Language Wars 17 fall in the same logical trap as in the search for invasions and immigration.

Tree or animal name evidence cannot fix a homeland. In a web of languages, different geographical areas will indicate tree or animal names that are specific to these areas. When the European side of the IE languages is examined, the tree or animal names will favour those found in its climate and when the Indian side of the languages are examined, the reference now will be to its flora and fauna.

Colin Renfrew has pointed out how a circular logic has been used by linguists to justify what has already been implicit in their assumptions. Speaking of the work by Paul Friedrich (1970) on “Proto-Indo-European trees”, Renfrew reminds us that the starting assumption there is that PIE was current in western Caspian and the Carpathians during the fourth millennium and the first centuries of the third millennium and then Friedrich proves that this was the PIE homeland! Reminds Renfrew:

[Friedrich’s] assumption is highly questionable. So complete an adoption of one specific solution to the question of Indo-European origins is bound to have a considerable impact upon his analysis of the origins of tree-names, and the historical conclusions he reaches. It is scarcely surprising if his theory harmonizes with the historical reconstruction upon which it is based. It is perhaps reasonable that the historical linguistics should be based upon the archaeology, but that the archaeological interpretation should simultaneously be based upon the linguistic analysis gives serious cause for concern. Each discipline assumes that the other can offer conclusions based upon sound independent evidence, but in reality one begins where the other ends. They are both relying on each other to prop up their mutual thesis.

Aryan and Dravidian

It was Bishop Caldwell (1875) who suggested that the South Indian languages of Tamil, Malayalam, Kannada, and Telugu formed the separate Dravidian family of languages. He further suggested that the speakers of the proto-Dravidian language entered India from the northwest. Other scholars argued against this Dravidian invasion theory. Scholars have argued that this attempt to see both the North and the South Indian languages coming to the subcontinent from outside (West Asia) as another example of the preoccupation with the notion of the “Garden of Eden’’.

In reality, the problem of what constitutes an Aryan or a Dravidian, in the biological or cultural sense in which it is generally posed, is insoluble. The problem of Aryan and Dravidian is a conflation of many categories. Indian texts do not use the term Arya or Aryan in a linguistic sense, only in terms  of culture.

There is reference in the Manu Smriti where even the Chinese are termed Aryan, proving that it is not the language that defines this term. The South Indian kings called themselves Aryan as did the South Indian travelers who took Indian civilization to Southeast Asia. One may have posed the problem in terms of the anthropological “distinction” between the speaker of the North and the South Indian languages. But the anthropologists tell us that there is no difference. When linguists in the last century insisted that the term “Aryan” be reserved for the North Indian languages alone, it was inevitable confusion would emerge.

The definition of Aryan and Dravidian are extrapolated from the culture of the speakers of the North and the South Indian languages. But the cultures of the North and the South are the same as far back as we can go. (There is some minor difference in kinship rules.) There is even a mirroring of the sacred geography. The North has Kashi and Mathura; the South has Kanchi and Madurai. Who is to say what the original was? If there is no cultural difference then the use of the term “Aryan” as defining the culture of just the speakers of the North Indian languages is misleading.

This following example puts the absurdity of the terminology in focus. There exist texts that state that Tamilian Hindus came and settled in Kashmir in the early 15th century in the liberal reign of Bada Shah. We don’t know how many people came, but that is the nature of such textual evidence anyway. Now what does that make a Kashmiri? An Aryan or a Dravidian?

Some scholars have claimed a Dravidian substratum for Marathi, but how do we know that prior to that Dravidian substratum there was not some other language that was spoken there? And maybe there has been more than one shift back and forth. Let’s imagine that everyone in India originally spoke Dravidian and then due to some process of “elite dominance” most people in the North started speaking Indo-Aryan and they kept their old traditions and legends.

The new speakers will still be culturally Dravidian and certainly they would be so “biologically”, if that could ever mean anything. If this is what happened in India then are the Aryans actually Dravidians and, by implication, are the Dravidians also Aryans?

There could be two groups of people speaking two different languages who culturally belong to the same tradition like the modern-day Hungarians and Czechs. We don’t know who the authors of the Vedas were. They could have been bilingual speakers who knew “Dravidian” and “Vedic”; maybe their first language was really Dravidian even though they had Sanskrit names as has been true in South India for much of historical times; or they were purely Sanskrit speaking. No rhetoric or ideology can resolve this question.

The use of a language in literature does not even mean that the speakers are a dominant elite. Let’s consider the use of Urdu in Pakistan. The Punjabi speaking Punjabis are the dominant group but Urdu is used for official work purely due to some historical factors. In fact, the only Urdu-speaking ethnic group in Pakistan, the Mohajirs, feel they are at the bottom of the totem pole. The texts cannot reveal the ethnic background just as Indians in the US who have adopted American names cannot be identified as ethnically Indian from their writing. The lesson is that the term “Aryan”, misused by so many different parties, should be retired from academic discourse.

Several Kinds of Families

The Indian linguistic evidence requires the postulation of two kinds of classification. The first is the traditional Indian classification where the whole of India is a single linguistic area of what used to be traditionally called the Prakrit family. Linguists agree that based on certain structural relationships the North and the South Indian languages are closer than Sanskrit and Greek.1, Second, we have a division between the North Indian languages that should really be called North Prakrit (called Indo-Aryan by the linguists) and the South Indian languages that may be called South Prakrit (or Dravidian).

There is also the Indo-European family to which the North Prakrit languages belong. Likewise, Dravidian has been assumed to belong to a larger family of agglutinative languages. This classification will allow us to get rid of the term Aryan in marking the families of languages, allowing us to move past the racist connotation behind its 19th century use. Its further virtue is that it recognizes that language families cannot be exclusive systems and they should be perceived as overlapping circles that expand and shrink with time.

Back to the Origins

Some Indologists driven by the old race paradigm have stood facts upside down to force them to fit their theory. We know that the internal evidence of the Indian texts shows that the Vedas precede the Puranas.

Since Puranic themes occur in the iconography of the Harappan times (2600-1900 BC), some take the Puranic material to precede the Vedas so that the Vedas could be placed in the second millennium BC.  I think the only logical resolution of all the archaeological and textual evidence is to assume that the Indic area became a single cultural area at least around 5000 BC. The Indian civilization was created by the speakers of many languages but the language of the earliest surviving literary expression was Vedic Sanskrit, that is itself connected to both the North and the South Prakrit languages.

This idea is supported not only by the internal evidence that shows that the Indic tradition from 7000 BC onwards is an indigenous affair, but also from the new analysis of ancient art. For example, David Napier argues that the forehead markings of the Gorgon and the single-eye of the cyclops in Greek art are Indian elements. Although he suggests that this may have been a byproduct of the interaction with the Indian foot soldiers who fought for the Persian armies, he doesn’t fail to mention the more likely possibility that the influence was through the 2nd millennium BC South Indian traders in Greece.

This is supported by the fact that the name of the Mycenaean Greek city Tiryns—the place where the most ancient monuments of Greece are to be found—is the same as that of the most powerful Tamilian sea-faring people called the Tirayans., Since the 2nd millennium interaction between Greece and India is becoming clear only now, it is appropriate to ask if our languages were frozen into fixed categories wrongly by the 19th century historical linguists. Consider the centum/satem divide in which European languages belong to the centum group and the North Indian languages to the satem group. The tree model is used to divide the PIE into these two sub-classes with the centum group representing the western branch and the satem group representing the eastern branch.

The discovery of Tocharian as a centum language was seen as an example of a heroic movement of centum-speaking people from the west. But now the discovery of Bangani, a centum language in India, has make the whole idea of a treelike division suspect. Consider also the question of our knowledge of the vocabulary of various languages. For some languages, this knowledge was primarily obtained in quick field-work done decades ago by scholars who were not native speakers. Could it be that they missed out on vital evidence?

One of the orthodox scholars informs us;that the word *mori “seems originally to have meant swamp, marsh land or lake, rather than a large body of open water. [I]t is found only in European languages and not in Indo-Iranian other than Ossetic—an Iranian language contiguous to Europe although originating further to the east.” This “fact” has lent itself to endless theorizing. But this “fact” is a result of incomplete surveys. The word mar, a cognate, is a common Kashmiri term for a swamp or even a lake. We see this word in the formation of Kashyapmar from which the word Kashmir is derived.

Even Kannada has a cognate. Also, many Hindi speakers pronounce the word for “hundred” as sainkara rather than saikara, which the field studies tell us is the “correct” form. Does that make Hindi a centum language? The archaeological findings from India and the discovery of the astronomy of the Vedic period are fatal for the constructions of historical linguistics that arose in the 19th century and are still being followed in schoolbooks in India although textbooks in the West have begun to present the new picture. While the general language categories seem reasonable, the concept of overlapping families seems essential to obtain better conceptual clarity. The breakdown of the old paradigm calls for considerable effort to create a new one to take its place.
In particular, the emerging chronological framework can be used to examine the relationships between Sanskrit and other ancient Indo-European languages. Etymological dictionaries should be revised to take note of the antiquity of Vedic Sanskrit. If PIE did not exist, can we extrapolate from the earliest layer of Vedic Sanskrit for correlations with life in prehistoric Harappan India?

(20908)

In the Vedic world view, the processes in the sky, on earth, and within the mind are connected. The Vedic seers insist that all rational descriptions of the universe lead to logical paradox. The one category transcending all oppositions is Brahman. Understanding the nature of consciousness is of paramount importance in this view but this does not mean that other sciences are ignored. Vedic ritual is a symbolic retelling of this world view. Knowledge is classified in two ways: the lower or dual, and the higher or unified. The seemingly irreconcilable worlds of the material and the conscious are taken as aspects of the same transcendental reality. The idea of complementarity is at the basis of the systematization of Indian philosophic traditions, so that complementary approaches are paired together.

We have the groups of: logic (Nyaya) and physics (Vaisheshika), cosmology (Sankhya) and psychology (Yoga), and language (Mimamsa) and reality (Vedanta). These six views are like the six sides of a cube. Although these philosophical schools were formalized in the post-Vedic age, we find the basis of these ideas in the Vedic texts.

The Sankhya and the Yoga systems take the mind as consisting of five components:

manas, ahamkara, chitta, buddhi, and atman.

Manas is the lower mind which collects sense impressions. Ahamkara is the sense of I-ness that associates some perceptions to a subjective and personal experience. Once sensory impressions have been related to I-ness by ahamkara, their evaluation and resulting decisions are arrived at by buddhi, the intellect. Chitta is the memory bank of the mind. These memories constitute the foundation on which the rest of the mindoperates. But chitta is not merely a passive instrument. The organization of the new impressions throws up instinctual or primitive urges which creates different emotional states. This mental complex surrounds the innermost aspect of consciousness,which is atman (Self or Brahman). In this view matter appears inert only because it has not expressed its potential. By process of transformation, nature (prakriti) attains the capacity for freedom. Sentient beings are free to varying degrees.

Physics and Chemistry

The Vaisheshika system considers nine classes of substances, some of which are nonatomic, some atomic, and others all-pervasive. The nonatomic ground is provided by the three substances ether, space, and time, which are unitary and indestructible; a further four, earth, water, fire, and air are atomic composed of indivisible, and indestructible atoms; self (atman), which is the eighth, is omnipresent and eternal; and, lastly, the ninth, is the mind (manas), which is also eternal but of atomic dimensions, that is, infinitely small. The atoms combine to form different kinds of molecules that break up under the influence of heat. The molecules come to have different properties based on the influence of various potentials (tanmatras). Heat and light rays are taken to consist of very small particles of high velocity. Being particles, their velocity is finite. The gravitational force was perceived as a wind. The other forces were mediated by atoms of one kind or the other. Indian chemistry developed many different alkalis, acids and metallic salts by processes of calcination and distillation, often motivated by the need to formulate medicines. Metallurgists developed efficient techniques of extraction of metals from ore.

Geometry and Mathematics

Indian geometry began very early in the Vedic period in altar problems as in the one where the circular altar (earth) is to be made equal in area to a square altar (heavens). Two aspects of the “Pythagoras” theorem are described in the texts by Baudhayana and others. The geometric problems are often presented with their algebraic counterparts. The solution to the planetary problems also led to the development of algebraic methods. Binary numbers were known at the time of Pingala’s Chhandahshastra. Pingala, who is believed to have lived about the fifth century BC used binary numbers to classify Vedic meters. The knowledge of binary numbers indicates a deep understanding of arithmetic.

Astronomy

For many years the mainstream view was to take Indian astronomy as being essentially derivative, based on Mesopotamian and Greek sources. This view arose from the belief that the Indians did not possess a tradition of sound observation. This view was proven wrong for the Siddhantic period by Roger Billard who, using computer analysis, showed that the parameters used in the Siddhantas were accurate for the date of the texts, establishing that they couldn’t have been borrowed from some old source outside of the country.

This was not accepted by all. In particular, David Pingree, who had invested his career in the paradigm that Greek astronomy was the source of Indian astronomy attacked Billard. The distinguished historian of astronomy B.L. van der Waerden stepped in as a referee. He wrote a famous paper called “Two treatises on Indian astronomy” in the Journal for History of Astronomy (1970), where he stated the problem as: “If Pingree is right, Billard is wrong, and conversely.” Proceeding to summarize the works of each, he concluded:

‘ Billard’s methods are sound, and his results shed new light on the chronology of Indian astronomical treatises and the accuracy of the underlying observations. We also have seen that Pingree’s chronology is wrong in several cases. In one case, his error amounts to 500 years … Billard’s book is reliable and contains very valuable new information. I have checked several of his results, and Billard always proved right’.

Meanwhile, our understanding of Vedic astronomy has changed in which my discovery of an astronomical code in the organization has played a role. These discoveries indicate that there was a long tradition of astronomical observation in India. The origins of Indian mathematics are also much ancient than previously thought. An amulet seal from Rehman Dheri (2400 BC) indicates that the nakshatra system is an old one. The seal shows a pair of scorpions on one side and two antelopes on the other. It has been argued that this seal represents the opposition of the Orion (Mrigashiras, or antelope head) and the Scorpio (Rohini) nakshatras. There exists another relationship between Orion and Rohini, this time the name of alpha Tauri, Aldebaran.

The famous Vedic myth of Prajapati as Orion, as personification of the year, desiring his daughter (Rohini) (for example Aitareya Brahmana 3.33) represents the age when the beginning of the year shifted from Orion to Rohini. For this transgression, Rudra (Sirius, Mrigavyadha) cuts off Prajapati’s head. It has been suggested that the arrow near the head It has been suggested that the arrow near the head of one of the antelopes represents the decapitation of Orion, and this seems a very reasonable interpretation of the iconography of the seal.

It is likely then that many constellations were named in the third millennium BC or earlier. This would explain why the named constellations in the Rigveda and the Brahmanas, such as the Rikshas (the Great Bear and the Little Bear), the two divine dogs (Canis Major and Canis Minor), the twin Asses (in Cancer), the Goat (Capricornus) and the Heavenly Boat (Argo Navis), are the same as in Europe. Other constellations described similar mythical events: Prajapati as Orion upon his beheading; Osiris as Orion when he is killed by Seth.

The Vedanga Jyotisha (VJ) of Lagadha (1300 BC) is one of the subsidiary Vedic texts, so its contents must be considered to be roughly coeval with the Brahmanas and other post-Vedic texts although the VJ text that has come down to us is definitely of a later period. The Puranas also contain a lot of very old material and their astronomy appears, on all counts, to be earlier than Aryabhata so they provide us with clues regarding the evolution of astronomical thought. It was long popular to consider the Siddhantic astronomy of Aryabhata to be based mainly on mathematical ideas that originated in Babylon and Greece. This view was inspired, in part, by the fact that two of the five pre-Aryabhata Siddhantas in Varahamihira’s Panchasiddhantika (PS), namely Romaka and Paulisha, appear to be connected to the West through the names Rome and Paul. But the planetary model of these early Siddhantas is basically an extension of the theory of the orbits of the sun and the moon in the Vedanga Jyotisha. Furthermore, the compilation of the PS occurred after Aryabhata and so the question of the gradual development of ideas can hardly be answered by examining it. I have presented the technical details of these discoveries elsewhere.

The main conclusion of these findings is that the earliest Indian astronomy is prior to the Mesopotamian one. We have traced certain Indian ideas in Mesopotamia in the second and the first millennium BC. There they were further developed and subsequently transmitted to Greece. Using hitherto neglected texts, an astronomy of the third millennium BC has been discovered. Yajnavalkya, who perhaps lived around 1800 BC, knew of a 95- year cycle to harmonize the motions of the sun and the moon and he also knew that the sun’s circuit was asymmetric. The second millennium text Vedanga Jyotisha of Lagadha went beyond the earlier calendrical astronomy to develop a theory for the mean motions of the sun and the moon. This marked the beginnings of the application of mathematics to the motions of the heavenly bodies. An epicycle theory was used to explain planThe Birth of Science 55 etary motions. Later theories consider the motion of the planets with respect to the sun, which in turn is seen to go around the earth.

Cosmology

The doctrine of the three constituent qualities: sattva, rajas, and tamas, plays an important role in the Sankhya physics and metaphysics. In its undeveloped state, cosmic matter has these qualities in equilibrium. As the world evolves, one or the other of these become preponderant in different objects or beings, giving specific character to each. The recursive Vedic world-view requires that the universe itself go through cycles of creation and destruction. This view became a part of the astronomical framework and ultimately very long cycles of billions of years were assumed. Indian evolution takes the life forms to evolve into an increasingly complex system until the end of the cycle. The categories of Sankhya operate at the level of the individual as well. Life mirrors the entire creation cycle and cognition mirrors a life-history. Cosmological speculations led to the belief in a universe that goes through cycles of creation and destruction with a period of 8.64 billion years. Related to this was the notion that light traveled with a speed of 186,000 miles per second. Since these numbers were not obtained through experimentation, the accuracy of these figures must be seen as remarkable coincidence.

Grammar

Panini’s grammar (5th century BC) provides 4,000 rules that describe the Sanskrit of his day completely. This grammar is acknowledged to be one of the greatest intellectual achievements of all time. The great variety of language mirrors, in many ways, the complexity of nature and, therefore, success in describing a language is as impressive as a complete theory of physics.

It is remarkable that Panini set out to describe the entire grammar in terms of a finite number of rules. Scholars have shown that the grammar of Panini represents a universal grammatical and computing system. From this perspective it anticipates the logical framework of modern computers.

Medicine

Ayurveda, the Indian medicine system, is a holistic approach to health that builds upon the tripartite Vedic approach to the world. Health is maintained through a balance between three basic humors (dosha) of wind (vata), fire (pitta), and water (kapha). Charaka and Sushruta are two famous early physicians. Indian surgery  was quite advanced. The caesarian section was known, bone-setting reached a high degree of skill, and plastic surgery was known.

The Yoga-Vasishtha

Let me take a single book, the Yoga-Vasishtha (YV), to summarize main ideas about space, time, matter, and man in the universe. The internal evidence indicates that it was authored or compiled later than the Ramayana. Scholars have dated it variously as early as first century AD or as late as the 13th or the 14th century. YV may be viewed as a book of philosophy or as a philosophical novel. It describes the instruction given by Vasishtha to Rama, the hero of the epic Ramayana. Its premise may be termed radical idealism and it is couched in a fashion that has many parallels with the notion of a participatory universe argued by Wheeler and others. Its most interesting passages from the scientific point of view relate to the description of the nature of space, time, matter, and consciousness. It should be emphasized that the YV ideas do not stand in isolation.

Similar ideas are to be found in the earlier Vedic books. At its deepest level the Vedic conception is to view reality in a monist manner; at the next level one may speak of the dichotomy of mind and matter. Ideas similar to those found in YV are also encountered in Puranas and Tantric literature. Three kinds of motion are alluded to in the Vedic books: these are the translational motion, sound, and light which are taken to be “equivalent” to earth, air, and sky. The fourth motion is assigned to consciousness; and this is considered to be infinite in speed. It is most interesting that the books in this Indian tradition speak about the relativity of time and space in a variety of ways. Universes defined recursively are described in the famous episode of Indra and the ants in Brahmavaivarta Purana 4.47.100-160, the Mahabharata 12.187, and elsewhere. These flights of imagination are to be traced to more than a straightforward generalization of the motions of the planets into a cyclic universe.

They must be viewed in the background of an amazingly sophisticated tradition of cognitive and analytical thought. Selected Passages YV consists of 6 books where the sixth book itself has two parts. The numbers in the square brackets refer to the book, (part), section, verse.

 Time

Time cannot be analyzed; for however much it is divided it survives indestructible. [1.23]

There is another aspect of this time, the end of action (kritanta), according to the law of nature (niyati). [1.25.6-7]

The world is like a potter’s wheel: the wheel looks as if it stands still, though it revolves at a terrific speed. [1.27]

Just as space does not have a fixed span, time does not have a fixed span either. Just as the world and its creation are mere appearances, a moment and an epoch are also imaginary. [3.20]

Infinite consciousness held in itself the notion of a unit of time equal to onemillionth of the twinkling of an eye: and from this evolved the time-scale right upto an epoch consisting of several revolutions of the four ages, which is the lifespan of one cosmic creation. Infinite consciousness itself is uninvolved in these, for it is devoid of rising and setting (which are essential to all time-scales), and it is devoid of a beginning, middle and end. [3.61]

Space There are three types of space—the psychological space, the physical space and the infinite space of consciousness. [3.17]

The infinite space of undivided consciousness is that which exists in all, inside and outside … The finite space of divided consciousness is that which created divisions of time, which pervades all beings…The physical space is that in which the elements exist. The latter two are not independent of the first. [3.97]

Other universes/wormholes. I saw within [the] rock [at the edge of the universe] the creation, sustenance and the dissolution of the universe…I saw innumerable creations in the very many rocks that I found on the hill. In some of these creation was just beginning, others were populated by humans, still others were far ahead in the passage of their times. [6.2.86]

I perceived within each molecule of air a whole universe. [6.2.92]

Space

There are three types of space—the psychological space, the physical space and the infinite space of consciousness. [3.17]

The infinite space of undivided consciousness is that which exists in all, inside and outside … The finite space of divided consciousness is that which created divisions of time, which pervades all beings…The physical space is that in which the elements exist. The latter two are not independent of the first. [3.97]

Other universes/wormholes. I saw within [the] rock [at the edge of the universe] the creation, sustenance and the dissolution of the universe…I saw innumerable creations in the very many rocks that I found on the hill. In some of these creation was just beginning, others were populated by humans, still others were far ahead in the passage of their times. [6.2.86]

I perceived within each molecule of air a whole universe. [6.2.92]

Matter

In every atom there are worlds within worlds. [3.20]

I saw reflected in that consciousness the image of countless universes. I saw countless creations though they did not know of one another’s existence. Some were coming into being, others were perishing, all of them had different shielding atmospheres (from five to thirty-six atmospheres). There were different elements in each, they were inhabited by different types of beings in different stages of evolution. [In] some there was apparent natural order in others there was utter disorder, in some there was no light and hence no time-sense. [6.2.59]

Experience

Direct experience alone is the basis for all proofs … That substratum is the experiencing intelligence which itself becomes the experiencer, the act of experiencing, and the experience. [2.19-20]

Everyone has two bodies, the one physical and the other mental. The physical body is insentient and seeks its own destruction; the mind is finite but orderly. [4.10]

I have carefully investigated, I have observed everything from the tips of my toes to the top of my head, and I have not found anything of which I could say, ‘This I am.’Who is ‘I’? I am the all-pervading consciousness which is itself not an object of knowledge or knowing and is free from self-hood. I am that which is indivisible, which has no name, which does not undergo change, which is beyond all concepts of unity and diversity, which is beyond measure. [5.52]

I remember that once upon a time there was nothing on this earth, neither trees and plants, nor even mountains. For a period of eleven thousand years the earth was covered by lava. In those days there was neither day nor night below the polar region: for in the rest of the earth neither the sun nor the moon shone. Only one half of the polar region was illumined. Then demons ruled the earth. They were deluded, powerful and prosperous, and the earth was their playground. Apart from the polar region the rest of the earth was covered with water. And then for a very long time the whole earth was covered with forests, except the polar region. Then there arose great mountains, but without any human inhabitants. For a period of ten thousand years the earth was covered with the corpses of the demons. [6.1]

Mind

The same infinite self conceives within itself the duality of oneself and the other. [3.1]

Thought is mind, there is no distinction between the two. [3.4]

The body can neither enjoy nor suffer. It is the mind alone that experiences. [3.115]

The mind has no body, no support and no form; yet by this mind is everything consumed in this world. This is indeed a great mystery. He who says that  he is destroyed by the mind which has no substantiality at all, says in effect that his head was smashed by the lotus petal … The hero who is able to destroy a real enemy standing in front of him is himself destroyed by this mind which is [nonmaterial].

The intelligence which is other than self-knowledge is what constitutes the mind. [5.14] Complementarity The absolute alone exists now and for ever. When one thinks of it as a void, it is because of the feeling one has that it is not void; when one thinks of it as notvoid, it is because there is a feeling that it is void. [3.10] All fundamental elements continued to act on one another—as experiencer and experience—and the entire creation came into being like ripples on the surface of the ocean. And, they are interwoven and mixed up so effectively that they cannot be extricated from one another till the cosmic dissolution. [3.12]

Consciousness

The entire universe is forever the same as the consciousness that dwells in every atom, even as an ornament is non-different from gold. [3.4]

The five elements are the seed of which the world is the tree; and the eternal consciousness is the seed of the elements. [3.13] Cosmic consciousness alone exists now and ever; in it are no worlds, no created beings. That consciousness reflected in itself appears to be creation. [3.13]

This consciousness is not knowable: when it wishes to become the knowable, it is known as the universe. Mind, intellect, egotism, the five great elements, and the world—all these innumerable names and forms are all consciousness alone. [3.14]

The world exists because consciousness is, and the world is the body of consciousness. There is no division, no difference, no distinction. Hence the universe can be said to be both real and unreal: real because of the reality of consciousness which is its own reality, and unreal because the universe does not exist as universe, independent of consciousness.} [3.14]

Consciousness is pure, eternal and infinite: it does not arise nor cease to be. It is ever there in the moving and unmoving creatures, in the sky, on the mountain and in fire and air. [3.55]

Millions of universes appear in the infinite consciousness like specks of dust in a beam of light. In one small atom all the three worlds appear to be, with all their components like space, time, action, substance, day and night. [4.2] 60 The Wishing Tree The universe exists in infinite consciousness. Infinite consciousness is unmanifest, though omnipresent, even as space, though existing everywhere, is manifest. [4.36]

The manifestation of the omnipotence of infinite consciousness enters into an alliance with time, space and causation. Thence arise infinite names and forms. [4.42]

Rudra is the pure, spontaneous self-experience which is the one consciousness that dwells in all substances. It is the seed of all seeds, it is the essence of this world-appearance, it is the greatest of actions. It is the cause of all causes and it is the essence of all beings, though in fact it does not cause anything nor is it the concept of being, and therefore cannot be conceived. It is the awareness in all that is sentient, it knows itself as its own object, it is its own supreme object and it is aware of infinite diversity within itself … The infinite consciousness can be compared to the ultimate atom which yet hides within its heart the greatest of mountains. It encompasses the span of countless epochs, but it does not let go of a moment of time. It is subtler than the tip of single strand of hair, yet it pervades the entire universe … It does nothing, yet it has fashioned the universe. All substances are non-different from it, yet it is not a substance; though it is non-substantial it pervades all substances. The cosmos is its body, yet it has no body. [6.1.36]

The YV Model of Knowledge

YV is not written as a systematic text. Its narrative jumps between various levels: psychological, social, and physical. But since the Indian tradition of knowledge is based on analogies that are recursive and connect various domains, one can be certain that our literal reading of the passages is valid. YV appears to accept the idea that laws are intrinsic to the universe. In other words, the laws of nature in an unfolding universe will also evolve. According to YV, new information does not emerge out of the inanimate world but it is a result of the exchange between mind and matter. It accepts consciousness as a kind of fundamental field that pervades the whole universe. One might speculate that the parallels between YV and some recent ideas of physics are a result of the inherent structure of the mind.

Other Texts

Our readings of the YV are confirmed by other texts such as the Mahabharata and the Puranas as they are by the philosophical systems of Sankhya and Vaisheshika, or the various astronomical texts.  Here is a reference to the size of the universe from the Mahabharata 12.182:36

‘The sky you see above is infinite. Its limits cannot be ascertained. The sun and the moon cannot see, above or below, beyond the range of their own rays. There where the rays of the sun and the moon cannot reach are luminaries which are self-effulgent and which possess splendor like that of the sun or the fire. Even these last do not behold the limits of the firmament in consequence of the inaccessibility and infinity of those limits. This space which the very gods cannot measure is full of many blazing and self-luminous worlds each above the other.’

The Mahabharata has a very interesting passage (12.233), virtually identical with the corresponding material in YV, which describes the dissolution of the world. Briefly, it is stated how a dozen suns burn up the earth, and how elements get transmuted until space itself collapses into wind (one of the elements). Ultimately, everything enters into primeval consciousness. If one leaves out the often incongruous commentary on these ideas which were strange to him, we find al-Biruni in his encyclopaedic book on India written in 1030 speaking of essentially the same ideas. Here are two little extracts:

‘The Hindus have divided duration into two periods, a period of motion, which has been determined as time, and a period of rest, which can only be determined in an imaginary way according to the analogy of that which has first been determined, the period of motion. The Hindus hold the eternity of the Creator to be determinable, not measurable, since it is infinite. They do not, by the word creation, understand a formation of something out of nothing. They mean by creation only the working with a piece of clay, working out various combinations and figures in it, and making such arrangements with it as will lead to certain ends and aims which are potentially in it. ‘

The mystery of consciousness is a recurring theme in Indian texts. Unfortunately, the misrepresentation that Indian philosophy is idealistic, where the physical universe is considered an illusion, has become very common. For an authoritative modern exposition of Indian ideas of consciousness one must turn to Aurobindo.

It appears that Indian understanding of physics was informed not only by astronomy and terrestrial experiments but also by speculative thought and by meditations on the nature of consciousness. Unfettered by either geocentric or anthropocentric views, this understanding unified the physics of the small with that of the large within a framework that included metaphysics.

This was a framework consisting of innumerable worlds (solar systems), where time and space were continuous, matter was atomic, and consciousness was atomic, yet derived from an all-pervasive unity. The material atoms were defined first by their subtle form, called tanmatra, which was visualized as a potential, from which emerged the gross atoms. A central notion in this system was that all descriptions of reality are circumscribed by paradox. The universe was seen as dynamic, going through ceaseless change.

The Medieval Period

Astronomical texts called siddhantas begin appearing sometime in the first millennium BC. According to tradition there were 18 early siddhantas of which only a few have survived. Each siddhanta is an astronomical system with its own constants. Some of the famous astronomer-mathematicians that arose in India’s long medieval period are listed below.

Aryabhata (born 476) took the earth to spin on its axis; this idea appears to have been his innovation. Aryabhata was aware of the relativity of motion as is clear from this passage in his book, Just as a man in a boat sees the trees on the bank move in the opposite direction, so an observer on the equator sees the stationary stars as moving precisely toward the west.

Brahmagupta, who was born in 598 in Rajasthan, wrote his masterpiece, Brahmasphuta Siddhanta, in 628. His school, which was a rival to that of Aryabhata, has been very influential in western and northern India. Brahmagupta’s work was translated into Arabic in the eighth century at Baghdad and it became famous in the Arabic world as Sindhind and it influenced Islamic astronomy. One of Brahmagupta’s chief contributions is the solution of a certain second order indeterminate equation which is of great significance in number theory.

Belonging to the Karnataka region, Bhaskara (born 1114), was an outstanding mathematician and astronomer. Amongst his mathematical contributions is the concept of differentials. He was the author of Siddhanta Shiromani, a book in four parts: (I) Lilavati on arithmetic, (ii) Bijaganita on algebra, (iii) Ganitadhyaya, (iv) Goladhyaya on astronomy. His epicyclic-eccentric theories of planetary motions are more developed than in the earlier siddhantas. Subsequent to Bhaskara we see a flourishing tradition of mathematics and astronomy in Kerala which saw itself as a successor to the school of Aryabhata.

Of these, Madhava (c. 1340-1425) developed a procedure to determine the positions of the moon every 36 minutes. He also provided methods to estimate the motions of the planets. He gave power series expansions for trigonometric functions, and for pi correct to eleven decimal places.

A very prolific scholar who wrote several works on astronomy, Nilakantha (c. 1444-1545) found the correct formulation for the equation of the center of the planets and his model must be considered a true heliocentric model of the solar system. He also improved upon the power series techniques of Madhava. The methods developed by the Kerala mathematicians were far ahead of the European mathematics of the day. Another noteworthy contribution was by the school of New Logic (Navya Nyaya) of Bengal and Bihar.

At its zenith during the time of Raghunatha (1475- 1550), this school developed a methodology for a precise semantic analysis of language. Its formulations are equivalent to mathematical logic. With all these brilliant achievements behind them, why didn’t the Indians create a scientific revolution that touched the entire fabric of society? Clearly, the social, political and economic conditions were not ripe for such change. Europe had the advantage of the wealth obtained from the New World part of which went to the support of institutions of higher learning and the development of instruments to aid navigation.

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Erwin Schrödinger

Perhaps the most remarkable intellectual achievement of the twentieth century was quantum theory, which is at the basis of our understanding of chemistry, biology, and physics and, consequently, it is at the basis of the century’s astonishing technological advances. One of the two creators of this theory was Erwin Schrödinger (1887-1961). In an autobiographical essay, he explains that his discovery of quantum mechanics was an attempt to give form to central ideas of Vedanta which, in this indirect sense, has played a role in the birth of the subject. In 1925, before his revolutionary theory was complete,

Erwin Schrödinger wrote:

This life of yours which you are living is not merely a piece of this entire existence,but in a certain sense the whole; only this whole is not so constituted that it can be surveyed in one single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear: tat tvam asi, this is you. Or, again, in such words as “I am in the east and the west, I am above and below, I am this entire world.”

Schrödinger’s influential What is Life? (1944) also used Vedic ideas.  The book became instantly famous although it was criticized by some for its emphasis on Indian ideas. Francis Crick, the co-discoverer of the DNA code, credited this book for key insights that led him to his revolutionary discovery. According to his biographer Walter Moore, there is a clear continuity between Schrödinger’s understanding of Vedanta and his research: The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles.

During the next few years, Schrödinger and Heisenberg and their followers created a universe based on superimposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One. He became a Vedantist, a Hindu, as a result of his studies in his search for truth. Schrödinger kept a copy of the Hindu scriptures at his bedside. He read books on Vedas, yoga, and Sankhya philosophy and he reworked them into his own words, and ultimately came to believe them. The Upanishads and the Bhagavadgita were his favourite scriptures.

According to his biographer Moore, “His system—or that of the Upanishads— is delightful and consistent: the self and the world are one and they are all. He rejected traditional western religious beliefs (Jewish, Christian, and Islamic) not on the basis of any reasoned argument, nor even with an expression of emotional antipathy, for he loved to use religious expressions and metaphors, but simply by saying that they are naive.” Schrödinger was a professor at several universities in Europe. He was awarded the Nobel Prize in 1933. During the Hitler era he was dismissed from his position for his opposition to the Nazi ideas and he fled to England. For some years he was in Ireland, but after the conclusion of the World War II he returned to Vienna where he died in 1961.

Quantum mechanics goes beyond ordinary logic. According to it reality is a superposition of all possibilities which is very different from classical physics. It is quantum mechanics which explains the mysteries of chemical reactions and of
life. In recent years, it has been suggested that the secrets of consciousness have a quantum basis. In a famous essay on determinism and free will, Schrödinger expressed very clearly the sense that consciousness is a unity, arguing that this

“insight is not new From the early great Upanishads the recognition Atman = Brahman (the personal self equals the omnipresent, all-comprehending eternal self) was in Indian thought considered, far from being blasphemous, to represent the quintessence of deepest insight into the happenings of the world. The striving of all the scholars of Vedanta was, after having learnt to pronounce with their lips, really to assimilate in their minds this grandest of all thoughts.”

He thought the idea of pluralization of consciousness and the notion of many souls to be naive. He considered the notion of plurality to be a result of deception (maya): “the same illusion is produced by a gallery of mirrors, and in the same way Gaurisankar and Mt. Everest turned out to be the same peak seen from different valleys.”

Schrödinger was a very complex person. But he had a sense of humor and paradox. He called his dog Atman. Perhaps he did this to honour Yudhishthira whose own dog, an incarnation of cosmic justice (Dharma), accompanied him on his last march to the Himalayas. More likely, he was calling attention to the unity that pervades the web of life.

Erwin Schrödinger Quotes

‘The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles. During the next few years, Schrodinger and Heisenberg and their followers created a universe based on super imposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One’

‘Vedanta teaches that consciousness is singular, all happenings are played out in one universal consciousness and there is no multiplicity of selves.’

‘Nirvana is a state of pure blissful knowledge.. It has nothing to do with individual. The ego or its separation is an illusion. The goal of man is to preserve his Karma and to develop it further – when man dies his karma lives and creates for itself another carrier.’

‘There is no kind of framework within which we can find consciousness in the plural; this is simply something we construct because of the temporal plurality of individuals, but it is a false construction….The only solution to this conflict insofar as any is available to us at all lies in the ancient wisdom of the Upanishad.’

‘The multiplicity is only apparent. This is the doctrine of the Upanishads. And not of the Upanishads only. The mystical experience of the union with God regularly leads to this view, unless strong prejudices stand in the West.’

‘After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense.’

“Some blood transfusion from the East to the West” to save Western science from spiritual anemia.”

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Only lunatics will support them, claiming that this proves that aliens have visited the earth from time to time. The high priests of the academy will say that even if the find was genuine it proves nothing;
at best it is a coincidence.

But what an astonishing coincidence! Just the right number out of an infinite different numbers!

The speed of light was first determined in 1675 by Roemer who looked at the difference in the times that light from Io, one of the moons of Jupiter, takes to reach earth based on whether it is on the near side of Jupiter or the far side. Until then light was taken to travel with infinite velocity. Even Newton assumed so.

But why are we talking about the absurd scenario of the archaeologists in Antarctica? Because, we are confronted with a situation that is quite similar!  I am an archaeologist of texts. I read old texts from the point of view of history of science. One such book is the celebrated commentary on the Rigveda by Sayana (c. 1315-1387), a minister in the court of King Bukka I of the Vijayanagar Empire in South India.

In a hymn addressed to the sun, he says that it is ``remembered that the sun traverses 2,202 yojanas in half a nimesha.”

This statement could either relate to the speed of the sun or to that of light. The units are well known. For example, the Indian epic “Mahabharata”, conservatively dated to 400 BC – 400 AD, defines 1 nimesha to be equal to 16/75.3 seconds; 1 yojana is about 9 miles.

Substituting in Sayana’s statement we get 186,536 miles per second. Unbelievable, you’d say! It cannot be the speed of light. Maybe it refers to the speed of the sun in its supposed orbit around the earth. But that places the orbit of the sun at a distance of over 2,550 million miles. The correct value is only 93 million miles and until the time of Roemer the distance to the sun used to be taken to be less than 4 million miles. This interpretation takes us nowhere.

What about the possibility of fraud? Sayana’s statement was printed in 1890 in the famous edition of Rigveda edited by Max Muller, the German Sanskritist. He claimed to have used several three or four hundred year old manuscripts of Sayana’s commentary, written much before the time of Roemer.  Is it possible that Muller was duped by an Indian correspondent who slipped in the line about the speed? Unlikely, because Sayana’s commentary is so well known that an interpolation would have been long discovered. And soon after Muller’s “Rigveda” was published, someone would have claimed that it contained this particular “secret” knowledge. The fact that the speed in the text corresponds to the speed of light was pointed out only recently by S.S. De and P.V. Vartak. Also a copy of Sayana’s manuscript, dated 1395 AD, is available.

Further support for the genuineness of the figure in the ancient book comes from another old book, the Vayu Purana. This is one of the earliest Puranas, considered to be at least 1,500 years old. (The same reference is to be found in the other Puranas as well.)

In Chapter 50 of this book, there is the statement that the sun moves 3.15 million yojanas in 48 minutes. This corresponds to about 10,000 miles per second if considered as speed of light, and 135 million miles for the distance to the sun, if considered as the speed of the sun. Sayana’s speed of light is exactly 18 times greater than this speed of the sun! Mere numerology? For the rationalists these numbers are a coincidence. Given the significance of these numbers, they’d look very carefully at the old manuscripts of Sayana’s commentary.

There are others who would say that consciousness, acting on itself can find universal knowledge. Look, they’d say, by examining biological cycles one can know the periods of the sun and the moon. So why shouldn’t it be possible to know other universal truths? They’d add that ancient texts speak — and this is true — of embryo transplants, multiple births from the same fetus, air and space travel, slowing or speeding of time, weapons that can destroy the entire world.

They’d say that it is more than ancient science fiction, it shows that the human imagination can envision all that can happen. This brings us back to the question of whether the figure of 186,000 miles per second in Sayana’s book is a astonishing coincidence, an example of the powers of intuition, or a meaningless number.

Notes:
1. The Rigvedic hymn number is 1.50.
2. For a discussion of the technical issues download the file speedlight.ps from the ftp directory on my homepage or see http://www.ee.lsu.edu/kak/ and then check the file speedlight.ps
You can also read this paper called “The speed of light and Puranic cosmology” on the Los Alamos Physics Archive hysics/9804020.

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