Sanskrit & Artificial Intelligence — NASA Knowledge Representation in Sanskrit and Artificial Intelligence

Abstract

In the past twenty years, much time, effort, and money has been expended on designing an unambiguous representation of natural languages to make them accessible to computer processing. These efforts have centered around creating schemata designed to parallel logical relations with relations expressed by the syntax and semantics of natural languages, which are clearly cumbersome and ambiguous in their function as vehicles for the transmission of logical data. Understandably, there is a widespread belief that natural languages are unsuitable for the transmission of many ideas that artificial languages can render with great precision and mathematical rigor.

But this dichotomy, which has served as a premise underlying much work in the areas of linguistics and artificial intelligence, is a false one. There is at least one language, Sanskrit, which for the duration of almost 1,000 years was a living spoken language with a considerable literature of its own. Besides works of literary value, there was a long philosophical and grammatical tradition that has continued to exist with undiminished vigor until the present century. Among the accomplishments of the grammarians can be reckoned a method for paraphrasing Sanskrit in a manner that is identical not only in essence but in form with current work in Artificial Intelligence. This article demonstrates that a natural language can serve as an artificial language also, and that much work in AI has been reinventing a wheel millenia old.

First, a typical Knowledge Representation Scheme (using Semantic Nets) will be laid out, followed by an outline of the method used by the ancient Indian Grammarians to analyze sentences unambiguously. Finally, the clear parallelism between the two will be demonstrated, and the theoretical implications of this equivalence will be given.

Semantic Nets
For the sake of comparison, a brief overview of semantic nets will be given, and examples will be included that will be compared to the Indian approach. After early attempts at machine translation (which were based to a large extent on simple dictionary look-up) failed in their effort to teach a computer to understand natural language, work in AI turned to Knowledge Representation.

Since translation is not simply a map from lexical item to lexical item, and since ambiguity is inherent in a large number of utterances, some means is required to encode what the actual meaning of a sentence is. Clearly, there must be a representation of meaning independent of words used. Another problem is the interference of syntax. In some sentences (for example active/passive) syntax is, for all intents and purposes, independent of meaning. Here one would like to eliminate considerations of syntax. In other sentences the syntax contributes to the meaning and here one wishes to extract it.

I will consider a "prototypical" semantic net system similar to that of Lindsay, Norman, and Rumelhart in the hopes that it is fairly representative of basic semantic net theory. Taking a simple example first, one would represent "John gave the ball to Mary" as in Figure 1. Here five nodes connected by four labeled arcs capture the entire meaning of the sentence. This information can be stored as a series of "triples":

give, agent, John

give, object, ball

give, recipient, Mary

give, time, past.

Note that grammatical information has been transformed into an arc and a node (past tense). A more complicated example will illustrate embedded sentences and changes of state:

John Mary

book past

Figure 1.

"John told Mary that the train moved out of the station at 3 o'clock."

As shown in Figure 2, there was a change in state in which the train moved to some unspecified location from the station. It went to the former at 3:00 and from the latter at 3:O0. Now one can routinely convert the net to triples as before.

The verb is given central significance in this scheme and is considered the focus and distinguishing aspect of the sentence. However, there are other sentence types which differ fundamentally from the above examples. Figure 3 illustrates a sentence that is one of "state" rather than of "event ." Other nets could represent statements of time, location or more complicated structures.

A verb, say, "give," has been taken as primitive, but what is the meaning of "give" itself? Is it only definable in terms of the structure it generates? Clearly two verbs can generate the same structure. One can take a set-theoretic approach and a particular give as an element of "giving events" itself a subset of ALL-EVENTS. An example of this approach is given in Figure 4 ("John, a programmer living at Maple St., gives a book to Mary, who is a lawyer"). If one were to "read" this semantic net, one would have a very long text of awkward English: "There is a John" who is an element of the "Persons" set and who is the person who lives at ADRI, where ADRI is a subset of ADDRESS-EVENTS, itself a subset of 'ALL EVENTS', and has location '37 Maple St.', an element of Addresses; and who is a "worker" of 'occupation 1'. . .etc."

The degree to which a semantic net (or any unambiguous, nonsyntactic representation) is cumbersome and odd-sounding in a natural language is the degree to which that language is "natural" and deviates from the precise or "artificial." As we shall see, there was a language spoken among an ancient scientific community that has a deviation of zero.

The hierarchical structure of the above net and the explicit descriptions of set-relations are essential to really capture the meaning of the sentence and to facilitate inference. It is believed by most in the AI and general linguistic community that natural languages do not make such seemingly trivial hierarchies explicit. Below is a description of a natural language, Shastric Sanskrit, where for the past millenia successful attempts have been made to encode such information.

Shastric Sanskrit

The sentence:

(1) "Caitra goes to the village." (graamam gacchati caitra)

receives in the analysis given by an eighteenth-century Sanskrit Grammarian from Maharashtra, India, the following paraphrase:

(2) "There is an activity which leads to a connection-activity which has as Agent no one other than Caitra, specified by singularity, [which] is taking place in the present and which has as Object something not different from 'village'."

The author, Nagesha, is one of a group of three or four prominent theoreticians who stand at the end of a long tradition of investigation. Its beginnings date to the middle of the first millennium B.C. when the morphology and phonological structure of the language, as well as the framework for its syntactic description were codified by Panini. His successors elucidated the brief, algebraic formulations that he had used as grammatical rules and where possible tried to improve upon them. A great deal of fervent grammatical research took place between the fourth century B.C and the fourth century A.D. and culminated in the seminal work, the Vaiakyapadiya by Bhartrhari. Little was done subsequently to advance the study of syntax, until the so-called "New Grammarian" school appeared in the early part of the sixteenth century with the publication of Bhattoji Dikshita's Vaiyakarana-bhusanasara and its commentary by his relative Kaundabhatta, who worked from Benares. Nagesha (1730-1810) was responsible for a major work, the Vaiyakaranasiddhantamanjusa, or Treasury of dejinitive statements of grammarians, which was condensed later into the earlier described work. These books have not yet been translated.

The reasoning of these authors is couched in a style of language that had been developed especially to formulate logical relations with scientific precision. It is a terse, very condensed form of Sanskrit, which paradoxically at times becomes so abstruse that a commentary is necessary to clarify it.

One of the main differences between the Indian approach to language analysis and that of most of the current linguistic theories is that the analysis of the sentence was not based on a noun-phrase model with its attending binary parsing technique but instead on a conception that viewed the sentence as springing from the semantic message that the speaker wished to convey. In its origins, sentence description was phrased in terms of a generative model: From a number of primitive syntactic categories (verbal action, agents, object, etc.) the structure of the sentence was derived so that every word of a sentence could be referred back to the syntactic input categories. Secondarily and at a later period in history, the model was reversed to establish a method for analytical descriptions. In the analysis of the Indian grammarians, every sentence expresses an action that is conveyed both by the verb and by a set of "auxiliaries." The verbal action (Icriyu- "action" or sadhyu-"that which is to be accomplished,") is represented by the verbal root of the verb form; the "auxiliary activities" by the nominals (nouns, adjectives, indeclinables) and their case endings (one of six).

The meaning of the verb is said to be both vyapara (action, activity, cause), and phulu (fruit, result, effect). Syntactically, its meaning is invariably linked with the meaning of the verb "to do". Therefore, in order to discover the meaning of any verb it is sufficient to answer the question: "What does he do?" The answer would yield a phrase in which the meaning of the direct object corresponds to the verbal meaning. For example, "he goes" would yield the paraphrase: "He performs an act of going"; "he drinks": "he performs an act of drinking," etc. This procedure allows us to rephrase the sentence in terms of the verb "to do" or one of its synonyms, and an object formed from the verbal root which expresses the verbal action as an action noun. It still leaves us with a verb form ("he does," "he performs"), which contains unanalyzed semantic information This information in Sanskrit is indicated by the fact that there is an agent who is engaged in an act of going, or drinking, and that the action is taking place in the present time.

Rather that allow the agent to relate to the syntax in this complex, unsystematic fashion, the agent is viewed as a one-time representative, or instantiation of a larger category of "Agency," which is operative in Sanskrit sentences. In turn, "Agency" is a member of a larger class of "auxiliary activities," which will be discussed presently. Thus Caitra is some Caitral or instance of Caitras, and agency is hierarchically related to the auxiliary activities. The fact that in this specific instance the agent is a third person-singular is solved as follows: The number category (singular, dual, or plural) is regarded as a quality of the Agent and the person category (first, second, or third) as a grammatical category to be retrieved from a search list, where its place is determined by the singularity of the agent.

The next step in the process of isolating the verbal meaning is to rephrase the description in such a way that the agent and number categories appear as qualities of the verbal action. This procedure leaves us with an accurate, but quite abstract formulation of the scntcnce: (3) "Caitra is going" (gacchati caitra) - "An act of going is taking place in the present of which the agent is no one other than Caitra qualified by singularity." (atraikatvaavacchinnacaitraabinnakartrko vartamaanakaa- liko gamanaanukuulo vyaapaarah:) (Double vowels indicate length.)

If the sentence contains, besides an agent, a direct object, an indirect object and/or other nominals that are dependent on the principal action of the verb, then in the Indian system these nominals are in turn viewed as representations of actions that contribute to the complete meaning of the sentence. However, it is not sufficient to state, for instance, that a word with a dative case represents the "recipient" of the verbal action, for the relation between the recipient and the verbal action itself requires more exact specification if we are to center the sentence description around the notion of the verbal action. To that end, the action described by the sentence is not regarded as an indivisible unit, but one that allows further subdivisions. Hence a sentence such as: (4) "John gave the ball to Mary" involves the verb Yo give," which is viewed as a verbal action composed of a number of auxiliary activities. Among these would be John's holding the ball in his hand, the movement of the hand holding the ball from John as a starting point toward Mary's hand as the goal, the seizing of the ball by Mary's hand, etc. It is a fundamental notion that actions themselves cannot be perceived, but the result of the action is observable, viz. the movement of the hand. In this instance we can infer that at least two actions have taken place:

(a) An act of movement starting from the direction of John and taking place in the direction of Mary's hand. Its Agent is "the ball" and its result is a union with Mary's hand.

(b) An act of receiving, which consists of an act of grasping whose agent is Mary's hand.

It is obvious that the act of receiving can be interpreted as an action involving a union with Mary's hand, an enveloping of the ball by Mary's hand, etc., so that in theory it might be difficult to decide where to stop this process of splitting meanings, or what the semantic primitives are. That the Indians were aware of the problem is evident from the following passage: "The name 'action' cannot be applied to the solitary point reached by extreme subdivision."

The set of actions described in (a) and (b) can be viewed as actions that contribute to the meaning of the total sentence, vix. the fact that the ball is transferred from John to Mary. In this sense they are "auxiliary actions" (Sanskrit kuruku-literally "that which brings about") that may be isolated as complete actions in their own right for possible further subdivision, but in this particular context are subordinate to the total action of "giving." These "auxiliary activities" when they become thus subordinated to the main sentence meaning, are represented by case endings affixed to nominals corresponding to the agents of the original auxiliary activity. The Sanskrit language has seven case endings (excluding the vocative), and six of these are definable representations of specific "auxiliary activities." The seventh, the genitive, represents a set of auxiliary activities that are not defined by the other six. The auxiliary actions are listed as a group of six: Agent, Object, Instrument, Recipient, Point of Departure, Locality. They are the semantic correspondents of the syntactic case endings: nominative, accusative, instrumental, dative, ablative and locative, but these are not in exact equivalence since the same syntactic structure can represent different semantic messages, as will be discussed below. There is a good deal of overlap between the karakas and the case endings, and a few of them, such as Point of Departure, also are used for syntactic information, in this case "because of". In many instances the relation is best characterized as that of the allo-eme variety.

To illustrate the operation of this model of description, a sentence involving an act of cooking rice is often quoted: (5) "Out of friendship, Maitra cooks rice for Devadatta in a pot, over a fire."

Here the total process of cooking is rendered by the verb form "cooks" as well as a number of auxiliary actions:

1. An Agent represented by the person Maitra

2. An Object by the "rice"

3. An Instrument by the "fire"

4. A Recipient by the person Devadatta

5. A Point of Departure (which includes the causal relationship) by the "friendship" (which is between Maitra and Devadatta)

6. The Locality by the "pot"

So the total meaning of the sentence is not complete without the intercession of six auxiliary actions. The action itself can be inferred from a change of the condition of the grains of rice, which started out being hard and ended up being soft.

Again, it would be possible to atomize the meaning expressed by the phrase: "to cook rice": It is an operation that is not a unitary "process", but a combination of processes, such as "to place a pot on the fire, to add fuel to the fire, to fan", etc. These processes, moreover, are not taking place in the abstract, but they are tied to, or "resting on" agencies that are associated with the processes. The word used for "tied to" is a form of the verbal root a-sri, which means to lie on, have recourse to, be situated on." Hence it is possible and usually necessary to paraphrase a sentence such as "he gives" as: "an act of giving residing in him." Hence the paraphrase of sentence (5) will be: (6) "There is an activity conducive to a softening which is a change residing in something not different from rice, and which takes place in the present, and resides in an agent not different from Maitra, who is specified by singularity and has a Recipient not different from Devadatta, an Instrument not different from.. .," etc.

It should be pointed out that these Sanskrit Grammatical Scientists actually wrote and talked this way. The domain for this type of language was the equivalent of today's technical journals. In their ancient journals and in verbal communication with each other they used this specific, unambiguous form of Sanskrit in a remarkably concise way.

Besides the verbal root, all verbs have certain suffixes that express the tense and/or mode, the person (s) engaged in the "action" and the number of persons or items so engaged. For example, the use of passive voice would necessitate using an Agent with an instrumental suffix, whereas the nonpassive voice implies that the agent of the sentence, if represented by a noun or pronoun, will be marked by a nominative singular suffix.

Word order in Sanskrit has usually no more than stylistic significance, and the Sanskrit theoreticians paid no more than scant attention to it. The language is then very suited to an approach that eliminates syntax and produces basically a list of semantic messages associated with the karakas.

An example of the operation of this model on an intransitive sentence is the following:

(7) Because of the wind, a leaf falls from a tree to the ground."

Here the wind is instrumental in bringing about an operation that results in a leaf being disunited from a tree and being united with the ground. By virtue of functioning as instrument of the operation, the term "wind" qualifies as a representative of the auxiliary activity "Instrument"; by virtue of functioning as the place from which the operation commences, the "tree" qualifies to be called "The Point of Departure"; by virtue of the fact that it is the place where the leaf ends up, the "ground" receives the designation "Locality". In the example, the word "leaf" serves only to further specify the agent that is already specified by the nonpassive verb in the form of a personal suffix. In the language it is rendered as a nominative case suffix. In passive sentences other statements have to be made. One may argue that the above phrase does not differ in meaning from "The wind blows a leaf from the tree," in which the "wind" appears in the Agent slot, the "leaf" in the Object slot. The truth is that this phrase is transitive, whereas the earlier one is intransitive. "Transitivity" can be viewed as an additional feature added to the verb. In Sanskrit this process is often accomplished by a suffix, the causative suffix, which when added to the verbal root would change the meaning as follows: "The wind causes the leaf to fall from the tree," and since English has the word "blows" as the equivalent of "causes to fall" in the case of an Instrument "wind," the relation is not quite transparent. Therefore, the analysis of the sentence presented earlier, in spite of its manifest awkwardness, enabled the Indian theoreticians to introduce a clarity into their speculations on language that was theretofore un- available. Structures that appeared radically different at first sight become transparent transforms of a basic set of elementary semantic categories.

It is by no means the case that these analyses have been exhausted, or that their potential has been exploited to the full. On the contrary, it would seem that detailed analyses of sentences and discourse units had just received a great impetus from Nagesha, when history intervened: The British conquered India and brought with them new and apparently effective means for studying and analyzing languages. The subsequent introduction of Western methods of language analysis, including such areas of research as historical and structural linguistics, and lately generative linguistics, has for a long time acted as an impediment to further research along the traditional ways. Lately, however, serious and responsible research into Indian semantics has been resumed, especially at the University of Poona, India. The surprising equivalence of the Indian analysis to the techniques used in applications of Artificial Intelligence will be discussed in the next section.

Equivalence

A comparison of the theories discussed in the first section with the Indian theories of sentence analysis in the second section shows at once a few striking similarities. Both theories take extreme care to define minute details with which a language describes the relations between events in the natural world. In both instances, the analysis itself is a map of the relations between events in the universe described. In the case of the computer-oriented analysis, this mapping is a necessary prerequisite for making the speaker's natural language digestible for the artificial processor; in the case of Sanskrit, the motivation is more elusive and probably has to do with an age-old Indo-Aryan preoccupation to discover the nature of the reality behind the the impressions we human beings receive through the operation of our sense organs. Be it as it may, it is a matter of surprise to discover that the outcome of both trends of thinking-so removed in time, space, and culture-have arrived at a representation of linguistic events that is not only theoretically equivalent but close in form as well. The one superficial difference is that the Indian tradition was on the whole, unfamiliar with the facility of diagrammatic representation, and attempted instead to formulate all abstract notions in grammatical sentences. In the following paragraphs a number of the parallellisms of the two analyses will be pointed out to illustrate the equivalence of the two systems.

Consider the sentence: "John is going." The Sanskrit paraphrase would be

"An Act of going is taking place in which the Agent is 'John' specified by singularity and masculinity."

If we now turn to the analysis in semantic nets, the event portrayed by a set of triples is the following:

1. "going events, instance, go (this specific going event)"

2. "go, agent, John"

3. "go, time, present."

The first equivalence to be observed is that the basic framework for inference is the same. John must be a semantic primitive, or it must have a dictionary entry, or it must be further represented (i.e. "John, number, 1" etc.) if further processing requires more detail (e.g. "HOW many people are going?"). Similarly, in the Indian analysis, the detail required in one case is not necessarily required in another case, although it can be produced on demand (if needed). The point to be made is that in both systems, an extensive degree of specification is crucial in understanding the real meaning of the sentence to the extent that it will allow inferences to be made about the facts not explicitly stated in the sentence

The basic crux of the equivalence can be illustrated by a careful look at sentence (5) noted in Part II.

"Out of friendship, Maitra cooks rice for Devadatta in a pot over a fire "

The semantic net is supplied in Figure 5. The triples corresponding to the net are:

cause, event, friendship

friendship, objectl, Devadatta

friendship, object2, Maitra

cause, result cook

cook, agent, Maitra

cook, recipient, Devadatta

cook, instrument, fire

cook, object, rice

cook, on-lot, pot.

The sentence in the Indian analysis is rendered as follows:

The Agent is represented by Maitra, the Object by "rice," the Instrument by "fire," the Recipient by "Devadatta," the Point of Departure (or cause) by "friendship" (between Maitra and Devadatta), the Locality by "pot."

Since all of these syntactic structures represent actions auxiliary to the action "cook," let us write %ook" uext to each karakn and its sentence representat(ion:

cook, agent, Maitra

cook, object, rice

cook, instrument, fire

cook, recipient, Devadatta

cook, because-of, friendship

friendship, Maitra, Devadatta

cook, locality, pot.

The comparison of the analyses shows that the Sanskrit sentence when rendered into triples matches the analysis arrived at through the application of computer processing. That is surprising, because the form of the Sanskrit sentence is radically different from that of the English. For comparison, the Sanskrit sentence is given here: Maitrah: sauhardyat Devadattaya odanam ghate agnina pacati.

Here the stem forms of the nouns are: Muitra-sauhardya- "friendship," Devadatta -, odana- "gruel," ghatu- "pot," agni- "fire' and the verb stem is paca- "cook". The deviations of the stem forms occuring at the end of each word represent the change dictated by the word's semantic and syntactic position. It should also be noted that the Indian analysis calls for the specification of even a greater amount of grammatical and semantic detail: Maitra, Devadatta, the pot, and fire would all be said to be qualified by "singularity" and "masculinity" and the act of cooking can optionally be expanded into a number of successive perceivable activities. Also note that the phrase "over a fire" on the face of it sounds like a locative of the same form as "in a pot." However, the context indicates that the prepositional phrase describes the instrument through which the heating of the rice takes place and, therefore, is best regarded as an instrument semantically. cause

Of course, many versions of semantic nets have been proposed, some of which match the Indian system better than others do in terms of specific concepts and structure. The important point is that the same ideas are present in both traditions and that in the case of many proposed semantic net systems it is the Indian analysis which is more specific.

A third important similarity between the two treatments of the sentence is its focal point which in both cases is the verb. The Sanskrit here is more specific by rendering the activity as a "going-event", rather than "ongoing." This procedure introduces a new necessary level of abstraction, for in order to keep the analysis properly structured, the focal point ought to be phrased: "there is an event taking place which is one of cooking," rather than "there is cooking taking place", in order for the computer to distinguish between the levels of unspecified "doing" (vyapara) and the result of the doing (phala).

A further similarity between the two systems is the striving for unambiguity. Both Indian and AI schools en-code in a very clear, often apparently redundant way, in order to make the analysis accessible to inference. Thus, by using the distinction of phala and vyapara, individual processes are separated into components which in term are decomposable. For example, "to cook rice" was broken down as "placing a pot on the fire, adding fuel, fanning, etc." Cooking rice also implies a change of state, realized by the phala, which is the heated softened rice. Such specifications are necessary to make logical pathways, which otherwise would remain unclear. For example, take the following sentence:

"Maitra cooked rice for Devadatta who burned his mouth while eating it."

The semantic nets used earlier do not give any information about the logical connection between the two clauses. In order to fully understand the sentence, one has to be able to make the inference that the cooking process involves the process of "heating" and the process of "making palatable." The Sanskrit grammarians bridged the logical gap by the employment of the phalu/ vyapara distinction. Semantic nets could accomplish the same in a variety of ways:

1. by mapping "cooking" as a change of state, which would involve an excessive amount of detail with too much compulsory inference;

2. by representing the whole statement as a cause (event-result), or

3. by including dictionary information about cooking. A further comparison between the Indian system and the theory of semantic nets points to another similarity: The passive and the active transforms of the same sentence are given the same analysis in both systems. In the Indian system the notion of the "intention of the speaker" (tatparya, vivaksa) is adduced as a cause for distinguishing the two transforms semantically. The passive construction is said to emphasize the object, the nonpassive emphasizes the agent. But the explicit triples are not different. This observation indicates that both systems extract the meaning from the syntax.

Finally, a point worth noting is the Indian analysis of the intransitive phrase (7) describing the leaf falling from the tree. The semantic net analysis resembles the Sanskrit analysis remarkably, but the latter has an interesting flavor. Instead of a change from one location to another, as the semantic net analysis prescribes, the Indian system views the process as a uniting and disuniting of an agent. This process is equivalent to the concept of addition to and deletion from sets. A leaf falling to the ground can be viewed as a leaf disuniting from the set of leaves still attached to the tree followed by a uniting with (addition to) the set of leaves already on the ground. This theory is very useful and necessary to formulate changes or statements of state, such as "The hill is in the valley."

In the Indian system, inference is very complete indeed. There is the notion that in an event of "moving", there is, at each instant, a disunion with a preceding point (the source, the initial state), and a union with the following point, toward the destination, the final state. This calculus-like concept fascillitates inference. If it is stated that a process occurred, then a language processor could answer queries about the state of the world at any point during the execution of the process.

As has been shown, the main point in which the two lines of thought have converged is that the decomposition of each prose sentence into karalca-representations of action and focal verbal-action, yields the same set of triples as those which result from the decomposition of a semantic net into nodes, arcs, and labels. It is interesting to speculate as to why the Indians found it worthwhile to pursue studies into unambiguous coding of natural language into semantic elements. It is tempting to think of them as computer scientists without the hardware, but a possible explanation is that a search for clear, unambigous understanding is inherent in the human being.

Let us not forget that among the great accomplishments of the Indian thinkers were the invention of zero, and of the binary number system a thousand years before the West re-invented them.

Their analysis of language casts doubt on the humanistic distinction between natural and artificial intelligence, and may throw light on how research in AI may finally solve the natural language understanding and machine translation problems.

Physics to Metaphysics - A Vedic Paradigm

For India's great realizers, the primary evidence in support of their theses is revealed scripture (sastra), such as the Vedanta-sutras. This evidence is considered to originate beyond the limits of human reasoning. Yet, especially for Westerners, as an introduction to the virtues of scriptural evidence, it may be prudent to first discuss the concept of a transcendental personal Godhead in the context of modern science and quantum mechanics in particular. Following the transition from Newtonian classical physics to quantum mechanics, several scientists have explored the possibility of a connection between physics and transcendence.

This may be due to the more abstract nature of quantum mechanics as opposed to classical physics. For example, classical physics attempts to describe the physical reality in concrete, easily understandable terms, while quantum mechanics deals in probabilities and wave functions. Quantum mechanics, however, is much more rigorous in its attempt to describe reality and explains phenomena that classical physics fails to account for. The "quantum leap" has given several physicists the hope that the transcendentalist's experience of consciousness can also be explained by the quantum mechanical theory. Although the quantum theory does not account for consciousness, it has become popular to attempt to bridge the gap between the transcendentalist's experience and the quantum mechanic world view. Some people have loosely called this the "new physics."

The rational spiritually-minded community cheered the appearance of Fritjof Capra's The Tao of Physics and Gary Zukav's Dancing Wu Li Masters. Later, David Bohm's The Implicate Order was similarly praised. Although there is good reason to applaud their work and the work of others like them, their theories, scientifically speaking, do not quite bridge the gap between physics and transcendence. However, these scientists have to some extent become "believers" and that is a major breakthrough. Furthermore, the theories have turned many educated persons in the spiritual direction.
Of all the recent attempts to show the "oneness" in what physicists and transcendentalists speak of, Bohm's implicate order theory is the most worthy of consideration. In comparison, Capra's "realization" that the dance of Shiva and the movement of atomic particles is one and the same — although profoundly beautiful — falls more in the realm of poetry than science.
Of course any attempt to find harmony between the scientific world view and the mystic's vision will be incomplete unless we adjust the scientific world view through an interface with the many realities it fails to account for (subtle bodies, consciousness, etc.). Taking that liberty, as Bohm has, Richard L. Thompson, Dr. of Mathematics and author of the book Mechanistic and Non-mechanistic Science, has postulated a new theory of "creation through sound" using what he calls The Vedic Paradigm.
Thompson advocates the philosophy of achintya bhedabheda, a transcendental conception which, interestingly enough, fits well with the example of the hologram (often used to illustrate Bohm's implicate order theory). This transcendental conception is different than the one Bohm advocates. Thompson attempts to show in his upcoming book, End of Physics, how some of the holes in Bohm's theory can be filled using an alternative view of transcendence, namely acintya bedhabedha.
Simply stated acintya bedhabedha means that reality is ultimately, inconceivably one and different at the same time. Bohm is an adherent of advaita vedanta or non-dualism. Non-dualists percieve reality as one homogenious substance. In their view all forms of variety and individuality are products of illusion. Acintya bedhabedha, holds that the world of material variety is illusory but not altogether false. It insists that there is a transcendental variety and spiritual individuality that lies beyond illusion. Acintya bedhabedha is a theistic conception and advaita vedanta is monistic or atheistic.
Thompson is a practicing scientist who has been pursuing transcendental disciplines for the last thirteen years. This kind of combination is rare. It is hard to find someone who is thoroughly familiar with science as well as with spirituality. In order to appreciate his theory of creation by sound it will be helpful to first briefly explain Bohm's theory of the implicate order and then proceed to further elaborate on the philosophy of acintya bedhabedha. Such explanations will serve as a peface to the discussion of creation, all of which shed new light on the nature of reality, helping to harmonize physics and metaphysics.
THE IMPLICATE ORDER
Bohm's explanation of reality involves an "implicate" and "explicate" order, with vague references to love, compassion, and other similar attributes that may lie beyond both the implicate and explicate. The implicate order is an ultimate physical substrate which underlies our present perception of reality. The reality that we perceive is what Bohm calls the explicate order. All order and variety, according to Bohm, are stored at all times in the implicate order in an enfolded or unmanifested state. Information continually unfolds or becomes manifest from the implicate order as the explicate order of our experience.

Of course any attempt to find harmony between the scientific world view and the mystic's vision will be incomplete unless we adjust the scientific world view through an interface with the many realities it fails to account for.

Bohm uses the example of the hologram to help explain his theory. A hologram is a photographic plate on which information is recorded as a series of density variations. Because holography is a method of lensless photography, the photographic plate appears as a meaningless pattern of swirls. When a coherent beam of light -- typically the laser -- interacts with the plate, the resultant emerging light is highly ordered and is perceived as an image in three dimensions. The image has depth and solidity, and by looking at it from different angles, one will see different sides of the image. Any part of the hologram will reproduce the whole image (although with less resolution). Bohm would say that the three-dimensional form of the image is enfolded or stored in the pattern of density variations on the hologram.
A further understanding of the nature of Bohm's implicate order is somewhat more difficult to grasp. In the transition from the classical description of physical objects to a quantum mechanical description, one is forced to use mutually incompatible descriptions. That is, to understand the behavior of electrons, it is necessary to describe them as point-like particles and extended waves. This concept of complementarity, devised in the 1920's by the physicist Niels Bohr, leads naturally to the thought that electrons, or their ultimate substrate, may not actually be fully describable in mathematical terms. Thus the ultimate physical reality may be an undefinable "something" which is only partially describable but not fully, because some of the partial descriptions will inevitably contradict each other. This is Bohm's idea regarding the nature of his implicate order.
Although Bohm accepts the reality of a whole containing distinguishable parts, he maintains that ultimately, reality at its most fundamental level is devoid of variety or individuality. Bohm believes that individuality is a temporal or illusory state of perception. According to his theory, although the parts appear to be distinct from the whole, in fact, because they "enfold" or include the whole, they are identical with the whole.
The intuitive basis behind this idea of wholeness is that when information is enfolded into a physical system, it tends to become distributed more or less uniformly throughout the system.
The hologram provides an easily understandable example. If portions of a hologram are blocked off, the resultant image remains basically the same. This, perhaps metaphorically, helps to illustrate the concept that the whole is present in each of its parts. Consider then a continuum in which all patterns ever manifested in any part of the continuum are represented equally in all parts. Loosely speaking, then one could say that the whole of the continuum in both space and time is present in any small part of the continuum. If we invoke the precedent of quantum mechanical indefinability, we could leap to the idea of a unified entity encompassing all space and time in which each part contains the whole and thus is identical to it. Because wholes are made up of parts, such an entity could not be fully described mathematically, although mathematical descriptions could be applied to the parts.
THOMPSON'S OBSERVATIONS
Although Bohm's theory of the implicate order is partially based on the standard methodology of physics, it is also apparent that it involves ideas that are not found in traditional science. Most of these ideas are clearly the influence of a preconceived notion of non-dualism.
Bohm's theory is sorely in need of a logical source of compassion which provides inspiration enabling finite beings to know the infinte. Ironically while Bohm emphatically states that it is not possible for unaided human thought to rise above the realm of manifest matter (explicate order) he proceeds to carry on a lengthy discussion about the unmanifest (implicate order). Although he speaks of compassion it is only in a vague reference to an abstract attribute. The logical necessity for an entity possesed of compassion is avoided by Bohm (although he almost admits the need). He retreats from this idea because the standard notions of a personal God are dualistic and thus undermine the sense that reality at the most fundamental plane is unified.
Bohm's idea that the parts of the implicate order actually include the whole is not fully supported by his physical examples alone. Indeed this is impossible to demonstrate mathematically. The part of the hologram is not fully representative of the whole. The part suffers from lack of resolution. It is qualitatively one but quantitatively different.
Bohm's account for the corruption in human society is also a short coming in an otherwise profound theory. The theory alleges that evil arises from the explicate order -- which is a contradiction of the basis of the theory which states that everything in the explicate order unfolds from the implicate order. This means that evil and human society at large or something at least resembling it must be originally present in the implicate order. But what would lead us to believe that an undifferentiated entity would store anything even remotely resembling human society? Or how could there be evil in or beyond the implicate order which is the source of love and compassion?
Bohm states that the totality of all things is timeless and unitary and therefore incapable of being changed. Later on he proposes that through collective human endeavor the state of arrairs can be changed. This is similar to the contradiction of advaita vedanta in which ultimate oneness is thought to be attained even though it is beyond time and forever uninfluenced by our actions.
These are some of the scientific and philosophical problems with the theory of the implicate order pointed out by Thompson. They are resolved by Thompson by replacing advaita vedanta with achintya bedhabedha.
ACHINTYA BHEDABHEDA
The history of philosophy bears evidence that neither the concepts of oneness (non-dualism) or difference (dualism) are adequate to fully describe the nature of being. Exclusive emphasis on oneness leads to the denial of the world and our very sense of self as an individual -- viewing them as illusion. Exclusive emphasis on difference divides reality, creating an unbridgeable gap between man and God. Both concepts at the same time seem necessary inasmuch as identity is a necessary demand of our reason while difference is an undeniable fact of our experience. Therefore a synthesis of the two can be seen as the goal of philosophy. In the theory of achintya bhedabheda, the concepts of both oneness and difference are transcended and reconciled in this higher synthesis, and thus they become associated aspects of an abiding unity in the Godhead. The word achintya is central to the theory. It can be defined as the power to reconcile the impossible. Achintya is that which is inconceivable on account of the contradictory notions it involves, yet it can be appreciated through logical implication.
Achintya, inconceivable, is different from anirvacaniya, or indescribable, which is said to be the nature of transcendence in the non-dualistic school. Anirvacaniya involves the joining of the opposing concepts of reality and illusion, producing a canceling effect -- a negative effect. Achintya, on the other hand, signifies a marriage of opposite concepts leading to a more complete unity -- a positive effect.

Just as the eye cannot see the mind but can be in connection with it if the mind chooses to think about it, so similarly the finite can know about the infinite only by the grace of the infinite.

It may be helpful to draw upon a reference from Vedic literature. Actually, the example of the hologram is similar to an explanation of the basis of reality recorded in the Brahma Samhita. There we find a verse in which, ironically, Godhead has been described as personal and individual and Who, at the same time one with and different from His energies.

He is an undifferentiated entity as there is no distinction between potency and possessor thereof. In His work of creation of millions of worlds, His potency remains inseparable. All the universes exist in Him and He is present in His fullness in every one of the atoms that are scattered throughout the universe at one and the same time. Such is the primeval Lord whom I adore. (Brahma Samhita 5.35)

In the material conception of form, the whole can be reduced to a mere juxtaposition of the parts. This makes the form secondary. In this verse the material conception of form is transcended. The supreme entity is fully present in all of the parts which make up the total reality and thus the supreme is one unified principle underlying all variegated manifestations. Yet He is personal and in this feature different from his parts or energies at the same time. The Brahma Samhita goes on to say that each of the parts of the Godhead's form are equal to each other and to the whole form as well. At the same time each of the parts remains a part. This is fundamental to the philosophical outlook of achintya bhedabheda. It allows for the eternal individuality of all things without the loss of oneness or harmony. It also allows for the possibility that man, even while possessed of limited mind and senses, can come to know about the nature of transcendence. The infinite, being so, can and does reveal Himself to the finite. Just as the eye can not see the mind but can be in connection with it if the mind chooses to think about it, so similarly the finite can know about the infinite by the grace of the infinite. The concept of non-dualism however allows for neither of these things.
In the Bhagavad Gita we find the following verse: (9.4)

By Me in My unmanifested form this entire universe is
pervaded. All beings are in Me, but I am not in them.

Although this is inconceivable -- achintya -- an example drawn from material nature may help us to understand this concept (logical implication). We cannot think of fire without the power of burning; similarly, we cannot think of the power of burning without fire. Both are identical. While fire is nothing but that which burns; the power of burning is but fire in action. Yet at the same time, fire and its burning power are not absolutely the same. If they were absolutely the same, there would be no need to warn our children that "fire burns." Rather it would be sufficient to say "fire." Furthermore, if they were the same, it would not be possible to neutralize the burning power in fire through medicine or mantra without causing fire to disappear altogether. In reality the fire is the energetic source of the energy which is the power to burn. From this example drawn from the world of our experience, we can deduce that the principle of simultaneous oneness and difference is all pervading, appearing even in material objects.
Just as there is neither absolute oneness nor absolute difference in the material example of fire and burning power, there is neither absolute oneness nor absolute difference between Godhead and His energies. Godhead consists of both the energetic and the energy, which are one and different. Godhead is also necessarily complete without His various emanations. This is absolute completeness. No matter how much energy He distributes, He remains the complete balance.
In this theory the personal form of God exists beyond material time in a trans-temporal state, There eternality and the passage of time are harmonized by the same principle of simultaneous oneness and variegatedness that applies to transcendental form. Thus within Godhead there may very well be something that resembles human society which could unfold as the explicate order.

The individual self is a minute particle of will or consciousness -- a sentient being -- endowed with a serving tendency. This self is transcendental to matter and qualitatively one with Godhead, while quantitatively different.

A personal, "human-like" Godhead replete with abode and paraphernalia is a perennial notion. In this conception the explicate order becomes in effect a perverted reflection of the ultimate reality existing in the transcendental realm. The reflection of that realm, appearing as the explicate order, amounts to the kingdom of God without God. It would be without God inasmuch as God, being the center of the ultimate reality, when expressed in reflected form no longer appears as the center. This produces illusion and the necessity for corruption. The basis of corruption is the misplaced sense of proprietorship resulting in the utterly false notions of "I" and "mine.
According to achintya bhedabheda,the individual self is a minute particle of will or consciousness -- a sentient being -- endowed with a serving tendency. This self is transcendental to matter and qualitatively one with Godhead, while quantitatively different. The inherent defect of smallness in size in the minute self in contrast to the quantitative superiority of Godhead makes the individual minute particle of consciousness prone to the influence of illusion. This is analogous to the example of the hologram in which only a portion of the holographic plate is illuminated with a coherent light source. The resultant image, although apparently complete, is slightly fuzzy and does not give the total three-dimensional view from all directions which one would observe when the entire holographic plate is illuminated.
Living in illusion, the atomic soul sees himself as separate from the Godhead. As a result of imperfect sense perception he is caused to make false distinctions such as good and bad, happiness and distress. The minute self can also live in an enlightened state in complete harmony with the Godhead by the latter's grace -- which is attracted by sincere petition or devotion. The very nature of devotion is that it is of another world, and for it to be devotion in the full sense, it must be engaged in for its own sake and nothing else. This act of devotion is the purified function of the inherent serving tendency of the self. It makes possible a communion with Godhead. In this communion the self becomes one in purpose with the one reality and eternally serves that reality with no sense of any separateness from Godhead. If we accept this theory then there is scope for action from within the explicate order, such as prayer or meditation, to have influence upon the whole. At least it would appear so, inasmuch as, in reality, the inspiration for such action has its origin in Godhead. Of course this idea is also found in varying degrees in many perennial theistic philosophies. It is perhaps most thoroughly dealt with, however, in the doctrine of achintya bhedabheda.
Although it is true that the human mind cannot possibly demonstrate the truth of this conception, this does not provide sufficient justification for rejecting the notion in favor of something more abstract, such as non-dualism. The fact is that any conception of the Godhead that is generated from the finite mind is subject to the same criticism. If we are limited to our mundane mind and senses for acquiring transcendental knowledge, then we may as well forego any speculation about transcendence and turn our attention exclusively to the manifest mundane world. The achintya bhedabheda theory of transcendence, however, at least allows for the possibility of the finite entity to approach the plane of transcendence through the acquisition of transcendental "grace." This conception provides for us something we can do in relation to Godhead (such as prayer or meditation) whereby our understanding can be enhanced. Alternatively, the non-dualistic approach really affords no method of approach.
Finally it must be emphasized that both the doctrines of non-dualism and achintya bhedabheda are quite extensive and impossible to deal with thoroughly in this short article. At least it should be clear that insistence on the non-dual conception of the ultimate reality creates problems for the theory of the implicate order. At the same time the theistic doctrine of inconceivable simultaneous oneness and difference at the very least deals with these problems adequately.

CREATION THROUGH SOUND

Thompson points out that the purely physical observations on which Bohm's theory is based provide insight as to how physics can be linked with transcendence. Thompson suggests that, scientifically speaking, the implicate order is limited to the observation that "organized macroscopic forms can arise by natural physical transformations from patterns of minute fluctuations that look indistinguishable from random noise." Such patterns could appear in many different forms such as electromagnetic fields (light waves) or the matter waves of quantum mechanics. These patterns which may later produce distinct macroscopic events can either be all-pervading or localized, and two such patterns could even occupy the same volume of space.
Thompson uses the philosophy of the Bhagavad Gita and other Vedic literatures as a source of metaphysical ideas. He offers a tentative proposal of a synthesis of physical and spiritual knowledge by introducing the necessary element of divine revelation.
He states that, "According to the Srimad Bhagavatam, the material creation is brought about and maintained through the injection of divinely ordered sound vibrations into a primordial material substrate called pradhana. According to this idea, the pradhana is an eternally existing energy of the supreme which is potentially capable of manifesting material space and time, the material elements, and their various possible combinations." In the absence of external influences no manifestations would take place. However, the pradhana will indeed produce various manifestations under the influence of intelligently directed sound vibrations generated by the Godhead. Thompson explains the meaning of "sound," coming from the Sanskrit word shabda, as "any type of propagating vibration, however subtle."
Keeping in mind that creation is a very complex affair, let's look at the final stages of creation in which organized forms are generated and controlled in a setting made up of the physical elements as we know them. According to the Vedic paradigm, at this stage, transcendental sound is introduced into the material continuum on the most subtle level. As a result, grosser elements are agitated, and finally organized structures such as the bodies of living organisms are produced.
Consider the phenomenon of optical phase conjugation -- a process that can reverse the motion of a beam of light and cause an image scrambled by frosted glass to return to its original, undistorted form. In a typical experiment, light is reflected from an object and passes through a pane of frosted glass. It then reflects from a device called a phase conjugate mirror and passes back through the glass. When the light enters the eye, one perceives a clear, undistorted image of the original object. This can be contrasted with the garbled blur one would observe if the light were reflected back through the glass by an ordinary mirror. See Figure left.
The explanation of this phenomenon is that the light on its first pass through the frosted pane is distorted in a complicated way by irregularities in the glass. The phase conjugate mirror reverses the distorted beam, and as it passes back through the glass it precisely retraces its steps and thus returns to its original undistorted form.
The beam reflected from the phase conjugate mirror has the curious property that it encodes information for the original image in a distorted, unrecognizable form, and as time passes, the distortion is reduced and the information contained by the beam becomes clearly manifest. Normally, we expect to see just the opposite -- a pattern containing meaningful information will gradually degrade until the information is irretrievably lost.
Thompson further elucidates the connection between the material and transcendental levels of existence with an example similar to that of optical phase conjugation. Suppose we have an arrangement in which pictures are being transmitted through a sheet of frosted glass. On one side of the glass we would see a series of images but we would not be able to determine the source of the images on the other side of the opaque glass. But in thinking about it, one would expect that the light coming through the frosted glass would become distorted. The fact that it does not seems to indicate that there is some sort of intelligence which is organizing or ordering the transmitted images. This is a simplified example of optical phase conjugation. Similarly, the order and complexity we find in matter must have intelligence behind it, although we at present cannot directly see that intelligence. The Vedic conception states that a veil of illusion called maya prevents living beings in the material domain from directly perceiving their origin, Godhead -- the supreme intelligent being. The Vedas further maintain that although God predominates the material nature, He is manipulating it in such an expert way that His influence cannot be detected; as Bohm states, "Complex patterns of events seem to unfold simply by material action and reaction."
As Thompson progresses in the formulation of his Vedic paradigm, a number of questions arise. How are the postulated organized vibrations introduced into the known physical continuum? How can some outside influence be accommodated? This would seem to involve violations of certain basic laws of physics such as conservation of energy, the second law of thermodynamics, and statistical laws of quantum mechanics.
In response to these objections, Thompson postulates a model involving levels of physical reality more subtle than quantum fields. "One can readily imagine a hierarchy of subtler and subtler levels culminating in an ultimate substrate which is transcendental and not amenable to mathematical description. Organized wave patterns could propagate through this hierarchy from the transcendental level to the level of gross matter. In such models the quantum fields will be reducible to these subtler levels, and phenomena on these levels will have effects on the level of the quantum fields." In the transition from Newtonian physics to quantum mechanics and further to quantum field theory, the conceptual framework diverges from the domain of familiar mechanical imagery. Thompson suggests that "The degree of subtlety of a level of reality corresponds to the degree of novelty and unfamiliarity of the concepts needed to adequately comprehend it. On the subtlest (or transcendental) level, the materially inconceivable principle of achintya bheda bheda tattva becomes applicable."

According to the Vedic paradigm, the conscious self is transcendental and has the same qualitative nature as the Godhead. Thus the link between conscious will and the initiation of physical action by the brain should also entail the transmission of patterns of information from transcendental to gross physical levels of reality.

The introduction of wave patterns into the gross material realm from an outside independent source should produce detectable violations of the conservation laws of physics. It would not be surprising to find violations of known laws if such subtler levels of material energy do exist. Indeed, the existence of the neutrino was postulated by Enrico Fermi in the 1930's because of an apparent violation of the principle of conservation of momentum in the radioactive decay of certain atomic nuclei. The discovery of the neutrino showed the existence of a subtle level which was previously unknown. It is therefore entirely reasonable to speak of the existence of more subtle levels which are as yet undiscovered. Also, in his forthcoming book, Thompson shows that models which receive influences from more subtle levels without undergoing any detectable change in momentum or energy may be constructed.
Thompson suggests, "Let us suppose for the moment that organized wave patterns are continually being injected into the known physical continuum perhaps from subtler levels of physical reality. Such patterns will appear to be random, especially if they encode information for many different macroscopic forms and sequences of events. For this reason they will be very difficult to distinguish from purely random patterns by experimental observation."
Consider a two-dimensional wave field -- exemplified by the surface of a body of water. This is illustrated in Figure 2, left. A two-dimensional wave field is capable of propagating waves which can be expressed by what is called the classical wave equation. In the first frame of Figure 2 we see the wave field moving in an apparently random way. As time passes it becomes apparent that this pattern of waves contains hidden information. This is illustrated in successive frames, where first in frame 2 we see that a letter "A" has appeared in the field. This form quickly takes shape and dissipates (frame 3), and it is replaced in frame 4 by the similar rapid appearance and disappearance of the symbol "" (Aum). Actually the information for both symbols is present in all 4 frames of the figure. This example is discussed in detail by Thompson in his forthcoming book:

Thus much of the random noise that surrounds us may consist of information for patterns that will 'unfold' in the future to produce macroscopic results, while the rest consists of the 'enfolded' or 'refolded' remnants of past macroscopic patterns.

Because the original source of these patterns is the inaccessible transcendental level, it is not possible to produce them at will. A thorough investigation of this phenomenon would necessarily depend on the analysis of observed spontaneous events.
Thompson believes that this type of study might be fruitful in the field of cognitive science. "According to the Vedic paradigm, the conscious self is transcendental and has the same qualitative nature as the Godhead. Thus the link between conscious will and the initiation of physical action by the brain should also entail the transmission of patterns of information from transcendental to gross physical levels of reality."
The concept of the unfolding of information is also useful in the field of natural history. The predominating scientific viewpoint is that the origin of living species can be explained by Darwin's theory of evolution by natural selection and random variation. Included in the group of those who have always dissented from this view is Alfred Russell Wallace, the co-inventor of Darwin's theory. Wallace felt that certain biological phenomenon, such as the brain, could not be accounted for properly without the action of some higher intelligence. Similarly, Bohm feels that "Natural selection is not the whole story, but rather that evolution is a sign of the creative intelligence of matter." Thompson has pointed out that "Bohm regards this intelligence as emanating either from his implicate order or from beyond."
The Vedic paradigm proposes that the supreme intelligent being can create or modify the forms of living beings by the transmission of organized wave patterns into the physical realm. Of course both this theory of creation by sound and the Darwinian theory of evolution are very difficult to verify. Thompson states, "The theory of creation by sound vibration involves transcendental levels of reality not accessible to the mundane senses, and thus in one sense it is more unverifiable than the purely physical Darwinian theory. However, if a purely physical theory turns out to be empirically unverifiable, then there is nothing further one can do to be sure about it. In contrast, a theory that posits a supreme intelligent being opens up the possibility that further knowledge may be gained through internal and external revelation brought about by the will of that being."
This entire approach is in line with the oft-mentioned need for a new paradigm, a new world view which is said to be in the making. Although the mechanistic world view founded by Descartes, Galileo, Newton, and Bacon has dominated thought since the seventeenth century -- now, as we approach the twenty-first century, the severe limitations of this view have become apparent. The mechanistic approach must be replaced with a holistic approach. Rather than torturing nature for her secrets, Thompson's idea calls for a reverence for nature and a humble appeal to Godhead for divine service.
Finally, in Thompson's own words, "This approach to knowledge and to life also constitutes one of the great perennial philosophies of mankind, but it has tended to be eclipsed in this age of scientific empiricism. To obtain the fruits of this path to knowledge, one must be willing to follow it, and one will be inclined to do this only if one thinks the world view on which it is based might possibly be true. Establishing this possibility constitutes the ultimate justification for constructing theories such as the one considered here: linking physics and metaphysics."